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APPLICATION AND ANALYSIS OF A
MICROSCOPE DIFFUSION CHAMBER

by

Keith D. Sherban

A THESIS

submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Mechanical Engineering

1987

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ABSTRACT

THE APPLICATION AND ANALYSIS OF A
MICROSCOPE DIFFUSION CHAMBER

by

Keith D. Sherban

A microscope diffusion chamber has been used to determine the
equilibrium and non-equilibrium osmotic response of individual cells.

The chamber allowed the direct observation of a cell subjected to a
change in concentration at a specified temperature. Cell systems used in
this work were egg lecithin liposomes and human lymphocytes. For each
cell system the normalized osmotically inactive volume, membrane
hydraulic permeability (for five specific temperatures) and membrane
activation energy have been determined.

The raw data generated were processed by a computer algorithm which
used a parameter estimation technique to yield the best statistical
estimate of the membrane permeability. The program was made "user
friendly" by setting up the algorithm to run in menu format and converted
to an IBM PC. In addition, the program also allowed the user to run
simulations for sensitivity studies and the design of experiments.

A major finding/result is that the estimated parameters using this
device and software matched previously reported results for egg lecithin
liposomes and human lymphocytes. This suggests that the device and
software can be applied successfully for determining water permeability

of cell membranes, including temperature effects.

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ACKNOWLEDGEMENTS

I would like to express my appreciation to my advisor Dr. McGrath. I
am grateful for his support, guidance and friendship.

I would like to thank my wife for her support, patients and never
ending encouragement.

I am deeply grateful to the members of my family who have also
patiently supported me.

I would like to thank John Tu, Mark Melkerson and Mosen Shabana of the
Bioengineering Transport Lab for their help and guidance.

I would like to thank the Ostrom's for their support and the use of
their computer systems.

I would also like to thank God for this opportunity and His never

ending patients and encouragement.

iii

TABLE OF CONTENTS

. LIST OF TABLES ..................................................... vii
LIST OF FIGURES .................................................... ix
NOMENCLATURE ....................................................... Xi
SUBSCRIPT NOMENCLATURE ............................................. xiii
GREEK NOMENCLATURE ................................................. xiv
CHAPTER

1. INTRODUCTION

1.1 Background and Motivation for Present Work .......... 1
1.2 Statement of Objective .............................. 3
2. ANALYSIS

2.1 System Definition ................................... 8

2.2 Modeling the System ................................. 10

2.2.1 The Concentration History .................. 10

2.2.2 The Kedem - Katchalsky Formulation ......... 13

2.2.3 The Volume Flow of a Cell .................. 21

2.3 The Estimation of Parameter P ....................... 24
2.4 The Effect of Temperature on P, (The Activation

Energy) ............................................. 29

3. THE PARAMETER ESTIMATION/SIMULATION PROGRAM, SENS

3.1 Introduction and Background (of J. Tu's Program).... 30
3.2 The Modified SENS ................................... 32
3.3 Converting SENS to the IBM PC ....................... 44

4. EXPERIMENTAL EQUIPMENT AND PROCEDURES

4.1 Preparing Cells for Experimental Runs ............... 46

4.1.1 Preparing Egg Lecithin Liposomes ........... 46

4.1.2 Preparing Human Lymphocytes ................ 48
4.2 Description of the Microscope Diffusion Chamber ..... 50
4.3 Description of the Overall Experimental System ...... 54
4.4 Description of an Experimental Run .................. 58
4.5 Description of Data Measurements .................... 61
4.6 Types of Experiments Performed ...................... 63

iv

5. THE EXPERIMENTAL RESULTS AND DISCUSSION

5.1 Introduction ........................................ 65
5.2 The Normalized Osmotically Inactive Cell Volume ..... 66
5.3 The Cell Membrane Water Permeability ................ 70
5.4 The Cell Membrane Water Permeability Activation
Energy .............................................. 79
6. SENSITIVITY STUDIES
6.1 Introduction ........................................ 83
6.2 The Liposome Base Case .............................. 84
6.2.1 The Effect of Varying D1 ................... 87
6.2.2 The Effect of Varying Hd ................... 90
6.2.3 The Effect of Varying RL2 .................. 92
6.2.4 The Effect of Varying LIP .................. 95
6.2.5 The Effect of Varying VINA ................. 97
6.2.6 The Effect of Varying DELAY ................ 99
6.2.7 The Effect of Varying DR ................... 101
6.2.8 The Effect of the Number of Data Points.... 104
6.2.9 The Effect of Varying Ea of the Dialysis
Membrane on the Ea of the Cell ............. 109
6.3. The Lymphocyte Base Case ............................ 111
6.3.1 The Effect of Varying D1 ................... 113
6.3 2 The Effect of Varying Hd ................... 115
6.3.3 The Effect of Varying RL2 .................. 117
6.3.4 The Effect of Varying LIP .................. 119
6.3 5 The Effect of Varying VINA ................. 120
6.3 6 The Effect of Varying DELAY ................ 122
6.3 7 The Effect of Varying DR ................... 124
6.3 8 The Effect of the Number of Data Points.... 126
6.3 9 The Effect of Varying E8 of the Dialysis
Membrane on the Ea of the Cell ............. 131
6.4 Discussion of Sensitivity Studies - Ranking the
Input Parameters .................................... 133
7. CONCLUSIONS .................................................. 135
8. SUGGESTIONS FOR FUTURE WORK .................................. 139
APPENDICES
A. THE NORMALIZED OSMOTICALLY INACTIVE VOLUME ................... 142
B. PRELIMINARY TESTING AND SET UP OF EXPERIMENTAL EQUIPMENT ..... 144
C. CLARIFICATION 0F SHABANA RESULTS ............................. 147
D. SENS - THE PRIME VERSION FORTRAN SOURCE CODE ................. 148

E. SENS - THE IBM PC VERSION FORTRAN SOURCE CODE ................ 189

BIBLIOGRAPHY ....................................................... 236

vi

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vii

.1 Normalized Osmotically Inactive Cell Volume ............... 69
.1 Permeability Results for Liposomes ........................ 74
.2 Permeability Results for Lymphocytes ...................... 76
.3 Comparison of Permeability Results ........................ 78
.1 Activation Energy Results ................................. 82
.1 Base Case Liposome ........................................ 84
.2 The Effect of Varying D1 .................................. 87
.3 The Effect of Varying Hd .................................. 90
.4 The Effect of Varying RL2 ................................. 92
.5 The Effect of Varying LIP ................................. 95
.6 The Effect of Varying VINA ................................ 97
.7 The Effect of Varying DELAY ............................... 99
.8 The Effect of Varying DR .................................. 101
.9 The Effect of the Number of Data Points ................... 104
.10 The Effect of Varying Ea of the Dialysis Membrane on
the Ea of the Cell ....................................... 109
.1 Base Case Lymphocyte ...................................... 111
.2 The Effect of Varying D1 .................................. 113
.3 The Effect of Varying Hd .................................. 115
.4 The Effect of Varying RL2 ................................. 117
.5 The Effect of Varying VINA ................................ 120
.6 The Effect of Varying DELAY ............................... 122
.7 The Effect of Varying DR .................................. 124
.8 The Effect of the Number of Data Points ................... 126
.9 The Effect of Varying Ea of the Dialysis Membrane on
the Ea of the Cell ........................................ 131

B.l Magnification Calibration ................................. 145
8.2 Temperature Bath Measurements ............................. 145

C.1 Summary of Shabana's Results .............................. 146

viii

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LIST OF FIGURES

Schematic Representation of the Microscope Diffusion
Chamber ................................................... 9

Schematic of Diffusion Chamber with Relevant Parameters... 12

The two compartment - two component system ................ 16
Flow Chart of SENS — Prime Version ........................ 33
Sample Output File of SEN — C_SMRY.DAT ................... 38

Sample Graphical Output - Concentration v.5. Normalized
Time ...................................................... 40

Sample Graphical Output - Sensitivity Coefficient v.5.

Time ...................................................... 41
Sample Graphical Output - Normalized Cell Volume v.5.
Time ...................................................... 42

Sample Graphical Output - Sum of the Squares v.s
Permeability .............................................. 43

Schematic Representation of the Microscope Diffusion
Chamber ................................................... 51

Schematic Cross Sectional View of Microscope Diffusion

Chamber ................................................... 52
Schematic of the Overall System ........................... 55

Normalized Cell Volume v.s. Normalized Inverse
Concentration - Liposome .................................. 67

Normalized Cell Volume v.s. Inverse Concentration -
Lymphocyte ................................................ 68

Estimated Permeability v.s. Inverse Temperature -
Liposome .................................................. 80

Estimated Permeability v.5. Inverse Temperature -

Lymphocytes ............................................... 81
P(est) v.s. D1 - Liposome ................................. 89
P(est) v.5. Hd - Liposome ................................. 91
P(est) v.5. RL2 - Liposome ................................ 94
P(est) v.s. LIP - Liposome ................................ 96

ix

.5 P(est) v.s. VINA - Liposome ............................... 98
.6 P(est) v.s. DELAY - Liposome .............................. 100
.7 S.D. v.s. DR - Liposome ................................... 103
.8 P(est) v.s. Number of Points - Liposome ................... 106
.9 S.D. v.s. 1/[Number of Pointslh - Liposome ................ 107
.10 SUMIN v.s. Number of Points - Liposome ................... 108
.11 Ea(Cell) v.s. Ea(Dialysis Membrane) - Liposome ........... 110
.1 P(est) v.s. D1 - Lymphocyte ............................... 114
.2 P(est) v.s. Hd - Lymphocyte ............................... 116
.3 P(est) v.s. RL2 - Lymphocyte .............................. 118
.4 P(est) v.s. VINA - Lymphocyte ............................. 121
.5 P(est) v.s. DELAY - Lymphocyte ............................ 123
.6 S.D. v.s. DR - Lymphocyte ................................. 125
.7 P(est) v.s. Number of Points - Lymphocyte ................. 128
.8 S.D. v.s. 1/[Number of Points]8 - Lymphocyte .............. 129
.9 SUMIN v.s. Number of Points - Lymphocyte .................. 130
.10 Ea(Cell) v.s. Ea(Dialysis Membrane) ...................... 132
Temperature Bath Measurements ............................... 146

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A Area
b Estimated Parameter
C Concentration
D Diffusivity of Solute in Specified Medium
Ea Activation Energy
Hd Convective Mass Transfer Coefficient
Ji Flux of Species i
Lij Phenomenlogical Coefficient
n Number of Data Points
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P Cell Membrane Water Permeability
Pest Estimated Permeability
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R Gas Constant
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S Entropy
S Sum of the Squares Function

T Temperature

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G Partial Molar Volume

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p Pressure

3 Solute

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1 Dialysis Membrane Region
2 Sample Region

3 Inside the Cell of Interest

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GREEK NOMENCLATURE

Parameter

Error

Osmotic Pressure

Molar Fraction

Volume Fraction
Reflection Coefficient
Chemical Potential
Dissipation Function
Standard Deviation
Predicted Parameter

Covariance of Errors

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CHAPTER 1

Introduction

1.1 Background and Motivation for Present Work

The cell is the most basic unit of living material. All biological
organisms are composed of one or more of these fundamentally similar
units. Understanding the reaction of a cell, due to an environmental
change, is a concern of biologists and other scientists. One particular
type of scientist, namely the cryobiologist, is interested in
understanding what happens to a cell and its membrane as the cell is
subjected to low temperatures. Since a cell is composed primarily of
water (50-90%), the temperature of 0°C is of considerable interest: the
freezing point of water (at atmospheric conditions). During the freezing
process, it has been shown that the membrane of the cell becomes damaged
or injured. It has been suggested that two distinct mechanisms of injury
occur, and this has been formulated into the "two-factor" hypothesis of
freezing injury.[1] Specifically, at low rates of cooling, all ice
formation is extracellular and injury is a direct result of osmotic
stress. At high rates of cooling, cells are damaged by the nucleation of
intracellular ice, and by its subsequent recrystallization during
warming. An optimal recovery is then observed at an intermediate rate of
cooling.[2]

The important phenomenon of interest for this paper deals with the
osmotic responses that occur during cooling and warming. The problem
that will be addressed is the equilibrium and non-equilibrium osmotic

behavior of a cell at a given temperature. To further explain, recall

 

 

 

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from above that during a low rate of cooling all ice formation is

extracellular. As the extracellular water freezes, the cell begins to
experience an increase in extracellular solute concentration which can be
quite large, depending on the environmental/experimental conditions. The
cell responds by expelling water from inside thus decreasing the cell
volume. In other words, the cell is trying to increase its intracellular
concentration in order to reestablish an equilibrium state. The cell
suffers damage due to dehydration.

Typical techniques for determining the equilibrium osmotic behavior
of cells includes one or more of the following undesirable
characteristics: individual cells cannot be monitored; relatively large
sample volumes are required; manipulation of the extracellular solute
concentration is inconvenient and/or time consuming; rather extensive
calibration procedures are required because the experimental technique is
an indirect one.[3] Optical techniques using light absorption and
scattering have been used in stopped-flow spectrophotometers in order to
determine the transient osmotic behavior of biological cells.[4'5'6]

This technique is indirect, requires relatively large sample volumes,
subjects cells to substantial shearing stresses, and yields no
information about individual cells, only the average.[3]

With these undesirable characteristics in mind, J.J. McGrath
developed the microscope diffusion chamber. The chamber attempts to
provide the following ideal characteristics: (1) allows real time direct
observation of individual cells in suspension, (2) requires small sample
volumes (10-1000 microliters), (3) allows rapid change of extracellular

concentrations (1-10 seconds), (4) allows repeated changes in

3
extracellular solutions, (5) allows temperature control of the medium,
'(6) allows the use of all standard microscope optical techniques, and (7)
is simple and economical to construct and use.[3] Although other
microscope diffusion chambers have been developed, none have all the

above characteristics, while the chamber developed by McGrath does.

 

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1.2 Statement of Objective

The work presented here is part of an ongoing study of the
microscope diffusion chamber developed by J.J. McGrath and was conducted
at the Bioengineering Transport Process Laboratory (BTPL) of Michigan
State University. Previous work performed by S.P. Nowlen, S.M. Tu and M.
Shabana, of the BTPL, initiated the testing and application of the
diffusion chamber along with developing parameter estimation software to
aid with data analysis. Their work consisted of using cell systems of
liposomes and unfertilized hamster ova and was carried out at room
temperature. The work in this thesis has accomplished the following: (1)
extends the diffusion chamber capabilities to allow experiments to be run
at different temperatures; (2) improves the software usability; (3)
applies the diffusion chamber to the cell systems of liposomes and human
lymphocytes; (4) uses the software to clarify previous results, and (5)
uses the software to study the sensitivity of the estimated parameter
(the membrane water permeability) with respect to a change in input
parameters.

The first step toward these goals was to research and gather
information about the work accomplished in the BTPL using the diffusion
chamber. At the time, S.M. Tu was conducting experiments using liposomes
as a cell system and developing a computer program to aid with data
analysis. It was determined that the best way to gain an understanding
of how the diffusion chamber operated was by trying to verify the results
Tu obtained. This was accomplished by using liposomes under the same

experimental conditions and analyzing the results using Tu's computer

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program.

Once this was accomplished, the next step was to adapt the
experimental system to allow for experiments to be carried out at
different temperatures. The diffusion chamber was already designed with
this consideration in mind. It had a heat exchange channel running along
the inside of the outer edge of the chamber body (see Figure 4.2.2). The
device used to control the Chamber's temperature was a refrigerated
circulating bath. The bath was connected directly to the diffusion
Chamber's heat exchange channel. The bath's fluid was also used to
control the temperature of the isotonic and hypertonic solutions (see
Figure 4.3.1). Once the experimental system was set up, thermocouples
and a digital display device were used to characterize the temperature
distribution of the diffusion chamber and to monitor of the temperature
at various points of the experimental system during an experimental run.

The computer program developed by Tu worked well, providing all of
the data and the parameters were entered correctly. However, if
something was not entered properly and/or the user encountered an error
during run time, it was often difficult to locate the cause. The main
thrust to improve the usability of the program was to have the program
explain to the user what the program required and accomplished. To do
this, the program was set up in a menu driven format which prompted the
user for the necessary input. In addition, the program was also adapted
so that it could be used with an IBM personal computer in conjunction
with the graphical software PLOTIT. The original program resided on the
PRIME 750, a minicomputer, available at the Case Center in the

Engineering building at M.S.U.

6
The experimental work included conducting experiments using
.liposomes and lymphocytes as cell systems because results existed in
literature for comparison. The types of experiments performed resulted
in the data necessary to generate cell inactive volumes, membrane
permeabilities and membrane activation energies for each cell system,
with the exception of conducting experiments for the liposomes cell
inactive volume. This work was previously performed by R. Callow of the
BTPL. These results were compared with those reported by S.M. Tu and R.
Callow for liposomes, and Porsche and Hempling for lymphocytes and were
found to be in good agreement. Therefore this establishes validity of
this approach.

Initially, the parameter estimation software was used to help
clarify work previously done by M. Shabana using unfertilized hamster
ova. When Shabana carried out his experiments and analyzed the data, the
zero time was taken to be when the cell started to "respond", by visually
detecting a fluctuation or shrinkage in the outer membrane of the cell.
However, this is not the true zero time. By reexamining the recorded
video tapes the delay time was approximated to be 6 seconds. Thus 6
seconds was added to each time interval for each set of data and new cell
membrane permeabilities were estimated. Then these newly calculated
permeabilities were compared to those calculated by Nowlen, using the
same sets of data but different parameter estimation techniques, and were
found to be in better agreement (see Appendix C for details).

The software was also applied to define the experimental conditions.
By having an approximate value for the cell membrane permeability (from

pervious work and published literature), the experimental conditions

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could be entered and the program could calculate a simulated volume time
history for the cell. Based on the outcome of the volume time history,
the experimental conditions could be adjusted to give a better or more
desirable volume history. The criteria used to here was to have the cell
radius shrink by 15% or more because this allowed for greater ease in
measuring volume history.

The most obvious use and primary reason for creating the software
was to enter the actual data from experimental runs to estimate a
membrane permeability for an individual cell. This was done for each set
of data obtained. The results are tabulated in Section 5.3, Tables 5.3.1
and 5.3.2.

Finally, the program was used for sensitivity studies. The
sensitivity studies were performed to help give a better understanding Of
the results generated in this thesis. The question was asked, if the
experimental conditions were similar to those encountered during
experiments with liposomes and lymphocytes, thus giving similar results,
what would happen to the estimated permeability if an input parameter was
increased or decreased? By doing such a study, one could determine how
"sensitive" the estimated parameter, in this case the cell permeability,
was with respect to a change in a particular input parameter of interest.

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CHAPTER 2

Analysis

2.1 System definition

A schematic representation of the diffusion chamber is given in
Figure 2.1.1. Initially the cell specimen is place into the diffusion
chamber sample region and the bulk flow region is filled with the
isotonic solution. At zero time, the bulk flow region is flushed with a
continuous flow of hypertonic solution. As a result, a concentration
boundary layer develops along the bottom surface of the dialysis
membrane. Solute diffuses through the boundary layer, through the
dialysis membrane and into the sample region. The cell responds
osmotically to the concentration increase. The analysis presented here
will model the solute diffusion process and the cell specimen's response,

which has been incorporated into a computer program.

 

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2.2 Modeling the system

The modeling of the system can be broken into two parts: the
diffusion of the solute into the sample region and the osmotic response

of the cell specimen.

2.2.1 The Concentration History

Since J.J. McGrath, in conjunction with S.M. Tu, has already
extensively analyzed the solute concentration history of the microscope
diffusion chamber, (see reference [7] in the bibliography), their
approach and results will only be summarized here.

The assumptions used to model the solute concentration are as

follows:[7]

1) one dimensional transient mass transfer
(developing mass transfer boundary layer is
accounted for with a mean coefficient, Hd).

2) a non-selective dialysis membrane, a - 0 [8],
(i.e. solute diffuses through the membrane as it
would through free solution (except the
diffusivity coefficient is lower).).

3) no net volume flow in the sample region of the
diffusion chamber.

4) fully developed, steady state laminar
hydrodynamic conditions in the bulk flow region.

5) the diffusion chamber is isobaric and
isothermal.

6) constant mass diffusivities.

7) negligible solute velocities normal to the
dialysis membrane.

8) the analysis does not account for the presence
of cells in the sample region.

.0
h «V
AAA '8
l

V.- ,
.-.0. .‘fi
U..§‘SAUAI

..
L .

“S

0. ..
. t . I
On... Ah...

 

 

ll

9) the bulk flow is assumed to step change from
C5,” to Cf at the zero time.

The problem considered is therefore one-dimensional transient
diffusion through two adjacent regions, one of which is bounded by an
impermeable plane and the other by convective flow.[7] A schematic
representation of the basic system can be seen in Figure 2.2.1. The

mathematics of the problem can be described by the following equations.

 

 

2
5Cs,1(xl:t) _ DI 5 Cs.1 0 5 x1 5 L1 ; c > 0 (2.2.1)
6t 6X12
2
5Cs,2(x2vt) _ D2 6 08.2 O 5 X2 5 L2 ; t > 0 (2.2.2)
8t 6X22

subject to the boundary conditions:

6C5’1(0,t)

 

 

 

 

Hd [Cs 0°(t) - Cs 1(0,t)] - —D1 (2.2.3)
6X1
Cs’1(L1,t) - CS’2(0,t) (2.2.4)
D1 6Cs’1(L1,t) _ D2 6C5’2(0,t) (2.2.5)
6X1 6X2
5C8.2(L2't) - 0 (2.2.6)
6X2
and the initial conditions:
Cs’1(X1,O) - Ci (2.2.7)
Cs’2(X2,0) - Ci (2.2.8)
Cs’m - Ci I t < 0 (2.2.9)

The technique used to solve these equations, and calculate the
concentration history, was the backwards finite difference approximation
method. These equations were formulated into a subroutine, MBCON, in the
program SENS. Refer to Appendices D and E for a listing of MBCON and
SENS. It should also be noted that to solve these equations the solute
diffusivity in free solution, D2, the solute diffusivity in the dialysis

membrane, D1, and the convective mass transfer coefficient, Hd, must be

 

4|.

‘0' drip-.QVDIU.

..:.~\/mw -

zgunv

Wh.‘ I,‘ E < n.-

U~V‘ - I

4% pb

LI

- 2

s L~A.-.~h.v- \

U

-ai~

a»...

UZ<3ES~¢S~

\

smw)

\ uni

~<sA~

hue

V

E

l h v§~\o ii‘

 

 

 

12

H.N.N 0.53m

 

 

 

 

 

 

 

\ X
\m \m
2.33%: Calcmo 8......o
304k XJDm
«D —D
A N.— VA «Jim,
[\I/Il
20—005 m2<¢m2m2
m412<w m_m>4<_o

mcmHmEocoa aco>mamm spa: coneocu coamnccam to uayosmcom

mu- "‘,‘;

’..'u. ...\

.

.- -o-le'\V"

a“ appsvrb A
I.

'. ‘n‘
.3: 50.-.?

>,.,.-

.-
-:HU.:~ bus C

Q A ‘
5-n‘-‘ 5. Or
b hvu V. b..-

n

O
14 -~‘. -y ’.
a..ttu.6. 0‘

"Av -

l
I'v.,\ .l.as de
in. ‘

“(ve‘oped b

:1. .F dEEVe l

a. .‘ ‘
{Effiggel p:

 

‘1
V H
m
“‘4' ‘a '.‘
~
I
1.53 a-
.
S‘;e:__
D - I
Ih‘s‘k'tn ‘5
a
'r
[as '

 

13
known. The solute diffusivity in free solution can readily be found in
.an appropriate handbook (e.g. CRC Handbook of Chemistry and Physics).
The solute diffusivity in the dialysis membrane has been claimed by the
manufacture (ENKA AG, Product Group Membrana) to be approximately one
tenth of the diffusion coefficient in free solution for compounds with a
molecular weight of 300 or less.[3] (For further discussion on the
dialysis membrane refer to reference [3].) Therefore, the value used for
the solute diffusivity in the dialysis membrane, throughout this work,
was Dl-D2*O.l. The convective mass transfer coefficient used in this
work was defined by J. Tu. He used an analogy from heat transfer
developed by Rays and Crawford[20]. By assuming 1) hydrodynamically
fully developed flow in the bulk flow region, 2) a two dimensional
parallel plate system and 3) no net volume flow in the sample region, he
approximated the convective mass transfer coefficient to be Hd-D2*10000

(which was also used though out this work).[21]

2.2.2 The Kedem - Katghalskvaormulation

The approach used to solve for the osmotic response of a cell
specimen is based on the principles developed in 1958 by Kedem and
Katchalsky. Their model, the K—K Formulation, has come to be known as
the classic model for membrane permeation using principles of
irreversible thermodynamics[9].

The development begins by considering the forces that cause the
flows across the membrane. In 1931, L. Onsager related these flows and
forces into equations called the "phenomenological equations". In

general these equations are written as,

1.-
,V

by,

‘8

 

-
I‘,‘

 

5“

R.

'u.

~u¢
.
.‘u
‘n
u
2.
~—
\
.
.‘t
..
-\.
.
Y-
.

14

J1 - L11X1 + L12X2 + ... + Llan
J2 a L21X1 + L22X2 + ... + L2an
. . (2.2.10)
Jn - Lnlxl + Ln2x2 + + Lnnxn

Note that each flow, Ji (i - l to n), is influenced linearly by its
conjugate force Xi and the nonconjugate forces Xj (jfi, j-l to n),
providing the "straight" coefficients, Lii: and the "cross" or "coupling"
coefficients, Lij (ifj), differ form zero. Having dimensions of flow per
unit force, Lij - (Ji/Xj)x1, the coefficients have general
characteristics of conductances or mobility. In addition to developing
these equations Onsager also discovered the matrix of coefficients to be
symmetrical; in other words Lik - Lki for i f k. It should be noted that
this linearity holds only for sufficiently slow processes occurring when
the system is not too far removed from a state of equilibrium. The
choice of a force conjugate to the flow Ji is restricted by the
requirement that the product Jixi has dimensions of the rate of entropy
production or decrease in free energy with time.[10] Thus this is the
starting point of the thermodynamic description. The total rate of
entropy change, dS/dt, is broken into the rate of entropy transfer
between the system and its surroundings, deS/dt, and the rate of internal
entropy production, diS/dt, which is generated by the irreversible
processes occurring within the system.

d3 dfii+dis (2.2.11)

dt dt dt

15
If all process within a closed system occur reversibly, the rate of

entropy change can be written as

= 1 (2.2.12)

where dQ is the heat gained, and T is the absolute temperature. However,
if the system undergoes an irreversible change the rate of entropy change
is written as

dS ldQ

__ (2.2.13)
dt T dc dc

When dealing with irreversible processes in an isothermal system it is
frequently convenient to consider the function Q given by

C - T fii (2.2.14)

dt

which Lord Rayleigh called the dissipation function. The particular
processes of interest for this paper are the movements of solute and
water across a cell membrane. The system which will be considered (see
Figure 2.2.2) consists of 1) two compartments separated by a membrane of
thickness Ax and surface area Ac and 2) two solutions of the same solvent
and solute, also separated by the membrane. The outer compartment is
designated by 2 and the inner compartment by 3.

The general dissipation function for the two component system of
solvent and solute, for an isothermal system, is written as

Q - Jwa + JSXs (2.2.15)

where w denotes the solvent and 5 denotes the solute. Focusing attention
within the membrane of a volume element of unit area and thickness dx,

the dissipation function becomes

.....V .g .L )3. ..~ ~71: ~Ave::fivuv Aw); ~ I .u FTQZ. d a ~UA=CAVC We); ~ ..u-x ~

16

N.N.N mcsmwu

 

 

 

 

m Hzm:pm<azou

xa

/

//|.
mz<mmzmz . m pszHm<azou

 

 

Emuw>m HCQCOQEOU 03H I ucmEpLDQEou 03H mzh

 

 

 

 

....

‘-"

 

-

a - Jw {-ffiy] + J5 {-ffii] (2.2.16)

.where p denotes the chemical potential. Since Jw and Js are independent

of x we can integrate across the membrane from x-O to x-Ax;

om - Jw ofo -353 dx + JS ofo -ff§ dx (2.2.17)
dt dt

Making the assumption that the chemical potentials at the surfaces of the
membrane are the same as those in the adjacent solutions the dissipation
function becomes
Qm - Jwpr + JSApS (2.2.18)

where pr - #w,2 - pw’3 and Aps - ps’z - ps,3. If the solution is
considered to be ideal, the chemical potential is approximated by

Apj - vjAp + RTA(ln1j) (j- w or 3) (2.2.19)
where G is the partial molar volume of j, Ap in the difference in
pressure between the outer and inner compartment, 7 the molar fraction of
constituent j. To further simplify equation (2.2.19), we also assume
both solutions dilute. This implies the volume fraction of solute is

small, 6 - C533 << 1, thus

 

Aps - vsAp + RT 3:: (2.2.20)
where C5
Es _ Cs’2(x2,t) + C5 3(t)
2
and
— ACS
pr = vap + RT ___ (2.2.21)

OI

W

 

.1.

in

\‘A

 

 

18

where

 

Introducing (2.2.19) and (2.2.23) into equation (2.2.18), the dissipation
function becomes

6,, - Jw (vap - Ems) + J5 (vap + Ems) (2.2.22)
0
W S

Re a rranging <I>In we get

em - (.vaw + Jsvs)Ap + is; - "Tl! RTACS (2.2.23)
Cs Cw

N'o 1:3 in equation (2.2.20) a new set of forces and flows represent the
:3. i S s ipation function. The new forces are the hydrostatic pressure, Ap=-=Xp
and the osmotic pressure, RTACS-XD. The new conjugate forces are the

C O- t al volume flow per unit area,

Jv - JwGw + .1565 (2.2.24)
and the velocity of solute relative to solvent,
JD-:- ”:3: (2.2.25)
Cs Cw

wh ich is called the exchange flow. Writing these new flows and forces in
C a this of phenomenological equations we get
Jv - LpAp + LpDAn (2.2.26)
JD - LDpAp + LDAvr (2.2.27)
whe he An-RTACS. Making use of Onsager's reciprocal relation, LpD‘LDp:

e
quation (2.2.26) and (2.2.27) become

JV = LpAp + Lpor (2.2.28)

,—

o“

‘_

...

.\~

 

 

 

19
JD - LpDAp + LDAn (2.2.29)
To further clarify the significance of these equations, the
phenomenological coefficients, Lp, LD and LpDv are transformed into other
coefficients that allow for more convenient comparison with experimental
data, ws, 1’15 and P.
Before deriving these new coefficients we must first look at the
fl ows that are defined. Instead of studying the exchange flow, JD, it
would be more advantageous to study the solute flow Js. By rearranging

equations (2.2.24) and (2.2.25) and assuming Cw w=1

Js - (JS +JD) E

_ _ 5 (2.2.30)
(vsCs + 1)

Al 8 o , by assuming the solution on both sides of the membrane dilute,

‘

VS C S<<l, (2.2.30) becomes

JS - (JV + JD)CS (2.2.31)

The first coefficient to be determined will be ws, the solute
p e rmeability. To accomplish this experimentally, it is more convenient
: 0 have conditions of zero volume flow across the membrane, Jv-O. If a
2 one entration difference exists across the membrane, a pressure
a i fference can be applied such that JV=0, according to equation (2.2.28).
Re arranging (2.2.28) becomes

Ap- [fl] Avr (2.2.32)
LP

3
Tbs tituting equation (2.2.29) and (2.2.32) into (2.2.31) yields

2
J5 - [LPLD ' LPD ]C5An (2.2.33)

LP

 

 

9‘..-
c Q Q

 

 

 

20

The solute permeability is defined to be:

2
ws - [LPLP ’ LPD 165 (2.2.34)
Lp

The second coefficient to be defined is the reflection coefficient,
wh ich was originally introduced by Staverman in 1951. This coefficient

1 5 defined by

J
as - -LPD - - _2 Afl=0 (2.2.35)
Lp Jv
Imposing similar conditions as described above, where Jv=0, (2.2.32)

be <2 omes

Ap - asRTACS

and rearranging
O's ‘ ___—AP (2.2.36)
RTACS
The Value of as ranges between 0 and l where for an ideal semipermeable

nemb rane as-l. In other words, all of the solute is reflected. Thus,

50 31‘ as<l implies only some of the solute is reflected.
Finally the last coefficient to be described is P, the membrane

h)TI‘dI‘Eiulic permeability. This coefficient is defined letting

p - LPRT (2.2.37)
vI»,

Wh _
ere Vw is the molar volume of the solvent.

By using these definition for ws, as and P, Jv and Js can be written
in
a more useful form. Recall form (2.2.28)

JV " LpAp + LpDAfl

Sn :-
bstituting in (2.2.35) and (2.2.37), the volume flux becomes

 

 

 

21

JV — va EB - OSACS (2.2.38)
RT

Also, recall the solute flux, J5, from (2.2.31)

Js - (Jv + JD)CS
155:5;r substituting (2.2.28), (2.2.29), (2.2.34) and (2.2.35) into (2.2.31)

‘ggr‘Ez. get

JS - 65(1 - as)Jv + wSAn (2.2.39)
Thus equations (2.2.38) and (2.2.39) are the equations commonly used to
(3.3 t ermine membrane characteristics and are known as the K-K formulation

Summarizing the conditions for which these equations are valid are

a S follows:

1) The system is two compartment - two component

2) The system is in thermal equilibrium

3) The membrane is permeable to the solvent and may
or may not be permeable to the solute.

4) The solutions are assumed to be ideal and dilute

5)

The driving forces are considered to be
sufficiently small such that a linear relation

exists between the driving forces and the
resulting flows.

2 r :21 - .33 The Volum§,Flow of a Cell

Recall from Figure 2.1.1, the cell specimen resides in the sample

rr.es: -
glen of the diffusion chamber. As hypertonic solution is flushed into

C
1t?“‘3= ‘Enulk flow region the solute diffuses into the sample region and the
C=-<Ea= 11.1~

responds osmotically. The equation that is most useful for

(jugs:
£3'<=’-1':ibing the response of the cell is the equation of volume flow

(2 ‘2-38)

 

'-
~

1;,

‘5

-~.-

1,...
.

..
D
....

A
..
H
..n,

 

 

.-
‘3‘—

 

 

 

22

Jv - va [53

RT

To further simplify this equation we must take a closer look at the
experimental conditions. As mentioned previously equation (2.2.38)
implies that the volume flow across the cell membrane can be caused by a
hydrostatic pressure difference, Ap, and/or a concentration difference
ACS . However with the experimental set up used in this work it is not
1. i kely for a hydrostatic pressure difference to exist across the
membrane. Therefore Ap is assumed to be zero. Also the cell's membrane
:7. S assumed to be an ideal semipermeable membrane to the solute that were
as e d which implies aS-l. Taking into account these assumptions, equation
C 2 - 2 -38) can be rewritten as
Jv - -GWPACS (2.2.40)
Th 1 S equation can be further simplified into a more useful form. First

re c o gnize that

 

J 1 ch(t)
VB
Ac(t) dt

”he 2:- e Ac(t)-41ch(t)2 for spherical systems (which was assumed), the
Sufi-:- face area of the cell and Vc(t)-(4/3)1ch(t)3, the volume of the cell.
le re fore (2.2.40) can be rearranged into

dRc(t) _
dt

-va [C5,2(X2,t) - Cs 3(t)] (2.2.41)

W i

th the equation in this form the only unknowns are P and CS’3(t).
R. _
Q ( t ) , the radius of the cell, can be measured, vw, the partial molar
V0

lume of the solvent is a constant which can be found in the appropriate

tar
19$ and Cs’2(X2,t) the concentration of solute outside the cell, is

9—1-4

 

..u

'-

Iv»

or
...

v
o

In

 

 

V”,
I

:g“~

 

 

 

23
obtained for from the equations described in section 2.2.1. However, the
concentration inside the cell CS,3(t) can be written in terms of the cell
v0 lume (which in related to the cell radius). This is accomplished by
us ing the definition of concentration (written here in terms of
m0 lality):

moles of solute
CS-

 

volume of solvent

Le tting Ns,3 represent the moles of solute inside the cell and Vw(t)

re present the volume of solvent inside the cell, the concentration is now

wr i tten as

N
cs,3<c) - .13...
mo

No t: e , Vw(t) can be written as

Vw - Vc(t) - Vb
Vhe re Vc(t) is the total volume of the cell and Vb is the "inactive
V0 lune". The inactive volume of the cell is that which is not "free"
3 0 lVent of the cell, i.e. the solute, bound solvent and any cell
0' rganelle material. This parameter is a constant and can be determined
exp e rimentally (see Appendix A). Therefore, the concentration within the

Cell is

Cs 3(t) - “5:3 (2.2.42)
Vc(t) - Vb
the

initial concentration (t=0) within the cell is

Ci , NS»3 (2.2.43)
Vc(0) “Vb

 

 

.HE

Ab

\U“

.h‘

‘.
‘
‘u

-\

 

24
Solving for Ns,3 and substituting into (2.2.42), the instantaneous

c oncentration becomes

cs,3<c> - Ci [w] (2.2.44)
Vc(t) - Vb

by substituting (2.2.44) into (2.2.41) we get

iRL‘E). - -fiw[cs,2<x2.t> - ci[v_c_(_‘_”_'32]] (2.2.45)
dt Vc(t) - Vb

Thus, the volume flow, JV, has been written in a more convenient form
wh ich now describes the rate of change of the cell radius. This equation
3’. s also used in the program SENS. The method used to solve this equation

we S the numerical method of Runge-Kutta (4th order). Since the

c o ncentration history within the sample region is known as a function of
p o S 1 tion and time, 3,, is a constant (the partial molar volume of water),
and Vb can be determined experimentally, the only unknown is P, the cell

membrane hydraulic permeability, in equation (2.2.45).

2 — 3 The Estmation of Para4meter P

As mentioned above in section 2.2.3 the membrane hydraulic
P e rmeability, P, is unknown and must be solved for. The method used to
3 Q lve for the parameter P is a. technique known as parameter estimation.
P a‘t‘a-l'meter estimation is a discipline that provides tools for the
a E f icient use of data in the estimation of constants appearing in
“a t}\ematica1 models and for aiding in modeling phenomena. [11] Typically
the solution to an equation is thought of as solving for the state of a

35,.
S tem given the initial conditions, the boundary conditions and the

QC)
tlsttants, or parameters, which can be found in appropriate handbooks.

‘¥—___¥

i

7.,

n»
(n

.0
b1.

vu

 

.

‘n.

'u
.

.-

‘a.
~v

'1
("I
/

(l‘
D

 

 

 

25
However in many circumstances the parameter(s), in this case P, is (are)
unknown. This is the problem that can be addressed using methods of
parameter estimation.
It should be noted that there is more than one parameter

e s timation method available. This work involves using the ordinary least
5 quares (OLS) method. This method, like the other estimation methods,
a t: tempts to minimize the error between the functional values generated by
the mathematical model and the experimentally measured functional values,
wi th respect to the parameter being estimated. The function used in the
OLS method is
s - 29-1 (Y1 - ni<3>>2 (2.3.1)

Whe re n is the number of data points. 8 is referred to as the sum of the
S quares function. This equation states that the differences between the
me a sured data values, Y1, and the corresponding predicted values from the

mo del, n, are squared and summed. The goal is to minimize S with

re 8 peat to the vector of parameters, 3. This is accomplished by taking

the derivative of S with respect to the parameters and setting it equal
2 Q 2 era.

2 - 6 (2.3.2)

5.3

Len the values of F are found that satisfy equation (2.3.2) the sum of
S q
“ares function has been minimized. In some cases it is possible to
ha
Ve more than one set of parameters that satisfy (2.3.2) due to the

p):—
esence of local minimums. The ultimate desire would be to find the

 

 

( I
(IV
,1

(I1

.-

s...

 

n
“.2

’A

‘9‘
’5
a.“

.

 

“h:

H. '

"A

I I

L)

 

26
global minimum. In general this is not a problem because most models
that are well posed only have one minimum.

Using equation (2.3.1), the sum of squares function for this work

5 - 29-1 [Rmi(t) - Rci(t)]2 (2.3.3)
wh ere Rmi(t) is the experimentally measured radius and Rci(t) is the
p redicted radius, using the model equation (2.2.45), at time t. Recall
the procedure normally used to minimize (2.3.3) would be to set the
de rivative of S with respect to P equal zero and solve for P. However,
the method used to minimize S, in the program SENS, was not as direct due
I: o the difficulty of solving for Rc(t) explicitly. Given a set of
exp erimental data, (i.e. (ti,Rmi) for i-l to n), S can be minimized by
having a computer program, SENS, generate theoretical sets of data, as
men t ioned in section 2.2, for a likely range of P’s supplied by the user,
wh i (:11 can be found in the published literature. Each set of data can
the n be plugged into (2.3.3) to calculate a S. The S with the smallest

Va 1 ue, Sminv corresponds to the set of data with the best curve fit of R

\r

‘ S - t and the best estimate of the cell permeability, Pest-
Now that a method exists for estimating P, it would be beneficial
to know how good of an estimate Pest is. This is accomplished by

c a
lculating the standard deviation of Pest- However, this is not an easy

2 a
3k because of the nonlinearity of S with respect to P. (S is said to
b e
nonlinear in P if the sensitivity coefficient,

68

SP

 

 

 

 

~ ‘

 

 

 

. _. ___—“kw-.. “MA—l- .—--‘-

27
is a function of the parameter, P.[11]) To get around this, J. Beck
formulated an approximate standard deviation by examining the covariance
ruatrix of the parameters for models that are linear with respect to the

I:sarameters. To calculate the standard deviation of P we must start with

1::t1e general sum of squares function for a linear model

5 - (Y - xp)T(Y - x,3) (2.3.4)
wh ere n - X]? and
x - xJ-ku) - 5’73“) ; i-l,...,n; j-l,...,n; k-l,...,p
65k

Taking the derivative of S with respect to p, setting the matrix of
de r :ivatives equal to zero and solving for fl-b we get
b - (xTX)'1XY (2.3.5)
33" making the following assumptions

1) Y1 - n1 + 5i? the error, 61, is in the measuring of Yi and is
additive,

2) E(ei) - 0; the expected mean value of the error is zero, (the
function E(x) is the statistical function of the expected
value of the variable x.)

3) Errorless independent variables,

A) Nonrandom parameters and no prior information regarding
the parameters,

tzlnl“EE== covariance of (2.3.5) is

cov(b) - (xTX)'1x¢X(xTX)'1 (2.3.6)
”ha be t - E(eeT). Equation (2.3.6) can now be used to approximate the
C:<:>“K"‘€53Lriance matrix of the parameters for nonlinear models;

cov(b) z (XTX)‘1XT¢X(XTX)'1 (2.3.7)
VJ i‘ 1::5‘TEL the additional assumptions of

l) constant variance errors,

2) uncorrelated errors,

3) covariance matrix of errors is known to within a
multiplicative constant,

 

-
tope‘
. :-
....

..
_...,
..tl‘

ut.

 

28

the estimate of (2.3.7) becomes

(Y - Y)T<Y - Y)
(n-p)

cov(b) z (xTxrls2 ; 52 z (2.3.8)

 

where n is the number of measurements, or data points, recorded, Y is the
experimental measured value, Y is the predicted value and p is the number
of parameters. Recall, in this work, there is only one parameter (P).

Rewriting (2.3.8) for one parameter the covariance matrix simplifies to

 

T
cov(b) - V(b) z (XTX)'152 ; 32 x (Y ' Y) (Y ' Y)(2.3.9)
(n-l)

where V(b) is the statistical function variance, which is related to the
standard deviation by 92(Pest) - V(b), (where 0 in the standard
deviation). Therefore, applying (2.3.9) the square (M3 the standard

deviation becomes

2E-1 [Rmi<c) - Rci<c)12

5Pest

02(Pest) z (2.3.10)

 

where 6Rci/6Pest is the so called sensitivity coefficient.

29

2.4 The Effect of Temperature on P. (The Activation Energyl

Several workers have studied the temperature dependence of the
movement. of 'water across cell membranes. The relationship used to
describe this dependence obeys the classical Arrhenius type equation

P - k exp[-AEa/RT] (2.4.1)

where k is a constant (frequency factor) and Ea is the activation energy.
This equation can be rewritten as

ln(P) - ln(k) - AEa (2.4.2)

RT

By plotting ln(P) v.s. l/T, the activation energy can determined from the

slope.

CHAPTER 3

The Parameter Estimation/Simulation Program, SENS

3.1 Introduction and Back round of J Tu's Pro ram

As mentioned in Section 1.2, J. Tu developed a FORTRAN computer
algorithm, SENS, to be used in conjunction with the microscope diffusion
chamber system to estimate membrane water permeabilities. Specifically,
the program was designed to estimate the permeability of a cell membrane
or run a simulation (pseudo) experiment to see what would happen during
an experiment under specified conditions. Prior to running the program
the (actual or simulated) experimental data and parameters were entered
into an input file. The input file was read by SENS and processed. The
output consisted of four optional graphs (sent to the screen and a
graphics file) and an output file containing tables. The first graph
plotted the normalized concentration change, in the dialysis membrane and
sample region, as a function of the normalized time. The second graph
plotted the sensitivity coefficient, 6Rc/6P, as a function of time. The
third plot was the normalized cell volume as a function of time. The
last graph plotted the sum of the squares function versus the
permeability. The first table in the output file was the input data, the
second a table containing the concentration distribution, in the dialysis
membrane and the sample region, as a function of time, the third a table
of the experimentally measured radius as function of time and finally the

best statistical estimate of the membrane hydraulic permeability, the

30

31
standard deviation of the best estimate of the permeability and the
.corresponding minimum sum.

Tu's program worked quite well, providing all of the parameters and
data were entered into the input file correctly. Therefore, the basic
structure of his program was left intact i.e. the processing of the
parameters and data. The major modifications made were at the input and
output stages. The input stage was revised to allow the user an option
of entering the necessary input by one of two ways: 1) a (modified)
input file or 2) by answering the prompted questions. The output was
arranged in a more logical manner and labelled more clearly as to what
was being (graphically) plotted and what tables were being generated.
Also, the best estimate of the permeability, the standard deviation and

the minimum sum were sent to the screen and to two output files.

32

.3.2 The Modified SENS

At first, the concept of making SENS user friendly seemed a
relatively simple task. But during the modification process it was
discovered that this would not be the case. The program grew 716
(FORTRAN) programming lines (which is about 24K) to 2002 programming
lines (which is about 68K).

The most efficient way to describe how SENS works would be to look
at the flow chart of SENS in Figure 3.2.1. The actual program can be
found in Appendix D. In addition, sample output, of the four graphs
describe in Section 3.1 and of one output file, can be seen in Figures
3.2.2 - 3.2.6. Note: this sample output is from actual experimental data
for an experiment using a lymphocyte at 25°C.

Once the modifications were made, the next step was to convert SENS

to an IBM Personal Computer.

33

Figure 3.2.1 - Flow Chart Of SENS - PRIME Version

I SENS |

lnternall g documented introduction
and list of variables

\I/

Initialization and declaration
of variables

 

 

 

 

 

 

 

 

 

 

 

 

Would uou like an 1 No
introduction to 'SENS'?J

Yes

 

 

 

Print introduction to screen

 

 

 

 

 

Yes Would you like a list
of the necessaru input?

 

 

 

 

 

No

 

 

 

Print a list of necessary
input to file I_DATA.LST

 

 

 

 

Yes

 

Would uou like a list
L ofa sample input file?

 

 

 

 

Print a list of sample No
input to file l_.SENS.EXP

 

 

 

 

 

 

 

 

Explain the output
34. capabilities

,---"" “-w i) Tabular
(Stop - End Program) 2) Graphical

 

 

 

 

 

 

 

lnternallg-
Set IRUNAG=0

 

 

 

34

Figure 3.2.1 (cont'd.)

 

 

 

Terminal I Would gou like to enter 1 Input file

 

Lg,

the necessarg input using

 

L an input file or the terminal?

 

7% gou want to use the program to
l) process experimental data
2) run a simulation ?

 

 

 

 

Enter control parameter -
IRELPSE
(l) = experimental data

(2) = simulation

 

 

 

 

 

 

 

 

Read the pre-existing
input file

 

 

Enter the phgsical parameters ofthe sustem:

l) RLl, dialgsis membrane thickness

2) RL2 ,-sample region (or cell chamber)
thickness

3) LIP ,location of cell (5 - it)

or choose Di=02/10
6) Hd; mass transfer coefficient or choose
Hd =10000*02

volume
9) RMAG ; magnification factor

 

4) DZ ;diffusivitg of solute in sample region
S) Di ,diffusivitg of solute in dial gsis membrane

7) CINIT , CINF ; Initial and final concentrations
8) VINA ; normalized osmoticallg inactive cell

 

 

 

 

 

 

\
[ Rewev parametersinput 1

 

 

 

y \
—-£s——-(Would you like to make em; changes?)

 

 

 

 

 

No
\ \
[flange the parameteq Internal question: 1
What is the value of lRUNAG"

_/

 

 

\1/

(3:0)] \Lm)

 

 

 

—:—-—-—-——————

35

Figure 3.2.1 (cont'd)

l

 

 

Enter :

l) IMO, Tl‘ll ,time range

2) OT ;time step

3) DP ; permeabilitg step

4) P0, Pl ;permeabilitg range

5) PSEN , permeabilitg value at
which the sensivitg
coefficients will be
calculated

 

 

 

 

 

 

Review this input

\I/

 

 

 

(Mum gou like to make ang changes’?)

 

Nol

 

 

 

 

 

 

W

Internal question: 55(1)
Change the parameter ‘ (0) What is the value of IRUNAG 7

 

 

 

 

 

 

 

 

delag in the data?

 

 

.. ..JU) (2)

 

 

 

 

 

 

No

Enter DELAY

 

 

 

 

l) PTRU ; permeabilitg value

2) RINIT ;initial cell radius
3) DR ; radius randomness

J
, Internal question:
(I) flernal WNW“: 7 (2) Ehat is the value
Real LWhat is the value of IRELPSE. Simulation of IRELPSE?
Experiment
Is there a time Y” EM" 3

of the radius historg
to generate

factor

 

 

 

 

(Time,

Enter the data pomts ;
THMI), RA(I)

Cell Radius)

 

 

 

 

 

 

[ERA

ew input data—1

 

 

Do gou want to make
ang changes7

 

 

 

N0

 

Yes

Wke changiF)

\/

<1)

 

 

 

 

 

 

| Review input
\I/

 

00
make em; changes?

gou want to Yes

 

 

 

No Wake changes

 

 

 

 

 

 

 

 

36

Figure 3.2.1 (cont'd.)

l

 

 

Select the desired graphical output :

1) Normalized concentration v.s. normalized time, IF I =Yes
2) Sensitivitg coeffiCient v.s. ti me, IF2=Yes

3) Normalized cell volume v.s. ti me, IF3=Yes

4) Sum of squares function v.s. permeabilitg, lF4=Yes

 

 

 

 

 

 

Dump the input parameters and data to
the output file 0.5ENS.DAT

 

 

 

 

 

Calculate the concentration historg in

the dialgsis membrane and sample region

use the backward difference method.
Tl‘1(l), CONC(I,J)

 

 

 

 

 

Dump Tl‘1(|), CONC(I,J) to 0.5ENS.DAT
using a pictoral representation of the
dial gsis membrane and sample region

 

 

 

 

 

 

If lFl =Yes, then plot normalized concentration (CA, CB)
v.s. normalized time (TM(I)/TMI)

 

 

 

Calculate radius historg for PSEN [RS(TMS,PSEN)I and
PSEN+PSEN*EPI [RB(TMB,PSEN+PSEN*EPI)]
using Runge- Kutta method

 

 

 

 

Calculate the sensivitg coefficient, SEN(I) adR/dP,
at each time step, TMSU)

 

 

 

 

 

Dump TMS(l) and SEN(|) to 0..SENS DAT

\I/

If IF2=Yes, then plot SEN(I) v.s. TMSU)
on the screen and graphics file G_PLOT

 

 

 

 

 

 

 

 

37

Figure 3.2.1 (cont'd)

l

If IRELPSE=2, then generate a simulated radius
historg using PTRU, TMAU), RA(|)

 

 

 

 

 

\
[Emulate normalized volume VOL(lfl

 

 

Calculate sum of squares function SUMO)
for the permeabiltig range P0 to Pl

 

 

 

 

 

Dump SUMO) v.s. P(l) to 0_.SENS.DAT

\l/

Determine the minimum SUM(l)=SUMIN and the
corresponding P(l)=PEST

 

 

 

 

 

 

 

 

 

If lF3=Yes, then plot YOL(I) v.s. TMA(I) on the
screen and graphics file G_PLOT

 

 

 

 

 

If IF4-Yes, then plot SUM(I) v.s. P(I) on the
screen and graphics file G_PLOT

 

 

 

 

\l/
[Emp input parameters and data to 0.5MRYDAfl
\l/
Dump PEST, SDP, SUMIN to the screen,
0.5MRYDAT AND 0_.SENS.DAT

 

 

 

 

 

 

Do gou wish to save the input data to YES

a specified file? I

 

 

 

 

Enter the name
No

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0f the file
Yes . .
Do gou wish to run the program again?
No
Would you like to
I) use the same input data, (making ang
necessarg modifications); set
IRUNAG = IPUNAG + l ___b.
2) enter all new parameters and data: ” _ ‘
set lRUNAG = 0 (Eton End Program)
w

 

 

 

 

same lnDUl data I all new data

 

 

38

FIGURE 3.2.2 - Sample Output File of SENS - O_SMRY.DAT

‘******************* THIS 13 FILE 0 SMRY.DAT ************************
THE INPUT PARAMETERS AND DATA WERE:

THE VALUES ENTERED SO FAR ARE:

1) DIALYSIS MEMBRANE THICKNESS - .160E+02 MICRONS
2) CELL CHAMBER THICKNESS - .915E+02 MICRONS

3) LIPOSOME POSITION (5-11) - 5

4) DIFFUSIVITY IN CELL CHAMBER - .148E-08 M*M/SEC.
5) DIFFUSIVITY IN DIALYSIS MEMBRANE - .148E-O9 M*M/SEC.
6) MASS TRANSFER COEFFICIENT - .148E-04

7) INITIAL CONCENTRATION - .291 OSMOLALITY

8) FINAL CONCENTRATION - .725 OSMOLALITY

9) INACTIVE VOLUME % - 34.70

10) MAGNIFICATION FACTOR - 11290.0

THE VALUES ENTERED ARE:
1) TIME STEP - 1.00 SEC.

2) TIME RANGE - .0 SEC. TO 60.0 SEC.
3) PERMEABILITY STEP - .10 MICRONS/SEC.
4) PERMEABILITY RANGE - .00 MICRONS/SEC. TO
15.00 MICRONS/SEC.
5) INVESTIGATING PERMEABILITY - 9.30 MICRONS/SEC.
THE DATA POINTS ENTERED WERE:
(INCLUDING THE TIME DELAY OF .0000 SEC.)
J TIME(J) RADIUS(J)
(SEC.) (CENTIMETERS)
1 .20 4.69
2 1.40 4.69
3 3.00 4.65
4 4.40 4.65
5 7.60 4.61
6 11.80 4.52
7 13.90 4.43
8 15.30 4.38
9 18.40 4.34
10 22.00 4.25
11 26.60 4.16
12 31.40 4.12
13 37.60 4.07
14 51.80 4.03
15 54.30 3.99
16 58.90 3.99

17 .00 .00

39

FIGURE 3.2.2 (cont'd.)

'********************** THE RESULTING PERMEABILITY ********************
THE LOCAL MINIMUM OCCURS AT P - 8.600 MICRONS/SEC.
THE STANDARD DEVIATION OF ESTIMATED P IS .267E+00 MICRONS/SEC.

THE MINIMUM VALUE OF SUM IS .004

40

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44

.3.3 Converting SENS to the IBM PC

Before SENS was adapted to the IBM PC, the primary concern that
needed to be addressed was which graphical software package should be
used. Originally SENS resided on the PRIME, which allowed the use of the
interactive graphical software, PRINTEX. The graphical software package
that was chosen to be used with the converted SENS version was PLOTIT.
PLOTIT was chosen because of its ease of use, the quality of graphs
produced (using a Hewlett Packard Plotter) and its availability at the
Engineering Computer Facility PC room.

Converting SENS from the PRIME to the IBM PC involved a two step
process. First SENS was adapted to function as though it were on an IBM
PC but was actually still on the PRIME. In other words, the interactive
graphical programming code was stripped from the original version of SENS
and replaced with code to generate four (optional) separate output files
which could be used with PLOTIT (on the PRIME). Then once all the "bugs"
were worked out SENS was converted to the IBM PC.

Another important consideration addressed was which FORTRAN compiler
should be used. The compiler that was used was MICROSOFT FORTRAN. This
compiler was chosen because the author was familiar with its operation
and it seemed to have a good error detecting mechanism which was very
helpful when SENS was converted.

Once the conversion process was completed, a sample input file was
used as a test to make sure both versions yielded the same results. It
should also be noted that after the conversion some minor programming

changes were made to both versions resulting in the programs recorded in

Appendices D and E.

45

 

 

CHAPTER 4

Experimental Equipment and Procedures

4.1 Preparing Cells for Experimental Runs
The methods used to prepare the cells used in this work will now be

described.

4.1.1 Preparing Egg Lecithin Liposomes

Before experiments using egg-lecithin liposomes were conducted, the
liposomes, the isotonic sucrose solution and the hypertonic sucrose
solution had to be prepared. The solutions were made by adding the
proper amount of sucrose to a known amount of distilled water. The
desired concentrations were 0.02 osmolality for the isotonic solution and
0.04 osmolality for the hypertonic solution. The concentrations were
measured using an osmometer.

Once these solutions were made the liposome cells were prepared.
0.07 grams of the egg lecithin lipid was measured into a 25 m1 erlenmeyer
flask. Next, the lipid was dissolved using 25 ml of a 2:1
chloroformzmethanol solution and a vortex mixer. Then 0.5 ml of this
solution was pipetted into a 50 ml round bottom flask which was fastened
to a rotavac and a vacuum was applied for approximately 8 hour. The
chloroformzmethanol solution evaporated leaving a thin film of lipid
dispersed on the bottom of the flask. The flask was detached and 10 ml
of isotonic solution was gently added, being careful not to disturb the

lipid film, and stoppered. The circulating bath, which had been

46

47

preheated to 60°C, was turned off, the flask was placed inside and
.steadied, and the bath was closed. This solution was left in the bath
overnight and by morning a small cloud of lipid had formed on the bottom
near the middle of the flask.

After a few tries, it was discovered that the best results for
obtaining what was believed to be "unilamillar" vesicles was to use a
pipetman, which was preadjusted to 18 pl samples, and extract a sample

from "near" the edge of the cloud.

48
4.1.2 Preparing Human Lymphocyteg

Prior to conducting experiments using lymphocytes, whole blood was
obtained and separated, and isotonic and hypertonic salt (sodium
chloride) solutions were prepared. Again, these solutions were prepared
in a similar fashion as those that were used in the liposome experiments.
The desired concentrations for the lymphocyte experiments was 0.291
osmolality for the isotonic solution and 0.725 osmolality for the
hypertonic solution. 0.291 osmolality was chosen for the isotonic
solution because this is the approximate osmolality of human blood.

0.725 was chosen because by increasing the concentration 2.5 times
allowed the final cell size to decrease about 40%, with respect to the
initial cell volume, which allowed for greater ease in recording the
change in the cell radius. Also, this was the approximate range used by
Hempling and Porsche, which allowed for comparisons to be made. In
addition to measuring the concentrations of the solution, the pH was also
measured. The pH of the solutions ranged form 7.0 to 7.3. The pH
measurements were made using an Orion pH electrode probe and meter.

The blood used was either obtained from the Red Cross in Lansing,
Michigan or was drawn from the author by a medical technologist on
campus. The blood was collected in vacuum tubes containing EDTA.
Therefore the age of the drawn blood ranged between 1 and 24 hours old by
the time the blood had undergone separation. Initially 3 ml of
Histopaque-1077 (SIGMA DIAGNOSTICS) medium was placed in 15 ml test tube.
Next 6 ml of blood was carefully layered on top of the medium. The tube
was then placed into a swing-bucket centrifuge and set at 387 6'5 for 30

minutes. This resulted in four distinct layers. The top layer contained

49
primarily plasma and platelets, the next layer contained the desired
.lymphocyte cells, while the last two layers contained the medium and
other blood cells (including red blood cells), respectively. The top
layer was suctioned off to approximately 5 mm above the lymphocyte layer.
Next the lymphocyte layer was pipetted off and placed into another 15 ml
test tube. These cells were then washed with 5 m1 of Bacto
Hemagglutination buffer solution [(0512-33-2) DIFCO LABORATORIES] (PH
7.3iO.l) and centrifuged at 387 6'5 for 10 minutes. The lymphocytes
remained at the bottom of the tube while platelets were suspended in the
buffer solution. The top layer of platelets was then suctioned off.
This washing procedure was repeated two more times. Note, clumping
sometimes occurred at any step of the washing. Clumping occurred
approximately one out of every five separation attempts. Sometimes the
clumps could be shook loose and sometimes the procedure was started over
with another sample of blood because the clumps would not readily break
apart. Finally, 0.8 ml of isotonic solution was added to the

lymphocyte/platelet medium and stored at 4°C for an average of one hour.

 

 

50
4.2 Description of the Microscope Diffusion Chamber
List of parts:

1) Chamber body, with heat exchange ducts

2) Clear plastic bottom cover slip

3) Dialysis membrane, (Cuprophan M80, ENKA AG, Product Group

Membrana)

4) Rubber membrane retaining ring

5) Top fitting

6) Top cover glass

7) Plastic membrane retainer

Schematic representations of the diffusion chamber are shown in

Figure 4.2.1 and 4.2.2. The chamber body was made of copper to allow for
effective heat transfer. There were two separate flow channels built
into the chamber body. The inner bulk flow channel ran down into the
entrance, near the middle area of the chamber body, across the bottom
clear plastic cover slip and up and out the exit. This channel provided
the introduction of the hypertonic solution during an experimental run.
The outer flow channel ran along the outer edge of the chamber, in a
square pattern, surrounding the inner channel region. This was the
channel used to control the temperature of the diffusion chamber. The
dialysis membrane separated the bulk flow region and the sample region.
The membrane has a dual purpose: 1) absorbing the shear of the bulk flow
region, thus keeping the cell specimen relatively stationary while 2)
providing a mechanism for solute transport (i.e. diffusion). The rubber
retaining ring held the dialysis membrane firmly to the top fitting, made
of brass, and also provided a seal between the top fitting and the

chamber body. The top cover glass was glued to the top fitting providing

a solid stationary boundary. The area between the dialysis membrane and

51

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52

Figure 4.2.2 - Schematic Cross Sectional View of Microsc0pe Diffusion Chamber

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Temperature
Regualting Bulk Flow Bulk Flow
Port Entrance Exit
. .// I '5 : llii ii 1 , : /:'.‘,:’, /[’.-l' I
/ . . L." #:l//
7 L-> —> -=; —>; —’r //_
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SIDE CROSS SECTIONAL VIEW

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Temperature
Regulating
Fluid

Exit

Temperature
Regulating
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Entrance

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TOP CROSS SECTIONAL VIEW

 

53
the top cover glass was called the sample region. This is where the cell

specimen resided.

54

4.3 Description of the Overall Experimental System

 

List of Equipment Used During Experimental Runs

1) Microscope diffusion chamber

2) Microscope, (Ziess Universal Research D-7082)

3) Pumping system - isotonic and hypertonic solutions

4) Discharge beaker (1000 ml)

5) Pressurized air supply (Engineering Building)

6) Vibration damping table

7) Digital temperature display device, (OMEGA Digicator C)

8) Copper-Constantan thermocouples, (OMEGA Engineering,
Inc., Model No. TT-T-24)

9) Endocal refrigerated circulating bath, (RTE-8DD, NESLAB)

10) Insulated Tub

11) Video monitor, (19" RCA Color Television)

12) Video camera, (Color JVC or Black and White)

13) Video cassette recorder (Sony-fil or Sony U-matic,VO-5600)

14) Video tape (Beta or 3/4")

15) Timer (Midwest Telecommunication)

l6) Vacuum grease

After having isolated and prepared the cells of interest in the isotonic
solution, the experimental system was set up. A schematic
representation of the experimental system is shown in Figure 4.3.1. The
system consisted primarily of three units: 1) the microscope diffusion
chamber and pumping system, 2) the temperature control system and 3) the
data recording equipment.

The microscope was set up on a vibration damping table. This table was
used due to the focusing problems that occurred when the microscope was
on a bench or counter top. Vibrations from other engineering labs were
conducted throughout the building which caused a blurring effect when
attempting to focus the microscope on a cell specimen.

First the microscope diffusion chamber body was placed on the specimen
stage of the microscope and fastened. Next the electronic solenoid

valves of the pumping system were connected to the specimen stage. Then

55

 

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56

the pumping system was connected to the entrance for the inner bulk flow
.channel, a discharge hose was connected from the exit bulk flow port to a
discharge beaker and the air supply was connected to the pumping system.
Subsequently the temperature control equipment was set up. The
circulating bath was placed on a table next to the vibration damping
table. The bath provided the fluid medium necessary to control the
temperature of the diffusion chamber and the isotonic and hypertonic
solution bottles. An internal circulating pump dispensed fluid to and
from the diffusion chamber while two external pumps provided and removed
the fluid necessary to heat/cool the solution bottles in the insulated
tub. The hoses connected to the external entrance and exit ports of the
diffusion chamber were insulated to minimized the heat transfer to/from
the surrounding lab environment. As mentioned above, the solution
bottles were placed in an insulated tub. The reason the solution bottles
were placed in a separate tank, and not directly into the circulating
bath, was to avoid vibration transfer from the compressor in the
circulating bath to the solution bottles and ultimately to the sample
region of the diffusion chamber. In addition, a series of thermocouples
were used to monitor the temperature at various points of the
experimental system. More specifically, the temperatures of the top
fitting of the diffusion chamber, the fluid in the insulated tank, the
fluid in the circulating bath, the fluid at the entrance of the inner
bulk flow channel and the fluid in each solution bottle were monitored.
Each of these thermocouples were connected to a digital temperature

display device.

57
Finally the data recording equipment was set up. First the video camera
.was attached to the vertical tube on top of the microscope. The video
cable from the camera was connected to timer. The timer projected a
digital stop watch on the upper left corner of the video monitor. The

timer cable was then connected to the video cassette recorder, which was

connected to the video monitor.

58

4.4 Description of an Experimental Run

After the system was set up one or more experimental runs could be
conducted. (It should be noted here that before any experiments were
performed some preliminary tests were conducted, see Appendix B.)
Initially the temperature controlling bath was started and allowed to
equilibrate to a desired temperature. This included having the diffusion
chamber, solution bottles and circulating fluid at approximately the same
temperature. Typically these three temperatures were equal to within
0.5°C. During this temperature transient, the dialysis membrane was
prepared. The membrane was shipped from the manufacture (ENKA) in sheets
measuring 88 x 11 inches, which were cut into 18 x 2 inch sections and
presoaked in isotonic solution for 30 minutes. After these preliminary
steps were taken, hoses leading from the solution bottles were
preflushed, using manual release valves, being careful to remove all air
bubbles from the lines. Next, the top fitting was removed and the
chamber body was flushed with isotonic solution. The top fitting was
then inverted, cover glass facing up, and an 18 pl sample, containing the
cell specimen, was pipetted on to the center of the glass. Then a
section of presoaked dialysis membrane was placed across the membrane
retainer. Extra care was taken in handling the dialysis membrane being
careful not to rip it. The membrane was then carefully lowered on to the
top fitting using the plastic membrane retainer. Holding the membrane
retainer in place, the rubber O-ring was applied to the fitted groove in
the top fitting. This O-ring held the membrane firmly in place. Next, a
small amount of vacuum grease was applied to the O-ring and then the top

fitting was placed into the chamber body. Note, at this point it was

59
also very important to make sure no air bubbles were present in the bulk
.flow region. Air bubbles in the bulk flow region would cause a pulsing
motion during an experimental run. The microscope was next focused on
the sample region. Then the pumping system was turned on flushing the
isotonic solution through the bulk flow region. This allowed for the
operator to check for air bubbles and any leaks before the hypertonic
solution was introduced thus "preserving" the cell specimen. The
isotonic solution was shut off and a search for a desirable specimen was
conducted. Once a cell was located the sample region thickness (RL2) and
cell position (LIP) were determined. The sample chamber thickness was
calculated using the grid marks on the fine adjustment focusing knob.
Each grid mark was calculated to be 1.5 pm deep. (This measurement was
performed by J. Tu). The number of grid marks counted between the top
cover glass and the dialysis membrane gave an approximate sample region
thickness. Note in the analysis it was assumed that the sample region
thickness remained constant, however in practice the sample region
thickness sometimes increased, on the average, 5 - 7%. Therefore an
average thickness was used based on the initial and final sample region
thicknesses. Also, the cell position was noted by counting the number of
grid marks from the dialysis membrane or the top cover glass. Again, in
the analysis the cell position was assumed constant; however in practice
the cell sometimes moved, on average 5%. Therefore an average cell
position was used based on the initial and final cell position. After
these calculation were made the isotonic solution was started again,
final focusing adjustment were made and the video recorder was started.

At: the desired time (t-O), the timer was started and the switch for the

60
hypertonic solution was engaged, which also cut the supply of isotonic
.solution. Note, the reason hypertonic solution was started while the
isotonic solution was flowing, and not from a dead start, was because the
shock from a dead start sometimes caused the cell to move out of the
plane of focus. The transition from flowing isotonic to hypertonic was
less abrupt. The cell response was recorded for a length of time based
upon calculations made using the simulation mode of the data reduction
program using reasonable estimates of anticipated permeability. At the
end of the time duration, the pumping system, timer and video recorder
were stopped.
At this point the experimental system could be set up for another run or
solution bottles could be exchanged and the system started up again,

further reducing the cell size.

61
4.5 Description of Data Measurements

After each run or after a set of runs, the data measurements were made.
It should be noted that all experimental runs had a time delay. This was
due to the small piece of tubing which connected the flow and the
diffusion chamber bulk flow entrance port. In the description above, it
was mentioned that a timer was started at the time the hypertonic
solution was switched on. At that moment, the solution in the connecting
tube still had isotonic solution in it. Based upon the length of the
tube, the tube diameter and the flow rate of the hypertonic solution, a
"time delay" was calculated (at the beginning of each experimental day).
The time delay did not need to be subtracted here because the program
SENS allowed the user to have a time delay (DELAY) subtracted from the
data if necessary. The typical time delay was between 2.2 seconds and
3.1 seconds with an average of 2.7 seconds.

The recorded video tape was played back and using the pause function the
time of the timer and cell radius was recorded. The number of data
points collected was about 20 to 30 for each cell. It should also be
noted here that during the play back of the tape, measuring the cell
radius was sometimes a difficult task for three reasons: 1) the cell
sometimes fluctuated such that the outer membrane of the cell was no
longer spherical in shape, particularly when experiments using liposomes
were conducted, (note: this fluctuation tended to diminish as the
temperature at which the experiment was conducted was decreased), 2) the
cell outer membrane was not clearly defined on the TV monitor, and 3) the
pause function for the VCR, particularly the SONY Beta machine, caused

the projected image on the TV monitor to vibrate slightly. These effects

62
will be studied in Sections 6.2.7 and 6.3.7. It should also be noted
.that when experiments using lymphocytes were conducted no distinction was
made between T-cells and B-cells (which could obviously lead to a
variability in the results presented in this paper).

The temperature was also recorded for each experimental run by using a
copper-constantan thermocouple which was placed on the top fitting.
During an experimental run the temperature sometimes changed slightly,
particularly if the temperature of the experiment was removed from room
temperature. However, this temperature change, on average, was no more

than l.5°C (which occurred when the temperature of the experimental run

was either at 10°C or 37°C).

63
4.6 Iypgs of Experimgnts Performed
As described previously, the experimental system was set up either to do
multiple experiments with different cells, at the same experimental
conditions, or to use the same cell and subject it to different
experimental conditions, e.g. continue to increase or decrease the
extracellular concentration or temperature. Using these two basic
configurations the normalized osmotically inactive volume of the cell,
the cell membrane water permeability and the cell membrane water
permeability activation energy could be determined.

To obtain the inactive volume of a cell, the cell was initially
subjected to the isotonic solution and the radius of the cell was
recorded. Then the cell was subjected to an increase in concentration
and allowed to come to an equilibrium cell volume. The cell radius was
again recorded for this new specified concentration. Next the original
isotonic solution was replaced by another solution with an even higher
concentration with which the cell had equilibrated. This procedure was
repeated until the cell had undergone five increases in concentration.
The inactive volume of the cell was obtained by developing a Boyle-Van't
Hoff plot (see Appendix A).

To obtain the permeability of a cell type at a specified temperature,
the cell was initially subjected to the isotonic solution at this
Specified temperature. At desired time a hypertonic solution was
imitroduced and the radius history of the cell was recorded as mentioned
it! Section 4.5. The parameter characterizing the system and the measured

cksta.were entered into SENS and an estimated permeability was formulated.

64
To obtain the activation energy of a cell type, experiments were
_performed at five different temperatures. At any given temperature, five
individual permeabilities were recorded and averaged to generate a mean
permeability. Recall by plotting the natural logarithm of the mean
permeability as a function of the inverse absolute temperature the

activation energy was obtained.

CHAPTER 5

The Experimental Results and Discussion
.5.1 Introduction

As mentioned previously, the objective of these experiments was to
apply the microscope diffusion chamber to cell systems that had
previously been examined by other scientists. The results obtained from
the diffusion chamber would then be compared with the results of these
other scientists. The specific parameters that were compared were the
normalized osmotically inactive cell volume, cell membrane water
permeability and cell membrane activation energy. The cells systems

tested were egg-lecithin liposomes and human lymphocytes.

65

66

.5.2 The Normglized Osmoticgllv Inactive Cell Volume

The normalized osmotically inactive cell volume of egg-lecithin
liposomes was not determined as a part of this work. Experiments using
the diffusion chamber were performed by R. Callow [18] of the BTPL, using
similar experimental conditions. The normalized osmotically inactive
volume reported by Callow was 6.0%. Therefore, this was the values used
to determine the liposome cell membrane permeability and activation
energy, (see Figure 5.2.1 for a schematic of Callow's results).

The normalized osmotically inactive volume for human lymphocytes was
determined to be Vb - 34.7%. See Figure 5.2.2 for the graphs of Vcell
v.s. l/Cs. This result is in good agreement with the inactive volumes
published by Hempling [14] (32.0%) and Porsche [15] (36.9%) (see Table
5.2.1). Therefore this inactive volume (34.7%) was used to formulate the

membrane permeability and activation energy for lymphocytes.

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69

TABLE 5.2.1 - Normalized Osmotically Inactive Cell Volume

cell type: human lymphocyte

 

Investigator Normalized Volume (%)
Hempling 32.0
Porshce 36.9

Sherban (*) 34.7

70
5.3 The Cell Membrgne Wgter Permeability

The membrane water permeability was calculated for 25 individual
liposome cells and 25 individual lymphocyte cells. The temperatures at
which the permeability was generated were 10°C, 16°C, 25°C, 30°C and 37°C
for liposomes and 10°C, 16°C, 25°C, 30°C and 35°C for lymphocytes, five
at each temperature. These results are summarized in Tables 5.3.1 and
5.3.2. The mean permeability at each temperature is also recorded.

A comparison can be made between the permeability calculated at 25°C
from this work and the work published by other scientists, for both
liposomes and lymphocytes (see Table 5.3.3). For example, Boroske [12]
reported the mean permeability (Pm) for egg-lecithin liposomes to be
4li4.9 pm/sec, Callow [13] reported Pm - 40.5i8.4 pm/sec, Melkerson [13]
reported Pm-4l.0i3.l pm/sec and Tu [7] reported Pm - 39.0:3.3 pm/sec.
The mean permeability generated for this work was 40.2i6.9 pm/sec. This
is in excellent agreement with the mean permeability reported by the
above investigators.

For the case of the lymphocyte, a similar comparison can be made.
Hempling [14] reported the mean permeability at 25°C to be 10.4iO.45
pm/sec, while Porshce [15] reported Pm - 4.2i0.42 pm/sec at 25°C. The
mean permeability calculated for this work was 9.3il.9 pm/sec at 25°C.
This is in good agreement with the permeability reported by Hempling.
However, there seems to be a discrepancy with the resulting mean
permeability reported by Porshce. By reviewing the paper published by
Porshce it was discovered that she devised a method to directly measure
the concentration change within the sample region of a diffusion chamber

similar to the one developed by McGrath. The solute she used was sodium

7l
chloride and the dialysis membrane had a wetted thickness of 20 pm. Her
_system was also similar in that there was a time delay of approximately 1
second due to the hypertonic solution front passing from the (switched)
valve to the chamber. Based on the information she reported in reference
[15] it was concluded that she treated the sample region (cell chamber)
as a "lumped" system. The thickness the sample region during these
concentration measurements was never specified. When the concentration
measurements were made she discovered that the concentration—time history
could be approximated by an exponential function. She calculated the
time constants with and with out a dialysis membrane to be r-2.08 sec
and r-l.48 sec, respectively. Therefore, she claimed the dialysis
membrane only played a secondary role as it did not cause much addition
to the delay and that the deviation from a step-like behavior seemed to
be caused mostly by a disturbance of the concentration profile due to
turbulence on its way toward the cell chamber. These results also
indicated that 95% of the final concentration was reached after about 5.6
seconds, when the cell has not yet started to shrink, and 99% was reached
after 8.6 seconds. In addition, she also stated that the zero time was
defined when shrinkage of more that 2% was detected. However, she did
realize that an under estimate of the delay time would result in an
underestimate of the membrane permeability. Based on the above argument
she concluded that the approximation of the measured concentration-
history by a step function impose at the corrected zero time seemed
therefore justified. These same experimental conditions that Porsche
used were entered into SENS, (i e. wetted dialysis membrane thickness -

20 pm, sample region thickness - 100 pm, the sodium chloride diffusivity

72

in free solution, D2, - 1.49E-9 m2/sec (at 25°C), the sodium chloride
diffusivity in the dialysis membrane, D1-0.1*D2, the convective mass
transfer coefficient, Hd-10000.*D2, the initial concentration - .310
osmol and the final concentration - 0.478 osmol), to see what the 95% and
99% concentration-time history results would be. Note, two assumptions
were made in this analysis since these parameters were not specified;
specifically, the sample region thickness was estimated at 100 pm and the
concentration readings were taken at the surface of the dialysis membrane
in the sample region, LIP-5. This analysis showed the 95% concentration
reading did not occur until approximately 45 seconds, while the 99%
concentration reading did not occur until approximately 85 seconds.
Consequently Porsche's analysis would lead to an underestimated membrane
permeability. Therefore, this is probably the cause for the discrepancy.

Note in Tables 5.3.1 and 5.3.2 two types standard deviations are
recorded: 1) the individual standard deviation for a single cell at a
specific temperature and 2) the standard deviation for the "population"
of cells at a specified temperature. The results show that the standard
deviation was less for an individual cell than for the population of
cells, at a specified temperature. Therefore it can be concluded that
there is a variation among the population.
Another way to look at it would be that for these cell types (liposomes
and lymphocytes) a given cell will have a specific cell membrane
permeability and that this membrane permeability will vary from cell to
cell (at a specified temperature). This result was not anticipated for
the liposome study but was not surprising for the lymphocyte study

because no distinction was made between B and T cells.

73

Another interesting observation was the ratio of the standard
deviation, both individual and population, to the resulting mean
permeability. These results show this ratio for the liposomes ranged
from 0.005 to 0.11 and on the average was 0.04 (for individual cells),
while this ratio for the lymphocytes ranged from 0.03 to 0.10 and on the
average was 0.05 (for individual cells). This ratio was higher for the
population because of the variance in population (0.14 for liposomes, on
the average and 0.17 for lymphocytes, on the average). There did not

appear to be any apparent patterns or trends.

74

TABLE 5.3.1 - Permeability Results for Liposomes

solute: sucrose
concentration: 0.02 - 0.04 osmolality

Temperature (Co) Permeability Standard Deviation (S.D.) S.D./Pm
(for an individual cell)

 

 

 

(um/see)l_ (um/sec)
10 25.4 2.6 0.11
10 26.5 1.6 0.07
10 22.0 0.6 0.03
10 24.2 0.5 0.02
10 21.9 0.5 0.02
16 27.7 1.7 0.06
16 32.0 0.7 0.02
16 33.2 1.0 0.03
16 30.4 1.6 0.05
16 32.2 1.6 0.05
25 39.0 0.7 0.02
25 37.2 2.4 0.06
25 38.0 1.4 0.03
25 45.9 0.2 0.005
25 41.0 1.0 0.02
30 65.6 3.7 0.06
30 62.0 4.1 0.06
30 66.0 3.4 0.05
30 64.8 2.8 0.04
30 70.3 3.0 0.05
37 92.5 2.1 0.02
37 104.2 1.9 0.02
37 95.8 8.5 0.09
37 95.8 3.9 0.04
37 94.1 3.5 0.04

75

TABLE 5.3.1 (cont'd.)

Average Permeability For Each Specified Temperature

Temperature (Co) Permeability, Pm Standard Deviation, S.D.p S.D.p/Pm

 

 

(pm/sec) (for population)
(um/sec)
10 24.0 4.1 0.17
16 30.7 4.8 0.16
25 40.2 6.9 0.17
30 65.7 6.0 0.09
37 96.5 9.1 0.09

76
TABLE 5.3.2 - Permeability Results for Lymphocytes
solute: sodium chloride

concentration: 0.291 - 0.725 osmolality

Temperature (C°) Permeability Standard Deviation (S.D.) S.D./Pm

 

 

 

“Elam/sec) (um/sec)
10 2.7 0.1 0.04
10 3.0 0.1 0.04
10 2.8 0.1 0.04
10 2.7 0.1 0.04
10 2.7 0.1 0.04
16 5.1 0.1 0.02
16 4.0 0.1 0.02
16 4.3 0.3 0.07
16 4.4 0.2 0.04
16 5.2 0.3 0.07
25 8.6 0.3 0.03
25 9.2 0.5 0.05
25 8.2 0.3 0.03
25 10.2 0.5 0.05
25 10.3 0.3 0.03
30 17.5 1.4 0.09
30 16.4 1.1 0.07
30 15.4 1.0 0.06
30 17.9 1.4 0.09
30 14.5 0.9 0.06
35 23.9 1.3 0.05
35 24.5 2.5 0.10
35 25.8 1.9 0.08
35 22.7 1.2 0.05
35 26.9 2.0 0.08

77

TABLE 5.3.2 (cont'd.)

Average Permeability For Each Specified Temperature

Temperature (C°) Permeability, Pm Standard Deviation, S.D.p S.D.P/Pm

 

(pm/sec) (for population)
(um/sec)
10 2.8 0.3 0.11
16 4.6 1.1 0.24
25 9.3 1.9 0.20
30 16.3 2.8 0.17
35 24.8 3.3 0.13

cell

78

type: egg lecithin liposomes

temperature: 25°C
solute: sucrose

 

TABLE 5.3.3 - Comparison of Permeability Results

 

 

Investigator Concentrgtion (osmolality) Mean Permegbility (um/sec) N
Boroske 0.0 - 0.04 41.1 i 4.9 13
Callow 0.0 - 0.02 40.5 i 8.4 23

0.0 - 0.04
Melkerson 0.0 - 0.04 41.0 i 3.1 6
Tu 0.02 - 0.04 39.0 i 3.3 9
Sherban (*) 0.02 - 0.04 40.2 i 6.9 5
cell type: human lymphocytes
temperature: 25°C
solute: sodium chloride

Investigator Concentrgtion (osmolglitv) Mggn Permeability (um/sec) N
Hempling 0.315 - 0.600 10.4 i 0.45 ?
Porshce 0.310 - 0.478 4.2 i 0.42 ?
Sherban (*) 0.291 - 0.725 9.3 i 1.9 5

 

 

Note: N is the number of cells used to determine the mean

permeability.

79

5.4 Th; Cell Membrgne Wgter Permeability Activation Energy

From the permeability data accumulated, the cell membrane activation
energy was formulated for both egg-lecithin liposomes and human
lymphocytes. Each activation energy, AEa, was obtained from the slope of
the lines in Figures 5.4.1 and 5.4.2. The activation energy resulting
from this work, AEa-8.9 Kcal/mole, for egg-lecithin liposomes compared
well with those published by other scientists. Specifically, Blok [16]
reported 9.5 Kcal/mole, while Reeves [l7] cited 8.25 Kcal/mole. In
addition, the activation energy calculated from this work for human
lymphocytes was 15.1 Kcal/mole. This result was in good agreement with
the activation energy reported by Hempling, AEa-l4.1 Kcal/mole. However,
the activation energy reported by Porsche, AEa-3.4 Kcal/mole, did not
compare well. She reported that her result was in good agreement with
the results reported by Hempling in reference [23], i.e. the activation
energy for lymphoid cells was 4.4 Kcal/mole, while the activation energy
for tumor cells was 5.7 Kcal/mole. Yet, the activation energies reported
by Hempling in reference [23] ranged between 13 and 18 Kcal/mole, rather
than 4.4 and 5.7 Kcal/mole. Therefore it is difficult to make a

comparison. These results are summarized in Table 5.4.1.

 

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TABLE 5.4.1 - Activation Energy Results

cell type: egg lecithin liposomes

 

 

Investigator Activation Energy (kcal/mole)
Blok 9.5
Reeves 8.25
Sherban (*) 8.9

cell type: human lymphocytes

 

Investigator Activation Energy (kcal/mole)
Hempling 14.1
Porsche 3.4
Sherban (*) 15.1

(*) - Results from this thesis

CHAPTER 6

Sensitivity Studies

6.1 Introduction

As mention in the objective statement of this thesis (Section 1.2),
the program SENS was used to study the sensitivity of the estimated
parameter with respect to a change in input parameters. This can more
clearly be stated by asking a key question. Specifically, what effect
would an under or over specified input parameter, which describes some
aspect of the experimental conditions, have on the resulting estimated
permeability, standard deviation and minimum sum produced by SENS? The
approach used to answer this question will be termed "sensitivity
studies". Since there are an infinite number of possible experimental
cases which could be studied, this discussion will be limited to two
"base" cases, which are relevant to the work presented in this paper.
From the study of these base cases some basic trends can be seen and some
generalized statements can be made. The two cases presented here involve
one for a liposome and one for a lymphocyte, both at room temperature.
Also, only those input parameters that could possibly have a value
different from the base case were studied. In other words, a value that
was specified for an input parameter for which there was confidence (for
that being the actual value) was not studied. More specifically, the
wetted dialysis membrane thickness (RLl), the diffusivity of the solute
in free solution (D2), the magnification factor (RMAG) and the initial

and final concentrations (CINIT and CINF) were not investigated.

83

84

6.2 The Liposome Base Case

The experimental conditions which were used to describe the base

case for the liposome were conditions commonly encountered in the lab

when experiments were performed at room temperature, i.e. 25°C.

Initially SENS was used, in the simulation mode, to generate a radius

history of a liposome which had an estimated permeability of 39.9 pm/sec.

The experimental conditions specified were as follows,

specified):

Variable

RL1
RL2
LIP
D2
D1

Hd
VINA
RINIT
DR
RMAG
CINIT
CINF
DP

DT
TMO
TMl
DELAY

TABLE 6.2.1 - The Liposome Base Case

cell type: liposome
solute: sucrose
temperature: 25°C

Description of Vgriable

Wetted dialysis membrane thickness

Sample region thickness

Cell position in sample region

Diffusivity of solute in free solution

Diffusivity of solute in dialysis
membrane

Mass Transfer coefficient

Normalized osmotically inactive volume

Initial cell radius

Imposed randomness factor

Magnification factor

Initial (isotonic) concentration

Final (hypertonic) concentration

Permeability step

Time step

Starting time

End time

Time delay

(unless otherwise

Specified Value

16 pm
100 pm
5

0.521‘11’10'9 mz/sec
D2*0.1

D2*10000

10 pm
.0 pm

.02 osmol
.04 osmol
pm/sec
.5 sec
.0 sec

0 sec
.0 sec

OU‘ONOOOI—‘O
...;

85

The resulting estimated permeability generated was 39.9 i 0.000 pm/sec

(with a minimum sum of 0.000). This generated data was then reentered,
using the (real) experimental parameter estimation mode, to yield a
permeability of 39.9 i 0.037 pm/sec (with a minimum sum of 0.000). Note,
when comparing the standard deviations there appears to be a discrepancy.
However, only the first three significant figures of a calculated radius,
Rci(t), were stored and the rest were truncated. Therefore, when this
radius history generated, in the simulation mode, reentered into SENS, in
the (real) experimental parameter estimation mode, the absolute value of
the difference between the simulated (pseudo) radius and the predicted
radius was greater than zero.

In each of the following sections (6.2.1 through 6.2.8) an input
parameter was varied (by increasing and then decreasing the value of the
parameter) to investigate the effect that this variation would have on
the resulting estimated permeability and standard deviation. Only one
input parameter was varied at a time and no other changes were made. The
resulting estimated permeability, standard deviation and minimum sum have
been tabulated for each varied input parameter. In addition, the varied
parameter has been plotted versus the resulting estimated permeability
(for most cases) or the standard deviation.

In the last section (6.2.9) the question was asked, what would be
the effect on the membrane activation energy of the liposome if the
activation energy of the dialysis membrane was changed? The results are
tabulated in Table 6.2.10. This is important because if the activation

energy of the dialysis membrane reported by the manufacture is not

86
correct, it could have a dramatic effect on the results presented in this

thesis. The magnitude of this difference would determine the severity.

87

6.2.1 The Effect of Varying Dl

TABLE 6.2.2 - The Effect of Varying D1

 

 

D1 E10 Permeability and Standard Deviation Minimum Sum
(Eliseo) (umzsgc)

10.0 31.3 i 0.400 0.077
3.0 32.2 i 0.348 0.054
2.0 32.9 i 0.311 0.040
1.5 33.6 i 0.274 0.029
1.0 35.1 i 0.201 0.014

* 0.521 39.9 i 0.037 0.000
0.3 49.5 i 0.225 0.006
0.25 55.2 i 0.286 0.006
0.16 81.6 i 0.832 0.013

* - original base case

The results show (Table 6.2.2 and Figure 6.2.1) that the estimated
permeability was inversely related to D1 in a non-linear way. For
example, by doubling D1 the estimated permeability decreased
approximately 10%, while increasing D1 by a factor of 20 only decreased
P(est) another 10%, (i.e a total of 20% more than the base case).
However, decreasing D1 by a factor of 2 increases P(est) by almost 40%
and decreasing D1 by a factor of 4 increase D1 by over 200%. Therefore
the value of the sucrose diffusivity in the dialysis membrane was on the
border line of being critically important and not so important. That is
to say that if D1 was under estimated the resulting estimated
permeability, P(est), would increase dramatically, while if D2 was over
estimated P(est) would not have a major effect. Thus it would be
desirable to increase D1 by some means. The manufacture (ENKA) has
claimed that the solute diffusivity in the dialysis membrane is

equivalent to the permeability of the membrane, Pmem times the wetted

88
membrane thickness, Ax, (i.e. Dl-Pmem*Ax). Therefore if the permeability
. of the membrane was increased, (possibly by making the dialysis membrane
out of a more permeable substance), the effect D1 would have on P(est)
would be diminished. Note, the maximum value D1 could every be, which
would not be very likely, would be the same value of the diffusivity of

sucrose in free solution (in this case water) 5.2lE-10 mz/sec (at 25°C).

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6.2.2 The Effect of Varying Hd

TABLE 6.2.3 - The Effect of Varying Hd

 

Hd E5 Permeability and Standard Deviation Minimum Sum
(mlsec) (amisec)
15.0 33.6 i 0.272 0.029
5.21 34.0 i 0.254 0.024
1.0 36.6 i 0.138 0.006

* 0.521 39.9 i 0.037 0.000
0.25 49.3 i 0.214 0.005
0.11 88.5 i 1.372 0.027

'7': - original base case

These results (Table 6.2.3 and Figure 6.2.2) show that the
.-:::ionvective mass transfer coefficient was also inversely related to P(est)
;:jiszn a non—linear way. Similarly, when Hd was doubled, P(est) decreased
approximately 8%, while when Hd was decreased by a factor of 2, P(est)
:jiE__:ITI<:reased by approximately 25%. Physically what this meant was that when
H d was decreased, the concentration boundary layer developing on the
S urface of the dialysis membrane, in the bulk flow region, was becoming
l a rge and visa versa, (i.e. when Hd was increased, the concentration
t3"‘EZZII-“_.1Lndary layer was becoming small). Obviously it would be more desirable
C O decrease the concentration boundary layer, thus minimizing the
L mp ortance of correctly estimating Hd, with respect to estimating the
“la m‘brane permeability. Experimental Hd can be increased by increasing

th «3 flow rate in the bulk flow region.

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6.2.3 The Effect of Varying RL2

TABLE 6.2.4 - The Effect of Varying RL2

 

 

RL2 Permeability and Standard Deviation Minimum Sum
_Iaml (um/sec)

10 28.4 i 0.562 0.206
50 32.7 i 0.283 0.034
75 36.1 i 0.129 0.005
* 100 39.9 i 0.037 0.000
150 49.0 i 0.090 0.001
200 59.2 i 0.699 0.028
250 68.8 i 2.092 0.145
300 76.7 i 4.088 0.372

* - original base case

For the above case, the relationship that exists between the sample
region thickness and P(est) appears to be slightly non-linear (see Figure
6.2.3) and was directly proportional. At first glance one might expect
that there should not be much of an effect here because the cell was at
the surface of the dialysis membrane; therefore the cell should be
experiencing the same increase in extracellular concentration no matter
what the sample region thickness. However, the developing concentration
boundary layer, at the surface of the dialysis membrane, and dialysis
membrane must also be taken into account. For example, let's say the
sample region thickness was small and at the beginning of an experiment
the bulk flow region was flushed with a hypertonic solution, thus
creating a step change in concentration in the bulk flow region. The
developing concentration gradient inside the sample region would be short

lived and the sample region can essentially be treated as a lumped

93
system. On the other hand if the sample region thickness was infinitely
large, a concentration gradient would always exist; therefore the cell in
the sample region, even though it’s at the surface of the dialysis
membrane, would never experience the final hypertonic solution
concentration. Looking at Figure 6.2.3 the curve appears to almost have
an S shape where the "ends" of the S will eventually approach asymptotes.
These two asymptotes are the two limiting cases discussed above. In most
of the experiments performed in this thesis the value of RL2 was usually
between 50 and 150 microns, which, for this case, could decrease P(est)
by 20% and increase P(est) by 20%, respectively. Ideally RL2 should be
made as small as possible (with respect to the cell diameter) because
this would decrease the concentration gradient across the sample region
thus decreasing the likelihood of incorrectly estimating RL2. However,
this was not an easy task to accomplish because the presoaked dialysis
membrane always has some unknown amount of isotonic solution on its
surface, which adds to the volume of the sample region. Note liposome
position was 5 (at the surface of the dialysis membrane) for all of the

above data sets.

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6.2.4 The Effect of Vgrying LIP

TABLE 6.2.5 - The Effect of Varying LIP

 

 

LIP Permeability and Standard Deviation Minimum Sum
___ (um/sec)
5 37.7 i 0.198 0.010
6 38.6 i 0.122 0.061
7 39.4 i 0.061 0.001
** 8 40.1 i 0.045 0.000
9 40.5 i 0.072 0.001
10 40.8 i 0.096 0.002
11 40.9 i 0.105 0.002
** : The base case was modified here in order to have the cell

position be in the middle, i.e. LIP-8, instead of 5.

The results in Table 6.2.5 show that the liposome position was
directly proportional to P(est) via an approximate linear relationship.
Clearly from this investigation of the effect of the cell position in the
sample region the estimated permeability did not change significantly
(see Figure 6.2.4) and would not be considered an important effect (for
this case). By mistakenly perceiving the cell to be at the middle
position (LIP-8) when the cell really was at the surface of the dialysis
membrane or at the surface of the top cover glass only decreases P(est)
by 6% or increases P(est) by 2%, respectively. Note, this trend, of RL2
not greatly effecting P(est), would continue if RL2 were decreased.
However, if RL2 were increased LIP would play a more significant role
because of the developing concentration gradient in the sample region.
Therefore, this would be another good reason to keep RL2 as small as

possible.

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6.2.5 The Effect of Varying VINA

TABLE 6.2.6 - The Effect of Varying VINA

 

 

VINA Permeability and Standard Deviation Minimum Sum
(3) (um/sec)
0.0 35.7 i 0.632 0.158
3.0 37.7 i 0.381 0.044
* 6.0 39.9 i 0.037 0.000
10.0 42.9 i 0.811 0.100
15.0 46.5 i 2.420 0.588
20.0 50.0 i 4.930 1.472
30.0 56.5 i 13.90 4.863

* - original base case

The results from this study show that the normalized osmotically
inactive volume of a cell was directly proportional to P(est) in a linear
fashion (see Figure 6.2.5). Decreasing VINA by a factor of 2 decreases
the estimated permeability by about 5% and increasing VINA by a factor of

2 increases P(est) by about 13%. Therefore an inaccurate VINA only has a

small to moderate effect on P(est).

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6.2.6 The Effect of Vagying DELAY

 

TABLE 6.2.7 - The Effect of Varying DELAY

 

 

DELAY Permeability and Standard Deviation Minimum Sum
sec (um/sec)
0.0 38.9 i 0.110 0.003
1.0 39 2 i 0.080 0.002
2.0 39.6 i 0.054 0.001
** 3.0 39.9 i 0.037 0.000
** : The base case was modified here because during an actual

experimental run there was a time delay (DELAY - defined in
Section 4.5) when the hypertonic solution was started, (due
to the time it took for the hypertonic solution to travel
from the electronic solenoid switch valve to the bulk flow
region under the dialysis membrane). Based on the
volumetric flow rate of the hypertonic solution, an average
time delay was calculated to be about 2.7 sec. A time delay
of 3.0 sec. was chosen for the new base case to allow for a
little extract delay in case the flow rate decreased.

The results from this study show the DELAY was directly and nearly
linearly related to P(est). By not accounting for a time delay when the
data was recorded P(est) would only ben under estimated approximately 3%.
Therefore, relationship that exists between the time delay and P(est)

does appear to be critically important (for this case) because the slope

of the line in Figure 6.2.6 is very small.

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6.2.7 Ihé Effect of Varying DR

TABLE 6.2.8 - The Effect of Varying DR

 

 

DR Permeability and Standard Deviation Minimum Sum
(gm) (umgsec)

* 0.000 39.9 i 0.037 0.000
0.001 40.0 i 0.040 0.000
0.005 40.0 i 0.083 0.002
0.01 39.8 i 0.152 0.005
0.05 39.8 i 0.768 0.134
0.1 39.6 i 1.513 0.524
0.2 39.2 i 2.983 2.105
0.5 38.0 i 7.144 13.260
1.00 36.5 i 13.43 52.895

* - original base case

The results from this study show that P(est) was not greatly
effected by DR, while the standard deviation increased linearly as DR
increased (see Figure 6.2.7). Recall from Figure 3.2.1, p.31 that DR was
defined to be the radius randomness factor. DR was implemented into SENS
to impose a (pseudo) randomness factor on the generated radius history of
a cell. This randomness factor was meant to incorporate the
uncertainties mentioned in Section 4.5, (i.e. the fluctuations of the
outer membrane of the cell and/or measurement errors that may have
occurred. An attempt was made to estimate the maximum magnitude of this
inaccuracy. Based on the TV monitor screen size, the video camera used
and the lens in the microscope the cell was magnified 5080 times. The
uncertainty in measuring the cell radius was estimate by approximating
the range the cell radius could be. For example, a cell with a 20 pm

diameter would measure 10.16 cm in the TV monitor. Based upon the

102
apparent thickness of the membrane projected on the screen and the
."steadiness" of the cell on the screen, which vibrated slightly on the
screen when the pause function was used, the uncertainty was approximated

to be 10.1 cm which corresponds to 0.1 pm uncertainty in the cell radius.

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6.2.8 The Effect of the Number of Data Points

 

TABLE 6.2.9 - The Effect of the Number of Data Points

 

 

# of points Permeability and Standard Deviation Minimum Sum
(um/sec)
4 51.4 i 2.85 0.006
6 49.4 i 5.63 0.064
10 46.6 i 3.74 0.088
15 42.4 i 3.25 0.242
20 40.0 i 2.48 0.305
25 39.3 i 2.06 0.350
30 39.2 i 1.77 0.375
35 39.3 i 1.65 0.422
40 39.4 i 1.57 0.527
45 39.4 i 1.45 0.570
50 39.5 i 1.38 0.644
100 39.6 i 0.93 1.151

Note: All of the input parameters used for this case were
the same as described for the base case except DR was
set at 0.1 pm. The rational for using 0.1 pm for DR
was described in Section 6.2.7, (i.e. this was the
best estimate for the uncertainty when the cell
radius measured). If DR was kept at 0.0 pm the
result would always be P(est) - 39.9 pm/sec, S.D. -
0.0 pm/sec and the SUMIN - 0.000. It should also be
note that the data points used for each of the above
cases were equally space within the 0 - 500 sec time
interval.

The above results appear to show that the number of data points,
used to generate a P(est), was related to the estimated permeability in a
non-linear way. The estimated permeability started at 51.4 pm/sec and
decreased until the number of data points was approximately 30, where
P(est) appears to level off around 39.5 pm/sec (see Figure 6.2.8).
Intuitively one would think that P(est) would oscillate about 39.9 pm/sec

when only a few data points were used and then level off, at

approximately 39.9 pm/sec, as the number of points was increased. It

105
should also be noted that it did not take very many points to get a
.reasonably good estimate for the membrane permeability - approximately 15
points or so. Also, recall from Section 4.5 that the number of data
points recorded for each experiment conducted was about 20 - 30.

The above results also show that the standard deviation was
inversely related to the number of points, with the exception of the case
for the number of points equal to 4. When the standard deviation was
plotted as a function of the inverse square root of the number of points
the relationship was approximately linear, (if the case for the number of
points equal to 4 was ignored), (see Figure 6.2.9). This was expected
based on the relationship between the number of data points and the
standard deviation given by equation (2.3.10).

Finally the number of data points was found to be related to the
minimum sum in an increasingly linear manner (see Figure 6.2.10). This

was also anticipated based on the relationship described in equation

(2.3.3).

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6.2.9 The Effect of Varying Ea of the Dialysis Membrane on the Ea of the Cell

TABLE 6.2.10 - The Effect of Varying Ea of the Dialysis Membrane
on the Ea of the Cell

 

 

Ea, Dialysis Membrane Ea, Liposome Membrane
(Kcal/mole) (Kcal/mole)
0.5 12.0
1.0 11.7
2.0 11.2
4.0 10.2
* 6.53 8.9
8.0 8.1
10.0 7.0
12.5 5.5
15.0 3.7

* - original base case

This investigation shows that the relationship between the two
membrane activation energies was slightly non-linear and inversely
proportional (see Figure 6.2.11). What this study suggested was that if
the manufacturer incorrectly stated the temperature effects, i.e. the
activation energy, with respect to the dialysis membrane, then the
activation energy reported in this work for the liposome would have to be
reevaluated. However, this is not likely but it is possible. The
original base case dialysis membrane E8 was 6.53 Kcal/mole. This data

was obtained from the manufacture (ENKA) and was published in reference

[3].

 

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6.3 e L oc te Base Ca
The experimental conditions used for the lymphocyte base case are
shown below in Table 6.3.1. The conditions specified were also commonly
encountered conditions when experiments were performed using lymphocytes
at 25°C. Again, SENS was used in the simulation mode to generate a

radius history for a cell with an estimated permeability of 9.3 pm/sec.

TABLE 6.3.1 - The Lymphocyte Base Case

cell type: lymphocyte
solute: sodium chloride
temperature: 25°C

ygzigble e t on V Specified Value
RL1 Wetted dialysis membrane thickness 16 pm
RL2 Sample region thickness 100 pm
LIP Cell position in sample region 5
D2 Diffusivity of solute in free solution 1.4831'r10‘9 m2/sec
Dl Diffusivity of solute in dialysis D2*O.l
membrane
Hd Mass Transfer coefficient D2*10000
VINA Normalized osmotically inactive volume 34.7%
RINIT Initial cell radius 5.5 pm
DR Imposed randomness factor 0.0 pm
RMAG Magnification factor 1
CINIT Initial (isotonic) concentration 0.291 osmol
CINF Final (hypertonic) concentration 0.725 osmol
DP Permeability step 0.1 pm/sec
DT Time step 1.0 sec
THO Starting time 0.0 sec
TMl End time 100 sec
DELAY Time delay 0.0 sec

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112

When these parameters and generated radius history data were reentered
into SENS, in the (real) experimental parameter estimation mode, the resulting
permeability was 9.3 i 0.042 pm/sec (with a minimum sum of 0.000).

The approach used to investigate the input parameter of interest was
the same approach as described for the liposome base case in Sections 6.2.1
through 6.2.9, (i.e. only the input parameter of interest was varied and any
deviation from this approach was specifically stated). The results were also

tabulated and graphs were produced where appropriate.

113

6.3.1 The f ect 0 Va in D1

TABLE 6.3.1 - The Effect of Varying D1

 

 

 

Dl E9 Permeability and Standard Deviation Minimum Sum
L9215ec) (qmisec)

1.5 5.2 i 0.055 0.002
1.0 5.4 i 0.060 0.002
0.5 5.9 i 0.070 0.002
0.2 7.8 i 0.068 0.001

* 0.148 9.3 i 0.042 0.000
0.1 12.7 i 0.348 0.004
0.05 35.8 i 11.38 0.106
0.04 73.5 i 63.06 0.211

* - original base case

The results show that the estimated permeability was inversely related to
D1 in a non-linear way (see Figure 6.3.1). When D1 was doubled P(est)
decreased approximately 30%, while when D1 was increased by a factor of 10
P(est) only decreased another 14%. When the value of D1 was half the base
case the estimated permeability increased approximately 250%. Therefore, a
similar conclusion that was made in 6.2.1 can be made here also, i.e. the
value used for D1 was on the border line of being critically important. Also
the goal here would be to either increase the dialysis membrane permeability,
thus diminishing the effect D1 has on P(est). The maximum value D1 could have
would be the same for the sodium chloride diffusivity in water, 1.48E-9 m2/sec

(at 25°C), however this would not be very realistic.

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6.3.2 The Effect of Varying Hd

 

TABLE 6.3.2 - The Effect of Varying Hd

 

 

Hd E4 Permeability and Standard Deviation Minimum Sum
(misec) (um/sec)
1.5 6.3 i 0.075 0.002
1.0 6.4 i 0.076 0.002
0.5 6.8 i 0.078 0.002
0.2 8.3 i 0.060 0.001
* 0.148 9.3 i 0.042 0.000
0.1 11.4 i 0.192 0.002
0.05 21.8 i 2.920 0.044
0.03 61.0 i 43.80 0.205

* - original base case

The result from this study show that the estimated permeability was
inversely related to the mass transfer coefficient in a non—linear manner also
(see Figure 6.3.2). For example, increasing ad by a factor of 2 decreased
P(est) 15%, while decreasing Hd by a factor of 2 increased P(est) 194%.

Again, as was mentioned Section 6.2.2, to minimize the importance of

accurately estimating “d by increasing the bulk flow rate.

 

 

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6-3-3 e e o Vari R

TABLE 6.3.3 - The Effect of Varying RL2

 

 

RL2 Permeability and Standard Deviation Minimum Sum
(gm) (um/sec)
10 4.0 i 0.039 0.002
50 5.8 i 0.097 0.005
75 7.4 i 0.112 0.003
* 100 9.3 i 0.042 0.000
150 12.9 i 0.786 0.020
200 15.7 i 2.261 0.082
250 17.3 i 2.716 0.163
300 18.1 i 5.070 0.242

* — original base case

The results show the RL2 was proportionally related to P(est) in a
Slightly non-linear way. Recall from Section 6.2.3 the two extreme cases of a
Small RL2, which resulted in treating the sample region as a lumped system,
51t1<3- of a large RL2, which resulted in a infinite concentration gradient in the
Sample region. These two extreme cases cause the curve in Figure 6.3.3 to
approach two asymptotes at about P(est)-4 pm/sec, for a small RL2, and about
P(est)-20 pm/sec, for larger RL2. Again, the approximate range that was used
“flnfiitl experiments were conducted was between 50 pm, which would decrease P(est)
by 38% if RL2 had been underestimated, and 150 pm, which would increase P(est)

by 39% if RL2 has been overestimated.

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6.3.4 The Effect of Varying LIP

 

Note, investigating LIP for the lymphocyte case will not be necessary
because the author was very certain that the position of the lymphocytes that
were tested were always next to the dialysis membrane. Therefore the position

was LIP - 5 for all five lymphocyte experiments for all five temperature

ranges.

120

6.3.5 The Ef ect 0 Va in VIN

TABLE 6.3.5 - The Effect of Varying VINA

 

 

VINA Permeability and Standard Deviation Minimum Sum
(31 (um/sec)
15.0 3.9 i 0.389 0.626
20.0 4.9 i 0.515 0.444
25.0 6.3 i 0.616 0.229
30.0 7.9 i 0.510 0.059
* 34.7 9.3 i 0.042 0.000
40.0 10.8 i 1.307 0.081
45.0 12.3 i 3.702 0.310
50.0 14.0 i 8.100 0.688
55.0 16.0 i 16.20 1.211

* - original base case

The relationship that resulted between VINA and P(est) in this study was
directly proportional and approximately linear (see Figure 6.3.4). It should
be noted that the curve in Figure 5.2.2, which the normalized osmotically
inactive cell volume obtained, appears to slightly non-linear. If one were to
trace a spline curve through the points and extrapolate the curve to the y-
axis the resulting Vb would approximately 45% which would increase the
resulting permeability to 12.3 pm/sec. However, this Vb was not used in order
to handle the resulting data the same as other investigators. To clarify this

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6.3.6 W

TABLE 6.3.6 - The Effect of Varying Delay

 

 

 

DELAY Permeability and Standard Deviation Minimum Sum
1&221 (unggc)
0.0 7.3 i 0.150 0.005
1.0 7.8 i 0.114 0.002
2.0 8.5 i 0.072 0.001
** 3.0 9.3 i 0.043 0.000
** : The base case was modified here because during an actual

experimental run there was a time delay (DELAY) when the
hypertonic solution was started, (due to the time it took for
the hypertonic solution to travel from the electronic solenoid
valve to the bulk flow entrance port). Base upon the volumetric
flow rate of the hypertonic solution, an average time delay was
calculated to be about 2.7 sec. A time of 3.0 was chosen for the
new base case to allow for a little extract delay in case the
flow rate decreased.

The results from this study show that DELAY was directly proportional and
approximately linearly related to P(est) (see Figure 6.3.5). Therefore,
under estimating the delay time would result in under estimating the membrane
permeability. For example, if the delay time of 3.0 seconds was not accounted
for when the data was recorded, (which would imply a delay time of 0.0

seconds), P(est) would be under estimated by approximately 22%.

 

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6.3.7 The Effect of Varying DR

DR
mm

.000
.001
.050
.010
.020
.040
.050
.060
.080
.100

0000000000

TABLE 6.3.7 - The Effect of Varying DR

Permeability and Standard Deviation
(umlgecl

 

* - original base case

Obezoool-‘bww

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.042
.091
.180
.373
.784
.030
.270
.880
.650

Minimum Sum

 

0000000000

.000
.000
.001
.003
.014
.055
.085
.123
.218
.338

The results from this study show that the estimated permeability,

most part, was not greatly effected as the imposed randomness, DR, was

for the

increased, while the standard deviation increased, non-linearly, as DR was

increased (see Figure 6.3.6).

As mentioned in Section 6.2.7 an attempt was

made to estimate the maximum possible inaccuracy obtained when measuring the

cell radius (after an experimental run).

determine the likely range of uncertainty for the lymphocyte case also.

uncertainty in measuring the cell radius for this case was i0.04 pm.

This same approach was used to

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6.3.8 The Effect of the Number of Data Points

TABLE 6.3.8 - The Effect of the Number of Data Points

 

 

 

# of points Permeability and Standard Deviation Minimum Sum
(um/sec)
4 12.0 i 1.76 0.003
6 12.0 i 1.37 0.011
10 11.8 i 1.29 0.014
15 11.3 i 1.29 0.033
20 10.7 i 1.02 0.044
25 10.0 i 0.81 0.055
30 9.5 i 0.65 0.060
35 9.3 i 0.58 0.071
40 9.2 i 0.55 0.084
45 9.1 i 0.50 0.091
50 9.1 i 0.47 0.103
100 9.2 i 0.32 0.184

Note: All of the input parameters used for this case
were the same as described for the base case
except DR was set at 0.04 pm. This approach was
based on the rational described in Section 6.2.8
and the uncertainty approximation made in Section
6.3.7. Also the number of data points used for
each of the above cases were equally space with
the 0 ~ 100 sec time range.

These results suggest that the estimated permeability was related to the
number of data points recorded in a non-linear fashion. The estimated
permeability started at about 12.0 pm/sec for a few points and decreased as
the number of points was increased until the number of points reached about
30, where P(est) began steady at about 9.2 pm/sec (see Figure 6.3.7). Recall
from section 4.5 that the number of data points recorded for each experimental
run was 20 - 30.

Also from the above results, the standard deviation was related to the

number of data points recorded in a decreasing non—linear manner, (as the

number of points increased). Again as was mentioned in Section 6.2.8, if the

127
case where the number of data points equalled 4 was ignored, the standard
deviation was then approximately linearly related to the inverse square root
of the number of data points (see Figure 6.3.8), which was to be expected
based on equation (2.3.10).
The relationship between the number of points and the minimum was

approximately linear, which was also expected based on equation (2.3.3) (see

Figure 6.3.9).

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6.3.9 The Effect of Varying Ea of thngialysis Membrane on the Ea of the Cell

TABLE 6.3.9 - The Effect of Varying Ea of the Dialysis Membrane
on the Ea of the Cell

 

Ea, Dialysis Membrane Ea, Liposome Membrane
(goal/mole) (KcaIZmole)

0.5 20.4

1.0 20.1

2.0 19.2

4.0 17.5

* 6.53 15.1
_8.0 13.6
10.0 11.7
12.5 9.0
15.0 6.2

* - original base case

The results for this study suggest the two membrane activation energies
were inversely proportional and slightly non-linear in relation to one another
(see Figure 6.3.10). Similarly, as mention in Section 6.2.9, if the
manufacturer misstated the activation energy for the dialysis membrane then

the resulting cell membrane activation energies would be effected.

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6.4 D s u o e s v t udie - Rankin n ut ar me ers

For the most part the sensitivity studies in Sections 6.2 and 6.3
produced similar results, when comparing the respective (general) shapes of
the curves, (e.g. Figure 6.2.1 and 6.3.1, etc.). Each input parameter that
was questioned effected the estimated membrane permeability to some degree.
This section will rank the importance of correctly estimating input
parameters, from most to least in terms of its "potential" to effect estimated
membrane permeability (for the two cases studied).

Clearly the input parameters which could effect the estimated
permeability the most are Md and D1 (see Figures 6.2.1, 6.2.2, 6.3.1 and
6.3.2). This can be explained by studying the resistance of the solute flow
through the boundary layer, dialysis membrane and sample region, which can be
written as l/Hd, RL1/D1 and RL2/D2, respectively. (Recall that Hd was the
convective mass transfer coefficient, RL1 was the thickness of the wetted
dialysis membrane, D1 was the solute diffusivity in the dialysis membrane, RL2
was the thickness of the sample region and D2 was the solute diffusivity in
free solution.) Calculating these resistances, l/Hd-0.625, RL1/D1-1.0 and
RL2/D2-0.625 (for the base case). Therefore, whenever Hd or D1 was decreased
its corresponding resistance became the dominant resistance to the solute flow
and when ever Hd or D1 was increased the resistance to solute flow in that
area diminished.

The input parameter which probably had the next most influence on P(est)
was RL2, the sample chamber thickness (see Figures 6.2.3 and 6.3.3). This can

also be explained by studying the resistance to solute flow. As mentioned

134
above, when the resistance to solute flow was changed, P(est) would then be
effected. More specifically, when RL2 was increased the resistance to solute
flow was increased and when RL2 was decreased the resistance to solute flow
was decreased, in the sample region.

Following RL2 would be VINA, the normalized osmotically inactive cell
volume (see Figures 6.2.5 and 6.3.4). This parameter was determined by
performing osmotic equilibrium experiments. It was observed that each cell
that was tested had its own osmotically inactive volume, which wasn't too
different for the average value used. The osmotically inactive cell volume
that was used for the liposome and lymphocyte experiments was average based on
a sample of the population.

The parameter with the next most influence, which wasn't a single input
parameter, was the number of data points used to estimate the membrane
permeability.

The last two input parameters that were studied were the time delay,
DELAY, and the cell position in the diffusion chamber, LIP. Varying these
parameters did not have much of an effect on P(est) (for these cases).
However, the time delay could have a substantial effect on P(est) if the time
duration of an experimental run is very short (less than about 15 seconds).
LIP would only become important if the sample region thickness was large where

a substantial concentration gradient could develop.

CHAPTER 7

Conclusions

Based upon the results of this work the following conclusions can be

:nuade:

1)

2)

3)

The two preparation techniques used to prepare egg-lecithin
liposomes and human lymphocytes can produce good yields, thus
providing a good population from which a cell specimen can be
chosen.

The microscope diffusion chamber system can effectively be used to
produce reliable data for calculating the equilibrium osmotic
response of liposomes and human lymphocytes because it is
relatively simple to task a cell in some isotonic solution and
expose it to a series of step-wise increases in concentration.
(Note: the cell is allowed to come to an equilibrium volume after
each step increase in concentration.) The cell system test in this
work was human lymphocytes which yielded a normalized osmotically
inactive cell volume of 34.7%. This normalized osmotically
inactive volume was in good agreement with inactive volumes
reported by other scientists. Therefore, the author believes the
microscope diffusion chamber could be applied to other cell systems
to determine their respective normalized osmotically inactive cell
volume.

The microscope diffusion chamber system, in conjunction with the
computer algorithm SENS, can be used to determine the dynamic non-

135

4)

136
equilibrium osmotic response of egg-lecithin liposomes and human
lymphocytes, (i.e. the cell membrane water permeability), at a
specified temperature. The cell membrane water permeabilities
determined for this work compared well with permeabilities
published by other scientists. Specifically, the mean permeability
calculated at 25°C for egg-lecithin liposomes was 40.2 pm/sec and
for human lymphocytes was 9.3 pm/sec. Based on these results the
author believes that the diffusion chamber, along with SENS, can be
used to determine the membrane water permeability for other cell
systems with similar membrane characteristics and could probably be
applied to cell systems with even higher membrane permeabilities.
However, there may be an upper limit, with respect to the
permeability, at which the diffusion chamber may not produce
reliable results.
Because the microscope diffusion chamber can be used at different
temperatures, the data produced by the microscope diffusion chamber
system can be used to determine the effect of temperature with
respect to the membrane permeability, i.e. the activation energy.
Based on the experiments conducted, for this work, it was
discovered the cell membrane permeability for both liposomes and
lymphocytes have a strong dependence on temperature. This
temperature dependence was quantified into an activation energy.
The activation energies calculated, for liposomes and lymphocytes,
were in good agreement with activation energies published by other
scientists, (8.9 Kcal/mole for egg-lecithin liposomes and 15.1

Kcal/mole for human lymphocytes). Based on these results the

5)

6)

7)

8)

137
author believes that the activation energy for other cell systems
can successfully be determined.
Egg-lecithin liposomes represent a good model system for
equilibrium and non-equilibrium osmotic studies because of the
similar behavior observed as compared to using a living cell
system, i.e. the osmotic shrinkage of liposomes is consistent with
the irreversible thermodynamic model developed by Kedem and
Katchalsky. As mentioned, the liposomes used for this work were
egg—lecithin in composition. Liposomes of other compositions could
be used in the diffusion chamber to determine the effect of the
membrane composition with respect to the cell membrane
permeability.
Human lymphocytes also behaved in a manner consistent with the
irreversible thermodynamic model and represent a good "hearty" cell
system to study, i.e. lymphocytes hold up well under adverse
conditions like increases in concentration.
The original version of SENS developed by J. Tu was an excellent
starting point for developing a user friendly program. The program
can easily be used by a user who has a general working knowledge of
the microscope diffusion chamber system.
The computer program SENS is a useful tool for setting up
experimental conditions. For example, if an investigator wishes to
know the approximate time duration of an experimental run, the
preliminary experimental conditions can be entered and the
normalized cell volume can be observed, (which will come to some

equilibrium volume). At the point when the cell has reached 99% of

9)

138
its new volume is the approximate time duration of an experimental
run.
The computer program SENS can effectively be used to study the
effect of under or over estimating an input parameter with respect
to the resulting estimated membrane permeability. Thus a
particularly "sensitive" parameter can be identified and procedures

can be implemented to carefully estimate this parameter.

CHAPTER 8

Suggestions for Future Work

'Ihe following suggestions are made for future work regarding the design

<>f the experimental system and the cell systems tested with the

nnicroscope diffusion chamber.

1)

2)

Redesign the pumping system used with the diffusion chamber system
to allow for more solution bottles to be accessible at one time.
The present design of the system only allows for only two solution
bottles to be used at a time. If a third (or fourth, or fifth,
etc.) solution were to be introduced, it would have to be changed
manually. By having five or more solution bottles readily
accessible the equilibrium osmotic response could more easily be
studied, i.e. the normalized osmotically inactive volume could more
easily be obtained.

Interface the switch which turns on the pumping system could also
be interfaced with the timer so that only one switch is necessary
to start an experiment. The present design of the microscope
diffusion chamber system has two separate switches, one to start
the hypertonic solution and one to start the timer, which take two
hands to start. In the mean time the focusing knob on the
microscope needs to have continual minor adjustments made. Having

a single switch would make this process easier.

139

3)

4)

5)

6)

7)

8)

9)

140
Incorporate electronically controlled valves to allow the solution
lines leading from the solution bottle to the electronic solenoid
valve to be preflushed. This would allow for more easily
controlling the temperature of the in coming solution and any air
bubbles in the solution lines to escape.
Make the bulk flow region thinner to allow for greater ease in
focusing the microscope condenser, which would result in a sharper
image project (and therefore video taped). The present design of
the diffusion chamber is such that the microscope condenser has to
be smashed into the plastic on the bottom of the diffusion chamber.
Modify to the diffusion chamber to allow more systematic control of
the sample region thickness.
Develop a better method of recording the cell radius (or volume)
history. This could be done by using an image analysis equipment
which can more accurately calculate the dynamic volume change of
the cell as it is exposed to the hypertonic solution.
Devise a method to verify the number of bilipid layers when
liposomes are used. Presently the method used to determine the
number of bilipid layers is based on the contrast of the liposome
projected on the screen.
Incorporate into the modelling, of the membrane water permeability,
the effect of internal and external solute concentration. The
concentration dependence was not mentioned, or studied, in this
work but has been shown by other investigators to have an effect.
Also incorporate into the modelling the estimation of the

individual cell osmotically inactive volume, in addition to the

10)

ll)

12)

141
cell membrane water permeability. This would result in a more
accurate estimate of the membrane permeability.
Do experiments to characterize the dialysis membrane permeability,
thus verifying the results of the manufacturer. As was shown in
the sensitivity studies the accurately knowing the solute
diffusivity in the dialysis membrane, which is related to the
membrane permeability by Pmem*Ax-D1, is extremely important.
Devise a method to study the convective mass transfer coefficient
and accurately determine its value. Also recall from the
sensitivity studies that accurately knowing the convective mass
transfer coefficient could be extremely important.
Apply the microscope diffusion chamber system to other cell
systems, particularly cells with higher membrane water
permeabilities, to determine if there are any problems in
accurately estimating the membrane permeability. The microscope
diffusion chamber system may produce misleading results if the cell
has a high membrane water permeability. To further explain, if the
dialysis membrane doesn't allow the passage of solute into the
sample region fast enough, (in other words the dialysis membrane is
too rate limiting with respect to solute transport), the resulting

volume history may lead to an inaccurate membrane permeability.

APPENDICES

APPENDIX A

The Normalized Osmotically Inactive Volume

Van't Hoff was the first to study and develop the laws to osmotic
equilibrium. His work was further expanded and applied to living cells
by Boyle and Van't Hoff. The result has come to be known as the Boyle-
Van't Hoff law, which has a form analogous to the perfect gas law
(PV-nRT):

«Vw - constant (A-l)

where Vw represents the volume of solvent (water) and z-RTCS represents
the osmotic pressure. This law states that if the intracellular solution
can be considered ideal and if all of the solvent can be considered
" free" or osmotically active then the osmotic pressure is inversely
proportional to the osmotic pressure, or extracellular concentration.
However, for many cell systems not all of the solvent can be considered
free. In 1932 Lucke’ and McCutheon developed a relationship to compensate
for the non-free solvent and anything else within the cell that can be
Considered non-solvent. This non-free solvent non-solvent volume is
t:ermed the "osmotically inactive cell volume".

The modified Boyle-Van't Hoff law, corrected for the osmotically
inactive volume, may then be stated as

"(vcell ‘ Vb) ' "0(V8ell ' Vb) (A'3)
where 1r is the osmotic pressure, (the extracellular and intracellular
osmotic pressures are equal at equilibrium), Vcell is the total volume of

the cell and Vb is the osmotically inactive volume. The superscript
142

143
values correspond to a reference initial states.[McGrath, Heat Trans...]

Dividing (A-3) by the initial cell volume, V8811, and rearranging, the

modified Boyle-Van't Hoff law becomes

0
ocell - :_(1 - Vb) + Vb (A-4)
1r

where Vcell = Vcell/Vgell (the normalized cell volume) and Vb - Vb/Vgell
(the normalized osmotically inactive cell volume). Therefore by plotting
Vcell v.s. 1/1 the normalized osmotically inactive volume can be found

from the intercept when l/1r equals zero or from the slope 1r°(l - Vb)

since both «0 is known.

Appendix B

Preliminary Testing and Set Up of Experimental Equipment

The magnification calibrations were necessary because a cell, which
appeared on the video monitor, was not only magnified by the lenses in
the microscope but was also magnified by the video camera and the video
monitor. These calibrations were performed using a Petroff-Haussen
Bacteria Counter. The counter had etches of a specific distance apart
marked on the surface of the glass. After focusing the microscope, the
length between the two etch marks projected on the video monitor was
measured. The ratio of the measured projected image and the known
specific distance on the bacteria counter resulted in a magnification
factor, RMAG. The results of these calibrations are summarized in Table
B.1. It should be noted here that the that SENS allowed the user to
enter the radius history measured from the video monitor, providing RMAG
was also entered.

In addition, before conducting any experiments the temperature
distribution of the diffusion chamber was investigated. These tests were
conducted to determine what temperature the controller (i.e. refrigerated
circulating bath) needed to be set at in order to obtain the desired
temperature at the cell chamber. The investigated temperature settings
of the circulating bath were 0.0°C, 8.9°C, 2l.l°C, 30.6°C, 35.2°C 50.800
and 60.7°C. The resulting temperatures detected at the top fitting are

summarized in Table 8.2 and Figure 8.1.

144

TABLE B.l - Magnification Calibration

 

 

 

 

Camera Obiective Power Optavar Power gmlmark Magnification, RMAG
Color 25 1.25 3.846 3175
Color 25 1.6 3.125 4064
Color 25 2.0 2.500 5080
Color 40 1.25 2.632 4683
Color 40 1.6 2.083 5994
Color 40 2.0 1.695 7492
Black/White 25 1.25 3.846 4750
Black/White 25 1.6 3.125 4064
Black/White 25 2.0 2.500 7600
Black/White 40 1.25 2.632 7005
Black/White 40 1.6 2.083 8968
Black/White 40 2.0 1.695 11209

TABLE 8.2 - Temperature Bath Measurements

Room Temperature - 23°C
(Note: All temperature are recorded in °C)

Circulating Bath Tempergture Temperature of Top Fittigg Difference

0.0 4.6 4.6

8.9 12.6 3.7
21.1 21.9 0.8
23.0 23.0 0.0
30.6 29.8 -0.8
35.2 33.8 -l.4
50.8 48.0 -2.8
60.7 56.9 -3.8

145

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APPENDIX C
As mentioned in section 1.2 SENS was used to clarify previous results
generated by M. Shabana using the microscope diffusion chamber. The cell
system he used was unfertilized hamster ova. After Shabana gathered the
experimental data he used a method devised be Terwilliger and Solomon
[19] to calculate the membrane water permeability, PMSI22]. To help

clarify this results his data was reentered into SENS to generate a new

permeability, PSENS- The results are summarized in Table C.1.
TABLE C.1 - Summary of Shabana's Results

cell type: unfertilized hamster ova
initial concentration: 0.3 osmol (NaCl)
temperature: 25°C

 

Exp. # Final Concentration (osmol) EMS (amfisec) ESENS (amisec)
l 0.5 18.38 28.1 i 1.6
2 0.5 21.26 51.3 i 5.6
5 0.5 22.40 33.0 i 3.4
6 0.5 20.75 42.8 i 3.6
7 0.5 21.86 61.0 i 13.0
3 0.8 20.35 28.1 i 3.0
4 0.8 17.21 24.8 i 1.7
8 0.8 16.96 15.2 i 1.5
9 0.8 14.72 33.1 i 2.0

10 0.8 18.64 36.4 i 3.6
11 0.8 18.26 31.9 i 1.8
12 1.5 17.68 35.3 i 4.0
13 1.5 15.89 37.2 i 5.6
14 1.5 15.36 22.3 i 1.6
15 1.5 15.21 33.2 i 4.5
16 1.76 17.05 29.3 i 2.9
17 1.76 14.62 29.5 i 2.4
18 1.76 ? 25.1 i 3.7
19 1.76 16.14 28.2 i 3.1

147

APPENDIX D

SENS - The Prime Version Fortran Source Code

00000000C)OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO000000

148
PROGRAM SENS
THIS PROGRAM INCLUDES THE COMPUTER MODEL FOR THE
DIFFUSION CHAMBER AND THE PARAMETER ESTIMATION FOR FINDING
PERMEABILITY OF A CELL INSIDE THE CELL CHAMBER OF THE
DIFFUSION CHAMBER.
THIS PROGRAM CONSISTS OF 1 MAIN PROGRAM AND 8 SUBROUTINES
AND 4 FUNCTIONS. THEY ALL ARE INSIDE THE FILES ’SENS',
'PAR.COUT', 'PLOT'. THE INPUT FILENAME IS SPECIFIED BY THE USER
AND THE NUMERICAL OUTPUT FILENAMES ARE 'O_SENS.DAT' AND 'O_SMRY.DAT',
AND THE GRAPHICAL OUTPUT FILENAME IS 'G_PLOT'
THE INPUT FORM REQUIRED IS AS FOLLOW
RL1: THICKNESS OF DIALYSIS MEMBRANE (M)
RL2: THICKNESS OF CELL CHAMBER (M)
LIP: APPROXIMATE LOCATION OF THE LIPOSOME (FROM 5 TO 11)
D1: DIFFUSIVITY OF SOLUTE INSIDE DIALYSIS MEMBRANE (M*M/SEC)
D2: DIFFUSIVITY OF SOLUTE INSIDE CELL CHAMBER (M*M/SEC)
CINIT: INITIAL CONCENTRATION (OSM)
CINF: FINAL CONCENTRATION (OSM)
H: MASS TRANSFER COEFF. (APPROXIMATELY 10000*D2)

IPRINT: NUMERICAL DATA OUTPUT FREQUENCY. (EVERY IPRINT*DT
SEC. PRINTS THE CONC. DIST. ON OUTPUT FILE)

IFl: CONTROL THE OUTPUT OF CONC. CHANCE INSIDE THE CELL
CHAMBER

IF2: CONTROL THE OUTPUT OF SENSITIVITY COEFF. VERSUS TIME

IF3: CONTROL THE OUTPUT OF NORMALIZED VOLUME RESPONSE
VERSUS TIME

IF4: CONTROL THE OUTPUT OF SUM OF ERROR OF SQUARE VERSUS
PERMEABILITY

(THE VALUES FOR ABOVE INTEGER OPTIONS ARE l-YES, O—NO)

IRELPSE: OPTION FOR EXPERIMENTAL DATA INPUT l-REAL-EXPERIMENT
2-PSUESO-EXPERIMENT

IMICCEN: OPTION FOR ENTERING DATA IN l=MICRONS 2-CENTIMETERS

COO0000000000000000000000OOOOOOOOOOOOOOOOOOO00000000

149
TMO, TMl: SETTING THE TIME RANGE ON THE PLOTS (SEC.)
DT: TIME STEP FOR PROCEEDING THE CALCULATION (SEC.)
(NOTE: IF DT IS SET TOO LARGE, THE RESULT WILL FLUCTUATE.
IN THIS CASE, REDUCE THE SIZE OF DT AND TRY AGAIN.
THIS IS DUE TO THE UNSTABLE OF THE NUMERICAL METHOD.)
DELAY: TIME DELAY SUBTRACTED FROM TIME ARRAY TM(I)

CABO, CAB1: WINDOW OF THE Y-DIRECTION ON FIRST GRAPH.
(UNLESS NECESSARILY, SET THE VALUES AS 0. AND 5.)

PSEN: THE PERMEABILITY VALUE AT WHICH WE INVESTIGATE THE
SENSITIVITY COEFF. (P'S EFFECT ON R'S CHANGE)

SENO, SENl: SETTING THE RANGE FOR THE SENSITIVITY COEFF. PLOT

PTRU: THE PERMEABILITY VALUE WITH WHICH THE PROGRAM GENERATES
PSUDO-EXPERIMENTAL DATA (R(TM,PTRU)).

DTl: THE TIME STEP FOR THE PSUDO-EXPT'L DATA DURING TMO TO
TMOl. (SEC.)

TMOl: THE PARTITION BETWEEN TWO DIFFERENT TIME STEPS RANGE.
(YOU CAN ASK THE PROGRAM TO GENERATES PSUDO-EXPT'L DATA
WITH TWO DIFFERENT INCREMENT IN TIME FOR TWO TIME
RANGE.)

DT2: THE TIME STEP FOR THE PSUDO-EXPT'L DATA DURING TMOl

TO TMl. (SEC.)

RINIT: INITIAL RADIUS (CM)

VINA: INACTIVE VOLUME (%)

RMAG: THE MAGNIFICATION OF THE MICROSCOPE

DR: MAGNITUDE FOR THE PSEUDO-RANDOMNESS IMPOSED ON THE
PREDICTED RADIUS RESPONSE (CM)

PO,P1: PERMEABILITY RANGE FOR THE FOURTH PLOT (MICRON/SEC.)

DP: INCREMENT OF PERMEABILITY IN CALCULATING SUM OF ERROR OF
SQUARE FOR EACH P VALUE

SUMO, SUMl: RANGE FOR THE FOURTH PLOT

OUTPUT CONFIGURATION OF 'O_SENS.DAT':

(1) INPUT DATA

OOOOOOOOOQOOOOOOOOOOOOOO

2000

150

(2) PRINT CONC. DIST. OF THE SYSTEM AS A FUNCTION OF
TIME.

(3) SENSITIVITY COEFF. CORESPOND TO PSEN.

(4) THE ESTIMATED PERMEABILITY (LOCAL MINIMUM ON SUM
VERSUS P GRAPH)

(5) THE STANDARD DEVIATION OF THIS ESTIMATED P

OUTPUT CONFIGURATION OF 'O_SUMR.DAT':

(1) SUMMARY OF INPUT PARAMETERS AND DATA
(2) SUMMARY OF RESULTING PERMEABILITY, STANDARD DEVIATION
AND MINIMUM SUM

OUTPUT CONFIGURATION OF THE GRAPHICS FILE G_PLOT CAN BE
ONE OR MORE OF THE FOLLOWING:

(l) CONCENTRATION V.S. DIMENSIONLESS TIME

(2) SENSITIVITY COEFFICIENTS V.S. TIME

(3) NORMALIZED VOLUME V.S. TIME

(4) SUM OF SQUARE OF ERRORS V.S. PERMEABILITY

INITIALIZATION AND DECLARATIONS

PARAMETER (N3-301,II-2,N1-301,N4-301,EPl-0.0l)

DIMENSION TMA(N3),TMB(N3),RA(N3),RB(N3),SEN(N3),SUM(N1),P(N1)
DIMENSION VOLC(N3),VOLA(N3),TMS(N3),RS(N3),RC(N3),RSAVE(N3)
CHARACTER*1 ICHANG, IGRAPH, IMORE, IAGAIN, IANOTH, ISAVE
CHARACTER*1 IMISTAK, IFIRST, IQUIT, IDEL

CHARACTER*11 XMICCEN,PROBLEM

CHARACTER*10 NAMFIL,ISENS

COMMON /C1/IPRINT,IF1,A1(II),A2(II),CABO,CABl

COMMON /C2/RINIT,VINA,DT,TM1,COUT(N4)

COMMON /C3/RL1,RL2,LIP,D1,D2,CINIT,CINF,H

EXTERNAL FCTO,F

EXPLANATION TO THE USER WHAT THE PROGRAM DOES.

IBACK - O

IRUNAG-O

IOPNAG=0

IMISTAK - 'N'

CONTINUE

WRITE(1,*)

WRITE(1,*)'WOULD YOU LIKE AN EXPLAINATION OF THIS PROGRAM, '
WRITE(1,*)’(SENS), (Y/N)?’

READ(1,'(A1)') IFIRST

CALL IYESNO(IFIRST)

IF(IFIRST.EQ.'N') GO TO 2002

WRITE(1,*)

WRITE(1,*)' WELCOME TO THE PROGRAM SENS. THIS PROGRAM WILL '

WRITE(1,*)'ALLOW THE USER TO (1) ANALYZE THE DATA OBTAINED USING '

151

WRITE(1,*)'THE MICROSCOPE DIFFUSION CHAMBER I.E. PARAMETER '
WRITE(1,*)'ESTIMATION OF THE PERMEABILITY OF A CELL OR (2) RUN '
WRITE(1,*)'A SIMULATION (PSEUDO) EXPERIMENT TO SEE WHAT MIGHT '
WRITE(1,*)'TO A CELL UNDER SPECIFIED CONDITIONS.’

OPTION TO HAVE A LIST OF THE NECESSARY PARAMETERS SENT TO

'I_DATA.LST'

WRITE(1,*)' IF THIS IS THE FIRST TIME YOU HAVE USED THIS '

WRITE(1,*)'PROGRAM

AND YOU WANT TO ENTER DATA FROM A REAL '

WRITE(1,*)'EXPERIMENT YOU MAY WANT TO OBTAIN A LIST OF THE '
WRITE(1,*)'PARAMETERS AND DATA NECESSARY TO RUN THE PROGRAM.’

WRITE(1,*)

WRITE(1,*)'WOULD YOU LIKE TO DO THIS, (Y/N)?’
READ(1,'(A1)') IFIRST

CALL IYESNO(IFIRST)

IF(IFIRST.EQ.'Y') THEN
OPEN(13,FILE-'I_DATA.LST')

WRITE(1,*)
WRITE(1,*)'THE

LIST OF THE NECESSARY INPUT TO RUN THE PROGRAM'

WRITE(1,*)'WILL BE IN FILE I_DATA.LST. THE PROGRAM WILL'
WRITE(1,*)'STOP NOW. HAVE I_DATA.LST PRINT AT THE PRINTER.’

WRITE(13,*)

WRITE(13,*)'THE PARAMETES AND DATA NEEDED TO RUN THE PROGRAM'
WRITE(13,*)'ARE:'

WRITE(13,*)
WRITE(13,*)'1)
WRITE(13,*)'2)
WRITE(13,*)'3)
WRITE(13,*)'
WRITE(13,*)'4)
WRITE(13,*)'
WRITE(13,*)'5)
WRITE(13,*)'6)
WRITE(13,*)'7)
WRITE(13,*)'8)
WRITE(13,*)'9)
WRITE(13,*)'10)
wa1ra<13,*)'11)
WRITE(13,*)'12)
WRITE(13,*)'13)
WRITE(13,*)'14)
WRITE(13,*)'15)
WRITE(13,*)'
WRITE(13,*)'16)
WRITE(13,*)'
WRITE(13,*)'
WRITE(13,*)
WRITE(13,*)'
WRITE(13,*)'
WRITE(13,*)'
CLOSE(13)

DIALYSIS MEMBRANE THICKNESS (RL1), MICRONS.’
CELL CHAMBER THICKNESS (RL2), MICRONS.’
DIFUSSIVITY OF SOLUTE IN MEMBRANE (D1), '
- METERS*METERS/SEC.'
DIFUSSIVITY OF SOLUTE IN FREE SOLUTION (D2),'
- METERS*METERS/SEC.'
MASS TRANSFER COEFFICIENT (H).'
INITIAL CONCENTRATION (CINIT), OSMOLALITY.’
FINAL CONCENTRATION (CINF), OSMOLALITY.’
INACTIVE VOLUME (VINA), %'
MAGNIFICATION FACTOR (RMAG).'
TIME STEP (DT), SEC.’
STARTING TIME (TMO), SEC.’
ENDING TIME (TMl), SEC.’
TIME DELAY (DELAY), SEC.’
PERMEABILITY STEP (DP), MICRONS/SEC.’
PERMEABILITY AT WHICH INVESTIGATE THE '
SENSITIVITY COEFFICIENTS (PSEN), MICRONS/SEC.’
THE DATA POINTS: TIME (TMA(I)), SEC. AND '
RADIUS (RA(I)), MICRONS OR'
CENTIMETERS.’

(NOTE: YOU ONLY NEED THE DATA POINTS IF YOU'
ARE USING THE PARAMETER ESTIMATION OPTION,’
I.E. A REAL EXPERIMENT.)'

152

GO TO 600
ENDIF

EXPLAINING THE OPTION TO ENTER DATA USING KEYBOARD OR AN INPUT FILE

WRITE(1,*)

WRITE(1,*)' THIS PROGRAM WILL ALLOW YOU TO ENTER THE DATA '
WRITE(1,*)'USING THE TERMINAL/KEYBOARD OR A PRE-EXISTING INPUT'
WRITE(1,*)'FILE SET UP BY THE USER. AN EXAMPLE OF AN INPUT FILE'
WRITE(1,*)'CAN BE SEEN BY QUITTING THIS PROGRAM AND PRINTING'
WRITE(1,*)'I_SENS.EXP AT THE PRINTER. DO YOU WISH TO QUIT AND '
WRITE(1,*)'PRINT THE EXAMPLE (Y/N)?’

READ(1,'(A1)') IQUIT

CALL IYESNO(IQUIT)

IF IQUIT IS YES THE PROGRAM WILL GENERATE I_SENS.EXP AND QUIT.

IF (IQUIT.EQ.'Y') THEN
0PEN(12,FILE-'I_SENS.EXP')
WRITE(12,*)'THIS IS THE EXAMPLE INPUT FILE I_SENS.EXP FOR THE'
WRITE(12,*)'PROGRAM SENS.FOR. THE PROGRAM WILL READ THE DATA'
WRITE(12,*)'ALINING THE VALUES UNDER THE LEFT MOST CHARACTER.’
RL1 - 16.

RL2 - 100.
LIP - 9

D1 - 5.21E-11
D2 - 5.21E-10
H - 5.21E-6
CINIT - 0.02
CINF - 0.04
VINA - 6.
RMAG -5080.
DT - 5.0

TMO - 0.0
TMl - 500.0
DELAY - 0.0
DP - 2.

P0 - 0.

P1 - 100.
PSEN - 40.
RINIT - 7.7
PTRU - 40.0
DR - 0.01
TMOl - 500.0
DTl - S.

DT2 - 5.0
IRELPSE - 1
IMICCEN - 2
IFl - 1

IF2 - 1

IF3 - 1

IF4 - 1

2002

153

IPRINT
CABO -
CABl -
SENO -
SENl -
VOLO -
VOL1
SUMO -
SUMl -
P0 - 0.0
Pl - 100.0
ICOUNT -40
RA(I) - 7.7
TMA(1) - 0.0
DO 1100 I - 2,40

TMA(1) - TMA(I-l) + 10.

RA(I) - RA(I-l) -0.05
CONTINUE
GO TO 331

ENDIF

mol
00H

0.1

0

I
HOV-'00
00000

EXPLAINING THE INPUT AND OUTPUT OPTIONS

WRITE(1,*)
WRITE(1,*)' THE PROGRAM WILL ALSO ALLOW THE USER TO VIEW THE'
WRITE(1,*)'RESULTS BY 1) TABLES AND/OR 2) GRAPHICALLY. THE'
WRITE(1,*)'TABLES GENERATED CAN BE FOUND IN A FILE CALLED'
WRITE(1,*)'"O_SENS.DAT". A SUMMARY OF THE INPUT PARAMETERS AND'
WRITE(1,*)'DATA CAN BE FOUND IN "O_SMRY.DAT". THE GRAPHICAL '
WRITE(1,*)'OUTPUT WILL BE DISPLAYED ON THE SCREEN AND STORED'
WRITE(1,*)'IN A GRAPHICS FILE G_PLOT.'
WRITE(1,*)'THE USER MUST THEN USE "PRINTX" T0 GENERATE A'
WRITE(1,*)'PRINTED COPY, (NOTE: THE FIRST GRAPHICS FILE WILL'
WRITE(1,*)'START ON PAGE 2 !!). THE PLOTS THAT CAN BE GENERATED'
WRITE(1,*)'ARE:'
WRITE(1,*)
WRITE(1,*)' 1) CONCENTRATION V.S. DIMENSIONLESS TIME'
WRITE(1,*)' 2) SENSITIVITY COEFFICIENTS V.S. TIME'
WRITE(1,*)' 3) NORMALIZED VOLUME V.S. TIME'
WRITE(1,*)' 4) SUM OF SQUARE OF ERRORS V.S. PERMEABILITY'
WRITE(1,*)
WRITE(1,*)'YOU ARE NOW READY TO START THE PROGRAM.’
CONTINUE
WRITE(1,*)
WRITE(1,*)'DO YOU WISH TO ENTER THE DATA USING (1) THE TERMINAL'
WRITE(1,*)'OR (2) A PRE-EXISTING INPUT FILE, (ENTER 1 OR 2)?’
WRITE(1,*)
READ(1,*,ERR-2000) ITERINP
CALL IONETWO(ITERINP)
IF(ITERINP.EQ.2) THEN

WRITE(1,*)

WRITE(1,*)'PLEASE ENTER THE NAME OF THE INPUT FILE TO BE '

. . WTJ
P» C C nzv C «,4

 

 

all

2100

2105

2106

154

WRITE(1,*)'USED, (ENTER NO MORE THAN 10 CHARACTERS).'
READ(1,'(A10)') ISENS
CALL CHANNAM(ISENS)
WRITE(1,*)
WRITE(1,*)'OKAY, THE PROGRAM IS CRUNCHING.’
GO TO 2999
ENDIF

IPRINT - 10

PROMPTING THE USER TO ENTER THE REQUIRED DATA AND PARAMETERS
NEEDED TO RUN THE PROGRAM.

CONTINUE

WRITE(1,*)

WRITE(1,*)'DO YOU WISH TO (1) ENTER DATA FROM A REAL EXPERIMENT'
WRITE(1,*)'OR (2) USE THE PROGRAM FOR A SIMULATION (PSEUDO-'
WRITE(1,*)'EXPERMINT), (ENTER 1 OR 2)?'

WRITE(1,*)

READ(1,*,ERR-2005) IRELPSE

CALL IONETWO(IRELPSE)

CONTINUE

WRITE(1,*)'ENTERING THE PHYSICAL PARAMETERS OP THE SYSTEM:'
WRITE(1,*)

WRITE(1,*)'PLEASE ENTER THICKNESS OF THE DIALYSIS MEMBRANE, '
WRITE(1,*)'(MICRONS).'

WRITE(1,*)

READ(1,*,ERR-2100) RL1

WRITE(1,*)

CONTINUE

WRITE(1,*)'PLEASE ENTER THE THICKNESS OF THE CELL CHAMBER,’
WRITE(1,*)'(MICRONS).'

WRITE(1,*)

READ(1,*,ERR—2105) RL2

WRITE(1,*)

CONTINUE

WRITE(1,*)'PLEASE ENTER THE CELL POSITION, (5-11).'
WRITE(1,*)'(SEE THE DIAGRAM BELOW FOR BETTER UNDERSTANDING.)'
WRITE(1,*)

WRITE(1,*)' DIALYSIS MEMBRANE CELL CHAMBER'
WRITE(1,*)’

WRITE(1,*)'B

WRITE(1,*)’U

WRITE(1,*)'L

WRITE(1,*)'K

WRITE(1,*)'F
WRITE(1,*)'L
WRITE(1,*)'0
WRITE(1,*)'W
WRITE(1,*)'
WRITE(1,*)

I I
I I
I I
I I
I I
WRITE(1,*)' 1 2 3 4 5 6 7 8 9 10 1
I l
I I
I l
I I
I l

___—_H_————

‘ Q Q ‘ ‘ ‘ ‘ . . ~ ‘

2110

2120

2130

2140

2150

2160

2170

READ(1,*,ERR-2106) LIP
WRITE(1,*)
CONTINUE

WRITE(1,*)'PLEASE ENTER THE DIFFUSIVITY OF THE SOLUTE INSIDE'
WRITE(1,*)'THE CELL CHAMBER, (METERS*METERS/SEC.), D2.’

WRITE(1,*)
READ(1,*,ERR-2110) D2
WRITE(1,*)

CONTINUE

WRITE(1,*)'DO YOU WISH TO ENTER (1) SEPARATE VALUES FOR THE'
WRITE(1,*)’DIFFUSIVITY OF THE SOLUTE INSIDE THE DIALYSIS'
WRITE(1,*)'MEMBRANE (METERS*METERS/SEC.), D1, AND THE MASS'
WRITE(1,*)'TRANSFER COEFFICIENT, H, OR (2) USE PRESET'

WRITE(1,*)'VALUES OF D1-D2/10 AND H-10000*D2?'
WRITE(1,*)

READ(1,*,ERR-2120) ISEPPRE

CALL IONETWO(ISEPPRE)

IF(ISEPPRE.EQ.1) THEN

CONTINUE

WRITE(1,*)'PLEASE ENTER D1 (METERS*METERS/SEC.).'

WRITE(1,*)
READ(1,*,ERR-2130) D1
WRITE(1,*)

CONTINUE

WRITE(1,*)'PLEASE ENTER H, (METERS*METERS/SEC.)'

WRITE(1,*)
READ(1,*,ERR—2140) H
ELSE IF (ISEPPRE.EQ.2) THEN

Dl - D2/10.0
H - 10000.*D2
ENDIF
CONTINUE
WRITE(1,*)

WRITE(1,*)'PLEASE ENTER THE INITIAL AND FINAL CONCENTRATION, '
WRITE(1,*)'CINIT CINF, (OSMOLALITY). (ENTER BOTH VALUES AND'

WRITE(1,*)’SEPARATE WITH A SPACE.)'
WRITE(1,*)

READ(1,*,ERR-2150) CINIT, CINF
CONTINUE

WRITE(1,*)

WRITE(1,*)'PLEASE ENTER THE INACTIVE VOLUME (%).'

WRITE(1,*)
READ(1,*,ERR-2160) VINA
WRITE(1,*)

CONTINUE

WRITE(1,*)

WRITE(1,*)'PLEASE ENTER THE MAGNIFICATION FACTOR.

wmiinki,“)'LAnbi CELL SILL ENIER l.U.)'
WRITE(1,*)

READ(1,*,ERR-2170) RMAG

WRITE(1,*)

(USE 5080 O '

2180

2190

2210

2215

156

CONTINUE

WRITE(1,*)

WRITE(1,2190) RL1,RL2,LIP,D2,Dl,H,CINIT,CINF,VINA,RMAG
FORMAT(1X,'THE VALUES ENTERED SO FAR ARE:',/,

. 1X,'l) DIALYSIS MEMBRANE THICKNESS - ',E11.3,' MICRONS',/,

. 1X,'2) CELL CHAMBER THICKNESS - ',E11.3,' MICRONS',/,

. 1X,'3) LIPOSOME POSITION (5-11) - ',12,/,

. 1X,'4) DIFFUSIVITY IN CELL CHAMBER - ',E11.3,' M*M/SEC.',/,

. 1X,'5) DIFFUSIVITY IN DIALYSIS MEMBRANE - ',E11.3,' M*M/SEC.',/,
. 1X,'6) MASS TRANSFER COEFFICIENT - ',E11.3,' ',/,

. 1X,'7) INITIAL CONCENTRATION - ',F7.3,' OSMOLALITY',/,

. 1X,'8) FINAL CONCENTRATION - ',F7.3,' OSMOLALITY',/,

. 1X,'9) INACTIVE VOLUME % - ',F5.2,/,

. 1X,'10) MAGNIFICATION FACTOR - ',F7.1,/)

WRITE(1,*)'DO YOU WISH TO CHANGE ANY OF THEM, (Y/N)?’
READ(1,'(A1)') ICHANC
CALL IYESNO(ICHANG)
IF(ICHANG.EQ.'Y') THEN
CONTINUE
WRITE(1,*)
WRITE(1,*)'PLEASE ENTER THE NUMBER BESIDE THE PARAMETER'
WRITE(1,*)'YOU WISH TO CHANGE, (1-10). '
READ(1,*,ERR-2210) NCHANC
CONTINUE
WRITE(1,*)
WRITE(1,*)'PLEASE ENTER THE NEW VALUE.’
IF(NCHANG.EQ.1) THEN
READ(1,*,ERR-2215) RL1
ELSE IF(NCHANC.EQ.2) THEN
READ(1,*,ERR-2215) RL2
ELSE IF(NCHANG.EQ.3) THEN
READ(1,*,ERR-2215) LIP
ELSE IF(NCHANG.EQ.4) THEN
READ(1,*,ERR=2215) D2
ELSE IF(NCHANG.EQ.S) THEN
READ(1,*,ERR-2215) D1
ELSE IF(NCHANG.EQ.6) THEN
READ(1,*,ERR-2215) H
ELSE IF(NCHANG.EQ.7) THEN
READ(1,*,ERR-2215) CINIT
ELSE IF(NCHANC.EQ.8) THEN
READ(1,*,ERR-221S) CINF
ELSE IF(NCHANG.EQ.9) THEN
READ(1,*,ERR—2215) VINA
ELSE IF(NCHANG.EQ.10) THEN
READ(1,*,ERR-2215) RMAG
ELSE IF(NCHANG.LE.0.0R.NCHANG.GE.ll) THEN
CALL INCORRES
GO TO 2210
ENDIF
GO TO 2180
ENDIF

2220

2223

2225

2230

2231

2235

2240

2245

157

IF(IRUNAG.GE.1.0R.IMISTAK.EQ.'Y') GO TO 2235

WRITE(1,*)

WRITE(1,*)'IN ORDER FOR THE PROGRAM TO RUN THE USER'
WRITE(1,*)'MUST ALSO ENTER THE FOLLOWING DATA:'

CONTINUE

WRITE(1,*)

WRITE(1,*)'THE TIME RANGE OF THE EXPERIMENT, TMO TM1, (SEC.),'
WRITE(1,*)'(NOTE: PLEASE MAKE SURE TM1 Is GREATER THAN THE '
WRITE(1,*)'TIME OF THE LAST DATA POINT TO BE ENTERED AND ENTER '
WRITE(1,*)'BOTH VALUES WITH A SPACE BETWEEN THEM.)'
READ(1,*,ERR-2220) TMO, TM1

CONTINUE

WRITE(1,*)

WRITE(1,*)'THE TIME STEP, DT, (SEC.). (NOTE: THIS TIME STEP IS'
WRITE(1,*)'USED FOR NUMERICAL INTEGRATION - CHOOSE DT SUCH THAT'
WRITE(1,*)'DT .GE. (TM1-TMO)/301 , TO PREVENT ARRAY OVERFLOW.)'
READ(1,*,ERR-2223) DT

CONTINUE

WRITE(1,*)

WRITE(1,*)'THE PERMEABILITY STEP, DP, (MICRONS/SEC.) (NOTE: '
WRITE(1,*)'CHOOSE DP SUCH THAT DP .GE. (THE MAGINTUE OF THE'
WRITE(1,*)'PERMEABILITY RANGE UNDER INVESTIGATION)/30l TO'
WRITE(1,*)'PREVENT ARRAY OVERFLOW.)'

READ(1,*,ERR-2225) DP

CONTINUE

WRITE(1,*)

WRITE(1,*)'THE PERMEABILITY RANGE UNDER INVESTIGATION, P0 P1,’
WRITE(1,*)’(MICRONS/SEC.). (NOTE: ENTER BOTH VALUES WITH A'
WRITE(1,*)'SPACE BETWEEN THEM.)'

READ(1,*,ERR-2230) P0, P1

CONTINUE

WRITE(1,*)

WRITE(1,*)'THE PERMEABILITY VALUE AT WHICH THE SENSITIVITY'
WRITE(1,*)'COEFFICIENT WILL BE EVALUATED, PSEN, (MICRONS/SEC ) '
READ(1,*,ERR-2230) PSEN

CONTINUE

WRITE(1,*)

WRITE(1,2240) DT,TMO,TM1,DP,PO,P1,PSEN

FORMAT(1X,'THE VALUES ENTERED ARE:',/,

1X,'l) TIME STEP - ',F7.2,' SEC.',/,

1X,'2) TIME RANGE - ',F8.1,' SEC.',' TO ',F8.1,' SEC.',/,
1X,'3) PERMEABILITY STEP - ',F7.2,' MICRONS/SEC.',/,
1X,'4) PERMEABILITY RANGE - ',F7.2,' MICRONS/SEC.',' TO '

,F7.2,' MICRONS/SEC.',/,
1X,'5) INVESTIGATING PERMEABILITY - ',F7.2,' MICRONS/SEC.',/)

WRITE(1,*)’DO YOU WISH TO CHANGE ANY OF THEM, (Y/N)?’

READ(1,'(A1)') ICHANC
CALL IYESNO(ICHANG)
IF(ICHANG.EQ.'Y')THEN
CONTINUE
WRITE(1,*)
WRITE(1,*)'PLEASE ENTER THE NUMBER BESIDE THE PARAMETER'

 

158

WRITE(1,*)'YOU WISH TO CHANGE, (1-5). '
READ(1,*,ERR-2245) NCHANC
2246 CONTINUE
' WRITE(1,*)
WRITE(1,*)'PLEASE ENTER THE NEW VALUE(S). '
READ(1,*,ERR-2246)
IF(NCHANG.EQ.1) THEN
READ(1,*,ERR-2246) DT
ELSE IF(NGHANG.EQ.2) THEN
WRITE(1,*)'(BOTH TMO AND TM1 - SEPARATE WITH A SPACE)’
READ (l,*,ERR-2246) TMO, TM1
ELSE IF(NCHANG.EQ.3) THEN
READ(1,*,ERR-2246) DP
ELSE IF(NCHANG.EQ.4) THEN
WRITE(1,*)'(BOTH P0 AND P1 - SEPARATE WITH A SPACE)’
READ(1,*,ERR-2246) P0, P1
ELSE IF(NCHANG.EQ.5) THEN
READ(1,*,ERR-2246) PSEN
ELSE IF(NCHANG.LE.0.0R.NCHANG.GE.6) THEN
CALL INCORRES

GO TO 2246
ENDIF
GO TO 2235
ENDIF
C
IF(IRELPSE.EQ.1) THEN
IF(IRUNAG.GE.1.0R.IMISTAK.EQ.'Y') THEN
2248 CONTINUE

WRITE(1,*)
WRITE(1,*)'DO YOU WISH TO (1) ENTER ALL NEW DATA POINTS'
WRITE(1,*)'OR (2) REVIEW THE PREVIOUS DATA POINTS,'
WRITE(1,*)'(Y/N)?’
READ(1,*,ERR-2248) INR
CALL IONETWO(INR)
IF(INR.EQ.2) GO TO 2261
IF(INR.EQ.1) THEN
I-O
WRITE(1,*)
GO TO 2250
ENDIF
ENDIF
I - O
WRITE(1,*)
WRITE(1,*)'SINCE YOU HAVE CHOSEN THE REAL-EXPERIMENTAL'
WRITE(1,*)'OPTION YOU MUST NOW ENTER THE DATA POINTS.'
2250 CONTINUE
WRITE(1,*)'BEFORE ENTERING THE DATA, Is THERE A TIME'
WRITE(1,*)'DELAY THAT YOU WOULD LIKE TO HAVE SUBTRACTED'
WRITE(1,*)'FROM THE TIME ARRAY YOU WILL BE ENTERING,’
WRITE(1,*)'(Y/N)?’
READ(1,'(A1)') IDEL
CALL IYESNO(IDEL)

2251

2252

2253

2255

2256
2257

2260

159

IF(IDEL.EQ.'N') THEN
DELAY - 0.0
ELSE IF(IDEL.EQ 'Y') THEN
CONTINUE
WRITE(1,*)
WRITE(1,*)'PLEASE ENTER THE TIME DELAY TO BE SUBTRACTED,’
WRITE(1,*)'(SEC.)'
READ(1,*,ERR-2251) DELAY
WRITE(1,2252) DELAY
FORMAT(/,' THE TIME DELAY THAT WILL BE SUBTRACTED IS ',
F7.4,' SEC. ',/,/,' DO YOU WISH TO CHANGE IT, (Y/N)?')
READ(1,'(A1)') ICHANC
CALL IYESNO(ICHANG)
IF(ICHANG.EQ.'Y') GO TO 2251
ENDIF
WRITE(1,*)
WRITE(1,*)'DO YOU WISH TO ENTER THE RADIUS USING UNITS'
WRITE(1,*)'OF (1) MICRONS OR (2) CENTIMETERS?’
READ(1,*,ERR-2253) IMICCEN
CALL IONETWO(IMICCEN)
WRITE(1,*)
WRITE(1,*)'PLEASE ENTER THE DATA POINTS,’
IF(IMICCEN.EQ.1)THEN
WRITE(1,*)'TIME(I) (SEC.) RADIUS(I) (MICRONS)'
ELSE IF(IMICCEN.EQ.2) THEN
WRITE(1,*)'TIME(I) (SEC.) RADIUS(I) (CENTIMETERS)'
ENDIF
WRITE(1,*)'(ENTER BOTH VALUES AND SEPARATE WITH A SPACE.)'
WRITE(1,*)'(NOTE: ENTER 0.0 0.0 FOR THE LAST DATA POINT.) '
WRITE(1,*)
I - I+1
WRITE(1,2256) I
FORMAT(IX,'ENTER POINT ',13)
READ(1,*,ERR-2257) TMA(I), RA(I)
IF((TMA(I).GT.O.).AND.(RA(I).GT.O.)) TMA(1)-TMA(I)-DELAY
IF(I.EQ.1) RAMAX - RA(I)
IF(I.GE.2.AND.RA(I).GT.RAMAX) RAMAX - RA(I)
IF((TMA(I).GT.O.).OR.(RA(I).CT.O.)) GO TO 2255
ICOUNT - I-l
IF(TM1.LE.TMA(ICOUNT)) THEN
WRITE(1,*)
WRITE(1,*)'PLEASE MAKE SURE THE TIME, LIMIT TM1 IS'
WRITE(1,*)'LARGER THAN THE TIME OF THE LAST DATA POINT.’
WRITE(1,*)'IF YOU DO NOT CHANGE THIS THE PROGRAM WILL STOP.’
WRITE(1,*)'(RELAX YOU WILL HAVE A CHANCE TO CHANGE IT.)'
WRITE(1,*)
ENDIF
CONTINUE
WRITE(1,*)'THE NEXT TABLE WILL SHOW YOU THE POINTS YOU HAVE'
WRITE(1,*)'JUST ENTERED. IF YOU HAVE ENTERED MORE THAN 20'
WRITE(1,*)'POINTS THE TABLE WILL STOP SPOOLING EVERY 20 POINTS'
WRITE(1,*)'T0 ALLOW YOU TO REVIEW THE POINTS ENTERED. MAKE’

160

WRITE(1,*)'A NOTE OF WHICH POINT YOU WISH TO CHANGE OR'
WRITE(1,*)'INSERT AND PRESS [RETURN] TO CONTINUE NOTE, YOU'
WRITE(1,*)'YOU WILL ONLY BE ABLE TO CHANGE ONE POINT AT'
WRITE(1,*)'A TIME.’
WRITE(1,*)'(NOW PRESS [RETURN] TO CONTINUE.)'
READ(1,'(A1)') ICHANC

2261 CONTINUE
WRITE(1,*)
WRITE(1,*)'THE DATA POINTS YOU HAVE ENTERED ARE: '
WRITE(1,2259) DELAY

2259 FORMAT(' (INCLUDING THE SUBTRACTED TIME DELAY 0F ',
. F10.4,' SEC.)')
WRITE(1,*)
WRITE(1,*)' J TIME(J) RADIUS(J)'
IF(IMICCEN.EQ.1) THEN
WRITE(1,*)' (SEC.) (MICRONS)'
ELSE IF(IMICCEN.EQ.2) THEN
WRITE(1,*)' (SEC.) (CENTIMETERS)'
ENDIF

DO 2265 J-1,ICOUNT+1
WRITE(1,2263) J, TMA(J), RA(J)
2263 FORMAT(lX,I3,5X,F8.2,SX,F8.2)
IF((J/20)*20.EQ.J) THEN
WRITE(1,*)
WRITE(1,*)'PRESS [RETURN] TO CONTINUE.’
READ(1,'(A1)') ICHANC
ENDIF
2265 CONTINUE
IF(IBACK.EQ.1) GO TO 2281
WRITE(1,*)
WRITE(1,*)'DO YOU WISH TO CHANGE OR INSERT ANY OF THE POINTS,’
WRITE(1,*)'(Y/N)?’
READ(1,'(A1)') ICHANC
CALL IYESNO(ICHANG)
IF(ICHANG.EQ.'Y') THEN
2266 CONTINUE
WRITE(1,*)
WRITE(1,*)'ENTER (1) TO CHANGE AND (2) TO INSERT.’
READ(1,*,ERR-2266) ICHAINS
CALL IONETWO(ICHAINS)
IF(ICHAINS.EQ.1) THEN
2267 CONTINUE
WRITE(1,*)
WRITE(1,*)'PLEASE ENTER THE INDEX NUMBER J'
READ(1,*,ERR-2267) JI
IF(JI.LE.0.0R.JI.CE.I+1) THEN
CALL INCORRES
GO TO 2267
ENDIF
WRITE(1,*)
WRITE(1,*)'PLEASE ENTER THE NEW VALUES FOR '
WRITE(1,*)'TIME(J) AND RADIUS(J). '

161

2270 READ(1,*,ERR-2270) TMA(JI), RA(JI)
GO TO 2261
ELSE IF(ICHAINS.EQ.2) THEN
2272 CONTINUE
WRITE(1,*)

WRITE(1,*)'ENTER THE INDEX NUMBER J YOU WISH TO '
WRITE(1,*)'CHANGE, (OR PUSH DOWN).'
READ(1,*,ERR-2272) JI
IF(JI.LE.0.0R.JI.GE.I+1) THEN
CALL INCORRES
GO TO 2272
ENDIF
I — I+1
ICOUNT - I-l
DO 2278 J-JI,I-1
TMA(I+JI-J) - TMA((I-1)+JI-J)
RA(I+JI-J) - RA((I-l)+JI-J)
2278 CONTINUE
WRITE(1,*)
WRITE(1,*)'PLEASE ENTER THE NEW VALUES FOR'
WRITE(1,*)'TIME(J) AND RADIUS(J).'
2280 READ(1,*,ERR—2280) TMA(JI), RA(JI)
GO TO 2261
ENDIF
ENDIF
2281 CONTINUE
IF(IRUNAG.GT.O) THEN
WRITE(1,*)
WRITE(1,*)'D0 YOU WISH TO HAVE A TIME DELAY SUBTRACTED'
WRITE(1,*)'FROM THE DATA POINTS, (Y/N)?’
READ(1,’(A1)') IDEL
CALL IYESNO(IDEL)
IF(IDEL.EQ.'Y') THEN
2282 CONTINUE
WRITE(1,*)
WRITE(1,*)'PLEASE ENTER THE DELAY TO BE SUBTRACTED.’
READ(1,*,ERR-2282) DELAY
WRITE(1,*)
WRITE(1,2283) DELAY
2283 FORMAT(' THE DELAY ENTERED IS ',F10.4,' (SEC.)',/,
' DO YOU WISH TO CHANGE IT, (Y/N)?')
READ(1,'(A1)') ICHANC
CALL IYESNO(ICHANG)
IF(ICHANG.EQ.'Y') GO TO 2282
ELSE IF(IDEL.EQ.'N') THEN
DELAY - 0.0
GO TO 2341
ENDIF
DO 2284 J-l,ICOUNT
TMA(J) - TMA(J) - DELAY
2284 CONTINUE
IBACK - 1

162

GO TO 2261
ENDIF
IBACK - 0

RINIT - RA(l)
ELSE IF(IRELPSE.EQ.2) THEN
IF(IRUNAG.CE.1.0R.IMISTAK.EQ.'Y') GO TO 2319
WRITE(1,*)
WRITE(1,*)'SINCE YOU HAVE CHOSEN THE PSEUDO-EXPERIMENTAL'
WRITE(1,*)'OPTION, THE FOLLOWING PARAMETERS MUST ALSO'
WRITE(1,*)'BE ENTERED.’
WRITE(1,*)
2300 CONTINUE
WRITE(1,*)'THE PERMEABILITY VALUE WITH WHICH THE PROGRAM'
WRITE(1,*)'GENERATES PSEUDO-EXPERIMENTAL DATA, PTRU, '
WRITE(1,*)'(MICRONS/SEC.).'
READ(1,*,ERR-2300) PTRU
2303 CONTINUE
WRITE(1,*)
WRITE(1,*)'DO YOU WISH TO ENTER THE INITIAL RADIUS USING UNITS'
WRITE(1,*)'0F (1) MICRONS OR (2) CENTIMETERS, (ENTER 1 OR 2)?'
READ(1,*,ERR-2303) IMICCEN
CALL IONETWO(IMICCEN)
2305 CONTINUE
WRITE(1,*)
WRITE(1,*)'PLEASE ENTER THE INITIAL RADIUS OF THE CELL, RINIT,’
IF(IMICCEN.EQ.1) WRITE(1,*)'(MICRONS).'
IF(IMICCEN.EQ.2) WRITE(1,*)'(CENTIMETERS).'
READ(1,*,ERR-2305) RINIT
2310 CONTINUE
WRITE(1,*)
WRITE(1,*)'SINCE THIS IS A SIMULATION THE DATA POINTS '
WRITE(1,*)'GENERATED WILL HAVE A RADIUS HISTORY THAT WILL'
WRITE(1,*)'LO0K EXACTLY LIKE THAT OF THEORY, THEREFORE'
WRITE(1,*)'THE PROGRAM ALLOWS THE USER TO IMPOSE A PSEUDO-'
WRITE(1,*)'RANDOMNESS FACTOR, DR, ON THE DATA. DR CAN BE'
WRITE(1,*)'THOUGHT OF AS THE MAGNITUDE OF THE VARIATION'
WRITE(1,*)'IN MEASURING THE RADIUS OF THE CELL.’
WRITE(1,*)'PLEASE ENTER DR NOW.’
IF(IMICCEN.EQ.1) WRITE(1,*)'(MICRONS).'
IF(IMICCEN.EQ.2) WRITE(1,*)'(CENTIMETERS).'
READ(1,*,ERR-2310) DR
WRITE(1,*)
WRITE(1,*)'WHEN USING THIS OPTION THE USER CAN CHANCE'
WRITE(1,*)'THE TIME STEP IN TWO REGIONS TO STUDY THE '
WRITE(1,*)'EFFECT OF DATA SPACING 0F PARAMETER ESTIMATION.'
WRITE(1,*)'DO YOU WISH TO DO THIS, (Y/N)? '
READ(1,'(A1)') IMORE
CALL IYESNO(IMORE)
IF(IMORE.EQ.'N') THEN
TMOl - TM1
DT1 - DT
DT2 - DT

163

ELSE IF(IMORE.EQ.'Y') THEN
2311 CONTINUE
WRITE(1,*)
WRITE(1,*)'PLEASE ENTER THE FIRST TIME STEP, DT1, (SEC.). '
READ(1,*,ERR-23ll) DT1
2312 CONTINUE
WRITE(1,*)
WRITE(1,*)'PLEASE ENTER THE SECOND TIME STEP, DT2, (SEC.) '
READ(1,*,ERR-2312) DT2
2313 CONTINUE
WRITE(1,*)

WRITE(1,*)'PLEASE ENTER THE INTERMEDIATE TIME LIMIT, TMOl,
WRITE(1,*)'(SEC.) FOR THE FIRST TIME INTERVAL. (TMOl '
WRITE(1,*)'TO TM1 IS ASSUMED TO BE THE SECOND TIME '
WRITE(1,*)'INTERVAL.)'

READ(1,*,ERR-2313) TMOl

‘

ENDIF
C
2319 CONTINUE
IF(IMICCEN.EQ.1) XMICCEN -'MICRONS'
IF(IMICCEN.EQ.2) XMICCEN -'CENTIMETERS'
WRITE(1,*)
WRITE(1,2320) PTRU,RINIT,XMICCEN,DR,XMICCEN,DT1,DT2,TMOl
2320 FORMAT(lX,'THE VALUES ENTERED FOR THE PSEUDO-EXPERIMENTAL’
,' OPTION ARE:',/,

. 1X,'1) PSEUDO-PERMEABILITY - ',F8.1,' MICRONS/SEC.',/,

. 1X,'2) INITIAL CELL RADIUS - ',E11.3,1X,A11,/,

. 1X,'3) RADIUS RANDOMNESS - ',E11.4,1X,A11,/,

. 1X,'4) FIRST TIME STEP - ',F7.2,' SEC.',/,

. 1X,'5) SECOND TIME STEP - ',F7.2,' SEC.',/,

. 1X,'6) INTERMEDIATE TIME LIMIT - ',F8.1,' SEC.',/)
WRITE(1,*)'DO YOU WISH TO CHANGE ANY OF THEM, (Y/N)?’
READ(1,'(A1)') ICHANG
CALL IYESNO(ICHANG)

IF(ICHANG.EQ.'Y') THEN
2330 CONTINUE
WRITE(1,*)
WRITE(1,*)'PLEASE ENTER THE NUMBER BESIDE THE PARAMETER'
WRITE(1,*)'YOU WISH TO CHANGE, (1-5). '
READ(1,*,ERR-2330) NCHANC
2340 CONTINUE

WRITE(1,*)
WRITE(1,*)'PLEASE ENTER THE NEW VALUE. '
IF(NCHANG.EQ.1) THEN
READ(1,*,ERR-2340) PTRU
ELSE IF(NGHANG.EQ.2) THEN
READ(1,*,ERR-2340) RINIT
ELSE IF(NCHANG.EQ.3) THEN
READ(1,*,ERR-2340) DR
ELSE IF(NCHANG.EQ.4) THEN
READ(1,*,ERR-2340) DT1
ELSE IF(NCHANG.EQ.5) THEN

C

164

READ(1,*,ERR-2340) DT2

ELSE IF(NCHANG.EQ.6) THEN
READ(1,*,ERR-2340) TM01

ELSE IF(NCHANG.LE.0.0R.NCHANG.GE.7) THEN
CALL INCORRES
GO TO 2330

ENDIF

GO TO 2319
ENDIF
ENDIF

2341 CONTINUE

2345

IF(IRUNAG.EQ.0) THEN
IFl - O
IF2 - O
IF3 - 0
IF4 - 0
CABO - 0.0
CABl - 5.0
SENO - -0.1
SENl - 0.0
SUMO - 0.0
SUMl - 100.0
ELSE IF(IRUNAG.GT.0) THEN
WRITE(1,*)
WRITE(1,*)'D0 YOU WISH TO CHANGE ANY OF THE LIMITS OF THE'
WRITE(1,*)'GRAPHICAL OPTIONS YOU HAVE CHOOSEN AND/OR '
WRITE(1,*)'WOULD YOU LIKE TO CHOOSE ANOTHER OPTION, (Y/N)?’
READ(1,'(A1)') ICHANG
CALL IYESNO(ICHANG)
IF(ICHANG.EQ.'N') GO TO 3999
IF(ICHANG.EQ.'Y') THEN
WRITE(1,*)
WRITE(1,*)'THE PROGRAM WILL NOW ALLOW TO CHANGE OR '
WRITE(1,*)'CHOOSE ANOTHER OPTION BY SELECTING ONE'
WRITE(1,*)'OF THE FOLLOWING OPTIONS.’
GO TO 2345
ENDIF
ENDIF
WRITE(1,*)'DO YOU WISH TO VIEW THE OUTPUT IN GRAPHICAL '
WRITE(1,*)'FORM, (Y/N)?’
READ(1,'(A1)') IGRAPH
CALL IYESNO(IGRAPH)
IF(IGRAPH.EQ.'Y') THEN
CONTINUE
WRITE(1,*)
WRITE(1,*)'THE OUTPUT CAN BE VIEWED IN THE FOLLOWING WAYS:'
WRITE(1,*)
WRITE(1,*)'1) CONCENTRATION V.S. DIMENSIONLESS TIME'
WRITE(1,*)'2) SENSITIVITY COEFFICIENT V.S. TIME'
WRITE(1,*)'3) NORMALIZED VOLUME V.S. TIME'
WRITE(1,*)'4) SUM OF ERRORS OF SQUARES V.S. PERMEABILITY'

2347

2348

2350

2360

2370

165

WRITE(1,*)
IF(IRUNAG.EQ.0) THEN

WRITE(1,*)'WHICH GRAPHICAL OPTION WOULD YOU LIKE (1-4),'

ELSE IF(IRUNAG.GT.0) THEN

WRITE(1,*)'WHICH GRAPHICAL OPTION WOULD YOU LIKE TO'

WRITE(1,*)'SELECT OR CHANGE LIMITS ON, (1-4)’

ENDIF
WRITE(1,*)'(PLEASE CHOOSE ONE GRAPH AT A TIME).'
CONTINUE
READ(1,*,ERR-2347) IOPTGR
IF(IOPTGR.LE.0.0R.IOPTGR.GE.5) THEN

CALL INCORRES

GO TO 2345
ENDIF

WRITE(1,*)'(NOTE: PLEASE ENTER BOTH LOWER AND UPPER LIMITS'

WRITE(1,*)' WITH A SPACE SEPARATING THE VALUES.)'
IF(IOPTGR.EQ.1) THEN

IFl - 1

CONTINUE

WRITE(1,*)

WRITE(1,*)'PLEASE ENTER THE CONCENTRATION LIMITS, CABO CABl.
WRITE(1,*)'(UNLESS NECESSARY TO CHANGE THESE SET THE VALUES'

WRITE(1,*)'AS 0.0 AND 5.0.)'
READ(1,*,ERR-2348) CABO, CABl
CALL CHANLIM(CABO,CAB1)
ELSE IF(IOPTGR.EQ.2) THEN
IF2 - 1
CONTINUE
WRITE(1,*)

WRITE(1,*)'PLEASE ENTER THE SENSITIVITY COEFFICIENT LIMITS,
WRITE(1,*)'(SUGGESTED LIMITS ARE -O.1 AND 0.0)'

WRITE(1,*)'SENO SENI.’
READ(1,*,ERR-2350) SENO, SENl
CALL CHANLIM(SENO,SEN1)
ELSE IF(IOPTGR.EQ.3) THEN
IF3 - 1
CONTINUE
WRITE(1,*)

WRITE(1,*)'PLEASE ENTER THE LIMITS FOR THE NORMALIZED'
WRITE(1,*)'VOLUME, VOLO VOLl. (UNLESS NECESSARY TO '
WRITE(1,*)'CHANGE THESE, SET THE VALUES AS 0.0 AND l.O).'

READ(1,*,ERR-2360) VOLO, VOLl
CALL CHANLIM(VOLO,VOL1)
ELSE IF(IOPTGR.EQ.4) THEN
IF4 - 1
CONTINUE
WRITE(1,*)

WRITE(1,*)'PLEASE ENTER THE SUM OF ERRORS LIMITS,
WRITE(1,*)'(SUGGESTED LIMITS 0.0 AND 20.0)'
READ(1,*,ERR-2370) SUMO, SUMl
CALL CHANLIM(SUMO,SUM1)

ENDIF

SUMO SUMl.

0

I

2400

3100

3110

3120

3125

3130

3140

3145

3150

3160

3170

3180

3190

166

WRITE(1,*)

WRITE(1,*)'DO YOU WISH TO CHOOSE ANOTHER GRAPH,

READ(1,'(A1)') IANOTH
CALL IYESNO(IANOTH)
IF(IANOTH.EQ.'Y') GO TO 2345
ENDIF
CONTINUE

(Y/N)? '

WRITE(1,*)'HAVE YOU MADE ANY MISTAKES THAT YOU WOULD LIKE '

WRITE(1,*)'ANOTHER CRACK AT ENTERING/CHANGING THE PARAMETERS '

WRITE(1,*)'OR DATA AGAIN, (Y/N)?’
READ(1,'(A1)') IMISTAK

CALL IYESNO(IMISTAK)
IF(IMISTAK.EQ.'Y') GO TO 2180
WRITE(1,*)

WRITE(1,*)'OKAY, THE PROGRAM IS NOW CRUNCHING.’

GO TO 3999
OPTION ITERINP - 2: ENTERING THE INPUT FILE

CONTINUE
OPEN(11,FILE-ISENS)

READ(11,'(A11)') PROBLEM

READ(11,3100) RL1,RL2,LIP
FORMAT(///,1X,F11.6,F11.6,12)
READ(11,3110) D1,D2,H
FORMAT(//,1X,Ell.2,Ell.2,E11.2)
READ(11,3120) CINIT, CINF
FORMAT(//,1X,F11.6,F11.6)

READ(11,3125) VINA,RMAG
FORMAT(//,1X,Ell.6,E11.6)

READ(11,3130) DT,TMO,TM1,DELAY
FORMAT(//,1X,F11.6,F11.6,F11.6,F11.6)
READ(11,3140) DP,PSEN
FORMAT(//,1X,F11.6,F11.6)

READ(11,3145) RINIT

FORMAT(//,1X,F11.6)

READ(11,3150) PTRU,DR,TM01,DT1,DT2
FORMAT(///,1X,Fll.6,F11.6,F11.6,F11.6,F10.6)
READ(11,3160) IRELPSE,IMICCEN
FORMAT(///,1X,I9,I9)

READ(11,3170) IF1,IF2,IF3,IF4,IPRINT
FORMAT(///,lX,Ill,Ill,Ill,I11,I2,/)
READ(11,3180) CABO,CAB1
FORMAT(//,1X,Fll.6,F11.6)

READ(11,3180) SENO,SEN1

READ(11,3180) VOL0,VOL1

READ(11,3190) PO,P1,SUMO,SUM1
FORMAT(//,1X,F11.6,F11.6,F11.6,F11.6,///)

IF(IMICCEN.EQ.1) XMICCEN-'MICRONS'
IF(IMICCEN.EQ.2) XMICCEN-'CENTIMETERS'

4020

4030

4040

4050

4060

4070

4080

4090

4100

4110

4120

4130

167

WRITING THE INPUT DATA TO THE OUTPUT FILE O_SENS.DAT'

WRITE(1,3195) ISENS

FORMAT(/,' THE INPUT FILE ',AlO,’ HAS BEEN ENTERED.')
CONTINUE

OPEN(10,FILE-'O_SENS.DAT')

WRITE(10,4000) ISENS

FORMAT(IX, ' ********************* THE INPUT FILE ' ’AIO
' ********************** ' ’ /)

WRITE(10,4005)

FORMAT(/,'RL1,RL2,LIP ARE',/)
WRITE(10,*) RL1,RL2,LIP
WRITE(10,4010)

FORMAT(/,'Dl,D2,H ARE',/)
WRITE(10,*) D1, D2, H
WRITE(10,4020)
FORMAT(/,'CINIT,CINF, ARE:',/)
WRITE(10,*)CINIT,CINF
WRITE(10,4030)

FORMAT(/,'VINA,RMAG ARE:',/)
WRITE(10,*)VINA,RMAG
WRITE(10,4040)
FORMAT(/,'DT,TMO,TM1,DELAY ARE:',/)
WRITE(10,*) DT,TMO,TM1,DELAY
WRITE(10,4050)

FORMAT(/,'DP,PSEN ARE:',/)
WRITE(10,*) DP, PSEN
WRITE(10,4060)

FORMAT(/,'RINIT IS:',/)
WRITE(10,*) RINIT

WRITE(10,4070)
FORMAT(/,'PTRU,DR,TM01,DT1,DT2 ARE:',/)
WRITE(10,*) PTRU,DR,TM01,DT1,DT2
WRITE(10,4080)
FORMAT(/,'IRELPSE,IMICCEN ARE:',/)
WRITE(10,*) IRELPSE, IMICCEN
WRITE(10,4090)
FORMAT(/,'IFl,IF2,IF3,IF4,IPRINT ARE:',/)
WRITE(10,*) IF1,IF2,IF3,IF4,IPRINT
WRITE(10,4100)

FORMAT(/,'CABO,CABl ARE:',/)
WRITE(10,*) CABO, CABl
WRITE(10,4110)

FORMAT(/,'SENO,SEN1 ARE:',/)
WRITE(10,*) SENO,SEN1
WRITE(10,4120)

FORMAT(/,'VOLO,VOL1 ARE:',/)
WRITE(10,*) VOLO,VOL1
WRITE(10,4130)
FORMAT(/,'P0,P1,SUMO,SUM1 ARE:',/)
WRITE(10,*) Po,P1,SUM0,SUM1

100

168

USING SUBROUTINE MBCON TO PREDICT THE CONCENTRATION CHANGE
INSIDE THE CELL CHAMBER

CALL MBCON(IOPNAG)
INITIALIZATION OF THE TIME VARIABLES AND RINIT

IT-INT((TM1-TMO)/DT)+1

DO 100 I-1,IT
TMS(I)-TMO+(I-l)*DT
TMB(I)-TMS(I)

CONTINUE

IF(IMICCEN.EQ.1) THEN
RINIT - RINIT/RMAG

ELSE IF(IMICCEN.EQ.2) THEN
RINIT - RINIT*10000./RMAG

ENDIF

CALCULATE R(TM,P) AND R(TM,P+DP)

CALL RGKT(TMS,RS,IT,DT,RINIT,PSEN)
CALL RGKT(TMB,RB,IT,DT,RINIT,PSEN+EP1*PSEN)

CALCULATE SENSITIVITY COEFF. (SEN)
WRITE(10,4175)

FORMAT(//,1X,'********* DIMENSIONLESS SENSIVITITY ',
'COEFFICIENT VERSUS TIME ********')

WRITE(10,4180)

4230

4235

FORMAT(/,6X,'TIME(I)',7X,'SEN(I)',/)

DO 4190 J-1,IT
SEN(J)-(RB(J)-RS(J))*PSEN/RINIT/(EP1*PSEN)
WRITE(10,*)TMS(J),SEN(J)

CONTINUE

PLOTTING SENSITIVITY VERSUS TIME (IF2-O STOP THE OUTPUT)

IF(IF2.EQ.0)GO TO 4230

CALL NEWPAG

CALL PLOT(TMO,TM1,10,SENO,SEN1,10,TMS,SEN,IT,FCTO,5,2)
CALL ANMODE

CALL HOME

WRITE(1,*)

WRITE(1,*)'PRESS [RETURN] TO CONTINUE.’
READ(1,'(A1)') IMORE

CONTINUE

WRITE(10,*)

WRITE(10,4235)

FORMAT< 1X ’ ' ************************ RADIUS VERSUS TIME ' ,
' ************************ ' )

4240
4250

4253
4255

4260

169

READING THE EXPERIMENTAL DATA AND CONVERTING TO MICRONS

IF (IRELPSE.EQ.1.AND.ITERINP.EQ.2) THEN

I-O
WRITE(IO,4240)
FORMAT(/,6X,'TM(I)',10X,'R(I)',/)
I-I+1
READ(11,*)TMA(I),RA(I)
RSAVE(I) - RA(I)
IF(RA(I).GT.0.) TMA(I) - TMA(1)-DELAY
WRITE(10,4253)TMA(I),RA(I)
IF(IMICCEN.EQ.1) THEN

RA(I) - RA(I)/RMAG
ELSE IF(IMICCEN.EQ.2) THEN

RA(I) - RA(I)*IOOOO./RMAG
ENDIF
IF(I.EQ.1) RAMAX - RA(I)
IF(I.GE.2) THEN

IF(RA(I).GT.RAMAX) RAMAX - RA(I)

ENDIF
IF ((TMA(I).GT.O.).OR.(RA(I).GT.0.)) GO TO 4250
ICOUNT-I-l
IF (TM1.LE.TMA(ICOUNT)) THEN

WRITE(1,*)

WRITE(1,*)'PLEASE MAKE SURE TM1 IS LARGER THAN THE TIME'

WRITE(1,*)'OF THE LAST DATA POINT, AND RUN IT AGAIN.’
GO TO 6000
END IF

CONVERTING INPUT DATA, ENTERED BY THE TERMINAL, TO MICRONS

ELSE IF(IRELPSE.EQ.1.AND.ITERINP.EQ.1) THEN
WRITE(10,4240)
DO 4255 K-1,ICOUNT+1
RSAVE(K) - RA(K)
WRITE(10,4253) TMA(K),RA(K)
FORMAT(SX,F7.2,5X,E11.4)
CONTINUE
IF(IMICCEN.EQ.1)THEN
DO 4260 K-1,ICOUNT
RA(K) - RA(K)/RMAG
CONTINUE
RAMAX - RAMAX/RMAG
ELSE IF(IMICCEN.EQ.2) THEN
DO 4270 K-1,ICOUNT
RA(K) - RA(K)*10000./RMAG
CONTINUE
RAMAX - RAMAX*10000./RMAG
ENDIF

GENERATING THE SIMULATED (PSEUDO) EXPERIMENTAL DATA

4280

4290

4292

4300

4301

FORMAT(//,1X,'***** SIMULATED RADIUS VERSUS TIME '

170

ELSE IF(IRELPSE.EQ.2) THEN
ICOUNT - ((TM01-TMO)/DT1+(TM1-TM01)/DT2+1)
CALL RGKT(TMS,RB,IT,DT,RINIT,PTRU)
DO 4280 J-1,IT
TMA(J) - TMS(J)
RC(J) - RB(J)
CONTINUE
TMA(1)-TMO
DO 4290 J-2,ICOUNT

IF (TMA(J-l).LT.TMOl) THEN
TMA(J)-TMA(J-1)+DT1

ELSE IF (TMA(J-l).GE.TMOl) THEN
TMA(J)-TMA(J-1)+DT2

END IF

CONTINUE

IF(IMICCEN.EQ.1) THEN
DR - DR/RMAG

ELSE IF(IMICCEN.EQ.2) THEN
DR - DR*10000./RMAG

ENDIF

RAMAXC - RC(1)

DO 4292 J-2,IT
IF(RC(J).GT.RAMAXC) RAMAXC - RC(J)

CONTINUE

RAMAX - RB(1)

DO 4300 J-l,ICOUNT

ITM-INT(TMA(J)/DT)+1

IF (ITM.GE.IT) THEN
RA(J)-RB(ITM)+DR*RANND()

ELSE
DRA-(RB(ITM+1)-RB(ITM))*(TMA(J)-(ITM-l)*DT)/DT
RA(J)-RB(ITM)+DRA+DR*RANND()

END IF

IF(RA(J).GT.RAMAX) RAMAX - RA(J)

CONTINUE
WRITE(10,*)
WRITE(10,4301)

’ *********** ' ’ /)

DO 4302 J-1,ICOUNT+1
IF(IMICCEN.EQ.1) RSAVE(J)-RA(J)*RMAG
IF(IMICCEN.EQ.2) RSAVE(J)-RA(J)*RMAG/10000.

CONTINUE

DO 4305 J-1,ICOUNT
WRITE(10,4253) TMA(J),RA(J)

CONTINUE

END IF

CALCULATING THE NORMALIZED VOLUME

DO 4315 I-l,ICOUNT

4315

4320
4330
c----
c----

4332

WRITE(10,4335)

4335

4336
4338

4340

171

VOLA(I)-(RA(I)/RAMAX)**3
CONTINUE
IF(IRELPSE.EQ.2) THEN
DO 4316 J-1,IT
VOLC(J) -(RC(J)/RAMAXC)**3
CONTINUE
ENDIF

CALCULATE SUM OF ERROR OF SQUARE FOR P VALUES FROM
P0 TO Pl

IP-(Pl-P0)/DP+1
DO 4330 I-1,IP
P(I)-P0+(I-1)*DP
CALL RCKT(TMB,RB,IT,DT,RINIT,P(I))
SUM(I)-0.
DO 4320 J-1,ICOUNT

ITM-INT(TMA(J)/DT)+1

IF (ITM.GE.IT) THEN
RN-RB(ITM)

ELSE
DRN-(RB(ITM+1)-RB(ITM))*(TMA(J)-(ITM-l)*DT)/DT
RN-RB(ITM)+DRN

END IF

SUM(I)-SUM(I)+(RN-RA(J))**2

CONTINUE
CONTINUE

WRITE(10,4332)

FORMAT(///,1X,'*********** SUM OF SQUARES OF ERRORS ',
’VERSUS PERMEABILITY *************')

FORMAT(/,' P(J) SUM(J)',/)
DO 4338 J-1,IP
WRITE(10,4336) P(J),SUM(J)
FORMAT(lX,F8.2,6X,E10.4)
CONTINUE

SUMIN-SUM(1)
PEST - P(l)
DO 4340 I-2,IP
IF (SUMIN.GT.SUM(I)) THEN
SUMIN-SUM(I)
PEST-P(I)
END IF
CONTINUE
CALL RGKT(TMB,RC,IT,DT,RINIT,PEST)
CALL RGKT(TMB,RB,IT,DT,RINIT,PEST+EP1*PEST)
DO 4350 J-1,IT
SEN(J)-(RB(J)-RC(J))/(EP1*PEST)

172

4350 CONTINUE
DO 4360 J-l,ICOUNT

ITM-INT(TMA(J)/DT)+1

IF (ITM.GE.IT) THEN
SEN(J)-SEN(ITM)

ELSE
DSEN-(SEN(ITM+1)-SEN(ITM))*(TMA(J)-(ITM-1)*DT)/DT
SEN(J)-SEN(ITM)+DSEN

END IF

4360 CONTINUE
SENSUM-O.

DO 4365 I-1,ICOUNT

SENSUM-SENSUM+SEN(I)**2

4365 CONTINUE

C - - .. -

c DUMPING SUMMARY INPUT PARAMETERS, INPUT DATA AND RESULTING

C PEST, SDP, SUMIN TO ’O_SMRY.DAT'

C - - - -

OPEN(14,FILE-'O_SMRY.DAT')
WRITE(14,*)
WRITE(14,4366)

4366 FORMAT(//,'********************* THIS IS FILE O_SMRY.DAT'
. ' ********************* ' , // )

WRITE(14,4367)

4367 FORMAT(/,'THE INPUT PARAMETERS AND DATA WERE:',//)
WRITE(14,2190)RL1,RL2,LIP,D2,Dl,H,CINIT,CINF,VINA,RMAG
WRITE(14,*)

WRITE(14,2240)DT,TMO,TM1,DP,P0,P1,PSEN
IF(IRELPSE.EQ.1) THEN
WRITE(14,*)
WRITE(14,*)'THE DATA POINTS ENTERED WEREz'
WRITE(14,2259) DELAY

WRITE(14,*)

WRITE(14,*)' J TIME(J) RADIUS(J)'
IF(IMICCEN.EQ.1) THEN

WRITE(14,*)' (SEC.) (MICRONS)'
ELSEIF(IMICCEN.EQ.2) THEN

WRITE(14,*)' (SEC.) (CENTIMETERS)'
ENDIF

DO 4368 J-1,ICOUNT+1
WRITE(14,2263) J,TMA(J),RA(J)
4368 CONTINUE
ELSE IF(IRELPSE.EQ.2) THEN

WRITE(14,*)
WRITE(14,2320)PTRU,RINIT,XMICCEN,DR,XMICCEN,DT1,DT2,TMOl
ENDIF
C
c--__
C THE ESTIMATED PERMEABILITY
c----

WRITE(10,4375)
WRITE(14,4375)

4375

173

FORMAT(///,'********************* THE RESULTING '
'PERMEABILITY *********************v,/)

SDP-SQRT(SUMIN/(ICOUNT-l)/SENSUM)

4380

4390

4395

4396

4397

6000

WRITE(10,4380)PEST

WRITE(14,4380)PEST

FORMAT(/,'THE LOCAL MINIMUN OCCURS AT P -',F8.3,' MICRONS/SEC.')
WRITE(10,4390)SDP

WRITE(14,4390)SDP

FORMAT(/,'THE STANDARD DEVIATION OF ESTIMATED P IS ',E8.3)
WRITE(10,4395)SUMIN

WRITE(14,4395)SUMIN

FORMAT(/,'THE MINIMUM VALUE OF SUM IS',F8.3)

CLOSE(14)

IF(IRELPSE.EQ.1) THEN
DO 4396 J-1,IT
IF(J.EQ.1) RAMAXC - RC(1)
IF(J.GE.2.AND.RC(J).GT.RAMAXC) RAMAXC-RC(J)
CONTINUE
DO 4397 J-1,IT
VOLC(J) - (RC(J)/RAMAXC)**3
CONTINUE
ENDIF

IF(IF3.EQ.O) GO TO 4398
PLOTTING NORMALIZED VOLUME CHART (IF3-0 STOP THE OUTPUT)

CALL NEWPAG

CALL PLOT(TMO,TM1,10,VOL0,VOL1,10,TMA,VOLA,ICOUNT,FCTO,1,3)
CALL PLOT(TMO,TM1,10,VOL0,VOL1,10,TMS,VOLC,IT,FCTO,S,3)
CALL ANMODE

CALL HOME

WRITE(1,*)

WRITE(1,*)'PRESS [RETURN] TO CONTINUE.’

READ(1,'(A1)') IMORE

CONTINUE
IF(IF4.EQ.0)GO TO 6000
PLOTTING SUM OF SQUARE OF ERRORS (IF4-0 STOP THE OUTPUT)

CALL NEWPAG

CALL PLOT(PO,P1,10,SUMO,SUM1,10,P,SUM,IP,FCTO,5,4)
CALL ANMODE

CALL HOME

WRITE(1,*)

WRITE(1,*)'PRESS [RETURN] TO CONTINUE.’
READ(1,'(A1)') IMORE

CONTINUE

174

WRITE(1,6100) PEST,SDP,SUMIN

6100 FORMAT(' ESTIMATED PERMEABILITY - ',F8.3,
. ' STANDARD DEVIATION - ',E8.3,
. ' MINIMUM SUM SQUARES - ',F8.3)
WRITE(1,*)
WRITE(1,*)'PRESS [RETURN] TO CONTINUE'
READ(1,'(A1)') IMORE

C RESETTING THE RA(I) - RSAVE(I) AND RINIT, RAMAX TO ORIGINAL VALUESS

IF(IMICCEN.EQ.1) THEN
RINIT - RINIT * RMAG
RAMAX - RAMAX * RMAG
IF(IRELPSE EQ.2) DR - DR *RMAG
DO 280 K - 1, ICOUNT+1
RA(K) - RSAVE(K)
280 CONTINUE
ELSE IF(IMICCEN.EQ 2) THEN
RINIT - RINIT *RMAG/IOOOO.
RAMAX - RAMAX *RMAG/IOOOO.
IF(IRELPSE.EQ.2) DR - DR*RMAG/10000.
DO 290 K-1,ICOUNT+1
RA(K) - RSAVE(K)

290 CONTINUE
ENDIF
c .....
C OPTION TO SAVE INPUT FILE
c .....
DELAY - 0.0
WRITE(1,*)

WRITE(1,*)'DO YOU WISH TO SAVE THE INPUT DATA IN A FILE,’
WRITE(1,*)'(Y/N)?’
READ(1,'(A1)') ISAVE
CALL IYESNO(ISAVE)
IF(ISAVE.EQ.'Y') THEN
320 CONTINUE
WRITE(1,*)
WRITE(1,*)'WHAT WOULD YOU LIKE TO NAME THIS FILE,’
WRITE(1,*)'(ENTER NO MORE THAN 10 CHARATERS)?’
READ(1,'(A10)',ERR-320) NAMFIL
OPEN(12,FILE-NAMPIL)
WRITE(12,325)
325 FORMAT(lX,'THIS IS THE FILE YOU HAD SAVED. YOU CAN '
,'USE THIS FILE AS',/,' AN INPUT FILE IF YOU DESIRE BY'
,' ACCESSING THIS FILE',/,' WHEN YOU ARE PROMPTED FOR'
. ,' THE NAME OF AN INPUT FILE.')
331 CONTINUE

WRITE(12,*)'RL1 RL2 LIP'
WRITE(12,332) RL1,RL2,LIP

332 FORMAT(IX,F5.2,6x,F7.2,4x,12,/)
WRITE(12,*)'D1 D2 H'

WRITE(12,333) Dl,D2,H

333

334

335

336

337

338

339

340

341

342

345

346

347

348

349

350
360

175

FORMAT(1X,E9.3,2X,E9.3,2X,E9.3,/)

WRITE(12,*)'CINIT CINF'

WRITE(12,334) CINIT,CINF

FORMAT(1X,F8.3,3X,F8.3,/)

WRITE(12,*)'VINA RMAG'

WRITE(12,335) VINA,RMAG

FORMAT(1X,F5.2,6X,F9.2,/)

WRITE(12,*)'DT TMO TM1 DELAY'
WRITE(12,336) DT,TMO,TM1,DELAY
FORMAT(1X,F6.3,5X,F7.2,4X,F7.2,4X,F7.2,/)
WRITE(12,*)'DP PSEN'

WRITE(12,337) DP,PSEN

FORMAT(1X,F5.2,6x,F6.2,/)

WRITE(12,*)'RINIT'

WRITE(12,338) RINIT

FORMAT(1X,E1O.4,/)

WRITE(12,339)

FORMAT(1X,'THE PARAMETERS FOR THE LINE BELOW ARE FOR ',

'SIMULATION OPTION:')

WRITE(12,*)'PTRU DR TM01 DT1 DT2'
WRITE(12,340) PTRU,DR,TM01,DT1,DT2
FORMAT(1X,F6.2,5X,F7.3,4x,F7.2,4x,F6.3,5X,F6.3,/)
WRITE(12,341)

FORMAT(1X,'THESE PARAMETERS BELOW ARE FOR DATA INPUT '
,'CONTROL:')

WRITE(12,*)'IRELPSE IMICCEN'

WRITE(12,342) IRELPSE, IMICCEN

FORMAT(2X,I1,9X,Il,/)

WRITE(12,*)'THESE PARAMETERS ARE FOR DATA OUTPUT CONTROL:'

WRITE(12,*)'IF1 IF2 IF3 IF4 IPRINT'

WRITE(12,345) IF1,IF2,IF3,IF4,IPRINT
FORMAT(1X,Il,10X,I1,10X,I1,10X,Il,10X,I2,/)
WRITE(12,346)
FORMAT(1X,'THESE PARAMETERS ARE FOR GRAPHICAL OUTPUT ',
'CONTROLz')
WRITE(12,*)'CABO CABl'
WRITE(12,347) CABO,CAB1
FORMAT(1X,F5.2,6X,F7.2,/)
WRITE(12,*)'SENO SENl'
WRITE(12,347) SENO, SENl
WRITE(12,*)'VOLO VOLl'
WRITE(12,347) VOL0,VOL1
WRITE(12,*)'P0 P1 SUMO SUMl'
WRITE(12,348) PO,P1,SUMO,SUM1
FORMAT(1X,F6.2,5X,F6.2,5X,F5.2,6X,F6.2,5x,/)
WRITE(12,349)
FORMAT(1X,'THE LAST GROUP BELOW IS THE DATA POINTS:')
WRITE(12,*)' TMA(I) RA(I)’
DO 360 I -1,ICOUNT
WRITE(12,350) TMA(1), RA(I)
FORMAT(1X,F9.4,5X,F7.2)
CONTINUE

00000

176

WRITE(12,*)' 0.0 0.0'

CLOSE(12)

IF(IQUIT.EQ.'Y') GO TO 600

WRITE(1,362) NAMFIL

FORMAT('OKAY, THE FILE ',AlO,' HAS BEEN SAVED.')
ENDIF
CLOSE(ll)

OPTION TO RUN THE PROGRAM AGAIN

WRITE(1,*)
WRITE(1,*)'DO YOU WISH TO RUN THE PROGRAM AGAIN, (Y/N)?’
READ(1,'(A1)') IAGAIN
CALL IYESNO(IAGAIN)
IOPNAG - IOPNAG + 1
IF(IAGAIN.EQ.'Y') THEN
CONTINUE

OPTION TO ENTER NEW DATA OR REVIEW OLD DATA

WRITE(1,*)
WRITE(1,*)'DO YOU WISH TO (1) ENTER ALL NEW DATA OR '

WRITE(1,*)'(2) USE AND REVIEW THE DATA ALREADY ENTERED,’

WRITE(1,*)'(ENTER 1 OR 2)?’
READ(1,*,ERR-500) INEWREV
CALL IONETWO(INEWREV)
DELAY - 0.0
IBACK - 0
IF(INEWREV.EQ.1) THEN
IRUNAG - 0
GO TO 2000
ELSE IF(INEWREV.EQ.2) THEN
ITERINP - 1
IRUNAG - IRUNAG + 1
GO TO 2180
ENDIF
ENDIF

STOPPING THE PROGRAM

WRITE(1,*)
WRITE(1,*)'OKAY, PROGRAM DONE.’
CALL CLOSTK(I)
CLOSE(IO)
CALL EXIT
END

SUBROUTINE RGKT(X,Y,N,DX,Y0,P)

USE RUNGE-KUTTA METHOD TO SOLVE ORDINARY DIFFERENTIAL
EQUATION

000000000

0

0000

00000000000000

177

X: INDEPENDENT VARIABE

Y: DEPENDENT VARIABLE

N: DIMENSION OF X(N) AND Y(N)

DX: INCREMENT OF X

Y0: INITIAL CONDITION OF Y

P: PARAMETER

F: THE SUPLLIED FUNCTION. (DY/DX-F(X,Y))

SUBROUTINE RGKT(X,Y,N,DX,YO,P)

DIMENSION X(N),Y(N)

Y(1)-YO

DO'l I-l,N-1
RKI-DX*F(X(I),Y(I),P)
RKZ-DX*F(X(I)+DX/2.,Y(I)+RK1/2.,P)
RK3-DX*F(X(I)+DX/2.,Y(I)+RK2/2.,P)
RK4-DX*F(X(I)+DX,Y(I)+RK3,P)
Y(I+1)-Y(I)+(RK1+2*RK2+2*RK3+RK4)/6.

CONTINUE

RETURN

END

FUNCTION F(X,Y,Z)

X: INDEPENDENT VARIABLE
Y: DEPENDENT VARIABLE
Z: PARAMETER

FUNCTION F(X,Y,Z)

PARAMETER N4-301,PI-3 14159

COMMON /C2/RINIT,VINA,DT,TM1,COUT(N4)

COMMON /C3/RL1,RL2,LIP,D1,D2,CINIT,CINF,H
V-0.018

I-INT(X/DT)+1
C0-COUT(I)+(COUT(I+1)-COUT(I))*(X-(I-l)*DT)/DT
V0-4.*PI*RINIT**3/3.

VIN-VINA*V0/100.
F--Z*V*(C0-CINIT*(VO-VIN)/(4.*PI*Y**3/3.-VIN))
RETURN

END

FUNCTION RANND()

RANDOM VARIABLE GENERATOR
NORMAL DISTRIBUTION WITH STANDARD DEVIATION EQUAL TO 1.

10

20

30

10

10

10

178

FUNCTION RANND()

DOUBLE PRECISION RANDOM
R-RANDOM()

AO-2.30753

A1-0.27O61

B1-o.99299

B2-O.O4481

IF (R-O.5) 10,10,20
AK-1.

GO TO 30

AK--1.

R-R-0.S
T-SQRT(ALOG(1./(R*R)))
E-T-(A0+A1*T)/(1.+B1*T+B2*T*T)
RANND-AK*E

RETURN

END

SUBROUTINE IONETWO(ITEST)

CONTINUE

IF(ITEST.LE.0.0R.ITEST.GE.3) THEN
WRITE(1,*)
WRITE(1,*)'** INCORRECT RESPONSE **'
WRITE(1,*)'PLEASE ENTER 1 OR 2'
WRITE(1,*)
READ(1,*) ITEST
GO TO 10

ENDIF

RETURN

END

SUBROUTINE IYESNO(ITEST)

CHARACTER *1 ITEST

CONTINUE

IF(ITEST.NE.'Y'.AND.ITEST.NE.'N') THEN
WRITE(1,*)
WRITE(1,*)'** INCORRECT RESPONSE **'
WRITE(1,*)'PLEASE ENTER "Y" OR "N"'
WRITE(1,*)
READ(1,'(A1)') ITEST
GO TO 10

ENDIF

RETURN

END

SUBROUTINE CHANLIM(ZO,Zl)

CHARACTER *1 ICHANGE

CONTINUE

WRITE(1,*)

WRITE(1,*)'THE VALUES ENTERED ARE: '
WRITE(1,*)

20

33

35

36

179

WRITE(1,*) 20, 21
WRITE(1,*)

WRITE(1,*)' DO YOU WISH TO CHANGE THEM,(Y/N)? '

READ(1,'(A1)') ICHANG
CALL IYESNO(ICHANG)
IF(ICHANC.EQ.'Y') THEN
WRITE(1,*)
CONTINUE
WRITE(1,*)'PLEASE ENTER THE NEW VALUES.
WRITE(1,*)
READ(1,*,ERR-20) 20,21
GO TO 10
ENDIF
RETURN
END
SUBROUTINE INCORRES
WRITE(1,*)
WRITE(1,*)'** INCORRECT RESPONSE **'
RETURN
END

SUBROUTINE CHANNAM(FILNAM)

CHARACTER*1 ICHANG

CHARACTER*1O FILNAM

CONTINUE

WRITE(1,*)

WRITE(1,35) FILNAM

FORMAT(1X,'THE FILE NAME ENTERED IS ',AlO)
WRITE(1,*)

WRITE(1,*)'DO YOU WISH TO CHANGE IT, (Y/N)?’

READ(1,'(A1)') ICHANG

CALL IYESNO(ICHANG)

IF(ICHANG.EQ.'Y') THEN
WRITE(1,*)
CONTINUE
WRITE(1,*)'PLEASE ENTER THE NEW NAME.
WRITE(1,*)
READ(1,'(A10)',ERR-36) FILNAM
GO TO 33

ENDIF

RETURN

END

I

180

SUBROUTINE MBCON(IOPNAG)

C .....
C JOB: 1. PREDICT THE CONCENTRATION CHANGE INSIDE THE CELL
C' CHAMBER
C 2. PLOTTING CONCENTRATION VERSUS TIME CHART
C .....
PARAMETER (N1-4,N2-6,II-2,N4-301)
REAL L1,L2,M
CHARACTER*1 ICONT
DIMENSION CN(NI+N2+1),CO(NI+N2+1),CE(N1+N2+1,N1+N2+1),
& W(N1+N2+2,N1+N2+2),CONC(N1+N2+1),CA(25),CB(25),
& DC(25),TM(25),X(II,II),Y1(II),Y2(II),W1(II+1,II+1)
COMMON /C1/IPRINT,IF1,A1(II),A2(II),CABO,CAB1
COMMON /C2/RINIT,VINA,DT,TM1,COUT(N4)
COMMON /CS/RL1,RL2,LIP,Dl,D2,CINIT,CINF,H
EXTERNAL FCTI,FCT2
C .....
C INITIALIZATION
C .....
L1-RL1*1.0E-6
L2-RL2*1.0E-6
TMAx-TMI
DX1-L1/N1
DX2-L2/N2
RX-DXZ/DXI
P1-DT*D1/Dx1/DX1
P2-DT*D2/Dx2/DX2
Bl-H*DX1/D1
M—2./(I+RX)
DO 1 I-1,N1+N2+l
CN(I)-0.
CO(I)-O.
DO 1 J-1,N1+N2+1
CE(I,J)-O.
1 CONTINUE
ICOUNT-O
C .....
C USING THE BACKWARD DIFFERENCE METHOD TO CALCULATE THE
C CONCENTRATION INSIDE THE CELL CHAMBER
C .....
WRITE(10,151)
151 FORMAT(///,1x,'************************ THE CONCENTRATION',
v HISTORY ************************v)
C .....
C INPUT VALUES TO THE COEFFICIENT MATRIX
C .....

CE(1,1)-1+2*P1+2*P1*B1

CE(1,2)--2*Pl

DO 2 I-2,N1
CE(I,I-1)--P1
CE(I,I)-l+2*P1
CE(I,I+l)--P1

201

202

181

CONTINUE

CE(N1+I,N1)--P1*M

CE(N1+1,Nl+1)-1+P1*M+P1*M*(D2/D1)/RX

CE(N1+1,N1+2)--P1*M*(D2/D1)/RX

D0 3 I-Nl+2,Nl+N2
CE(I,I-1)--P2
CE(I,I)-1+2*P2
CE(I,I+1)--P2

CONTINUE

CE(N1+N2+1,NI+N2)—-2*P2

CE(N1+N2+1,N1+N2+1)-1+2*P2

C0(1)—CO(1)+2*B1*P1

CALCULATE THE COEFFICIENT MATRIX
CALL LINEQ(CN,CO,CE,W,N1+N2+1,N1+N2+2,I)
PUT CN INTO GO FOR NEXT CALCULATION

ICOUNT-ICOUNT+1
DO 4 I-1,N1+N2+l
CO(I)-CN(I)
CONTINUE
COUT(ICOUNT)-CN(LIP)*(CINF-CINIT)+CINIT
COUT(ICOUNT)-CINF+(CINIT-CINF)*EXP(-(ICOUNT-1)*DT/19.6)

CHECK TO SEE WHETHER IT IS TIME TO OUTPUT THE DATA

IF (ICOUNT/IPRINT*IPRINT.EQ.ICOUNT) THEN
WRITE(10,101)ICOUNT*DT
FORMAT(/,'CONCENTRATION DIST. AT TIME-',F10.4,'SEC. IS',/)
DO 5 I-1,N1+N2+1
CONC(I)-CN(I)*(CINF-CINIT)+CINIT
CONTINUE
WRITE(10,*)
WRITE(10,*)' DIALYSIS MEMBRANE CELL CHAMBER'
WRITE(10,*)' I |
WRITE(10,*)'B | |
WRITE(10,*)'U I |
WRITE(10,*)'L | |
WRITE(10,*)'K I |
WRITE(IO,*)' | |
WRITE(IO,*)' 1 3 5 7 9

WRITE(10,201) CONC(1),CONC(3),CONC(5),CONC(7),CONC(9),CONC(11)

FORMAT(1X,E9.3,1X,E9.3,1X,E9.3,1X,E9.3,1X,E9.3,1X,E9.3)
WRITE(10,*)' I I

WRITE(10,*)' I 2 4 I 6 8 10
WRITE(10,202) CONC(2),CONC(4),CONC(6),CONC(8),CONC(10)
FORMAT(3X,E9.3,2X,E9.3,1X,E9.3,1X,E9.3,1X,E9.3)
WRITE(10,*)'F I I

WRITE(10,*)'L I I

WRITE(10,*)'O I I

1

l
I
l
I
I
I
1

‘ ‘ ‘

‘ ‘ ‘ ‘ ‘ ‘ ‘

Q ~

10

11

103

182

WRITE(10,*)'W I I

WRITE(10,*)

WRITE(10,*)
IP-ICOUNT/IPRINT
IF (CN(Nl+l).GE.1.) CN(N1+1)-1.-1.E-6
IF (CN(N1+N2+1).GE.1.) CN(N1+N2+1)-1.-1.E-6
CA(IP)--LOG(l-CN(N1+1))
CB(IP)--LOG(l-CN(N1+N2+1))
DC(IP)-CONC(N1+1)-CONC(N1+N2+1)
TM(IP)-ICOUNT*DT/TMAX

END IF

CHECK TO SEE WHETHER IT IS TIME TO STOP THE EXECUTION
IF (ICOUNT*DT.LT.TMAX+DT) GO TO 6

FINDING THE BEST LINEAR FIT FOR THE CONCENTRATION VERSUS
TIME POINTS

DO 10 I-1,2
X(I,2)-O.
Y1(I)-O.
Y2(I)-0.

CONTINUE

DO 11 I-1,IP
X(1,2)-X(1,2)+TM(I)
X(2,2)-X(2,2)+TM(I)**2
Y1(1)-Y1(1)+CA(I)
Y1(2)-Y1(2)+CA(I)*TM(I)
Y2(1)-Y2(1)+CB(I)
Y2(2)-Y2(2)+CB(I)*TM(I)

CONTINUE

X(2,1)-X(1,2)

X(1,1)-IP

CALL LINEQ(A1,Y1,X,W1,2,3,I)

CALL LINEQ(A2,Y2,X,W1,2,3,I)

WRITE(10,103)A1(1),A1(2)

FORMAT(/,' THE EQUATION FOR THE LINEAR BEST FIT FOR THE',/,

' CONCENTRATION VERSUS TIME IS,',/,
I Y - ',F6.3,' + ',F6.3,' *X',/)

.WRITE(10,103)A2(1),A2(2)

IF(IOPNAG.EQ.O) CALL PLOTINIT
IF (IF1.EQ.O) GO TO 12

PLOTTING THE CONCENTRATION VERSUS TIME CHART
(IFl-O STOP THE OUTPUT)

CALL PLOT(0.,1.,10,CABO,CAB1,10,TM,CA,IP,FCT1,l,1)
CALL PLOT(0.,1.,10,CABO,CAB1,10,TM,CB,IP,FCT2,2,0)
CALL ANMODE

CALL HOME

WRITE(1,*)

183

WRITE(1,*)'PRESS [RETURN] TO CONTINUE.’
READ(1,'(A1)') ICONT

RETURN

END

FUNCTIONS FOR THE INPUT OF THE SUBROUTINE 'PLOT'

FUNCTION FCT1(X)

PARAMETER II-2

COMMON /Cl/IPRINT,IF1,A1(II),A2(II),CABO,CABl
FCTl-A1(l)+Al(2)*X

RETURN

END

FUNCTION FCT2(X)

PARAMETER II-2

COMMON /Cl/IPRINT,IF1,A1(II),A2(II),CABO,CABl
FCT2-A2(1)+A2(2)*X

RETURN

END

000000000000000000000000000000000000

184

OPEN THE GRAPHIC FILE

SUBROUTINE PLOTINIT

CALL INITT(480)

CALL OPENTK('G_PLOT',I)

RETURN

END

SUBROUTINE PLOT(XO,X1,NX,YO,Y1,NY,X,Y,N,FCT,IMARK,IFX)
THIS SUBROUTINE PLOT THE GRAPH WITH WINDOW X0,X1,YO,Y1.
X0, X1: RANGE ON X-AXIS

Y0, Y1: RANGE ON Y-AXIS

NX: NUMBER OF SCALE MARK ON X-AXIS

NY: NUMBER OF SCALE MARK ON Y-AXIS

X, Y: THE SUPPLIED DATA POINTS TO BE PLOTTED ON THE GRAPH
N: TOTAL NUMBER OF DATA POINTS

FCT: SUPPLIED FUNCTION TO COMPARE WITH THE DATA POINTS
(MIGHT BE THE EXACT SOLUTION CURVE)

IMARK: SELECT THE KIND OF SYMBOL TO MARK THE DATA POINTS.

SQUARE

. TRIANGLE (POINTS UPWARD)
TRIANGLE (POINTS DOWNWARD)
DIAMAND SHAPE

CONTINUOUS CURVE

UIJ-‘UJNH

IFX: GRAPH TO BE PLOTTED.

CONCENTRATION V.S. DIMENSIONLESS TIME

SENSITIVITY COEFFICIENT V.S. TIME

NORMALIZED VOLUME V.S. TIME

SUM OF THE SQUARES OF THE ERRORS V.S. PERMEABILITY

bWNH

SUBROUTINE PLOT(XO,X1,NX,YO,Y1,NY,X,Y,N,FCT,IMARK,IFX)
PARAMETER IN-1,EP1-1E-15

DIMENSION X(N),Y(N)

CHARACTER*10 LABEL(2,21)

CHARACTER*24 YTITLE

CHARACTER*1 A

RNX-NX

RNY-NY

102

185

RGX-Xl-XO

RGY-Yl-YO

IF (ABS(RGX).LT.EP1.0R.ABS(RGY).LT.EP1) THEN
WRITE(1,102)
FORMAT(/,'THE SIZE OF THE WINDOW IS ZERO',/)
GO TO 11

END IF

CALL DWINDO(0.5*(X1+X0)-RGX,0.5*(X1+XO)+RGX,O.5*(Y1+Y0)

&-RGY,O.5*(Y1+YO)+RGY)

0000

0

DRAW HORIZONTAL AND VERTICAL GRID TICKS

NOTICE TYPE CONVERSION IN THE STATEMENTS INVOLVING
RNX AND RNY

CALL MOVEA(X0,YO)

CALL DRAWA(X1,YO)

DO 1 I-2,NX+1
P—(I-l.)*RGX/RNX+XO
CALL MOVEA(P,YO)

CALL DRAWA(P,Y0+RGY/20)

CONTINUE

CALL MOVEA(XO,YO)

CALL DRAWA(XO,Y1)

DO 2 I-2,NY+1
Q-(I-l.)*RGY/RNY+YO
CALL MOVEA(X0,Q)

CALL DRAWA(XO+RGX/20,Q)

CONTINUE

WRITING CHARACTERS

DO 3 I-I,NX+I,2
P-(I-l.)*RGX/RNX+XO-RGX/15.
Q-(I-l.)*RGX/RNX+XO
CALL MOVEA(P,YO-RGY/9.)
WRITE(LABEL(1,I),101) Q
CALL CHARTK(LABEL(1,I),O.7)

CONTINUE

DO 4 I-1,NY+1,2
P-(I-l.)*RGY/RNY+YO
CALL MOVEA(Xo-RGX/6 ,P)
WRITE(LABEL(2,I),101) P
FORMAT(E8.2)

CALL CHARTK(LABEL(2,I),O.7)

CONTINUE

LABELLING THE AXES

CALL MOVEA(XO+(RGX*O.25),Y0-3.*(RCY/10.))
IF(IFX.EQ.1) THEN

186

CALL CHARTK('DIMENSIONLESS TIME',0.85)
ELSE IF(IFX.EQ.2.OR.IFX.EQ.3) THEN
CALL CHARTK('TIME (SEC.)’,0.85)
ELSE IF(IFX.EQ.4) THEN
CALL CHARTK('PERMEABILITY (UM/SEC.)',O.85)
ENDIF
IF(IFX.EQ.1) THEN
YTITLE - 'CONCENTRATION'
NCHAR - I3
ELSE IF(IFX EQ 2) THEN
YTITLE - 'SENSITIVITY COEFFICIENT'
NCHAR - 23
ELSE IF(IFX.EQ.3) THEN
YTITLE - 'NORMALIZED VOLUME'
NCHAR - 17
ELSE IF(IFX.EQ.4) THEN
YTITLE - 'SUM OF SQUARES OF ERRORS'
NCHAR - 24
ENDIF

IF(IFX.EQ.1.OR.IFX.EQ.2.OR.IFX.EQ.3.OR.IFX.EQ.4) THEN
DO 200 I-1,NCHAR
AINDEX - I-l
YYY - (Y0+RGY)-(AINDEX*RGY*0.0533)
CALL MOVEA((X0-0.3*RCX),YYY)
A - YTITLE(I:I)
CALL CHARTK(A,O 85)
CONTINUE
ENDIF

PLOTTING THE CURVES

CALL MOVEA(XO,FCT(X0))
D0 5 I-l,IN*N
XF-X0+I*RCX/IN/N
CALL DRAWA(XF,FCT(XF))
CONTINUE
IF (IMARK.EQ.1) THEN
DO 6 I-1,N
CALL SQUARE(X(I),Y(I),RGX/60,RGY/60)
CONTINUE
ELSE IF (IMARK EQ 2) THEN
DO 7 I-1,N
CALL TRI(X(I),Y(I),RGX/60,RGY/60)
CONTINUE
ELSE IF (IMARK.EQ.3) THEN
DO 8 I-1,N
CALL TRI2(X(I),Y(I),RGX/60,RGY/60)
CONTINUE
ELSE IF (IMARK.EQ.4) THEN
DO 9 I-l,N
CALL DIAMAND(X(I),Y(I),RGX/60,RGY/60)

10

00000

187

CONTINUE
ELSE IF (IMARK.EQ.5) THEN
CALL MOVEA(XO,YO)
DO 10 I-1,N
CALL DRAWA(X(I),Y(I))
CONTINUE
END IF

CALL MOVEA(X0,0.5*(Y1+YO)+RGY)
CALL DRAWA(XO+0.0000000001,0.5*(Y1+Y0)+RGY)

RETURN
END

SUBROUTINE SQUARE(X,Y,DX,DY)
X, Y: POSITION TO PLACE THIS MARK
DX, DY: SIZE OF THIS MARK

SUBROUTINE SQUARE(X,Y,DX,DY)
CALL MOVEA(X-DX/2,Y-DY/2)
CALL DRAWA(X-DX/2,Y+DY/2)
CALL DRAWA(X+DX/2,Y+DY/2)
CALL DRAWA(X+DX/2,Y-DY/2)
CALL DRAWA(X-DX/2,Y-DY/2)
RETURN

END

SUBROUTINE TRI(X,Y,DX,DY)

SUBROUTINE TRI(X,Y,DX,DY)
CALL MOVEA(X—DX/2,Y-DY/2)
CALL DRAWA(X,Y+DY/2)
CALL DRAWA(X+DX/2,Y-DY/2)
CALL DRAWA(X-DX/2,Y-DY/2)
RETURN

END

SUBROUTINE TRI2(X,Y,DX,DY)

SUBROUTINE TR12(X,Y,DX,DY)
CALL MOVEA(X-DX/2,Y+DY/2)
CALL DRAWA(X,Y-DY/2)

CALL DRAWA(X+DX/2,Y+DY/2)
CALL DRAWA(X-DX/2,Y+DY/2)
RETURN

END

SUBROUTINE DIANAMD(X,Y,DX,DY)

SUBROUTINE DIAMAND(X,Y,DX,DY)

188

CALL MOVEA(X,Y+DY/2)
CALL DRAWA(X-DX/2,Y)
CALL DRAWA(X,Y-DY/2)
CALL DRAWA(X+DX/2,Y)
CALL DRAWA(X,Y+DY/2)
RETURN

END

FUNCTION FCTO(X)

TRIVIAL CURVE, IT PLOTS A STRAIGHT LINE AT Y-O.
FUNCTION FCTO(X)

FCTO-O.

RETURN
END

APPENDIX E

SENS - The IBM PC Version Fortran Source Code

0
t—‘
He
5
(D
1“:

00VO‘U‘L‘WNH

000000000000000000000000000000000000000000000

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Page
07-20-87
19:28:31
1 7 Microsoft FORTRAN77 V3.31 August 1985
PROGRAM SENS
C$DEBUG

THIS PROGRAM INCLUDES THE COMPUTER MODEL FOR THE

DIFFUSION CHAMBER AND THE PARAMETER ESTIMATION FOR FINDING
PERMEABILITY OF A CELL INSIDE THE CELL CHAMBER OF THE
DIFFUSION CHAMBER.

THIS PROGRAM CONSISTS OF 1 MAIN PROGRAM, 5 SUBROUTINES

AND 2 FUNCTIONS. THEY ALL ARE INSIDE THE FILES 'SENS.FOR',
'MBCON.FOR'.

THE INPUT DATA CAN BE ENTERED ONE OF TWO WAYS, VIA THE
TERMINAL/KEYBOARD OR BY USING A PRE-EXISTING INPUT FILE SET
UP BY THE USER; FOR EXAMPLE 'I_SENS.DAT'.

THE OUTPUT CAN BE VIEWED BY (1) LOOKING AT THE TABLES GENERATED,
WHICH RESIDE IN FILE ’O_SENS.DAT' AND 'O_SMRY.DAT', AND/OR (2)
HAVING THE PROGRAM GENERATE FILES TO BE USED IN CONJUNCTION WITH
PLOTIT TO VIEW THE OUTPUT GRAPHICALLY.

THE INPUT DATA REQUIRED IS AS FOLLOWS:

RL1: THICKNESS OF DIALYSIS MEMBRANE (M)

RL2: THICKNESS OF CELL CHAMBER (M)

LIP: APPROXIMATE LOCATION OF THE LIPOSOME (FROM 5 TO 11)

D1: DIFFUSIVITY OF SOLUTE INSIDE DIALYSIS MEMBRANE (M*M/SEC)
D2: DIFFUSIVITY OF SOLUTE INSIDE CELL CHAMBER (M*M/SEC)

CINIT: INITIAL CONCENTRATION (OSM)

CINF: FINAL CONCENTRATION (OSM)

H: MASS TRANSFER COEFF. (APPROXIMATELY 10000*D2)

IPRINT: NUMERICAL DATA OUTPUT FREQUENCY. (EVERY IPRINT*DT
SEC. PRINTS THE CONC. DIST. ON OUTPUT FILE)

IRELPSE: OPTION FOR EXPERIMENTAL DATA INPUT l-REAL-EXPERIMENT
2-PSUESO-EXPERIMENT

IMICCEN: OPTION FOR ENTERING DATA IN l-MICRONS 2-CENTIMETERS

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D Line#
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000000000

0000000000000000000000000C§000000000000I---'|

190
TMO, TM1: SETTING THE TIME RANGE ON THE PLOTS (SEC.)

DT: TIME STEP FOR PROCEEDING THE CALCULATION (SEC.)
(NOTE: IF DT IS SET TOO LARGE, THE RESULT WILL FLUCTUATE.
IN THIS CASE, REDUCE THE SIZE OF DT AND TRY AGAIN.
THIS IS DUE TO THE UNSTABLE OF THE NUMERICAL METHOD.)

DELALY: TIME DELAY SUBTRACTED FROM TIME ARRAY TM(I).
Page
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19:28:31
7 Microsoft FORTRAN77 V3.31 August 1985
PSEN: THE PERMEABILITY VALUE AT WHICH WE INVESTIGATE THE
SENSITIVITY COEFF. (P'S EFFECT ON R'S CHANGE)

PTRU: THE PERMEABILITY VALUE WITH WHICH THE PROGRAM GENERATES
PSUDO-EXPERIMENTAL DATA (R(TM,PTRU)).

DT1: THE TIME STEP FOR THE PSUDO-EXPT'L DATA DURING TMO TO
TM01. (SEC.)

TM01: THE PARTITION BETWEEN TWO DIFFERENT TIME STEPS RANGE.
(YOU CAN ASK THE PROGRAM TO GENERATES PSUDO-EXPT'L DATA
WITH TWO DIFFERENT INCREMENT IN TIME FOR TWO TIME
RANGE.)

DT2: THE TIME STEP FOR THE PSUDO-EXPT'L DATA DURING TM01

TO TM1. (SEC.)

RINIT: INITIAL RADIUS (MICRONS OR CM)

VINA: INACTIVE VOLUME (%)

RMAG: THE MAGNIFICATION OF THE MICROSCOPE

DR: MAGNITUDE FOR THE PSEUDO-RANDOMNESS IMPOSED ON THE
PREDICTED RADIUS RESPONSE (MICRONS OR CM)

P0, P1: PERMEABILITY RANGE UNDER INVESTIGATION (MICRONS/SEC.)

DP: INCREMENT OF PERMEABILITY IN CALCULATING SUM OF ERROR OF
SQUARE FOR EACH P VALUE

CONl: NAME OF THE FILE CONTAINING CA V.S.
DIMENSIONLESS TIME

CON2: NAME OF THE FILE CONTAINING CB V.S.
DIMENSEIONLESS TIME

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D Line#
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000000000000000000

(30000000000000000000000000000'“J

191

SENC: NAME OF THE FILE CONTAINING THE SENSITIVITY COEFFICIENTS V.
TIME

IF IRELPSE - 1

VOLl: NAME OF THE FILE CONTAINING THE NORMALIZED VOLUME V.
TIME (REAL EXPERIMENTAL DATA).

VOL2: NAME OF THE FILE CONTAINING THE NORMALIZED VOLUME V.
TIME (THEORETICAL CURVE BASED OF THE ESTIMATED
PERMEABILITY WHICH IS CALCULATED).

IF IRELPSE - 2

VOLl: NAME OF THE FILE CONTAINING THE NORMALIZED VOLUME V.
TIME (WITH AN IMPOSED RANDOMNESS), BASED ON THE TRUE
PERMEABILITY ENTERED, PTRU.

VOL2: NAME OF THE FILE CONTAINING THE NORMALIZED VOLUME V.
TIME (N0 RANDOMNESS), ALSO BASED ON PTRU.

Page

07-20-87
19:28:31
7 Microsoft FORTRAN77 V3.31 August 1985

SUMR: NAME OF THE FILE CONTAINING THE SUM OF THE SQUARE OF THE ER
V.S. PERMEABILITY.

OUTPUT CONFIGURATION OF 'O_SENS.DAT':

(1) INPUT DATA

(2) PRINT CONC. DIST. OF THE SYSTEM AS A FUNCTION OF
TIME.

(3) SENSITIVITY COEFF. CORRESPOND TO PSEN.

(4) THE ESTIMATED PERMEABILITY (LOCAL MINIMUN ON SUM
VERSUS P GRAPH)

(5) THE STANDARD DEVIATION OF THIS ESTIMATED P

OUTPUT CONFIGURATION OF 'O_SMRY.DAT':

(1) SUMMARY OF INPUT PARAMETERS AND DATA
(2) SUMMARY OF RESULTING PERMEABILITY, STANDARD DEVIATION
AND MINIMUM SUM

THE OUTPUT FILES THAT CAN BE CREATED BY THE PROGRAM IF THE
USER DESIRES.

THE FILES CREATED WILL BE COMPATABLE TO USE WITH
PLOTIT USING FREE FORMAT.

(1) CONCENTRATION V.S. DIMENSIONLESS TIME
(2) SENSITIVITY COEFFICIENTS V.S. TIME
(3) NORMALIZED VOLUME V.S. TIME

142
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'145
146

C
C
c .....
C
c .....

192

(4) SUM OF SQUARE OF ERRORS V.S. PERMEABILITY

INITIALIZATION AND DECLARATIONS

147 $INCLUDE: 'IMSL'
1 $LARGE: DMY327

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D Line# 1

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DIMENSION DMY327(1)

PARAMETER (N3-301,II-2,N1-301,N4-301,EP1-o.01,N5-25)
DIMENSION TMA(N3),TMB(N3),RA(N3),RB(N3),SEN(N3),SUM(N1),P(N1)
DIMENSION VOLC(N3),VOLA(N3),TMS(N3),RS(N3),RC(N3),RSAVE(N3)
DIMENSION CA(N5),CB(N5)

CHARACTER*1 ICHANG, IGRAPH, IMORE, IAGAIN, IANOTH, ISAVE
CHARACTER*1 IMISTAK, IFIRST, IQUIT, IDEL

CHARACTER*11 XMICCEN,PROBLEM

CHARACTER*10 NAMFIL,CON1,SENC,VOL1,SUMR,CON2,VOL2,ISENS
COMMON /C1/IPRINT,IF1,A1(II),A2(II)

COMMON /02/RINIT,VINA,DT,TM1,COUT(N4)

COMMON /C3/RL1,RL2,LIP,Dl,D2,CINIT,CINF,H

EXTERNAL F

XSEED -566387.0

ISC - O

IBACK - O

IRUNAG-O

IOPNAG-O

IMISTAK - 'N'

Page
07-20-87
19:28:31
7 Microsoft FORTRAN77 V3.31 August 1985
EXPLANATION TO THE USER WHAT THE PROGRAM DOES.
CONTINUE
WRITE(*,*)

WRITE(*,*)'WOULD YOU LIKE AN EXPLANATION OF THIS PROGRAM, '
WRITE(*,*)'(SENS), (Y/N)?’

READ(*,'(A1)') IFIRST

IF(IFIRST.EQ.'N') GO TO 1200

WRITE(*,*)

WRITE(*,*)’ WELCOME TO THE PROGRAM SENS. THIS PROGRAM WILL '
WRITE(*,*)'ALLOW THE USER TO (1) ANALYZE THE DATA OBTAINED USING '
WRITE(*,*)’THE MICROSCOPE DIFFUSION CHAMBER I.E. PARAMETER '
WRITE(*,*)'ESTIMATION OF THE PERMEABILITY OF A CELL OR (2) RUN '
WRITE(*,*)'A SIMULATION (PSEUDO) EXPERIMENT TO SEE WHAT MIGHT '
WRITE(*,*)'TO A CELL UNDER SPECIFIED CONDITIONS.’

OPTION TO HAVE A LIST OF THE NECESSARY PARAMETERS SENT TO
'I_DATA.LST'

WRITE(*,*)' IF THIS IS THE FIRST TIME YOU HAVE USED THIS '

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D Line# 1
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193

WRITE(*,*)'PROGRAM AND YOU WANT TO ENTER DATA FROM A REAL '
WRITE(*,*)'EXPERIMENT YOU MAY WANT TO OBTAIN A LIST OF THE '
WRITE(*,*)'PARAMETERS AND DATA NECESSARY TO RUN THE PROGRAM.’
WRITE(*,*)

WRITE(*,*)'WOULD YOU LIKE TO DO THIS, (Y/N)?’

READ(*,'(A1)') IFIRST

CALL IYESNO(IFIRST)

IF(IFIRST.EQ.'Y') THEN

OPEN(13,FILE-'I_DATA.LST',STATUS-‘NEW')

WRITE(*,*)
WRITE(*,*)'THE

WRITE(*,*)'WILL BE IN FILE "I_DATA.LST".
WRITE(*,*)'STOP NOW.

WRITE(13,*)

LIST OF THE NECESSARY INPUT TO RUN THE PROGRAM'
THE PROGRAM WILL'
HAVE I_DATA.LST PRINT AT THE PRINTER.’

WRITE(13,*)'THE PARAMETES AND DATA NEEDED TO RUN THE PROGRAM'
WRITE(13,*)'ARE:'

WRITE(13,*)
WRITE(13,*)'1)
WRITE(13,*)'2)
WRITE(13,*)'3)
WRITE(13,*)'4)
WRITE(13,*)'
WRITE(13,*)'5)
WRITE(13,*)'
WRITE(13,*)'6)
WRITE(13,*)'
WRITE(13,*)'7)
WRITE(13,*)'8)
WRITE(13,*)'9)
WRITE(13,*)'10)
WRITE(13,*)'11)
WRITE(13,*)'12)
WRITE(13,*)'13)
WRITE(13,*)'14)
WRITE(13,*)'15)
WRITE(13,*)'16)

DIALYSIS MEMBRANE THICKNESS (RL1), MICRONS.’
CELL CHAMBER THICKNESS (RL2), MICRONS.’
CELL POSITION IN THE CELL CHAMBER (5-11).'
DIFUSSIVITY OF SOLUTE IN MEMBRANE (D1), '
- METERS*METERS/SEC.'
DIFUSSIVITY OF SOLUTE IN FREE SOLUTION (D2),'
- METERS*METERS/SEC.'
MASS TRANSFER COEFFICIENT (H).'
- METERS/SEC.’
INITIAL CONCENTRATION (CINIT), OSMOLALITY.’
FINAL CONCENTRATION (CINF), OSMOLALITY.'
INACTIVE VOLUME (VINA), %'
MAGNIFICATION FACTOR (RMAG).'
TIME STEP (DT), SEC.’
STARTING TIME (TMO), SEC.’
ENDING TIME (TM1), SEC.’
TIME DELAY (DELAY), SEC., (0.0 IF NO DELAY)‘
PERMEABILITY STEP (DP), MICRONS/SEC.’
THE LIMITS OF THE PERMEABILITY RANGE UNDER '

CLOSE(13,STATUS

Page
07-20-87
19:28:31
7 Microsoft FORTRAN77 V3.31 August 1985
WRITE(13,*)' INVESTIGATION (P0 TO P1), MICRONS/SEC.’
WRITE(13,*)'17) PERMEABILITY AT WHICH INVESTIGATE THE '
WRITE(13,*)' SENSITIVITY COEFFICIENTS (PSEN), MICRONS/SEC.’
WRITE(13,*)'18) THE DATA POINTS: TIME (TMA(I)), SEC. AND '
WRITE(13,*)' RADIUS (RA(I)), MICRONS OR'
WRITE(13,*)' CENTIMETERS.’
WRITE(13,*)
WRITE(13,*)' (NOTE: YOU ONLY NEED THE DATA POINTS IF YOU'
WRITE(13,*)' ARE USEING THE PARAMETER ESTIMATION OPTION,’
WRITE(13,*)' I.E. A REAL EXPERIMENT.)'

-'KEEP')

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D Line#
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GO TO 600

ENDIF

WRITE(* *)
WRITE(* *)'

IEXP -0
IF (IQUIT.EQ.'Y') THEN

194

EXPLAINING THE OPTION TO ENTER DATA USING KEYBOARD OR AN INPUT
FILE (WHICH IS SPECIFIED BY THE USER).

, THIS PROGRAM WILL ALLOW YOU TO ENTER THE DATA'
WRITE(*,*)'USING THE TERMINAL/KEYBOARD OR A PRE-EXISTING INPUT'
WRITE(*,*)'FILE SET UP BY THE USER. AN EXAMPLE OF AN INPUT FILE'
WRITE(*,*)'CAN BE SEEN BY QUITTING THIS PROGRAM AND PRINTING '
WRITE(*,*)'I_SENS.EXP AT THE PRINTER. DO YOU WISH TO QUIT AND '
WRITE(*,*)'PRINT THE EXAMPLE,
READ(*,'(A1)') IQUIT

CALL IYESNO(IQUIT)

(Y/N)?’

IF IQUIT IT YES THE PROGRAM WILL GENERATE I_SENS.EXP AND QUIT.

OPEN(12,FILE-'I_SENS.EXP',STATUS-'NEW’)

WRITE(12,*)'THIS IS THE EXAMPLE INPUT FILE I_SENS.EXP FOR THE '
WRITE(12,*)'PROGRAM SENS.FOR. THE PROGRAM WILL READ THE DATA'
WRITE(12,*)'ALINING THE VALUE UNDER THE LEFT MOST CHARACTER.’

RL1-16.

RL2 - 100.
LIP - 9

D1 - 5.21E-11
D2 - 5.21E-10
H - 5.21E-6
CINIT - 0.02
CINF - 0.04
VINA - 6.
RMAG - 5080.
DT - 5.0

TMO - O.

TM1 -500.
DELAY -0.0
DP - 2.

PO - 0.

P1 - 100.
PSEN - 40.
RINIT - 7.7
PTRU - 40.
DR - 0.01

TM01 - 500.
DT1 - 5.0

Page

07-20-87
19:28:31
Microsoft FORTRAN77 V3.31 August 1985

 

H

H

281
282
283

‘284

285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332

1100

1200

195

DT2 - 5.0

IRELPSE - 1

IMICCEN - 2

IF1 - 1

IF2 - 1

IF3 - 1

IF4 - 1

IPRINT - 10

CONl -'O_CON1.DAT'

CON2 -'0_CON2.DAT'

SENC -'O_SENC.DAT'

VOL1 -'O_VOL1.DAT'

VOL2 -'O_VOL2.DAT'

SUMR -'0_SUMR.DAT'

ICOUNT - 4O

RA(l) - 7.7

TMA(1) - 0.0

DO 1100 I - 2,40
TMA(I) - TMA(I-l) + 10.
RA(I) - RA(I-l) - 0.05

CONTINUE

IEXP - 1

ISAVE - 'Y'

GO TO 319

ENDIF

EXPLAINING THE INPUT AND OUTPUT OPTIONS

WRITE(*,*)

WRITE(*,*)' THE PROGRAM WILL ALSO ALLOW THE USER TO VIEW THE'
WRITE(*,*)'RESULTS BY 1) TABLES AND/0R 2) HAVING FILES CREATED'
WRITE(*,*)'WHICH THE USER USES "PLOTIT" TO GENERATE GRAPHICAL'
WRITE(*,*)'0UTPUT. THE TABLES GENERATED CAN BE FOUND IN A FILE'
WRITE(*,*)'CALLED "O_SENS.DAT". A SUMMARY OF THE INPUT '
WRITE(*,*)'PARAMETERS, INPUT DATA AND RESULTING PERMEABILITY'
WRITE(*,*)'CAN BE FOUND IN "O_SMRY.DAT".'

WRITE(*,*)'THE FILES THAT CAN BE CREATED FOR PLOTIT ARE'
WRITE(*,*)'FOR THE FOLLOWING DATA SETS.’

WRITE(*,*)

WRITE(*,*)'1) CONCENTRATION V.S. DIMENSIONLESS TIME'
WRITE(*,*)'2) SENSITIVITY COEFFICIENTS V.S. TIME'

WRITE(*,*)'3) NORMALIZED VOLUME V.S. TIME'

WRITE(*,*)'4) SUM OF THE SQUARE OF THE ERRORS v.s. PERMEABILITY'
WRITE(*,*)

WRITE(*,*)'THE PROGRAM WILL PROMPT THE USER TO ENTER A FILE'
WRITE(*,*)'NAME FOR EACH OF THE DESIRED DATA SETS TO BE PLOTTED.’
WRITE(*,*)

WRITE(*,*)'YOU ARE NOW READY TO START THE PROGRAM.'

CONTINUE

WRITE(*,*)

WRITE(*,*)'DO YOU WISH TO ENTER THE DATA USING (1) THE TERMINAL'
WRITE(*,*)'OR (2) A PRE-EXISTING INPUT FILE, (ENTER 1 OR 2)7'

333
334

D Line#
335
336
337
338
339
340
341
342
343
344
345
346
347
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349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379

2100

2105

2106

196

WRITE(*,*)
READ(*,*,ERR-1200) ITERINP
Page
07-20-87
19:28:31
7 Microsoft FORTRAN77 V3.31 August 1985

CALL IONETWO(ITERINP)
IF(ITERINP EQ.2) THEN
WRITE(*,*)
WRITE(*,*)'PLEASE ENTER THE NAME OF THE INPUT FILE TO BE USED,’
WRITE(*,*)'(ENTER NO MORE THAN 10 CHARACTERS).'
READ(*,'(A10)') ISENS
CALL CHANNAM(ISENS)
WRITE(*,*)
WRITE(*,*)'OKAY, THE PROGRAM IS CRUNCHING.’
GO TO 2999
ENDIF

IPRINT - 10

PROMPTING THE USER TO ENTER THE REQUIRED DATA AND PARAMETERS
NEEDED TO RUN THE PROGRAM.

CONTINUE

WRITE(*,*)

WRITE(*,*)'DO YOU WISH TO (1) ENTER DATA FROM A REAL EXPERIMENT'
WRITE(*,*)'OR (2) USE THE PROGRAM FOR A SIMULATION (PSEUDO-'
WRITE(*,*)'EXPERMINT), (ENTER 1 OR 2)?’

WRITE(*,*)

READ(*,*,ERR-ZOOS) IRELPSE

CALL IONETWO(IRELPSE)

CONTINUE

WRITE(*,*)'ENTERING THE PHYSICAL PARAMETERS OF THE SYSTEM:'
WRITE(*,*)

WRITE(*,*)'PLEASE ENTER THICKNESS OF THE DIALYSIS MEMBRANE, '
WRITE(*,*)'(MICRONS).'

WRITE(*,*)

READ(*,*,ERR-ZlOO) RL1

WRITE(*,*)

CONTINUE

WRITE(*,*)'PLEASE ENTER THE THICKNESS OF THE CELL CHAMBER,’
WRITE(*,*)'(MICRONS).'

WRITE(*,*)

READ(*,*,ERR-ZlOS) RL2

WRITE(*,*)

CONTINUE

WRITE(*,*)'PLEASE ENTER THE CELL POSITION, (5-11).'
WRITE(*,*)'(SEE THE DIAGRAM BELOW FOR BETTER UNDERSTANDING.)'
WRITE(*,*)

WRITE(*,*)' DIALYSIS MEMBRANE CELL CHAMBER'
WRITE(*.*)' I I '

380
381
382
‘383
384
385
386
387
388
389
390

D Line#
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426

2110

2120

2130

2140

2150

197

WRITE(* *)'B I
WRITE(* *)'U I
WRITE(* *)'L I
WRITE(* *)'K I
WRITE(* *)' 1 2 3 4
|
I
|
|
I

___—.... LII—__—

C"

\J

m

\0

H

O

H
_____ H————

‘ ~ ‘ ‘ ‘ ‘ ‘ 0 ‘ ‘

WRITE(*,*)'F
WRITE(*,*)'L
WRITE(*,*)'O
WRITE(*,*)'W
WRITE(*,*)'
WRITE(*,*)
Page
07-20-87
19:28:31
7 Microsoft FORTRAN77 V3.31 August 1985
READ(*,*,ERR-2106) LIP
WRITE(*,*)
CONTINUE

WRITE(*,*)'PLEASE ENTER THE DIFFUSIVITY OF THE SOLUTE INSIDE'
WRITE(*,*)'THE CELL CHAMBER, (METERS*METERS/SEC.), D2.’
WRITE(*,*)
READ(*,*,ERR—2110) D2
WRITE(*,*)
CONTINUE
WRITE(*,*)'DO YOU WISH TO ENTER (1) SEPARATE VALUES FOR THE'
WRITE(*,*)'DIFFUSIVITY OF THE SOLUTE INSIDE THE DIALYSIS'
WRITE(*,*)'MEMBRANE (METERS*METERS/SEC.), D1, AND THE MASS'
WRITE(*,*)'TRANSFER COEFFICIENT, H, OR (2) USE PRESET'
WRITE(*,*)'VALUES OF D1-D2/10 AND H-10000*D2?'
WRITE(*,*)
READ(*,*,ERR-2120) ISEPPRE
CALL IONETWO(ISEPPRE)
IF(ISEPPRE EQ.1) THEN
CONTINUE
WRITE(*,*)'PLEASE ENTER D1 (METERS*METERS/SEC.).'
WRITE(*,*)
READ(*,*,ERR-2130) D1
WRITE(*,*)
CONTINUE
WRITE(*,*)'PLEASE ENTER H, (METERS/SEC.)'
WRITE(*,*)
READ(*,*,ERR-2140) H
ELSE IF (ISEPPRE.EQ.2) THEN
D1 - D2/10.0
H - 10000.*DZ
ENDIF
CONTINUE
WRITE(*,*)
WRITE(*,*)'PLEASE ENTER THE INITIAL AND FINAL CONCENTRATION, '
WRITE(*,*)'CINIT CINF, (OSMOLALITY). (ENTER BOTH VALUES AND'
WRITE(*,*)'SEPARATE WITH A SPACE.)'

427
428
429
'430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446

D Line#
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473

2160

2170

2180

2190

1

2210

2215

198

WRITE(*,*)
READ(*,*,ERR-2150) CINIT, CINF
CONTINUE
WRITE(*,*)
WRITE(*,*)'PLEASE ENTER THE INACTIVE VOLUME (%).'
WRITE(*,*)
READ(*,*,ERR-2160) VINA
WRITE(*,*)
CONTINUE
WRITE(*,*)
WRITE(*,*)'PLEASE ENTER THE MAGNIFICATION FACTOR. (USE 5080.0 '
WRITE(*,*)'FOR BTP MEASUREMENTS. IF YOU ARE ENTERING THE'
WRITE(*,*)'EXACT CELL SIZE ENTER 1.0.)'
WRITE(*,*)
READ(*,*,ERR-2170) RMAG
WRITE(*,*)
CONTINUE
WRITE(*,*)
WRITE(*,2190) RL1,RL2,LIP,D2,Dl,H,CINIT,CINF,VINA,RMAG
FORMAT(1X,'THE VALUES ENTERED SO FAR ARE:',/,
Page

07-20-87
19:28:31
7 Microsoft FORTRAN77 V3.31 August 1985

. 1X,'l) DIALYSIS MEMBRANE THICKNESS - ',E11.3,' MICRONS',/,

. 1X,'2) CELL CHAMBER THICKNESS - ',E11.3,' MICRONS',/,

. 1X,'3) LIPOSOME POSITION (5-11) - ',12,/,

. 1X,'4) DIFFUSIVITY IN CELL CHAMBER - ',E11.3,' M*M/SEC.',/,

. 1X,'5) DIFFUSIVITY IN DIALYSIS MEMBRANE - ',E11.3,' M*M/SEC.',/,
. 1X,'6) MASS TRANSFER COEFFICIENT - ',E11.3,' M/SEC ',/,

. 1X,'7) INITIAL CONCENTRATION - ',F7.3,' OSMOLALITY',/,

. 1X,'8) FINAL CONCENTRATION - ',F7.3,' OSMOLALITY',/,

. 1X,'9) INACTIVE VOLUME % - ',F5.2,/,

. 1X,'10) MAGNIFICATION FACTOR - ',F7.1,/)

WRITE(*,*)'DO YOU WISH TO CHANGE ANY OF THEM, (Y/N)?’
READ(*,‘(A1)') ICHANG
CALL IYESNO(ICHANG)
IF(ICHANG.EQ.'Y') THEN
CONTINUE
WRITE(*,*)
WRITE(*,*)'PLEASE ENTER THE NUMBER BESIDE THE PARAMETER'
WRITE(*,*)'YOU WISH TO CHANGE, (1-10). '
READ(*,*,ERR-2210) NCHANC
CONTINUE
WRITE(*,*)
WRITE(*,*)'PLEASE ENTER THE NEW VALUE.’
IF(NCHANG.EQ.1) THEN
READ(*,*,ERR-2215) RL1
ELSE IF(NCHANG.EQ.2) THEN
READ(*,*,ERR—2215) RL2
ELSE IF(NCHANG.EQ.3) THEN

474
475
476
'477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502

2220

D Line# 1

503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520

2223

2225

2226

199

READ(*,*,ERR-2215) LIP
ELSE IF(NCHANG.EQ.4) THEN
READ(*,*,ERR-2215) D2
ELSE IF(NCHANG.EQ.5) THEN
READ(*,*,ERR-2215) D1
ELSE IF(NCHANG.EQ.6) THEN
READ(*,*,ERR-2215) H
ELSE IF(NCHANG.EQ.7) THEN
READ(*,*,ERR-2215) CINIT
ELSE IF(NCHANG.EQ.8) THEN
READ(*,*,ERR-2215) CINF
ELSE IF(NCHANG.EQ.9) THEN
READ(*,*,ERR-2215) VINA
ELSE IF(NCHANG.EQ.10) THEN
READ(*,*,ERR-2215) RMAG
ELSE IF(NCHANG.LE.0.0R.NCHANG.GE.11) THEN
CALL INCORRES
GO TO 2210
ENDIF
GO TO 2180
ENDIF
IF(IRUNAG.GE.1.0R.IMISTAK.EQ.'Y') GO TO 2235
WRITE(*,*)
WRITE(*,*)'IN ORDER FOR THE PROGRAM TO RUN THE USER'
WRITE(*,*)'MUST ALSO ENTER THE FOLLOWING DATA:'
CONTINUE
WRITE(*,*)
WRITE(*,*)'THE TIME RANGE OF THE EXPERIMENT, TMO TM1, (SEC.),'
WRITE(*,*)'(NOTE: PLEASE MAKE SURE TM1 IS GREATER THAN THE '
Page

07-20-87
19:28:31
7 Microsoft FORTRAN77 V3.31 August 1985
WRITE(*,*)'TIME OF THE LAST DATA POINT TO BE ENTERED AND ENTER '
WRITE(*,*)'BOTH VALUES WITH A SPACE BETWEEN THEM.)'
READ(*,*,ERR-ZZZO) TMO, TM1
CONTINUE
WRITE(*,*)
WRITE(*,*)'THE TIME STEP, DT, (SEC.). (NOTE: THIS TIME STEP IS'
WRITE(*,*)'USED FOR NUMERICAL INTEGRATION - CHOOSE DT SUCH THAT'
WRITE(*,*)'DT .GE. (TM1-TMO)/301 TO PREVENT ARRAY OVERFLOW.)'
READ(*,*,ERR-2223) DT
CONTINUE
WRITE(*,*)
WRITE(*,*)'THE PERMEABILITY RANGE WHICH YOU ARE INVESTIGATING, '
WRITE(*,*)'P0 P1, (MICRONS/SEC.). (ENTER BOTH VALUES WITH '
WRITE(*,*)'A SPACE BETWEEN THEM.)'
READ(*,*,ERR-2225) P0, P1
CONTINUE
WRITE(*,*)
WRITE(*,*)'THE PERMEABILITY STEP, DP, (MICRONS/SEC.) (NOTE: '

521
522
523
“524 2230
525
526
527
528
529 2235
530
531
532 2240
533
534
535
536
537
538
539
540
541
542
543 2245
544
545
546
547
548 2246
549
550
551
552
553
554
555
556
557
558

D Line# 1
559
560
561
562
563
564
565
566
567

200

WRITE(*,*)'CHOOSE DP SUCH THAT DP .GE. (Pl-PO)/301 TO '
WRITE(*,*)'PREVENT ARRAY OVERFLOW.)'
READ(*,*,ERR—2226) DP
CONTINUE
WRITE(*,*)
WRITE(*,*)'THE PERMEABILITY VALUE AT WHICH THE SENSITIVITY'
WRITE(*,*)'COEFFICIENT WILL BE EVALUATED, PSEN, (MICRONS/SEC ) '
READ(*,*,ERR-2230) PSEN
CONTINUE
WRITE(*,*)
WRITE(*,2240) DT,TMO,TM1,DP,PO,P1,PSEN
FORMAT(1X,'THE VALUES ENTERED ARE:',/,
1X,'1) TIME STEP - ',F7.2,' SEC.',/,
1X,'2) TIME RANGE - ',F8.1,' SEC.',' TO ',F8.1,' SEC.',/,
1X,’3) PERMEABILITY STEP - ',F7.2,' MICRONS/SEC.',/,
1X,'4) PERMEABILITY RANGE - ',F7.2,' MICRONS/SEC. TO',/,
1x,' ',F7.2,' MICRONS/SEC.',/,
1X,'5) INVESTIGATING PERMEABILITY - ',F7.2,' MICRONS/SEC.',/)

WRITE(*,*)'DO YOU WISH TO CHANGE ANY OF THEM, (Y/N)?’

READ(*,‘(A1)') ICHANG
CALL IYESNO(ICHANG)
IF(ICHANG.EQ.'Y')THEN
CONTINUE
WRITE(*,*)
WRITE(*,*)'PLEASE ENTER THE NUMBER BESIDE THE PARAMETER'
WRITE(*,*)'YOU WISH TO CHANGE, (1-5). '
READ(*,*,ERR-2245) NCHANC
CONTINUE
WRITE(*,*)
WRITE(*,*)'PLEASE ENTER THE NEW VALUE(S). '
IF(NCHANG.EQ.1) THEN
READ(*,*,ERR-2246) DT
ELSE IF(NGHANG.EQ.2) THEN
WRITE(*,*)'(BOTH TMO AND TM1 - SEPARATE WITH A SPACE)’
READ (*,*,ERR-2246) TMO, TM1
ELSE IF(NCHANG.EQ.3) THEN
READ(*,*,ERR-2246) DP
ELSE IF(NCHANG.EQ.4) THEN
Page

07-20-87
19:28:31
7 Microsoft FORTRAN77 V3.31 August 1985
WRITE(*,*)'(BOTH P0 AND Pl - SEPARATE WITH A SPACE)’
READ(*,*,ERR-2246) P0,P1
ELSE IF(NCHANG.EQ.5) THEN
READ(*,*,ERR-2246) PSEN
ELSE IF(NCHANG.LE.0.0R.NCHANG.GE.6) THEN
CALL INCORRES
GO TO 2246
ENDIF
GO TO 2235

568

569 C
570
‘571

572 2248
573

574

575

576

577

578

579

580

581

582

583

584

585

586

587

588

589 2250
590

591

592

593

594

595

596

597

598

599 2251
600

601

602

603

604

605 2252
606

607

608

609

610

611

612

613

614 2253

D Line# 1

201

ENDIF

IF(IRELPSE.EQ.1) THEN

IF(IRUNAG.GE.1.0R.IMISTAK.EQ.'Y') THEN
CONTINUE
WRITE(*,*)
WRITE(*,*)'DO YOU WISH TO (1) ENTER ALL NEW DATA POINTS'
WRITE(*,*)'OR (2) REVIEW THE PREVIOUS DATA POINTS, (Y/N)?’
READ(*,*,ERR—2248) INR
CALL IONETWO(INR)
IF(INR.EQ.2)GO TO 2261
IF(INR.EQ.1) THEN
I-O
WRITE(*,*)
GO TO 2250
ENDIF
ENDIF
I - 0
WRITE(*,*)
WRITE(*,*)'SINCE YOU HAVE CHOSEN THE REAL-EXPERIMENTAL'
WRITE(*,*)'OPTION THE DATA POINTS MUST BE ENTERED. BUT'
CONTINUE
WRITE(*,*)'BEFORE ENTERING THE DATA, IS THERE A TIME'
WRITE(*,*)'DELAY THAT YOU WOULD LIKE TO HAVE SUBTRACTED'
WRITE(*,*)’FROM THE TIME ARRAY YOU WILL BE ENTERING,’
WRITE(*,*)’(Y/N)?'
READ(*,'(A1)')IDEL
CALL IYESNO(IDEL)
IF(IDEL.EQ.'N') THEN
DELAY - 0.0
ELSE IF(IDEL.EQ.'Y') THEN
CONTINUE
WRITE(*,*)
WRITE(*,*)'PLEASE ENTER THE TIME DELAY TO BE SUBTRACTED,’
WRITE(*,*)'(SEC.).'
READ(*,*,ERR-2251) DELAY
WRITE(*,2252) DELAY
FORMAT(/,' THE TIME DELAY THAT WILL BE SUBTRACTED IS ',
F7.4,' SEC.',/,/,' DO YOU WISH TO CHANGE IT, (Y/N)?')
READ(*,'(A1)') ICHANG
CALL IYESNO(ICHANG)
IF(ICHANG.EQ.'Y') GO TO 2251
ENDIF
WRITE(*,*)
WRITE(*,*)'DO YOU WISH TO ENTER THE RADIUS USING UNITS'
WRITE(*,*)'OF (1) MICRONS OR (2) CENTIMETERS?’
READ(*,*,ERR-2253) IMICCEN
Page

07-20-87
19:28:31
Microsoft FORTRAN77 V3.31 August 1985

615
616
617
'618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666

2255

2256
2257

2260

2261

2262

202

CALL IONETWO(IMICCEN)
WRITE(*,*)
WRITE(*,*)'PLEASE ENTER THE DATA POINTS,’
IF(IMICCEN.EQ.1)THEN
WRITE(*,*)'TIME(I) (SEC.) RADIUS(I) (MICRONS)'
ELSE IF(IMICCEN.EQ.2) THEN
WRITE(*,*)'TIME(I) (SEC.) RADIUS(I) (CENTIMETERS)'
ENDIF
WRITE(*,*)'(ENTER BOTH VALUES AND SEPARATE WITH A SPACE.)'
WRITE(*,*)'(NOTE: ENTER 0.0 0.0 FOR THE LAST DATA POINT.) '
WRITE(*,*)
I - I+1
WRITE(*,2256) I
FORMAT(1X,'ENTER POINT ',13)
READ(*,*,ERR-2257) TMA(I), RA(I)
IF((TMA(I).GT.0.).AND.(RA(I).GT.0.)) TMA(I) - TMA(I) - DELAY
IF(I.EQ.1) RAMAX - RA(I)
IF(I.GE.2.AND.RA(I).GT.RAMAX) RAMAX - RA(I)
IF((TMA(I).GT.O.).OR.(RA(I).GT.0.)) GO TO 2255
ICOUNT - I-l
IF(TM1.LE.TMA(ICOUNT)) THEN
WRITE(*,*)
WRITE(*,*)'PLEASE MAKE SURE THE TIME LIMIT, TM1, IS'
WRITE(*,*)'LARGER THAN THE TIME OF THE LAST DATA POINT.’
WRITE(*,*)'IF YOU DO NOT CHANGE THIS THE PROGRAM WILL STOP.’
WRITE(*,*)'(RELAX YOU WILL HAVE A CHANCE TO CHANGE IT.)'
WRITE(*,*)
ENDIF
CONTINUE
WRITE(*,*)'THE NEXT TABLE WILL SHOW YOU THE POINTS YOU HAVE'
WRITE(*,*)'JUST ENTERED. IF YOU HAVE ENTERED MORE THAN 20'
WRITE(*,*)'POINTS THE TABLE WILL STOP SPOOLING EVERY 20 POINTS'
WRITE(*,*)'TO ALLOW YOU TO REVIEW THE POINTS ENTERED. MAKE'
WRITE(*,*)'A NOTE OF WHICH POINT YOU WISH TO CHANGE OR'
WRITE(*,*)'INSERT AND PRESS [RETURN] TO CONTINUE NOTE, YOU'
WRITE(*,*)'YOU WILL ONLY BE ABLE TO CHANGE OR INSERT ONE '
WRITE(*,*)'POINT AT A TIME.’
WRITE(*,*)'(NOW PRESS [RETURN] TO CONTINUE.)'
READ(*,'(A1)') ICHANG
CONTINUE
WRITE(*,*)
WRITE(*,*)'THE DATA POINTS YOU HAVE ENTERED ARE: '
WRITE(*,2262) DELAY
FORMAT(' (INCLUDING THE TIME DELAY OF ',F8.4,' SEC.)')
WRITE(*,*)

WRITE(*,*)' J TIME(J) RADIUS(J)’
IF(IMICCEN.EQ.1) THEN

WRITE(*,*)' (SEC.) (MICRONS)'
ELSE IF(IMICCEN.EQ.2) THEN

WRITE(*,*)' (SEC.) (CENTIMETERS)'
ENDIF

DO 2265 J-l,ICOUNT+1

667
668
669
'670

>r-r-r-r-

H
U)

Line#
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712

l 713

P‘P‘F‘P‘U

2263

2265

2266

2267

2270

2272

203

WRITE(*,2263) J, TMA(J), RA(J)
FORMAT(1X,I3,5X,F8.2,5X,F8.2)
IF((J/20)*20.EQ.J) THEN
WRITE(*,*)
Page

07-20-87
19:28:31
Microsoft FORTRAN77 V3.31 August 1985
WRITE(*,*)'PRESS [RETURN] TO CONTINUE.’
READ(*,'(A1)') IMORE
ENDIF
CONTINUE
IF(IBACK.EQ.1) GO TO 2281
WRITE(*,*)
WRITE(*,*)'DO YOU WISH TO CHANGE OR INSERT ANY OF THE POINTS,’
WRITE(*,*)'(Y/N)?'
READ(*,'(A1)') ICHANG
CALL IYESNO(ICHANG)
IF(ICHANG.EQ.'Y') THEN
CONTINUE
WRITE(*,*)
WRITE(*,*)'ENTER (1) TO CHANGE AND (2) TO INSERT.’
READ(*,*,ERR-2266) ICHAINS
CALL IONETWO(ICHAINS)
IF(ICHAINS.EQ.1) THEN
CONTINUE
WRITE(*,*)
WRITE(*,*)'PLEASE ENTER THE INDEX NUMBER J'
READ(*,*,ERR-2267) JI
IF(JI.LE.0.0R.JI.GE.I+1) THEN
CALL INCORRES
GO TO 2267
ENDIF
WRITE(*,*)
WRITE(*,*)'PLEASE ENTER THE NEW VALUES FOR '
WRITE(*,*)'TIME(J) AND RADIUS(J). '
READ(*,*,ERR-2270) TMA(JI), RA(JI)
GO TO 2260
ELSE IF(ICHAINS.EQ.2) THEN
CONTINUE
WRITE(*,*)
WRITE(*,*)'ENTER THE INDEX NUMBER J YOU WISH TO '
WRITE(*,*)'CHANGE, (OR PUSH DOWN).'
READ(*,*,ERR-2272) JI
IF(JI.LE.0.0R.JI.GE.I+1) THEN
CALL INCORRES
GO TO 2272
ENDIF
I - 1+1
DO 2278 J-JI,I-1
TMA( I+JI-J ) - TMA( (I-1)+JI-J )

H

714
715 2278
716

“717

718
719 2280
720
721
722
723 2281
724
725
726

D Line# 1

P‘P‘

727
728
729
730
731 2282
732
733
734
735
736
737 2283
738
739
740
741
742
743
744
745
746
747 2284
748
749
750
751
752
753
754
755
756
757
758
759
760 2300

204

RA( I+JI-J ) - RA( (I-1)+JI-J )
CONTINUE
WRITE(*,*)
WRITE(*,*)'PLEASE ENTER THE NEW VALUES FOR'
WRITE(*,*)'TIME(J) AND RADIUS(J).'
READ(*,*,ERR-2280) TMA(JI), RA(JI)

GO TO 2260
ENDIF
ENDIF
CONTINUE
IF((IRUNAG.GT.0).OR.(IMISTAK.EQ.'Y')) THEN
WRITE(*,*)
WRITE(*,*)'DO YOU WISH TO HAVE A TIME DELAY SUBTRACTED'
Page
07-20-87
19:28:31
7 Microsoft FORTRAN77 V3.31 August 1985

WRITE(*,*)'FROM THE DATA POINTS, (Y/N)?’
READ(*,‘(A1)') IDEL
CALL IYESNO(IDEL)
IF(IDEL.EQ.'Y') THEN
CONTINUE
WRITE(*,*)
WRITE(*,*)'PLEASE ENTER THE DELAY TO BE SUBTRACTED.’
READ(*,*,ERR—2282) DELAY
WRITE(*,*)
WRITE(*,2283) DELAY
FORMAT(' THE DELAY ENTERED IS ',F10.4,' (SEC.)',/,
' DO YOU WISH TO CHANGE IT, (Y/N)?')
READ(*,'(A1)') ICHANG
IF(ICHANG.EQ.'Y') GO TO 2282
ELSE IF(IDEL.EQ.'N') THEN
DELAY - 0.0
GO TO 2341
ENDIF
DO 2284 J - 1,1COUNT
TMA(J) - TMA(J) - DELAY
CONTINUE
IBACK - 1
GO TO 2261
ENDIF
IBACK - O
RINIT - RA(l)

ELSE IF(IRELPSE EQ.2) THEN
IF(IRUNAG.GE.1.0R.IMISTAK.EQ.'Y') GO TO 2319
WRITE(*,*)

WRITE(*,*)'SINCE YOU HAVE CHOSEN THE PSEUDO-EXPERIMENTAL'
WRITE(*,*)'OPTION, THE FOLLOWING PARAMETERS MUST ALSO'
WRITE(*,*)'BE ENTERED.’

WRITE(*,*)

CONTINUE

761
762
763
'764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782

D Line#
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807

2303

2305

2310

1

2311

2312

205

WRITE(*,*)'THE PERMEABILITY VALUE WITH WHICH THE PROGRAM'

WRITE(*,*)‘GENERATES PSEUDO-EXPERIMENTAL DATA, PTRU, '

WRITE(*,*)'(MICRONS/SEC.).'

READ(*,*,ERR-2300) PTRU

CONTINUE

WRITE(*,*)

WRITE(*,*)‘DO YOU WISH TO ENTER THE INITIAL RADIUS USING UNITS'

WRITE(*,*)'OF (1) MICRONS OR (2) CENTIMETERS, (ENTER 1 OR 2)?’

READ(*,*,ERR-2303) IMICCEN

CALL IONETWO(IMICCEN)

CONTINUE

WRITE(*,*)

WRITE(*,*)‘PLEASE ENTER THE INITIAL RADIUS OF THE CELL, RINIT,‘

IF(IMICCEN.EQ.1) WRITE(*,*)'(MICRONS).'

IF(IMICCEN.EQ.2) WRITE(*,*)'(CENTIMETERS).'

READ(*,*,ERR-2305) RINIT

CONTINUE

WRITE(*,*)

WRITE(*,*)'SINCE THIS IS A SIMULATION THE DATA POINTS '

WRITE(*,*)'GENERATED WILL HAVE A RADIUS HISTORY THAT WILL'

WRITE(*,*)‘LOOK EXACTLY LIKE THAT OF THEORY, THEREFORE'

WRITE(*,*)'THE PROGRAM ALLOWS THE USER TO IMPOSE A PSEUDO-'
Page

07-20-87
19:28:31
Microsoft FORTRAN77 V3.31 August 1985
WRITE(*,*)'RANDOMNESS FACTOR, DR, ON THE DATA. DR CAN BE'
WRITE(*,*)'THOUGHT OF AS THE MAGNITUDE OF THE VARIATION'
WRITE(*,*)'IN MEASURING THE RADIUS OF THE CELL.’
WRITE(*,*)‘PLEASE ENTER DR NOW.’
IF(IMICCEN.EQ.1) WRITE(*,*)‘(MICRONS).'
IF(IMICCEN.EQ.2) WRITE(*,*)'(CENTIMETERS).'
READ(*,*,ERRa2310) DR
WRITE(*,*)
WRITE(*,*)'WHEN USING THIS OPTION THE USER CAN CHANGE'
WRITE(*,*)'THE TIME STEP IN TWO REGIONS TO STUDY THE '
WRITE(*,*)'EFFECT OF DATA SPACING OF PARAMETER ESTIMATION.’
WRITE(*,*)'DO YOU WISH TO DO THIS, (Y/N)? '
READ(*,'(A1)') IMORE
CALL IYESNO(IMORE)
IF(IMORE.EQ.'N') THEN
TM01 - TM1
DT1 - DT
DT2 - DT
ELSE IF(IMORE.EQ.'Y') THEN
CONTINUE
WRITE(*,*)
WRITE(*,*)'PLEASE ENTER THE FIRST TIME STEP, DT1, (SEC.). '
READ(*,*,ERR-23ll) DT1
CONTINUE
WRITE(*,*)

206

808 WRITE(*,*)'PLEASE ENTER THE SECOND TIME STEP, DT2, (SEC.) '

809 READ(*,*,ERR-2312) DT2

810 2313 CONTINUE

'811 WRITE(*,*)

812 WRITE(*,*)'PLEASE ENTER THE INTERMEDIATE TIME LIMIT, TMOl,’

813 WRITE(*,*)'(SEC.) FOR THE FIRST TIME INTERVAL. (TM01 '

814 WRITE(*,*)‘TO TM1 IS ASSUMED TO BE THE SECOND TIME '

815 WRITE(*,*)'INTERVAL.)'

816 READ(*,*,ERR-2313) TM01

817 ENDIF

818 C

819 2319 CONTINUE

820 IF(IMICCEN.EQ.1) XMICCEN -'MICRONS'

821 IF(IMICCEN.EQ.2) XMICCEN -'CENTIMETERS'

822 WRITE(*,*)

823 WRITE(*,2320) PTRU,RINIT,XMICCEN,DR,XMICCEN,DT1,DT2,TMOl

824 2320 FORMAT(1X,'THE VALUES ENTERED FOR THE PSEUDO-EXPERIMENTAL'

825 . ,' OPTION ARE:',/,

826 . 1X,'1) PSEUDO-PERMEABILITY - ',F8.1,' MICRONS/SEC.',/,

827 . 1X,'2) INITIAL CELL RADIUS - ',E11.3,1X,A11,/,

828 . 1X,'3) RADIUS RANDOMNESS - ',E11.4,1X,A11,/,

829 . 1X,'4) FIRST TIME STEP - ',F7.2,' SEC.',/,

830 . 1X,'5) SECOND TIME STEP - ',F7.2,' SEC.',/,

831 . 1X,'6) INTERMEDIATE TIME LIMIT - ',F8.1,' SEC.',/)

832 WRITE(*,*)'DO YOU WISH TO CHANGE ANY OF THEM, (Y/N)?’

833 READ(*,‘(A1)') ICHANG

834 CALL IYESNO(ICHANG)

835 IF(ICHANG.EQ.'Y') THEN

836 2330 CONTINUE

837 WRITE(*,*)

838 WRITE(*,*)'PLEASE ENTER THE NUMBER BESIDE THE PARAMETER'
AH Page
16

07-20-87
19:28:31
D Line# 1 7 Microsoft FORTRAN77 V3.31 August 1985

839 WRITE(*,*)'YOU WISH TO CHANGE, (1-5). '

840 READ(*,*,ERR-2330) NCHANC

841 2340 CONTINUE

842 WRITE(*,*)

843 WRITE(*,*)'PLEASE ENTER THE NEW VALUE. '

844 IF(NCHANG.EQ.1) THEN

845 READ(*,*,ERR-2340) PTRU

846 ELSE IF(NCHANG.EQ.2) THEN

847 READ(*,*,ERR-2340) RINIT

848 ELSE IF(NCHANG.EQ.3) THEN

849 READ(*,*,ERR-2340) DR

850 ELSE IF(NCHANG.EQ.4) THEN

851 READ(*,*,ERR-2340) DT1

852 ELSE IF(NCHANG.EQ.5) THEN

853 READ(*,*,ERR-2340) DT2

854 ELSE IF(NCHANG.EQ.6) THEN

855
856
857
'858
859
860
861
862
863 C
864 2341
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880 2342
881
882
883
884
885
886
887
888
889
890
891 2343
892
893
894

D Line# 1
895
896
897
898
899
900
901

207

READ(*,*,ERR-2340) TM01

ELSE IF(NCHANG.LE.0.0R.NCHANG.GE.7) THEN
CALL INCORRES
GO TO 2330

ENDIF

GO TO 2319
ENDIF
ENDIF

CONTINUE
IF1 - O
IF2 - O
IF3 - O
IF4 - O
CON1 -'O_CON1.DAT'
CON2 -'O_CON2.DAT'
SENC -'O_SENC.DAT'
VOL1 -'O_VOL1.DAT'
VOL2 -'O_VOL2.DAT'
SUMR -'O_SUMR.DAT'
WRITE(*,*)‘DO YOU WISH TO HAVE FILES CREATED SO THAT YOU CAN'
WRITE(*,*)'USE PLOTIT TO GENERATE GRAPHICAL OUTPUT, (Y/N)?’
READ(*,'(A1)') IGRAPH ,
CALL IYESNO(IGRAPH)
IF(IGRAPH.EQ.'Y') THEN
CONTINUE
WRITE(*,*)
WRITE(*,*)'THE OUTPUT CAN BE VIEWED IN THE FOLLOWING WAYS:'
WRITE(*,*)
WRITE(*,*)'1) CONCENTRATION V.S. DIMENSIONLESS TIME'
WRITE(*,*)'2) SENSITIVITY COEFFICIENT V.S. TIME'
WRITE(*,*)'3) NORMALIZED VOLUME V.S. TIME'
WRITE(*,*)'4) SUM OF SQUARE OF ERRORS V.S. PERMEABILITY'
WRITE(*,*)
WRITE(*,*)'WHICH GRAPHICAL OPTION WOULD YOU LIKE (1-4), -'
WRITE(*,*)'(PLEASE CHOOSE ONE GRAPH AT A TIME).'
CONTINUE
READ(*,*,ERR-2343) IOPTGR
IF(IOPTGR.LE.0.0R.IOPTGR.GE.S) THEN
CALL INCORRES

Page
07-20-87
19:28:31
7 Microsoft FORTRAN77 V3.31 August 1985
GO TO 2342
ENDIF
WRITE(*,*)

WRITE(*,*)‘(NOTEz WHEN ENTERING THE FILE NAME USE 10'
WRITE(*,*)' CHARACTERS OR LESS.)'
IF(IOPTGR.EQ.1) THEN

IF1 - l

902 2344
903
904

‘905

906
907
908
909
910
911 2345
912
913
914
915
916
917
918
919 2346
920
921
922
923
924
925
926
927 2347
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949 2348
950

208

CONTINUE

WRITE(*,*)'THE DATA GENERATED FOR THE GRAPH CONCENTRATION'
WRITE(*,*)'V.S. DIMENSIONLESS TIME REQUIRES THE USER TO '
WRITE(*,*)'CHOOSE TWO FILE NAMES.’

WRITE(*,*)

WRITE(*,*)'PLEASE ENTER THE NAME FOR THE FIRST DATA SET,’
WRITE(*,*)'(CA(I) V.S. TIME(I)/TMAX).'
READ(*,’(A10)',ERR-2344) CON1

CALL CHANNAM(CONl)

CONTINUE

WRITE(*,*)

WRITE(*,*)'PLEASE ENTER THE NAME FOR THE SECOND DATA SET,’
WRITE(*,*)'(GB(I) V.S. TIME(I)/TMAX).'
READ(*,'(A10)',ERR-234S) CON2

CALL CHANNAM(CONZ)

ELSE IF(IOPTGR.EQ.2) THEN

IF2 - 1

CONTINUE

WRITE(*,*)'PLEASE ENTER THE FILE NAME YOU DESIRE FOR THE'
WRITE(*,*)'GRAPH - SENSITIVITY COEFFICIENT V.S. TIME.’
WRITE(*,*)'(SEN(I) V.S. TIME(I)).'
READ(*,'(A10)',ERR—2346) SENC

CALL CHANNAM(SENC)

ELSE IF(IOPTGR.EQ.3) THEN

IF3 - 1
CONTINUE
WRITE(*,*)'THE DATA GENERATED FOR THE GRAPH OF NORMALIZED'
WRITE(*,*)'VOLUME V.S. TIME REQUIRES THE USER TO CHOOSE'
WRITE(*,*)'TWO FILE NAMES. THE FIRST FILE WILL CONTAIN'
IF(IRELPSE.EQ.1) THEN
WRITE(*,*)'THE ACTUAL DATA POINTS ENTERED (WHICH ARE'
WRITE(*,*)'CONVERTED TO NORMALIZED VOLUME). THE '
WRITE(*,*)'SECOND FILE WILL CONTAIN THE DATA FOR THE'
WRITE(*,*)'BEST FIT CURVE BASED OF THE PERMEABILITY'
WRITE(*,*)'ESTIMATED FROM THE DATA ENTERED.’
ELSE IF(IRELPSE.EQ.2) THEN
WRITE(*,*)'THE SIMULATED DATA POINTS, WITH AN IMPOSED'
WRITE(*,*)'RANDOMNESS TO THE DATA, BASED ON THE TRUE'
WRITE(*,*)'PERMEABILITY ENTERED. THE SECOND FILE WILL'
WRITE(*,*)'CONTAIN THE DATA FOR THE BEST FIT CURVE'
WRITE(*,*)'BASED ON THE TRUE PERMEABILITY ENTERED ALSO.’
ENDIF
WRITE(*,*)
WRITE(*,*)'PLEASE ENTER THE NAME FOR THE FIRST DATA SET,’
WRITE(*,*)'(VOLA(I) V.S. TIME(I)).'
READ(*,'(A10)',ERR-2347) VOL1
CALL CHANNAM(VOLl)
CONTINUE
WRITE(*,*)
Page

07-20-87

D Line#
951
'952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000

1

2349

3100

3110

3120

3125

3130

3140

3145

209

19:28:31
7 Microsoft FORTRAN77 V3.31 August 1985
WRITE(*,*)'PLEASE ENTER THE NAME FOR THE SECOND DATA SET,’
WRITE(*,*)'(VOLC(I) V.S. TIME(I)).'
READ(*,'(A10)',ERR~2348) VOL2
CALL CHANNAM(VOLZ)
ELSE IF(IOPTGR.EQ.4) THEN
IF4 - 1
CONTINUE
WRITE(*,*)'PLEASE ENTER THE FILE NAME YOU DESIRE FOR THE'
WRITE(*,*)'GRAPH - SUM OF SQUARE OF ERRORS V.S. PERMEABILITY,’
WRITE(*,*)'(SUM(I) V.S. P(I)).'
READ(*,‘(A10)',ERR-2349) SUMR
CALL CHANNAM(SUMR)
ENDIF
WRITE(*,*)
WRITE(*,*)’DO YOU WISH TO CHOOSE ANOTHER FILE NAME FOR'
WRITE(*,*)'ANOTHER DATA SET, (Y/N)?’
READ(*,'(A1)') IANOTH
CALL IYESNO(IANOTH)
IF(IANOTH.EQ.'Y') GO TO 2342
ENDIF
WRITE(*,*)
WRITE(*,*)'HAVE YOU MADE ANY MISTAKES THAT YOU WOULD LIKE '
WRITE(*,*)'ANOTHER CRACK AT ENTERING/CHANGING THE PARAMETERS '
WRITE(*,*)'OR DATA AGAIN, (Y/N)?’
READ(*,'(A1)') IMISTAK
CALL IYESNO(IMISTAK)
IF(IMISTAK.EQ.'Y') GO TO 2180
WRITE(*,*)
WRITE(*,*)'OKAY, THE PROGRAM IS NOW CRUNCHING.’
GO TO 3999

OPTION ITERINP - 2: ENTERING THE INPUT FILE

CONTINUE
OPEN(11,FILE-ISENS,STATUS-‘OLD')
READ(11,'(A11)') PROBLEM
READ(11,3100) RL1,RL2,LIP
FORMAT(///,1X,F11.6,F11.6,12)
READ(11,3110) D1,D2,H
FORMAT(//,1X,E9.3,2X,E9.3,2X,E9.3)
READ(11,3120) CINIT, CINF
FORMAT(//,1X,F11.6,F11.6)
READ(11,3125) VINA,RMAG
FORMAT(//.1X,F11.6,F11.6)
READ(11,3130) DT,TMO,TM1,DELAY
FORMAT(//,1X,Fll.6,F11.6,F11.6,F11.6)
READ(11,3140) DP,PO,P1,PSEN
FORMAT(//,1X,F11.6,F11.6,F11.6,Fll.6)
READ(11,3145) RINIT
FORMAT(//,1X,F11.6)

1001
1002
1003
1004
1005
1006

D Line#

1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047

3150

3160

3170

4000

4005

4010

4020

4030

4040

4050

4060

210

READ(11,3150) PTRU,DR,TM01,DT1,DT2
FORMAT(///,1X,F11.6,F11.6,F11.6,F11.6,F10.6)
READ(11,3160) IRELPSE,IMICCEN
FORMAT(///,1X,I1,10X,Il)
READ(11,3170) IF1,IF2,IF3,IF4,IPRINT
FORMAT(///,1X,I1,10X,Il,10X,Il,10X,Il,10X,I2,/)

Page

07-20-87

19:28:31
7 Microsoft FORTRAN77 V3.31 August 1985
READ(11,3175) CON1,CON2,SENC,VOL1,VOL2,SUMR
FORMAT(//,1X,A10,1X,A10,/,1X,A10,/1X,AlO,lX,A10,/,1X,A10,///)

IF(IMICCEN.EQ.1) XMICCEN-'MICRONS'
IF(IMICCEN.EQ.2) XMICCEN-'CENTIMETERS'

WRITING THE INPUT DATA TO THE OUTPUT FILE O_SENS.DAT

WRITE(*,3180) ISENS

FORMAT(/,’ THE INPUT FILE ',AlO,' HAS BEEN ENTERED.')

CONTINUE

IF(IOPNAG.EQ.O) THEN
OPEN(10,FILE-'O_SENS.DAT',STATUS-'NEW')
OPEN(ZO,FILE-'O_SMRY.DAT',STATUS-'NEW')

ENDIF

WRITE(10,4000) ISENS

FORMAT(IX , ' *********************** THE INPUT FILE ' , A10 ,

' *********************** ' , / )

WRITE(10,4005)

FORMAT(/,'RL1,RL2,LIP ARE',/)
WRITE(10,*)RL1,RL2,LIP
WRITE(10,4010)
FORMAT(/,'D1,D2,H ARE:',/)
WRITE(10,*) D1,D2,H
WRITE(10,4020)
FORMAT(/,'CINIT,CINF ARE:',/)
WRITE(10,*) CINIT,CINF
WRITE(10,4030)
FORMAT(/,'VINA,RMAG ARE:’,/)
WRITE(10,*) VINA,RMAG
WRITE(10,4040)
FORMAT(/,'DT,TMO,TM1,DELAY ARE:',/)
WRITE(10,*) DT,TMO,TM1,DELAY
WRITE(10,4050)
FORMAT(/,'DP,P0,P1,PSEN ARE:',/)
WRITE(10,*) DP,PO,P1,PSEN
WRITE(10,4060)
FORMAT(/,'RINIT IS:',/)
WRITE(10,*) RINIT
WRITE(10,4O7O)

1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062

D Line#

h‘h‘h‘h‘

1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094

4070

4080

4090

211

FORMAT(/,'PTRU,DR,TM01,DT1,DT2 ARE:',/)
WRITE(10,*) PTRU,DR,TM01,DT1,DT2
WRITE(10,4080)

FORMAT(/,’IRELPSE,IMICCEN ARE:',/)
WRITE(10,*) IRELPSE, IMICCEN

WRITE(10,4O9O)
FORMAT(/,'IF1,IF2,IF3,IF4,IPRINT ARE:',/)
WRITE(10,*) IF1,IF2,IF3,IF4,IPRINT
WRITE(10,4100)
FORMAT(/,'CON1,CON2,SENC,VOL1,VOL2,SUMR ARE:'

./)

WRITE(10,4110) CON1,CON2,SENC,VOL1,VOL2,SUMR

4135
4140

4142

4150
C .....
C

C .....

FORMAT(AIO,5x,AIO,/,AIO,/,A10,5X,A1O,/,A1O)

Page

07-20-87
19:28:31
7 Microsoft FORTRAN77 V3.31 August 1985
USING SUBROUTINE MBCON TO PREDICT THE CONCENTRATION
CHANGE INSIDE THE CELL CHAMBER

WRITE(*,*)

WRITE(*,*)'ENTERING SUBROUTINE MBCON.’
CALL MBCON(TMS,CA,CB,IP)

WRITE(*,*)

WRITE(*,*)'LEAVING MBCON.’

IF IF1-1 (YES), WRITE DATA TO CON1 AND CON2

IF(IFI EQ 0) GO TO 4150
OPEN(14,FILE—CON1,STATUS—'NEW')
OPEN(15,FILE—CON2,STATUS-'NEW')
DO 4140 I-1,IP
WRITE(14,4135) TMS(I),CA(I)
WRITE(15,4135) TMS(I),CB(I)
FORMAT(1X,F6.4,1X,',',1X,E9.3)
CONTINUE
WRITE(*,*)
WRITE(*,*)'THE DATA FOR THE GRAPH CONCETRATION V.S. '
WRITE(*,*)'DIMENSIONLESS TIME HAS BEEN SENT TO FILES -'
WRITE(*,4142) CON1, CON2
FORMAT(1X,A10,' AND ',AlO)
CLOSE(14,STATUS-'KEEP')
CLOSE(15,STATUS-'KEEP')
CONTINUE

INITIALIZATION OF THE TIME VARIABLES AND RINIT

IT—INT((TM1-TMO)/DT)+1
DO 4170 I-1,IT

1
1
l

1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118

D Line#

P‘P‘P‘H‘

...;

1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141

4170

4210
4220

WRITE(*,*)

212

TMS(I)-TMO+(I-1)*DT
TMB(I)-TMS(I)
CONTINUE
IF(IMICCEN.EQ.1) THEN
RINIT - RINIT/RMAG
ELSE IF(IMICCEN.EQ.2) THEN
RINIT - RINIT*1000O./RMAG
ENDIF

CALCULATE R(TM,P) AND R(TM,P+DP)

WRITE(*,*)

WRITE(*,*)'CALCULATING R(TM,P).'

CALL RGKT(TMS,RS,IT,DT,RINIT,PSEN)
WRITE(*,*)

WRITE(*,*)'CALCULATING R(TM,P+DP).'

CALL RGKT(TMB,RB,IT,DT,RINIT,PSEN+EP1*PSEN)
CALCULATE SENSITIVITY COEFF. (SEN)
WRITE(10,4175)

FORMAT(//,1X,'************** DIMENSIONLESS SENSIVITITY ',
'COEFFICIENT VERSUS TIME ************')

Page

07-20-87

19:28:31

7 Microsoft FORTRAN77 V3.31 August 1985

WRITE(*,*)'CALCULATING SENSITIVITY COEFFICIENT, SEN.’

WRITE(10,4180)

FORMAT(/,6X,'TIME(I)',7X,'SEN(I)',/)

DO 4190 J-1,IT
SEN(J)-(RB(J)-RS(J))*PSEN/RINIT/(EP1*PSEN)
WRITE(10,4185)TMS(J),SEN(J)
FORMAT(SX,F7.2,5X,E10.3)

CONTINUE

IF IF2 - 1 (YES), WRITE DATA TO SENC
IF(IF2.EQ.O)GO TO 4230

OPEN(16,FILE-SENC,STATUS-'NEW')
DO 4220 I-1,IT
WRITE(16,4210) TMS(I),SEN(I)
FORMAT(1X,F8.2,1X,',',1X,E9.3)
CONTINUE
WRITE(*,*)
WRITE(*,*)'THE DATA FOR THE GRAPH OF THE SENSITIVITY '
WRITE(*,*)'COEFFICIENTS V.S. TIME HAS BEEN SENT TO FILE -'
WRITE(*,'(1X,A10)') SENC
CLOSE(16,STATUS-'KEEP')

 

 

 

1111

 

1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174

4240
4250

D Line# 1

P‘h‘h‘h‘

1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188

c----

C----

4253
4255

213

CONTINUE

WRITE(10,*)

FORMAT(IX,'****************************** RADIUS VERSUS TIME',
' ***************************I)

READING THE EXPERIMENTAL DATA AND CONVERTING TO MICRONS

IF (IRELPSE.EQ.1.AND.ITERINP.EQ.2) THEN
WRITE(10,4235)
I-O
WRITE(10,4240)
FORMAT(/,6X,'TM(I)',lOX,'R(I)',/)
I-I+1
READ(11,*)TMA(I),RA(I)
RSAVE(I) - RA(I)
IF(RA(I).GT.0.) TMA(I) -TMA(I)-DELAY
WRITE(10,4253) TMA(I), RA(I)
IF(IMICCEN.EQ.1) THEN
RA(I) - RA(I)/RMAG
ELSE IF(IMICCEN.EQ.2) THEN
RA(I) - RA(I)*10000./RMAG
ENDIF
IF(I.EQ.1) RAMAX - RA(I)
IF(I.GE.2) THEN
IF(RA(I).GT.RAMAX) RAMAX - RA(I)
ENDIF
IF ((TMA(I).GT.O.).OR.(RA(I).GT.O.)) GO TO 4250
ICOUNT-I-l
IF (TM1.LE.TMA(ICOUNT)) THEN
WRITE(*,*)
WRITE(*,*)'PLEASE MAKE SURE TM1 IS LARGER THAN THE TIME'
WRITE(*,*)'OF THE LAST DATA POINT, AND RUN IT AGAIN.’

GO TO 6000
Page
07-20-87
19:28:31
7 Microsoft FORTRAN77 V3.31 August 1985
END IF

CONVERTING INPUT DATA, ENTERED BY THE TERMINAL, TO MICRONS

ELSE IF(IRELPSE.EQ.1.AND.ITERINP.EQ.1) THEN
WRITE(10,4235)
WRITE(10,4240)
DO 4255 K-1,ICOUNT+1
RSAVE(K) - RA(K)
WRITE(10,4253) TMA(K),RA(K)
FORMAT(SX,F7.2,5X,E11.5)
CONTINUE
IF(IMICCEN.EQ.1)THEN
DO 4260 K-1,ICOUNT

H). ..
111111 11 111A. 2 Dailllll

 

 

H

H

h‘h‘

h‘h‘h‘h‘h‘h‘

P‘h‘

>h‘h‘h‘

214

P‘h‘h‘h‘h‘C’

1189 RA(K) - RA(K)/RMAG
1190 4260 CONTINUE
1191 RAMAX - RAMAX/RMAG
1192 ELSE IF(IMICCEN.EQ.2) THEN
1193 DO 4270 K-l,ICOUNT
1194 RA(K) - RA(K)*10000./RMAG
1195 4270 CONTINUE
1196 RAMAX - RAMAX*10000./RMAG
1197 ENDIF
1198 C----
1199 C GENERATING THE SIMULATED (PSEUDO) EXPERIMENTAL DATA
1200 C -----
1201 ELSE IF(IRELPSE.EQ.2) THEN
1202 ICOUNT - ((TM01-TMO)/DT1+(TM1-TM01)/DT2+1)
1203 CALL RGKT(TMS,RB,IT,DT,RINIT,PTRU)
1204 DO 4280 J-1,IT
1205 TMA(J) - TMS(J)
1206 RC(J) - RB(J)
1207 4280 CONTINUE
1208 TMA(1) - TMO
1209 DO 4290 J-2,ICOUNT
1210 IF (TMA(J-l).LT.TM01) THEN
1211 TMA(J)-TMA(J-1)+DT1
1212 ELSE IF (TMA(J-l).GE.TMOl) THEN
1213 TMA(J)-TMA(J-1)+DT2
1214 END IF
1215 4290 CONTINUE
1216 IF(IMICCEN.EQ.1) THEN
1217 DR - DR/RMAG
1218 ELSE IF(IMICCEN.EQ.2) THEN
1219 DR - DR*10000./RMAG
1220 ENDIF
1221 RAMAXC - RC(1)
1222 DO 4292 J-2,IT
1223 IF(RC(J).GT.RAMAXC) RAMAXC - RC(J)
1224 4292 CONTINUE
1225 RAMAX - RB(1)
1226 RA(l) - RB(1)
1227 DO 4300 J-2,ICOUNT
1228 ITM-INT(TMA(J)/DT)+1
1229 IF (ITM.GE.IT) THEN
1230 RA(J)-RB(ITM)+DR*RANND(XSEED,ISC)
Page
07-20-87
19:28:31
Line# 1 7 Microsoft FORTRAN77 V3.31 August 1985
1231 ELSE
1232 DRA-(RB(ITM+1)-RB(ITM))*(TMA(J)-(ITM-1)*DT)/DT
1233 RA(J)-RB(ITM)+DRA+DR*RANND(XSEED,ISC)
1234 END IF
1235 IF(RA(J).GT.RAMAX) RAMAX - RA(J)

P‘F‘P‘F‘P‘P‘

P‘P‘

F‘F‘h‘

HNNNNNNNNNHHHH

1236 4300
1237
1238
1239 4302
1240
1241
1242
1243
1244
1245
1246
1247
1248 4305
1249
1250
1251
1252 4310
1253

1254 C----

1255 C

1256 C----

1257
1258
1259
1260 4315

1261 C----

1262 C
1263 C

1264 C----

1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281 4320
1282 4330

1283 C----

1284 C

1285 C----

1286

215

CONTINUE
WRITE(10,*)

WRITE(10,4302)

FORMAT(1X,’********** SIMULATED RADIUS VERSUS TIME'
' ************** ' )
WRITE(10,*)
DO 4305 J-1,ICOUNT+1
IF(IMICCEN.EQ.1) THEN
RSAVE(J) - RA(J)*RMAG
ELSE IF(IMICCEN.EQ.2) THEN
RSAVE(J) - RA(J)*RMAG/10000.
ENDIF
CONTINUE
WRITE(10,4240)
DO 4310 J - 1,1COUNT
WRITE(10,4253) TMA(J), RSAVE(J)
CONTINUE
ENDIF

CALCULATING THE NORMALIZED VOLUME

DO 4315 I-1,ICOUNT

VOLA(I)-(RA(I)/RAMAX)**3

IF(IRELPSE.EQ.2) VOLC(I) -(RC(I)/RAMAXC)**3
CONTINUE

CALCULATE SUM OF ERROR OF SQUARE FOR P VALUES FROM
P0 TO P1

WRITE(*,*)
WRITE(*,*)'CALCULATING SUM OF SQUARE OF ERRORS FROM PO TO P1.’
IP-(Pl-P0)/DP+1
DO 4330 I-1,IP
P(I)-PO+(I-l)*DP
CALL RGKT(TMB,RB,IT,DT,RINIT,P(I))
SUM(I)-0.
DO 4320 J-1,ICOUNT

ITM-INT(TMA(J)/DT)+1

IF (ITM.GE.IT) THEN
RN-RB(ITM)

ELSE
DRN-(RB(ITM+1)-RB(ITM))*(TMA(J)-(ITM-1)*DT)/DT
RN-RB(ITM)+DRN

END IF

SUM(I)-SUM(I)+(RN-RA(J))**2

CONTINUE
CONTINUE

WRITE(10,4332)
Page

24

D Line# 1

P‘F‘F‘P‘P‘F‘F‘P‘ h‘h‘ P‘F‘F‘P‘P‘ P‘h‘

H

1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334

4332

4335

4338
C

4340

4350

4360

4365
c----

c----

4366

4367

WRITE(10,4335)

216

07-20-87
19:28:31
7 Microsoft FORTRAN77 V3.31 August 1985
FORMAT(///,1X,'************** SUM OF SQUARES OF ERRORS ',
'VERSUS PERMEABILITY ***************')

FORMAT(/,' P(J) SUM(J)',/)
DO 4338 J-1,IP

WRITE(10,4460) P(J),SUM(J)
CONTINUE

SUMIN-SUM(1)
PEST - P(l)
D0 4340 I-2,IP

IF (SUMIN.GT.SUM(I)) THEN
SUMIN-SUM(I)

PEST-P(I)

END IF
CONTINUE
CALL RGKT(TMB,RC,IT,DT,RINIT,PEST)
CALL RGKT(TMB,RB,IT,DT,RINIT,PEST+EP1*PEST)
DO 4350 J-1,IT

SEN(J) - (RB(J)-RC(J))/(EP1*PEST)
CONTINUE
D0 4360 J-1,ICOUNT

ITM-INT(TMA(J)/DT)+1

IF (ITM.GE.IT) THEN
SEN(J)-SEN(ITM)

ELSE
DSEN-(SEN(ITM+1)-SEN(ITM))*(TMA(J)-(ITM-1)*DT)/DT
SEN(J)-SEN(ITM)+DSEN

END IF

CONTINUE
SENSUM-O.
D0 4365 I-1,ICOUNT

SENSUM-SENSUM+SEN(I)**2

CONTINUE

DUMPING SUMMARY INPUT PARAMETERS, INPUT DATA AND RESULTING
PEST, SDP, SUMIN TO 'O_SMRY.DAT'

WRITE(20,*)
WRITE(20,4366)
FORMAT ( // ’ ' ************************ THI S I S FILE 0 ,
' O_SMRY _ DAT ************************ ' ’ // )

WRITE(20,4367)

FORMAT(/,'THE INPUT PARAMETERS AND DATA WERE:',//)
WRITE(20,2190) RL1,RL2,LIP,D2,D1,H,CINIT,CINF,VINA,RMAG
WRITE(20,*)

WRITE(20,2240) DT,TMO,TM1,DP,PO,P1,PSEN
IF(IRELPSE.EQ.1) THEN

1335
1336
1337
1338
1339
1340
1341
1342

D Line#

F‘P‘

P‘F‘P‘

H

1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381

4368

c----

C

C----

4375

4380

4385

4390

217

WRITE(20,*)
WRITE(20,*)'THE DATA POINTS ENTERED WEREz'
WRITE(20,2262) DELAY

WRITE(20,*)

WRITE(20,*)' J TIME(J) RADIUS(J)’
IF(IMICCEN.EQ.1) THEN
WRITE(20,*)' (SEC.) (MICRONS)'
ELSEIF(IMICCEN.EQ.2) THEN
Page
07-20-87
19:28:31
7 Microsoft FORTRAN77 V3.31 August 1985
WRITE(20,*)' (SEC.) (CENTIMETERS)'

ENDIF
DO 4368 J-1,ICOUNT+1
WRITE(20,2263) J,TMA(J),RA(J)

CONTINUE
ELSEIF(IRELSPE.EQ.2) THEN

WRITE(20,*)

WRITE(20,2320) PTRU,RINIT,XMICCEN,DR,XMICCEN,DT1,DT2,TM01
ENDIF

THE ESITMATED PERMEABILITY

WRITE(10,437S)

WRITE(20,4375)

FORMAT ( /// ’ ' ************************** THE RESULTING '
' PERMEABILITY ************************ ' ’ / )

SDP-SQRT(SUMIN/(ICOUNT-1)/SENSUM)

WRITE(10,4380)PEST

WRITE(20,4380)PEST

FORMAT(/,'THE LOCAL MINIMUM OCCURS AT P -',F8.3,
' MICRONS/SEC.')

WRITE(10,4385)SDP

WRITE(20,4385)SDP

FORMAT(/,'THE STANDARD DEVIATION OF ESTIMATED P IS
WRITE(10,4390)SUMIN

WRITE(20,4390)SUMIN

FORMAT(/,'THE MINIMUM VALUE OF SUM IS',F8.3)

',E8.3)

IF(IRELPSE.EQ.1) THEN
D0 4400 J-1,IT
IF(J.EQ.1) RAMAXC - RC(1)
IF(J.GE.2.AND.RC(J).GT.RAMAXC) RAMAXC - RC(J)
CONTINUE
D0 4410 J-l,IT
VOLC(J) - (RC(J)/RAMAXC)**3
CONTINUE
ENDIF

P‘P‘h‘

P‘P‘

1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398

D Line#

P‘F‘P‘

1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428

C

c .....
IF(IF3.EQ.0) GO TO 4450

4420
4430

4431

4432

4460
4470

218

IF IF3 - 1 (YES), WRITE THE DATA TO VOL1 AND VOL2

OPEN(17,FILE-VOL1,STATUS-'NEW')
OPEN(18,FILE-VOL2,STATUS-‘NEW’)
DO 4430 J-1,ICOUNT
WRITE(17,4420) TMA(J),VOLA(J)
FORMAT(1X,F7.2,1X,',',1X,F7.5)
CONTINUE
DO 4431 J-1,IT
WRITE(18,4420) TMS(J), VOLC(J)
CONTINUE
WRITE(*,*)
WRITE(*,*)'THE DATA FOR THE GRAPH NORMALIZED VOLUME V.S.'
WRITE(*,*)'TIME HAS BEEN SENT TO FILES -'
WRITE(*,4432) VOL1, VOL2
FORMAT(1X,A10,' AND ',AlO)
Page

07-20—87

19:28:31

Microsoft FORTRAN77 V3.31 August 1985
CLOSE(17,STATUS-'KEEP')
CLOSE(18,STATUS-'KEEP')

CONTINUE
IF IF4 - 1 (YES), WRITE THE DATA TO SUMR

IF(IF4.EQ.0) CO TO 6000

OPEN(19,FILE-SUMR,STATUS-'NEW')
DO 4470 J-1,IP
WRITE(19,4460) P(J),SUM(J)
FORMAT(1X,F8.2,1X,',',1X,E9.2)
CONTINUE
WRITE(*,*)
WRITE(*,*)'THE DATA FOR THE GRAPH OF THE SUM OF SQUARE OF'
WRITE(*,*)'ERRORS V.S. PERMEABILITY HAS BEEN SENT TO FILE - '
WRITE(*,‘(1X,A10)') SUMR
CLOSE(19,STATUS-'KEEP')

CONTINUE

WRITE(*,*)

WRITE(*,6100) PEST,SDP,SUMIN

FORMAT(' THE ESTIMATED PERMEABILITY Is ',F8.3,' MICRONS/SEC.',//,

' THE STANDARD DEVIATION IS ',E9.3,' MICRONS/SEC.',//,
' THE MINIMUM SUM OF THE SQUARE OF THE ERRORS IS ',E9.3)

RESETTING THE RA(I) - RSAVE(I) AND RINIT, RAMAX TO ORIGNAL VALUES

IF(IMICCEN.EQ.1) THEN

RINIT - RINIT * RMAG
RAMAX - RAMAX * RMAG

hard

H

1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454

280

319

320

D Line# 1

1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475

325

331

332

333

334

335

219

IF(IRELPSE.EQ.2) DR - DR * RMAG
D0 280 K - 1, ICOUNT+1
RA(K) - RSAVE(K)
CONTINUE
ELSE IF(IMICCEN.EQ.2) THEN
RINIT - RINIT *RMAG/IOOOO.
RAMAX - RAMAX *RMAG/lOOOO.
IF(IRELPSE.EQ.2) DR - DR *RMAG/IOOOO.
DO 290 K - 1,ICOUNT+1
RA(K) - RSAVE(K)
CONTINUE
ENDIF

OPTION TO SAVE THE INPUT FILE

WRITE(*,*)
WRITE(*,*)'DO YOU WISH To SAVE THE INPUT DATA IN A FILE,’
WRITE(*,*)'(Y/N)?’
READ(*,‘(A1)') ISAVE
CALL IYESNO(ISAVE)
CONTINUE
IF(ISAVE.EQ.'Y') THEN
IF(IEXP.EQ.1) GO To 331

CONTINUE
WRITE(*,*)
WRITE(*,*)'WHAT WOULD YOU LIKE TO NAME THIS FILE,’
Page
07-20-87
19:28:31

Microsoft FORTRAN77 V3.31 August 1985
WRITE(*,*)'(ENTER NO MORE THAN 10 CHARATERS)?’
READ(*,'(A10)',ERR-320) NAMFIL
OPEN(12,FILE-NAMFIL,STATUS-'NEW')
WRITE(12,325)
FORMAT(1X,'THIS IS THE FILE YOU HAD SAVED. YOU CAN '
,'USE THIS FILE AS',/,' AN INPUT FILE IF YOU DESIRE BY'
,' ACCESSING THIS FILE ',/,' WHEN YOU ARE PROMPTED FOR'
,' THE NAME OF AN INPUT FILE.')
CONTINUE

WRITE(12,*)'RL1 RL2 LIP'
WRITE(12,332)RL1,RL2,LIP
FORMAT(1X,F5.2,6X,F7.2,4X,12,/)
WRITE(12,*)'D1 D2 H'

WRITE(12,333) D1,D2,H
FORMAT(1X,E9.3,2X,E9.3,2X,E9.3,/)
WRITE(12,*)'CINIT CINF'
WRITE(12,334) CINIT,CINF
FORMAT(1X,F8.3,3X,F8.3,/)
WRITE(12,*)'VINA RMAG'
WRITE(12,335) VINA,RMAG
FORMAT(1X,F5.2,6X,F7.2,/)

220

1476 WRITE(12,*)'DT TMO TM1 DELAY'

1477 WRITE(12,336) DT,TMO,TM1,DELAY

1478 336 FORMAT(1X,F6.3,5X,F7.2,4X,F7.2,4X,F7.2,/)

1479 WRITE(12,*)'DP P0 P1 PSEN'

1480 WRITE(12,337) DP,PO,P1,PSEN

1481 337 FORMAT(1X,F5.2,5X,F6.2,6X,F6.2,5X,F6.2,5X,/)

1482 WRITE(12,*)'RINIT'

1483 WRITE(12,338) RINIT

1484 338 FORMAT(1X,E9.3,/)

1485 WRITE(12,339)

1486 339 FORMAT(1X,'THE PARAMETERS FOR THE LINE BELOW ARE FOR ',

1487 . 'SIMULATION OPTIONz')

1488 WRITE(12,*)'PTRU DR TM01 DT1 DT2'

1489 WRITE(12,340) PTRU,DR,TM01,DT1,DT2

1490 340 FORMAT(1X,F6.2,5X,F7.3,4X,F7.2,4X,F6.3,5X,F6.3,/)

1491 WRITE(12,341)

1492 341 FORMAT(1X,'THESE PARAMETERS BELOW ARE FOR DATA INPUT '

1493 . ,'CONTROL:')

1494 WRITE(12,*)'IRELPSE IMICCEN'

1495 WRITE(12,342) IRELPSE, IMICCEN

1496 342 FORMAT(1X,II,10X,Il,/)

1497 WRITE(12,*)'THESE PARAMETERS ARE FOR DATA OUTPUT CONTROL:'

1498 WRITE(12,*)'IF1 IF2 IF3 IF4 IPRINT'

1499 WRITE(12,345) IF1,IF2,IF3,IF4,IPRINT

1500 345 FORMAT(1X,11,10X,11,10X,Il,10X,Il,10X,12,/)

1501 WRITE(12,346)

1502 346 FORMAT(1X,'THESE ARE THE FILE NAMES FOR THE GRAPHICAL ',

1503 . 'OUTPUTz')

1504 WRITE(12,347) CON1,CON2,SENC,VOL1,VOL2,SUMR

1505 347 FORMAT(/,1X,A10,1X,A10,/1X,A10,/1X,A10,1X,A10,/1X,A10,/)

1506 WRITE(12,349)

1507 349 FORMAT(1X,'THE LAST GROUP BELOW ARE THE DATA POINTS:')

1508 WRITE(12,*)' TMA(I) RA(I)’

1509 DO 360 I -1,ICOUNT
1 1510 WRITE(12,350) TMA(I), RA(I)
AH Page
28

07-20-87
19:28:31

D Line# 1 7 Microsoft FORTRAN77 V3.31 August 1985
1 1511 350 FORMAT(1X,F9.4,5X,F9.4)
1 1512 360 CONTINUE

1513 WRITE(12,*)' 0.0 0.0'

1514 CLOSE(12,STATUS-'KEEP')

1515 IF(IQUIT.EQ.'Y') GO TO 600

1516 WRITE(*,*)

1517 WRITE(*,362) NAMFIL

1518 362 FORMAT(' OKAY, THE FILE ',A10,’ HAS BEEN SAVED.')

1519 ENDIF

1520 CLOSE(11,STATUS-'KEEP')

1521 C -----

1522 C OPTION TO RUN THE PROGRAM AGAIN

1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558

Name

Type

A1
A2
CA
CB
CINF
“H
29

REAL
REAL
REAL
REAL
REAL

D Line# 1
CINIT REAL

CON1
CON2

CHAR*10
CHAR*10

221

WRITE(*,*)
WRITE(*,*)'DO YOU WISH TO RUN THE PROGRAM AGAIN,
READ(*,‘(A1)') IAGAIN
CALL IYESNO(IAGAIN)
IOPNAG - IOPNAG + 1
IF(IAGAIN.EQ.'Y') THEN
CONTINUE

(Y/N)?’

OPTION TO ENTER NEW DATA OR REVIEW OLD DATA

WRITE(*,*)
WRITE(*,*)'DO YOU WISH TO (1) ENTER ALL NEW DATA OR '
WRITE(*,*)'(Z) USE AND REVIEW THE DATA ALREADY ENTERED,’
WRITE(*,*)’(ENTER 1 OR 2)?’
READ(*,*,ERR-SOO) INEWREV
CALL IONETWO(INEWREV)
DELAY - 0.0
IBACK - O
IF(INEWREV.EQ.1) THEN
IRUNAG - 0
GO TO 2000
ELSE IF(INEWREV.EQ.2) THEN
ITERINP - 1
IRUNAG - IRUNAG + 1
GO TO 2180
ENDIF
ENDIF

STOPPING THE PROGRAM.

WRITE(*,*)

WRITE(*,*)'OKAY, PROGRAM DONE.’
CLOSE(10,STATUS-'KEEP')
CLOSE(20,STATUS-'KEEP')

END
Offset P Class
8 /C1 /
16 /C1 /
15668
15768
24 /C3 /
Page
07-20-87
19:28:31
7 Microsoft FORTRAN77 V3.31 August 1985
20 /C3 /
15964

15974

COUT
D1

D2
DELAY

DMY327

DP
DR
DRA
DRN
DSEN
DT
DT1
DT2
EP1
F

H

I

IAGAIN
IANOTH

IBACK

ICHAIN
ICHANG
ICOUNT

IDEL
IEXP
IF1
IF2
IF3
IF4

IFIRST
IGRAPH

II

IMICCE
IMISTA

IMORE

INEWRE

INR
INT

IOPNAG
IOPTGR

IP

IPRINT

IQUIT

IRELPS
IRELSP
IRUNAG

ISAVE
ISC
ISENS

ISEPPR

IT

ITERIN

REAL
REAL
REAL
REAL
REAL
REAL
REAL
REAL
REAL
REAL
REAL
REAL
REAL
REAL

REAL
INTEGER*4
CHAR*1
CHAR*1
INTEGER*4
INTEGER*4
CHAR*1
INTEGER*4
CHAR*1
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
CHAR*1
CHAR*1
INTEGER*4
INTEGER*4
CHAR*1
CHAR*1
INTEGER*4
INTEGER*4

INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
CHAR*1
INTEGER*4
INTEGER*4
INTEGER*4
CHAR*1
INTEGER*4
CHAR*10
INTEGER*4
INTEGER*4
INTEGER*4

16
12
16
15904

15908
15928
19444
19560
19732

15936
15940

28
16028
21420
18080
15876
17444
16748
16024
17212
15892

15952
15956
15960
15889
18074

15948
15888
17442
21422
17208

15884
18076
18972

15890
15944
19904
15880
16032
15872
16038
16048
19024
16034

222

/C2 /

/C3 /

/C3 /

LARGE

/C2 /

PARAMETER
EXTERNAL

/C3 /

/Cl /

PARAMETER
INTRINSIC
/Cl /

ITM INTEGER*4
AH

30 .

D Line# 1 7
J INTEGER*4
JI INTEGER*4
K INTEGER*4
LIP INTEGER*4
N1 INTEGER*4
N3 INTEGER*4
N4 INTEGER*4
N5 INTEGER*4
NAMFIL CHAR*10
NCHANC INTEGER*4
0 REAL

P REAL

P0 REAL

P1 REAL

PEST REAL
PROBLE CHAR*11
PSEN REAL
PTRU REAL

RA REAL
RAMAX REAL
RAMAXC REAL
RANND REAL

RB REAL

RC REAL
RINIT REAL

RL1 REAL

RL2 REAL
RMAG REAL

RN REAL

RS REAL
RSAVE REAL

SDP REAL

SEN REAL
SENC CHAR*10
SENSUM REAL
SQRT

SUM REAL
SUMIN REAL
SUMR CHAR*10
TMO REAL

TM01 REAL

TM1 REAL

TMA REAL

TMB REAL

TMS REAL
VINA REAL

19440

17410
17448
19384

20516
16750
18472
14464
15912
15916
19716
18081
15920
15924

6036
17358
19428

7240
13260

15896
19556
10852
12056
20024

8444
15984
19736

9648
19712
16014
15900
15932
12
16
1220

4832

223

/C3 /

PARAMETER
PARAMETER
PARAMETER
PARAMETER

FUNCTION

/C2 /
/C3 /
/C3 /

INTRINSIC

/C2 /

/C2 /

Page

07-20-87
19:28:31
Microsoft FORTRAN77 V3.31 August 1985

224

VOL1 CHAR*10 15994
VOL2 CHAR*10 16004
VOLA REAL 3628
VOLC REAL 2424
XMICCE CHAR*11 17558
XSEED REAL 15868
1559 C -----
1560 C SUBROUTINE RGKT(X,Y,N,DX,Y0,P)
AH Page
31
07-20-87
19:28:31
D Line# 1 7 Microsoft FORTRAN77 V3.31 August 1985
1561 C
1562 C USE RUNGE-KUTTA METHOD TO SOLVE ORDINARY DIFFERENTIAL
1563 C EQUATION
1564 C
1565 C X: INDEPENDENT VARIABE
1566 C
1567 C Y: DEPENDENT VARIABLE
1568 C
1569 C N: DIMENSION OF X(N) AND Y(N)
1570 C
1571 C DX: INCREMENT 0F X
1572 C
1573 C Y0: INITIAL CONDITION OF Y
1574 C
1575 C P: PARAMETER
1576 C
1577 C F: THE SUPLLIED FUNCTION. (DY/DX-F(X,Y))
1578 C -----
1579 SUBROUTINE RGKT(X,Y,N,DX,Y0,P)
1580 DIMENSION X(N),Y(N)
1581 Y(1)-Y0
1582 D0 1 I-1,N-1
1 1583 RKl-DX*F(X(I),Y(I),P)
1 1584 RK2-DX*F(X(I)+DX/2.,Y(I)+RK1/2.,P)
1 1585 RK3-DX*F(X(I)+DX/2.,Y(I)+RK2/2.,P)
1 1586 RK4-DX*F(X(I)+DX,Y(I)+RK3,P)
1 1587 Y(I+1)-Y(I)+(RK1+2*RK2+2*RK3+RK4)/6.
1 1588 1 CONTINUE
1589 RETURN
1590 END
Name Type Offset P Class
DX REAL 12 *
F REAL FUNCTION
I INTEGER*4 21426
N INTEGER*4 8 *

225

P REAL 20 *
RK1 REAL 21434
RK2 REAL 21438
RK3' REAL 21442
RK4 REAL 21446
X REAL 0 *
Y REAL 4 *
Y0 REAL 16 *
1591 C -----
1592 C FUNCTION F(X,Y,Z)
1593 C
1594 C X: INDEPENDENT VARIABLE
1595 C
1596 C Y: DEPENDENT VARIABLE
1597 C
1598 C 2: PARAMETER
1599 C -----
AH Page
32
07-20-87
19:28:31
D Line# 1 7 Microsoft FORTRAN77 V3.31 August 1985
1600 FUNCTION F(X,Y,Z)
1601 PARAMETER (N4-301,PI-3.14159)
1602 COMMON /CZ/RINIT,VINA,DT,TM1,COUT(N4)
1603 COMMON /C3/RL1,RL2,LIP,D1,D2,CINIT,CINF,H
1604 V-0.018
1605 I-INT(X/DT)+1
1606 CO-COUT(I)+(COUT(I+1)-COUT(I))*(X-(I-1)*DT)/DT
1607 V0-(4.*PI*(RINIT**3))/3.
1608 VIN-VINA*V0/100.
1609 F--Z*V*(CO-CINIT*(V0-VIN)/(4.*PI*Y**3/3.-VIN))
1610 RETURN
1611 END
Name Type Offset P Class
C0 REAL 21458
CINF REAL 24 /C3 /
CINIT REAL 20 /C3 /
COUT REAL 16 /C2 /
D1 REAL 12 /C3 /
D2 REAL 16 /C3 /
DT REAL 8 /C2 /
H REAL 28 /C3 /
I INTEGER*4 21454
INT INTRINSIC
LIP INTEGER*4 8 /C3 /
N4 INTEGER*4 PARAMETER
PI REAL PARAMETER

RIN
RL1
RL2

IT

TM1'

V0
VIN

VINA

1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626

D Line#

1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645

00000

10

12
21450
21462
21466

OObOb
x-a-x-

/C2
/C3
/C3
/C2

/C2

226

\\\\

FUNCTION RANND(XSEED,ISC)

RANDOM VARIABLE GENERATOR

NORMAL DISTRIBUTION WITH STANDARD DEVIATION EQUAL TO 1.

FUNCTION RANND(XSEED,ISC)
DOUBLE PRECISION RANDOM

GENERATING A UNIFORM RANDOM NUMBER

INTEGER A,X

IF(ISC.EQ.0) X - XSEED

A - 2**1O + 3

Page
07-20-87
19:28:31
7 Microsoft FORTRAN77 V3.31 August 1985
M - 2**20
FM - M
X - MOD(A*X, M)
FX - X
XSEED - X
Z - FX/FM

CONVERTING THE RANDOM NUMBER WITH A UNIFORM DISTRIBUTION TO A
RANDOM NUMBER HAVING A NORMAL DISTIBUTION

R - RANDOM()
R - Z
A0-2.30753
A1-0.27061
B1-0.99299
82-0.04481

IF (R-0.5) 10,10,20

AK-l.
GO TO 30

227

1646 20 AK--1.
1647 RPR'O.S
1648 30 T-SQRT(ALOG(1./(R*R)))
.1649 E-T-(A0+A1*T)/(1.+Bl*T+B2*T*T)
1650 RANND-AK*E
1651 ISC - ISC + 1
1652 RETURN
1653 END
Name Type Offset P Class
A INTEGER*4 21474
A0 REAL 21498
Al REAL 21502
AK REAL 21514
ALOG INTRINSIC
Bl REAL 21506
B2 REAL 21510
E REAL 21522
FM REAL 21482
EX REAL 21486
ISC INTEGER*4 4 *
M INTEGER*4 21478
MOD INTRINSIC
R REAL 21494
SQRT INTRINSIC
T REAL 21518
X INTEGER*4 21470
XSEED REAL 0 *
Z REAL 21490
1654 C
1655 SUBROUTINE IONETWO(ITEST)
1656 31 CONTINUE
1657 IF(ITEST.LE.0.0R.ITEST.GE.3) THEN
1658 WRITE(*,*)
AH Page
34
07-20-87
19:28:31
D Line# 1 7 Microsoft FORTRAN77 V3.31 August 1985
1659 WRITE(*,*)'** INCORRECT RESPONSE **'
1660 WRITE(*,*)'PLEASE ENTER 1 OR 2'
1661 WRITE(*,*)
1662 READ(*,*) ITEST
1663 GO TO 31
1664 ENDIF
1665 RETURN
1666 END
Name Type Offset P Class

ITEST INTEGER*4

1667 C

1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680

Name

ITEST CHAR*1

1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702

32

Type

C

33

35

36

D Line# 1

228

0*

SUBROUTINE IYESNO(ITEST)

CHARACTER *1 ITEST

CONTINUE

IF(ITEST.NE.'Y'.AND.ITEST.NE.'N') THEN
WRITE(*,*)
WRITE(*,*)'** INCORRECT RESPONSE **'
WRITE(*,*)'PLEASE ENTER "Y" OR "N"'
WRITE(*,*)
READ(*,‘(A1)') ITEST
GO TO 32

ENDIF

RETURN

END

Offset P Class

0*

SUBROUTINE CHANNAM(FILNAM)
CHARACTER *1 ICHANG
CHARACTER *10 FILNAM
CONTINUE
WRITE(*,*)
WRITE(*,35) FILNAM
FORMAT(1X,'THE FILE NAME ENTERED IS ',AlO)
WRITE(*,*)
WRITE(*,*)' DO YOU WISH TO CHANGE IT,(Y/N)? '
READ(*,'(A1)') ICHANC
CALL IYESNO(ICHANG)
IF(ICHANG.EQ.'Y') THEN
WRITE(*,*)
CONTINUE
WRITE(*,*)'PLEASE ENTER THE NEW NAME. '
WRITE(*,*)
READ(*,'(A10)',ERR-36) FILNAM
GO TO 33
ENDIF
RETURN
END

Page

07-20-87
19:28:31
7 Microsoft FORTRAN77 V3.31 August 1985

229

Name Type Offset P Class
FILNAM CHAR*10 0 *
ICHANG CHAR*1 21562

1703 SUBROUTINE INCORRES

1704 WRITE(*,*)

1705 WRITE(*,*)'** INCORRECT RESPONSE **'

1706 RETURN

1707 END
Name Type Offset P Class
Name Type Size Class
Cl 24 COMMON
C2 1220 COMMON
C3 32 COMMON
CHANNA SUBROUTINE
F REAL FUNCTION
INCORR SUBROUTINE
IONETW SUBROUTINE
IYESNO SUBROUTINE
MBCON SUBROUTINE
RANND REAL FUNCTION
RGKT SUBROUTINE
SENS PROGRAM
Pass One No Errors Detected

1707 Source Lines
“2

“H
1
D Line# 1 7
l SUBROUTINE MBCON(TM,CA,CB,IP)
2 C$DEBUG
3 $INCLUDE: 'IMSL'
1 $LARGE: DMY327
2 DIMENSION DMY327(1)
4 C -----
S C
6 C CHAMBER
7 C
8 C -----
9 PARAMETER (II-2,III-3,N4-301)
10 REAL L1,L2,M
ll
12 &
13 &
14
15
16
17 C -----
18 C INITIALIZATION
19 C -----
20 N1 - 4
21 N2 -6
22 L1-RL1*1.0E-6
23 L2-RL2*1.0E-6
24 TMAX-TMI
25 DXl-Ll/Nl
26 DX2-L2/N2
27 RX-DXZ/DXl
28 P1-DT*Dl/DX1/DX1
29 P2-DT*D2/DX2/DX2
30 Bl-H*DX1/D1
31 M-2./(1+RX)
32 DO 1 I-1,N1+N2+1
l 33 CN(I)-O.
1 34 CO(I)-O.
1 35 D0 1 J-1,N1+N2+1
2 36 CE(I,J)-0.
2 37 l CONTINUE
38 ICOUNT-0
39 C -----
40 C
41 C
42 C -----
43 WRITE(10,151)
44 151
45

230

Page

06-28-87
20:18:55
Microsoft FORTRAN77 V3.31 August 1985

JOB: 1. PREDICT THE CONCENTRATION CHANGE INSIDE THE CELL

2. PLOTTING CONCENTRATION VERSUS TIME CHART

DIMENSION CN(11),CO(11),CE(11,11),

WK1(154),CONC(11),CA(25),CB(25),
DC(25),TM(25),X(II,II),Y1(II),Y2(II),WK2(10)

COMMON /Cl/IPRINT,IF1,A1(II),A2(II)
COMMON /C2/RINIT,VINA,DT,TM1,COUT(N4)
COMMON /C3/RL1,RL2,LIP,D1,D2,CINIT,CINF,H

USING THE BACKWARD DIFFERENCE METHOD TO CALCULATE THE
CONCENTRATION INSIDE THE CELL CHAMBER

FORMAT(///,IX,'************************* THE CONCENTRATION',
v HISTORY *************************v)

46
47
48
49
50
51
52
53
54

>F‘P‘F‘

N

D Line#

56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87

F‘P‘F‘P‘

90
91
92

H

231

INPUT VALUES TO THE COEFFICIENT MATRIX

CE(1,1)-1+2*P1+2*P1*Bl
CE(1,2)--2*P1
DO 2 I-2,N1
CE(I,I-1)--P1
CE(I,I)-1+2*P1
CE(I,I+1)--P1
Page

06-28-87
20:18:55
7 Microsoft FORTRAN77 V3.31 August 1985
CONTINUE
CE(N1+1,N1)--P1*M
CE(N1+1,N1+1)-1+P1*M+P1*M*(DZ/D1)/RX
CE(N1+1,N1+2)--P1*M*(DZ/D1)/RX
DO 3 I-N1+2,N1+N2
CE(I,I-1)—-P2
CE(I,I)-1+2*P2
CE(I,I+1)--P2
CONTINUE
CE(N1+N2+1,N1+N2)--2*P2
CE(N1+N2+1,N1+N2+1)-1+2*P2
WRITE(*,*)
WRITE(*,*)'CALCULATING THE COEFFICIENT MATRIX -'
WRITE(*,*)'ENTERING LEQTZF (1)'
CO(1)-CO(1)+2*BI*P1

CALCULATE THE COEFFICIENT MATRIX

NXl - N1+N2+1
MX - 1
IDGTl - 3
CALL LEQT2F(CE,MX,NX1,NX1,CO,IDGT1,WK1,IER1)
IX -1
IF(IER1.NE.0) THEN
WRITE(*,*)
WRITE(*,llO) IX,IER1,ICOUNT
FORMAT(' IER',Il,' - ',IS,5X,'ICOUNT-'I4)
ENDIF

PUT CO INTO CN FOR NEXT CALCULATION

ICOUNT-ICOUNT+1
DO 4 I-1,N1+N2+1
CN(I)-CO(I)
CONTINUE
COUT(ICOUNT)-CN(LIP)*(CINF-CINIT)+CINIT
COUT(ICOUNT)-CINF+(CINIT-CINF)*EXP(-(ICOUNT-1)*DT/l9.6)

 

93 C
94 C -----
95
96
97 101
98
99
100
1 101 5
102
103
104
105
106
107
108
109
110

H

D Line# 1
111
112 201
113
114
115
116 202
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133 C -----
134 C
135 C -----
136
137
138
139 C -----

232
CHECK TO SEE WHETHER IT IS TIME TO OUTPUT THE DATA

IF (ICOUNT/IPRINT*IPRINT.EQ.ICOUNT) THEN

WRITE(10,101)ICOUNT*DT

FORMAT(/,'CONCENTRATION DISTRIBUTION AT TIME-',

F8.2,'SEC. IS',)
D0 5 I-1,N1+N2+1
CONC(I)-CN(I)*(CINF-CINIT)+CINIT

CONTINUE
WRITE(10,*)
WRITE(10,*)' DIALYSIS MEMBRANE CELL CHAMBER'
WRITE(10,*)'
WRITE(10,*)'B
WRITE(10,*)'U
WRITE(10,*)'L
WRITE(10,*)'K
WRITE(10,*)'

m———_——

WRITE(10,*)' 3 7 9 1
Page
06-28-87
20:18:55
7 Microsoft FORTRAN77 V3.31 August 1985

WRITE(10,201) CONC(1),CONC(3),CONC(5),CONC(7),CONC(9),CONC(11)
FORMAT(1X,E9.3,1X,E9.3,1X,E9.3,1X,E9.3,1X,E9.3,1X,E9.3)
WRITE(10,*)' | | I'
WRITE(10,*)' | 2 4 | 6 8 10 1'
WRITE(10,202) CONC(2),CONC(4),CONC(6),CONC(8),CONC(10)
FORMAT(3x,E9.3,2x,E9.3,Ix,E9.3,1x,E9.3,1x,E9.3)
WRITE(10,*)' | |
WRITE(10,*)'F | |
WRITE(10,*)'L | |
WRITE(10,*)'O | I
WRITE(10,*)'W | |
WRITE(10,*)' | |
WRITE(10,*)
WRITE(10,*)
IP-ICOUNT/IPRINT
IF (CN(N1+1).GE.1.) CN(N1+1)-1.-1.E-6
IF (CN(N1+N2+1).GE.1.) CN(N1+N2+1)-1.-l.E-6
CA(IP)—-LOG(l-CN(N1+1))
CB(IP)--LOG(1-CN(N1+N2+1))
DC(IP)-CONC(N1+1)-CONC(N1+N2+1)
TM(IP)-ICOUNT*DT/TMAX
END IF

CHECK TO SEE WHETHER IT IS TIME TO STOP THE EXECUTION
IF (ICOUNT*DT.LT.TMAX+DT) GO TO 6

WRITE(*,*)
WRITE(*,*)'LEAVING LEQT2F (1)'

F‘h‘h‘k‘

h‘h‘h‘h‘h‘h‘h‘

140 C
141 C

142 C .....
- 143

144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166

10

11

D Line# 1

H

167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186

120

200

233

FINDING THE BEST LINEAR FIT FOR THE CONCENTRATION VERSUS
TIME POINTS

DO 10 I-1,2
X(I,2)-0.
Y1(I)-0.
Y2(I)-0.

CONTINUE

DO 11 I-1,IP
X(1,2)-X(1,2)+TM(I)
X(2,2)-X(2,2)+TM(I)**2
Y1(1)-Y1(1)+CA(I)
Y1(2)-Y1(2)+CA(I)*TM(I)
Y2(1)-Y2(1)+CB(I)
Y2(2)-Y2(2)+CB(I)*TM(I)

CONTINUE

X(2,1)-X(1,2)

X(1,1)-IP

NX2 - 2

IDGT2 - 3

IDGT3 - 3

WRITE(*,*)

WRITE(*,*)'FINDING BEST LINEAR FIT FOR CONCENTRATION V.S. TIME —'

WRITE(*,*)

WRITE(*,*)'ENTERING LEQT2F (2)'

CALL LEQT2F(X,MX,NX2,NX2,Y1,IDGT2,WK2,IER2)

WRITE(*,*)
Page
06-28—87
20:18:55
7 Microsoft FORTRAN77 V3.31 August 1985
WRITE(*,*)'LEAVING LEQT2F (2)'
IX - 2
IF(IER2.NE.0) THEN
WRITE(*,*)
WRITE(*,120) IX, IER2
FORMAT(' IER',Il,' - ',I3)
ENDIF

D0 200 K - 1,2
A1(K) - Y1(K)

CONTINUE
WRITE(*,*)
WRITE(*,*)'ENTERING LEQT2F (3)'
CALL LEQT2F(X,MX,NX2,NX2,Y2,IDGT3,WK2,IER3)
WRITE(*,*)
WRITE(*,*)'LEAVING LEQT2F (3)'
IX - 3
IF(IER3.NE.0) THEN

WRITE(*,*)

WRITE(*,IZO) IX, IER2
ENDIF

234

187 D0 210 K -1,2
1 188 A2(K) - Y2(K)
1 189 210 CONTINUE
'190 WRITE(10,103)A1(1),A1(2)
191 103 FORMAT(/,' THE EQUATION FOR THE LINEAR BEST FIT FOR THE',/,
192 . ' CONCENTRATION VERSUS TIME IS,',/,
193 . ' Y - ',F6.3,' + ',F6.3,' *X',/)
194 WRITE(10,103)A2(1),A2(2)
195 RETURN
196 END

Name Type Offset P Class

A1 REAL 8 /C1 /

A2 REAL 16 /C1 /

B1 REAL 1460

CA REAL 4 *

CB REAL 8 *

CE REAL 936

CINF REAL 24 /C3 /

CINIT REAL 20 /C3 /

CN REAL 704

CO REAL 748

CONC REAL 792

COUT REAL 16 /C2 /

D1 REAL 12 /C3 /

D2 REAL 16 /C3 /

DC REAL 836

DMY327 REAL 0 LARGE

DT REAL 8 /CZ /

DXl REAL 1440

DX2 REAL 1444

H REAL 28 /C3 /

I INTEGER*4 1468

ICOUNT INTEGER*4 1484

IDGTl INTEGER*4 1632

AH Page

5
06-28-87
20:18:55

D Line# 1 7 Microsoft FORTRAN77 V3.31 August 1985

IDGT2 INTEGER*4 1876

IDGT3 INTEGER*4 1880

IERl INTEGER*4 1636

IER2 INTEGER*4 1884

IER3 INTEGER*4 1912

IF1 INTEGER*4 4 /C1 /

II INTEGER*4 PARAMETER

III INTEGER*4 PARAMETER

1P INTEGER*4 12 *

IPRINT INTEGER*4 0 /Cl /

IX INTEGER*4 1640

235

 

J INTEGER*4 1476
K INTEGER*4 1908
L1 REAL 1428
L2' REAL 1432
LIP INTEGER*4 8 /C3 /
LOG INTRINSIC
M REAL 1464
MX INTEGER*4 1628
N1 INTEGER*4 1420
N2 INTEGER*4 1424
N4 INTEGER*4 PARAMETER
NXl INTEGER*4 1624
NX2 INTEGER*4 1872
P1 REAL 1452
P2 REAL 1456
RINIT REAL 0 /C2 /
RL1 REAL 0 /C3 /
RL2 REAL 4 /C3 /
RX REAL 1448
TM REAL 0
TM1 REAL 12 /C2 /
TMAX REAL 1436
VINA REAL 4 /C2 /
WKl REAL 16
WK2 REAL 664
X REAL 632
Y1 REAL 648
Y2 REAL 656
197
198
199
Name Type Size Class
C1 24 COMMON
C2 1220 COMMON
C3 32 COMMON
LEQT2F SUBROUTINE
MBCON SUBROUTINE
Pass One No Errors Detected

199 Source Lines
“Z

BIBLIOGRAPHY

10.

11.

12.

BIBLIOGRAPHY

Mazur, P., ”Cryobiology: The freezing of biological systems,"
Science 168, 939-949 (1970).

Morris, G.J., "Liposomes as a Model System for Investigating

Freezing Injury," Effects of Low Temperatures of Biological
Membranes, Academic Press Inc. (London) LTD., 241-262 (1981).

McGrath, J.J., "A Microscope Diffusion Chamber for the Determination
of the Equilibrium and Non-equilibrium Response of Individual
Cells," Submitted to the Journal of Microscopy, March 1985.

Blok, M.C., vanDeenan, L.L.M. & deGeir, J., ”The Effect of
Cholesterol Incoporation on the Temperature Dependence of Water
Permation Through Liposomal Membranes Prepared From

Phosphatidycholines," Biochemica Biophysica ACTAI 464 509-518
(1977).

Hempling, M.C., "Permeability of the Ehrlich ascites Tumor Cells to
Water," Journal of General Physiology, 44 365-379 (1960).

Savitz, D., Sidel, V.M. & Solomon, A.K., "Osmotic Properties of
Human Red Cells," Journal of General Physiology, 48 79-94 (1964).

McGrath, J.J. & Tu, S.M., "On the Determination of Cell Membrane
Water Permeability Using a Microscope Diffusion Chamber - I. Solute
Concentration History Within a Diffusion Chamber," Submitted to the

quppal of Membrane Biology.

Wendt, R.P., Klein, E., Bresler, E.H., Holland, F.F., Serino, R.M. &
Villa, H., "Sieving Properties of Hemodialysis Membranes," gppppal
of Membrane Science 5, 23-49 (1979).

Kedem, O. & Katchalsky, A., "Thermodynamic Analysis of the
Permeability of Biological Membranes to Non-Electrolytes,"
Biochimica Et Biophysica ACTA 27, 229 (1958).

 

Katchalsky, A. & Curran, P.F., Noneguilibrium Thermodynamics in
Biophysics, Havrard University Press, Cambridge, Massachusetts, p.87
(1965).

Beck, J.V. & Arnold, K.J., Parameter Estimation in Engineering and
Science, John Wiley & Sons, New York, pp.1,l8 (1977).

Boroske, E., Elwenspoek, M. and Helfrich, W., "Osmotic Shrinkage of

Giant Egg-Lecithin Vesicles", Journal of Biophysics 34, pp.95-109
(1981).

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