‘PvisSIbl RETURNING MATERIALS: Place in book drop to LIBRARIES remove this checkout from .—c—- your record. FINES will be charged if book is returned after the date stamped below. . £33 2 Kim 08921922903 OCT 1 96 €00; {1'0 0 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 n- ~..~I o... -..¢ .u» .x. AU 5 ~ 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. J. u. .: .Hu up. u c .u» 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 ‘\ (T\ '\ (h I“ LIST OF TABLES 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 [Q ;d to LO [0 f0 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 1 N I; '0‘ ‘ v uvhcnbus PA-...... . yx..-C...‘ ,.. _ I‘ .‘eo..... U v.s.-o); I ‘ , |' ~‘-‘--s A I p. “in on...\“. n" An-v‘~.‘-‘ .... Snug-y _ - Q‘.. g. " r"'v- '5. ...:._ Q d ‘ I v \..-_‘_' a. ‘ p. . g. " \ (‘v- ~ '...-. a P ‘Q A 9} . 'v“ to: M. all '5_ L; \C. 1:. Ve‘? P u a S n "no A“. ”A-“ V I -". . ‘ C V 'l. ck cf ‘ s g - 0-.- ‘vn Lv. r*;: o ‘_ ‘ 1"- a“: .1 n ‘ 'C '\ A‘m‘. ‘ \, ‘ ' Q :Q": . t_‘; '\A 'I’ q . r . o““a ‘5 NOMENCLATURE 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 Q Work Due to Heat P Cell Membrane Water Permeability Pest Estimated Permeability p Pressure p Number of Parameters R Gas Constant Rc Cell Radius - Predicted Rm Cell Radius - Measured S Entropy S Sum of the Squares Function T Temperature t Time V Volume G Partial Molar Volume w Solute Permeability xi X Length x Length Xi Force Xij Sensitivity Coefficient Y Measured Parameter xii r “ vast C u;-;,. a n.v~....h nu» §‘&: 55:- W SUBSCRIPT NOMENCLATURE b Osmotically Inactive c Cell D Diffusion i Initial Condition i Species i j Species j m Membrane p Pressure 3 Solute w Solvent 1 Dialysis Membrane Region 2 Sample Region 3 Inside the Cell of Interest xiii (I! HI GREEK NOMENCLATURE Parameter Error Osmotic Pressure Molar Fraction Volume Fraction Reflection Coefficient Chemical Potential Dissipation Function Standard Deviation Predicted Parameter Covariance of Errors xiv Q q ‘ ..-.., i C O.‘ ~U~ .. —&— up L..€ C‘ . na‘ -— ..4 .‘~‘-h.~~- ‘ . rev-.0 1. V‘ KMS. c.. n.- “ ' ‘ ~a a- Véuzt. .S i 0v . ' I‘,‘ ‘ mu 1'; ’ A\1 ‘11-» ' "v ‘ G. p p a ‘v-c V I N.“ara \ ‘~. "~ I:‘ .‘_~ ens .'-.l r i 6 ._“:~ 5. ‘- l!- ..e r:‘e.;° 4 ‘r l‘ V‘ l 6‘ ._‘ N. '. c_ "'I \ Q“ o_v .b"~‘ '.fl' ‘ 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 ~ -. ‘V p- n-..v .u . uw .7- v.«-- r fix vvg. .u. , a "n- n....,..,._ ,- v~..»....... ‘ ‘ - :~- , .h -m .“- ‘\. h.‘- N‘ --<‘. l r “— '\. rm A-‘ u a. a at , ‘l ’. . ,-’ v. ~ V‘ U-‘: ' -‘a J‘ ‘ ~65 w A . ’-, . d.-:-.‘ -., v. ‘ ".1 2 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. L, 0. 0a to (I (‘1 (i v - C‘-‘~ Tn“ brun- V \“""v\- ( 'N-oou-nnh I-‘D . latch,‘ _. h““=§~'.. 5”: :5- ‘ \. . ‘5': t, ' . E_H"c ‘h l ‘¢.e f :‘: e‘ P‘ _ "t -‘ VH‘Q~1C br‘:I,_|L D an. , '0 9 u w v.-. \,.= \ ._ ‘ “.q‘»_ an» . . "vi-v U .‘ 5 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 . A .— ‘7'9flltficc n. w u . . . 5"... .5.“ . 'o.>u.g- ‘l. . , I ‘l ””‘n ~v h...‘._. t. S Q FE.."“. ’p ~\v....1i g” . . a o ‘7 ‘ ”L“ *.J i 3" a d:~: "‘ “~~ \r - _. ‘ o :5 ‘v.‘,‘ "a u. .. 5 H“v‘ an "a t..- C .1 ~ V ‘. a fl:.q . t..- '“»d a C‘s."_. .‘u ‘ 'I‘s Ha. .1..“5 ‘~ V‘!" 5 ‘u.‘ -.. a . h'u ‘- u.tb‘:“h ‘q . ‘V L 3 ‘L‘e '- .;Ev (A. a )- ‘ LJ‘ k C.- .9 -‘ ‘- m “1 . I ‘y. C “ . .‘ \‘ne 6 K v 7:r 1 JJ 9 'n~. :‘r. _ ~“'.':Ly“ '. . L 4‘ 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 V :c:.c‘ be e‘ 3'55 CC ' «\- . n-—-,,'_ - “mutint u o , . ‘ F. 4.... - I V H »:-a v Y t - ."A ' O‘A‘: es.~~ 7 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. Thus estimates of experimental uncertainties could be made. . en’s. "Av-p VE...-..‘U ‘3 v0. 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. OQOOuOLO.S. L 32.23279 :3— 3: u .5 «Au UnafiuUUOLU a: OZU LO .~D~ a ~ud-UmQLnahvz U~ ungtpéaxuun H.H.N 0.59”. oocaom Em: >nom 21.35 conEmco _ l \ / w._<0m OF #02 _ \\K\\\\\\\\D AU c2255 —\K\N\\\\\\\\ >8: ism AHU \\\\\\\\\N\ +_ ~— J. co_mmm \ gaEmmk 7 \\\m\\\K\\\\ Us M o cummmnhwmh lyz , |\ mama co>oo 3:330 oaoomocfls. ill, .\ J ‘(I d/l 9.5:. no» mc_m coomam umnEOr—u .533“:me $2950.32..— mcu k0 coZoucmmmuamm ofiuoEmcum 10 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 ~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:pmm 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 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< - Ci [w] (2.2.44) Vc(t) - Vb by substituting (2.2.44) into (2.2.41) we get iRL‘E). - -fiw[cs,2 - 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 cofiuoupcmocou . uzayzo Hoofica0to mflasom uoiioiiueouog 41 4.3. 8%: Adomv oEfi 0.00 0.00 0.044 0.00 0.0m 0.0V 0.0 L t . h . IL L L . IL L 00.0l 1.0.0.. 18.0.. / 18.0.. 10.0! , I I. 00.0 maze .m.> “cmfiofiuemou >HL>_Hmemm . osauzo Hooficaoto mfiaeom nasdp/oap ilaog A . iIAiiisueS uegoi ‘ 1. itll IQIEIL f\I-ul\p.v 42 Own 8%: noomv oEfi 00 om 0+. on 0m 0_ 0 r ....i L .lLl... InkllsiLll. r ILilll.Ll.. .LI.IILIO.O _ Bum _Hcoanaxo 630.0 0 Aoom\mcotowEv ndflm. m u Cmovd .0230 0: ...mon ole . 0N0 14.0 m . o 10 0 C jig _ was» .m.> me:_o> “Lou umNfi_oEtoz I osapso HooHcQOLG m_anm A !)/\/(ISU!)/\ on lies pezuowon i l 3, (l0 eLuri )9 u .— «a::i::-gnun& . ”U. .\/ M...MvL~b~:bMJ. C~\.~ KO :=~rfi I ..wfiqfih,us-v N~UnU-xn§huismV niv Nakzkvfia 43 .F____...-.__.- -..... .. ----..._._--..._.._ -..- I F‘“ "" 'f F) m.m.m mesa; A.oom\mcoto_Ev bzfiooEtoa O F NF L i. [ill—ll. OFF 0 0 ¢ LN L—l Lil) h .7 IF L111 1P IlauL...o. I1 F 0 Ir "WWII—T T— F —l N S ‘uonounj saJonbg sq; ,io bung >uzfinom=tmm .m.> mmLozom 9:90 .Ezm i “Dunno 25:30.5 QHQEDw 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 fimé 950$ outaom Em: m4pom osmmE . tonEmco M. _ fl _ K\N\\\\\\\\\H ~\\\N\\\\\\\N AU 333:0 3o: 5.5 Avllu +_ L.“ :o.mom \ \\\\\\\\N\\\ \ o.o.Emm \/ NHNKWN NNNNNN o cmm_.mn>e_:mo_fl 7////V /, V// j |\ .nxxi. .lluv mama to>oo 05m $0.25 3:330 oaoomocozz Q/IL toasocu coamzLefin oncomOLULZ on“ L0 coeo0ucmmmtamm oHpoEmcom 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 //_ .- l.’ , A . . 7? [I . _ . . . //"“/ /'/./,/ SIDE CROSS SECTIONAL VIEW /Temperature Regulating Channel Temperature Regulating Fluid Exit Temperature Regulating Fluid Entrance ———-\. - r/ 775- f// // //// //// ////)/ T— (Bulkx Flow ”Entrancex// IN ./h/1’/ Bulk Flow ‘- ’./ I .,/Exic .’ \ V ' t . .' '.. I / I : / _ o _ ‘//4' r74 If / ._,i —> —l—> L.) / , ' / _ I I I . // - 4:; ////' // / 7/ / / .,/,f:iii / /‘ 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 I— ~ Pust‘ ... umxmom umumnomwo _ I s.m.s messes odoomouuas yonemzo con=MMWQ odoumouowz xo>IL u0uwcoz >8 ., NHNENO oaaa> .L ousumuooEmHm .Lii _ «any 1 coauzaom mo>am> aficOuuonzm pfiocoaom coHDSHow cacouuooam owsouomH a5: 7] one Q pounaomcu L,~Nu :umm L wcaumaswom - muaumumaeoe .Iu.. ”mu i. o>am> Hopscoo ua< pmuwusmmoum aoumzm Hamum>0 mnu mo afiumSonom 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. 0; oEomoa: H :oo o 67 0.0 L 3.... 839.1 cozobcoocoo omto>E pomzoEtoz 0.0 5.0 0.0 0.0 4.0 0.0 N0 ...L._._._.L._. W00 1 F0 1N0 10.0 14.0 10.0 10.0 15.0 10.0 10.0 0.? msomoafim - :o_H0tucmo:ou mmtm>:H umNfifioEtoz .m.> msafio> __mu umNLLoetoz 2/\ (IDilIUI)/\//\ awngoA Hag pazllouuoN oLmoocaEz n __oo o ucwoa comm Low muz mmm.oum 8 6 mum 8%: 3:20:53 .0} cozobcmocoo @952: 0+ 0.0 0.0 m.N 0.N 04 04 0.0 0.0 bnpnb-pub—bH—L—nbub—bnkbbbP-n—Pnhb—-b1ph 0.0 1 F0 1¢.0 15.0 H0.0 I mu>uocQE>4 . i cowuogucmucou 09.02.: .m.> mED~0> :00 00:35.52 0., =0 (IDIlIUI)/\//\ ewnIOA 118:) PGZIIDWJON 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. 80 0.0 2% 8%: hEZox $8003 .00 L.\F otgotanoH omto>E mum in NM NM . . oEomoa: .1. :oo o — 550.011m Jan coco ..2 01.2 0 TN T 1v W0 00 L10— .47 a. 10¢ W00 . .100 mm co, mEomoaLm -mLDLOLQQEmL mmtm>cH .m.> >ufifianometma umooe_pmm foes/3110131111) ‘(ise)d Ki! 0 paivwnss icoeuua 1 81 0.0 New 8%: ”£2.90 8383 .mm C; otzyotanoH om..o>c. mhn NM NM. N0 onozaEb ...u __mo 0 F Radium .358 zoom .2 mnz o 1N 14. M0 00 10F .. tom T 10% T wow wow 00F mmu>oocae>m - mtzsotmaame mmto>ca .m.> >D_Hunometoa umpoefiumm WIT ('oes/suonltu) ( 01412183 l fiiilqoewed :8 82 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). Rs 839.1 A.oom\m**mtoLoEV .20 F0 ocoEEoE @9520 E omOLozm 00 336320 0.0 O.N Oé 0.0 E L .h 1P 1P _ L 5 u — F 1- th b O oEomoo: .11. :8 910 080 owes n 10_ 10m 10m. I!!!" #04 89 d 100 100 lllqOSLUJS -‘ T... ('oos/suomlw) ‘(isa)d 105 100 o——-""' 00 mEOmoaHm 1 Ha .m.> Aummva 90 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. oEomOQ: .11. :oo omoo omon 91 O D m. was 830 A.oom\mcoLoEv .40 p: EoMoEooo toamcofi mmoE 0.? 0.0 1— L P In P — h n F —|] n In P ].r 1 new row row 100 r...____ -. ..-.-m-..... ...--_.....__._._......._.c 3'11 Q. o\ -4000! .-.-Ii ‘1": '0... II- 'Qa ’I I‘D. tall I.-. .la. II.-IIIII.(III”PAI.OI .Ull Cl 0E0m00w4 i 0: .w.> Auwmvm 00 ('OSS/SUOJOIUJ) ‘(isa)d fiiilqoewed Peiowiisa 92 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. 94 mama 839.1 AmcotBEv .NIE mmoconH cofiom oEEom 00m. 00m F. 1P b] L - 0m: 0 b r p b h L b b O oEomoaz u __oo 6.10 38 once a 0 F 1 10m 100 T 10¢ 050mm: 1 NIE .m.> 38E ('OSS/SUOJOIUJ) ‘(ise)d 0111409de paiowlisa 95 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. “2825 o? u 35 ole 96 once omon D FF is 8%: a: 85601 oEomoaj 0 a” 0 mm a m” _w P 0 1% L .17 1% Ir L C) i onomm mmmz4 Aummvm (oas/suomiw) ‘(isa)d A1111<11>6>Lwea1 peiowiisa 97 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). oEOmoa: u :8 01¢ 98 QmOO GMOQ D 03 8%: ooLxSoEé>E> n at . oEEo> :oo o>zoo£ \EoozoEmo poNLLoELoz 0.0m. 0.¢N 0.0m 0.0— 0.N— 0.0 L L f]. L L L . L 1 L L I'LII. .a all-L l. (pas/3110101111) ‘(ise)d All 06 0.0 L TO Lu TOP L. T8 T fi05 T T00 T r“! I I... I'ITIII!‘ ‘I. 0.-.... .Ilul I- ..--‘1 a‘t‘Iil'l. tr om 388: .. <2; .m.> 38E qoauued peiowgisg l .1! 99 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. oEomoa: n :oo @16 100 omoo omen U 93 239.1 coma 85mg >060 oEc. T405 100 L00 mEomoaS .. >500 .m.> 33E ('oes/suomiw) ‘(isa)d 353 Aiigiqoeuued paiouu 101 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. mEomoa: 1]. :00 010 800 omon u 103 0.” 0.0 0.0 5.0 L L r 53 95m: nmcoLoLEv .mo mmocEOUcom pomoog 0.0 0.0 To 0.0 N0 r L L L L —.0 0.0 L \. \ \ \ 0 meomoaLm - mo .m.> .0.m 0F ('oas/suomgul) “Q's uoliogAeg plopuoig 104 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). mum mam: 8.an Lo LonEzz 00 F 00 00 05 00 0L0 0% 00 ON 0 F 5 L 5 p L L F L oEomoo: H __oo 61¢ 106 0.0 10.2 10.8 10.0... Tod... roam T98 Tod.“ 10.00 oeomoaLJ - mLcLoa Lo Lmnsaz .m.> LmeLL 0.00 (pas/$110010) ‘(ise)d fiiiiqoewed peiowiisa a . ...L’C+r;CC kc 1:005:0th .W.> .Q.W oEowoa: H :00 107 O 0.0 was 8%: xmmELoa Lo LonEJZHTQ To No No _..0 F L O 8883 .. £358 .8 $9523.. .m.> .0.m «e—IL O O LAT- O O f—o ('oes/suoniui) "G's uoiipiAaQ pJopuoig oEomoo: H :8 o 108 00? 2.3 $ng 350a Lo LonEzz 00 05 00 00 men 00 ON 0 F P F _ _ L L 5 0.0 080000“; 1 wagon L0 .5952 .0.) ZHZDm “1.. 7N0 woo m... 10.0 ....00 NIWI’lS LLll'lS 0nw1u1w 6.2. 1138?; pro the ac: 109 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]. DZLDAJDIL a I. oEomoaLL n. :00 01¢ 38 moon 0 110 0w f :.N.m 2%: Ao_oE\._ooxv .om ocoLnEoE 29520 .6 38:0 cozo>00< h L I» [P 1F PI .F a Li lP .L‘l’l’llhllli'i /. 0— 0 0 L l O FTITrTTTTTU—FTI l I!) '- ITI—TfilTfiTIT 080000: .. Ame—0.23.0: mHmLSUfiQvom .m.> Sfimuvom I!) O O N In N (slow/10354) ‘03 113:) ,10 KBJaug uogpAiiov 6.3 show ERCO1 at radiu jg 111 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 We into SEES permeabil '1”: the same through 6 dEViation tabulated 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. mu>oocQE>q I HQ .m.> apnoea cc 33050.83 ...... :00 114 omoo moon 0 D 'hi IV and 2%: A.oom\m**mt3oEv .mm 5 20582,. $9390 E 8:25 £28m. .6 323:5 n ngu _Li in |r if L LIIP o.F MI. m.w w Au Thy? musuocas>4 - Ha .m.> Aumova (‘oes/suomgw) 1139):} Mmqoewed pelownsa 6.3. inver (See P(est Again 115 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. 330:9»; n. :00 coco omon 116 «.2 8%: A.oom\mtoyoEv.vm Ur. E20580 tocmcob. mmoz m; 0.“ who Lbh4+LLLLIIF 1— I 0.0 n in. _ . u . V _ Flu‘ It-“ II“. Volt, zi'il‘ ‘16’n‘ul‘ Q! 1“." III 1‘1 mp>oocae>4 - u: .m.> Aummva ..'- .I’L T T: row Ton ('oas/suomguu) ‘(ise)d Kaizlqoeuuea pewwnsa 117 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. 03.60an2 n :8 Ole omoo moon 0 118 0.00m. 03 839.1 nmcotflEv .msm 3656:: cofiom oEEom Odom 0.00— r h LP .- F L—[t b b L b b IF \@\6\V\- l\\\\\¢\\\\9 llllOlI‘l mu>uocae>4 I mnE .m.> Aummvm (“oes/suoniw) ‘(ise)d Knuqoew-Jed pawns}; 119 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 more experiments should be conducted. and 8:9... oExSoon>E> u now . mE:_o> :00 m>zooc_ >__ooBoEmO noN:oc.toz 06m owmau Divan. 9mm own" afloocaEb n =3 0.6 T I 2.-- ..--..f- . do once omen a $13 Elie-‘ liéflulitéllilol To P Txikt e w ,n“ M——- - 121 "r“?— 0 q- Fl... ”a .-..o—u-o...¢n-‘o. 330:an .. <2; .m.> Emmi (Des/sumogw) ‘(ise)d K‘mqoeuued PSQDWEEH 122 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%. o onocaEz H :3 Ole 123 080 moon 0 fl r.____.. .... .. one 959.1 38v £3.65 >260 Etc. 3 o; . mu #3- .....--_.-f.i..Lllll.. ll! LI L I! F row {on Tom 830:an .. Elma .m.> Cami om ('oes/suomguu) 1139):} Annabell-wad peaownsa 124 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 H- l+l+l+l+l+l+l+l+l+ NHHH000000 .042 .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 The oSoocaEb n.. :00 ole omoo moon 0 125 and 8%: AmcoLQLEV .mo mmochocom ommOQE_ 0rd 00.0 00.0 no.0 00.0 00.0 tno.0 no.0 No.0 0.0 00.0 L L L L L L L L L 0H>UOEQE>0 .. mm .m.> .Q.w ('oes/suomgw) "(J‘s UOIlolAeQ pJopuoig 126 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). otAoocaEb u :00 I 128 53 83: 9.an Lo 89:32 on LrLHLFLLPFL 0x. L F LI _ L 00 L mu>uocae>m - mucLoa Lo Lmae:z .m.> Aummva Tor (oes/suwogw) ‘(1se)d Kmqoewed pawns; 3305953 n :60 129 0 who 6.35 xfimocooa Son .6 oooE3253 0.0 To 0.0 N0 _..0 0.0 Ll L P LI L L n L h L»0.0 fl. \6 .\ onoo T ox .\ \Q x lo; \M. o .\\ \\\ r \ Aw \\ .\\\\ InfiN o 0u>uocoE>4 I wfiwucflom mo LmoEon\H .m.> .Q.m foes/suomguu) "Q's uonogAaQ pJopuoig 3>oofiE3 n... :8 130 0 QB 8%: EEOQ Son .5 $9.52 0.00” o._om 0._om o._o\. 0.Loo 0.Lom 0.“: o._on 0._0N o.Lo_ 0.0. 00 03302953 I 002202 upo 202532 .m.> zHZDM No NlWflS umg Lumugugw 131 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. onozaEz H :00 I 132 mmoo moon D ocoLnEoE $9320 00 >920 cozo>zo< or b [P 8.3 8%: Ao_oE\.ooxv .00 o_ m b L F b b b In P n P O ./ TTTITTTTTITjiIITrIrTfiWII AmcoLaEmz wLm>HoLovom .m.> flammovom [0 C) '— l0 O N mm. (elow/looy) ‘03 ”so 40 ABJeug uogioAgov 133 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 -3.8 145 146 pm 8:5 o mmoLooo mLEOLoQEoF 500 0:52:85 0.05 0.00 0.00 0.0a. 0.0m, 0.0m o.o~ 0.0 L L r L _ L L L Hi L .VII b i? if r'!.'|a-llll IIII|II III-II" ,'|l| muc0E02 00002 2u0m 02 3 “0200802. 3 seerep SOUSJBHIQ emimedwei einlosqv 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 189 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 48 49 50 51 52 53 54 55 56 D Line# 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 88 89 90 91 92 93 94 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 07-20-87 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 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 D Line# 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 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 142 143 144 '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 2 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 D Line# 1 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 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 ' 187 188 189 '190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 D Line# 1 223 224 225 226 227 228 229 230 231 232 233 193 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') 234 235 236 ‘237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 D Line# 279 280 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# 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 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. 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