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MICHIGAN STATE UNIVERSITY
EAST LANSING, MICI-I 48824-1048

This is to certify that the
thesis entitled

TEMPERATURE CONSIDERATIONS FOR A WIRELESS
IMPLANTABLE MEMS PRESSURE SENSOR

presented by

ROBERT DOYLE CABLE III

has been accepted towards fulfillment
of the requirements for the

MS. degree in MECHANICAL ENGINEERING

 

 

 

12m, 74424 fizz 200%

Date

MSU is an Affirmative Action/Equal Opportunity Institution

PLACE IN RETURN Box to remove this checkout from your record.
To AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

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6/01 cJClRC/DatoDuopGS—pJS

 

TEMPERATURE CONSIDERATIONS FOR A WIRELESS IMPLANTABLE MEMS
PRESSURE SENSOR

By

Robert Doyle Cable III

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
MASTER OF SCIENCE
Department of Mechanical Engineering

2004

ABSTRACT
TEMPERATURE CONSIDERATIONS FOR A WIRELESS IMPLANTABLE MEMS
PRESSURE SENSOR
By

Robert Doyle Cable III

Elevated Intraocular Pressure (IOP) is the main risk factor associated with
glaucoma. A continuous IOP monitoring system is being developed as a research tool to
study glaucoma and ultimately reduce the number of people suffering from glaucoma
related blindness. The main component of the system is a MEMS pressure sensor. The
sensor, based on a RLC circuit, utilizes capacitive sensing and is powered by wireless
telemetry, a requirement for implantation in the eye. The temperature range of the
sensor’s environment is investigated using a finite element model of the eye and by
impinging an air jet with varying velocities, temperatures, and relative humidities on the
eye of a cat. The sensitivity of the sensor and its associated circuit elements to
temperature changes is examined. This research confirms that IOP readings are sensitive
to temperature variations in the sensor’s environment and further demonstrates the

potential of the sensor to record temperature independent of pressure.

This thesis is dedicated to my family who made many sacrifices while supporting me
financially and mentally through all my years of schooling, and to my friends who urged
me to never quit and reminded me of the light at the end of the tunnel. I would not have

come this far without you.

iii

ACKNOWLEDGEMENTS

I would like to express my thanks to Dr. John R. Lloyd for his patience and

guidance as my advisor. My master’s committee members Dr. Arthur J. Weber and Dr.

Timothy A. Grotjohn provided a great deal of assistance in my research.

This work was funded in part by Alcon Incorporated.

iv

TABLE OF CONTENTS

LIST OF TABLES .................................................................................. vii

LIST OF FIGURES .................................................................................. ix

NOMENCLATURE ............................................................................... xiii

INTRODUCTION .................................................................................... 1
CHAPTER 1

INTRODUCTION .................................................................................... 1

1.1 Glaucoma Background .................................................................. 1

1.2 Currently Available Glaucoma Tests ................................................. 2

1.3 IOP Sensor as a Superior Glaucoma Research Tool ................................ 3
CHAPTER 2

SENSOR INFORMATION ......................................................................... 5

2.1 Description of Pressure Monitoring System ......................................... 5

2.2 Overview for Determining IOP ....................................................... 8

2.3 Description of how the System Works ............................................. 11

2.4 Location of Implantation .............................................................. 26
CHAPTER 3

TEMPERATURE AND PRESSURE CONSIDERATIONS ................................. 29

3.1 Fabrication .............................................................................. 29

3.2 RLC Considerations ................................................................... 30

3.2.1 Resistor Considerations ................................................... 30

3.2.2 Inductor Considerations ................................................... 48

3.2.3 Capacitor Considerations .................................................. 55

3.3 Cavity Pressure Considerations ...................................................... 66
CHAPTER 4

EYE CONSIDERATIONS ........................................................................ 75

4.1 Eye Models Available in Literature ................................................. 75

4.2 Heat Transfer Model of the Human Eye ............................................ 80

4.3 Cat Testing .............................................................................. 83

4.4 Simulation Comparison to Cat Testing ............................................. 89
CHAPTER 5

FUTURE WORK .................................................................................... 97

5.1 Sensor .................................................................................... 97

5.2 Extraocular Components .............................................................. 98

5.3 Chamber Testing ....................................................................... 98

5.4 Implantation ........................................................................... 101

CHAPTER 6
SOCIAL AND ETHICAL CONSIDERATIONS ............................................. 103
CHAPTER 7
CONCLUSIONS .................................................................................. 1 05
BIBLIOGRAPHY ................................................................................. 108

vi

LIST OF TABLES

Chapter 2. Sensor Information

Table 2.1 Plate Spacing, Capacitance and Natural Frequency ....................... 23
Table 2.2 Diaphragm Properties and Dimensions .................................... 24
Table 2.3 Pressure Limits and Characteristics .......................................... 25

Chapter 3. Temperature and Pressure Considerations

Table 3.1 Sensitivities of Resistor models .............................................. 38
Table 3.2 Additional Capacitance Effects on Natural Frequency Range ........... 51
Table 3.3 fr , Operating Range of the Sensor .......................................... 53
Table 3.4 Inductance Equation Parameters ............................................. 54
Table 3.5 Constant Thermal Conductivities ............................................ 69
Table 3.6 Thermal Conductivity of Air ................................................. 69
Table 3.7 FEM Analysis Results ......................................................... 73

Chapter 4. Eye Considerations

Table 4.1 Steady-state Temperatures (Control Values) ............................... 76
Table 4.2 Steady-state Temperatures (Increased Ambient) ........................... 76
Table 4.3 Steady-state Temperatures (Increased Body-core) ........................ 77
Table 4.4 Corneal Surface Temperatures for 2100 W/m2 Incident Irradiation ..... 78

Table 4.5 The Effect of Ambient Temperature on Temperature Rises2 Experienced
in the Eye Exposed to an Incident Irradiance Of 1250 W/m .....79

Table 4.6 Experimental Rabbit Data ..................................................... 80

Table 4.7 Tissue Thermal Conductivities ............................................... 81

vii

Table 4.8 Cat Testing Initial Conditions ................................................ 86

Table 4.9 Cat Testing Results ............................................................ 86
Table 4.10 Constants for Nust Correlation .............................................. 90
Table 4.11 Jet Properties .................................................................. 92
Table 4.12 Simulation Comparison to Cat Testing .................................... 95

viii

LIST OF FIGURES

Chapter 1. Introduction
Figure 1.1 Representation of the Eye ..................................................... 1

Chapter 2. Sensor Information

Figure 2.1 Pressure Sensor with Overall Dimensions .................................. 5
Figure 2.2 Base of the Sensor .............................................................. 6
Figure 2.3 Data Acquisition and Processing Device .................................... 7
Figure 2.4 Process for Determining IOP ................................................ 10
Figure 2.5 Equivalent Circuit ............................................................. 11
Figure 2.6 Current, Voltage Relationship - Resistor .................................. 12
Figure 2.7 Current, Voltage Relationship — Capacitor ................................ 13
Figure 2.8 Current, Voltage Relationship — Inductor ................................. 14
Figure 2.9 RLC Phasor Diagrams ........................................................ 14
Figure 2.10 Phasor Diagram of Impedance for the Internal Circuit ................. 15
Figure 2.11 Internal Component Voltage Drops vs. Frequency ...................... 17
Figure 2.12 Equivalent Circuit During Mutual Inductance ........................... 19
Figure 2.13 External Voltage Drop vs. Frequency ..................................... 20
Figure 2.14 External Current vs. Frequency ............................................ 21
Figure 2.15 Sensor Location .............................................................. 26
Figure 2.16 Resonance Curves for Coupled Circuits .................................. 27

Chapter 3. Temperature and Pressure Considerations

Figure 3.1 Effect of Frequency on Skin Depth ......................................... 31

ix

Figure 3.2 Skin Depth vs. Frequency .................................................... 32

Figure 3.3 Resistance vs. Frequency ..................................................... 33
Figure 3.4 Resistance vs. Temperature .................................................. 34
Figure 3.5 Line Width Variation of Coil for Different Temperatures ............... 36
Figure 3.6 R(CTE) vs. Temperature ..................................................... 37
Figure 3.7 Resistance Variations with Temperature ................................... 37
Figure 3.8 Resistance Change on Internal Peak Current Curve ...................... 39
Figure 3.9 Resistance Change on Internal Voltage Curve ............................ 39
Figure 3.10 Resistance Change on External Peak Current Curve ................... 40
Figure 3.11 Resistance Change on External Voltage Curve .......................... 41
Figure 3.12 Internal Circuit Phase Angle ............................................... 42
Figure 3.13 Resistance Change on Internal Phase Curve ............................. 42
Figure 3.14 External Circuit Phase Angle .............................................. 43
Figure 3.15 Resistance Change on External Phase Curve ............................ 44
Figure 3.16 Instantaneous Power in Internal Circuit .................................. 45
Figure 3.17 Pms in Internal Circuit ...................................................... 46
Figure 3.18 Thermal Noise vs. Temperature ............................................ 47
Figure 3.19 Dip Measurement from Re,“ Voltage Profile ............................. 48
Figure 3.20 Sensor Equivalent Circuit Showing Additional Capacitance .......... 50
Figure 3.21 The Q Variation of an Inductor with Frequency ........................ 52
Figure 3.22 Layout for a Square Spiral Inductor ....................................... 54
Figure 3.23 Inductance vs. Temperature ................................................ 55
Figure 3.24 Hinged Plate Capacitor Model ............................................. 56

Figure 3.25 Capacitance Derivation Schematic ........................................ 56

Figure 3.26 Comparison of Capacitance Models ....................................... 58
Figure 3.27 Capacitance vs. Cavity Temperature ....................................... 59
Figure 3.28 Model of a Spherical Segment ............................................. 60
Figure 3.29 C8(p-v) vs. Plate Spacing .................................................... 62
Figure 3.30 C803-“ vs. Pressure .......................................................... 63
\
Figure 3.31 CT vs. Temperature ........................................................... 64
Figure 3.32 FEM Model .................................................................. 67
Figure 3.33 Close-up of Cavity ........................................................... 67
Figure 3.34 Entire Meshed Model ....................................................... 70
Figure 3.35 Meshed Cavity ............................................................... 71
Figure 3.36 Temperature Distribution in the Sensor .................................. 72
Figure 3.37 Cavity Temperature Distribution .......................................... 72
Figure 3.38 Cavity Pressure vs. Temperature ........................................... 74

Chapter 4. Eye Considerations

Figure 4.1 FEM Human Eye Model ..................................................... 81
Figure 4.2 Temperature Distributions in the Eye ....................................... 83
Figure 4.3 Test Rig for Cat Testing ...................................................... 84
Figure 4.4 Hypodermic Needle Thermocouple Probe ................................. 85

Figure 4.5 Effect of Jet Relative Humidity on Ocular Temperature Changes. . ....87

Figure 4.6 Effect of Jet Velocity on Ocular Temperature Changes .................. 88
Figure 4.7 Nusselt, Reynolds Numbers From Cat Testing ........................... 93
Figure 4.8 Region for Temperature Recording from Simulations ................... 94

xi

Chapter 5. Future Work

Figure 5.1 Top View of Sensor ........................................................... 97
Figure 5.2 Bottom View of Sensor ...................................................... 98
Figure 5.3 Pressure Chamber ............................................................ 100
Figure 5.4 Pressure Chamber Close-up ................................................ 101

xii

Ce(P-T)

Ca(P-V)

Iint

NOMENCLATURE

Overlapping Capacitor Plate Area (m2), Cross-sectional Area of a
Conductor (m )

Nominal Overlapping Capacitor Plate Area (m2)

Temperature Dependant Overlapping Capacitor Plate Area (m2)
Bandwidth (Hertz)

Capacitance (Farads)

Equivalent Capacitance (Farads)

Hinged Plate Capacitance (Farads)

Capacitance between Inductor Windings (Farads)

Average Plate Spacing Capacitance (F arads)

Silicon Recess to Inductor Capacitance (Farads)

Temperature Dependant Capacitance (Farads)

Capacitance as a Function of Temperature Dependant Pressure (Farads)

Capacitance as a Function of Volume Dependant Pressure (Farads)

Impingement Surface Diameter (Meters), Eye Diameter (Meters)
Young’s Modulus (Pascals)

Current (Amps)

Sensor Current (Amps)

xiii

LET

LMON

Current Amplitude (Amps)

Current through Resistor (Amps)

Inductance (Henries), Length of a Conductor (Meters), Sensor Cavity
Width (Meters), Nozzle-to-surface Distance (Meters)

External Circuit Inductance (Henries)

Sensor Inductance (Henries)

Line Height of Inductor (Meters)

Temperature Dependant Inductor Line Height (Meters)

Line Length of Inductor (Meters)

Temperature Dependant Inductor Line Length (Meters)

Calculated Inductance (Henries)

Nominal Length (Meters)

Line Width of Inductor (Meters)

Temperature Dependant Inductor Line Width (Meters)

Mutual Inductance (Henries)

Stagnation Point Nusselt Number

Pressure (Atmospheres)

Partial Pressure of Air (Pa)

Pressure of Fluid Mixture (Pa)

xiv

Pext

Pint

Partial Pressure of Steam (Pa)

Pressure on External Diaphragm Surface (atm, mmHg)

Pressure on Internal Diaphragm Surface (atm, mmHg)

Root Mean Square Power (Watts)

Ratio of Inductor Reactance to Resistance

Resistance (Ohms)
Rayleigh Number
Reynolds Number

External Circuit Impedance (Ohms)

Sensor Resistance (Ohms)

Nominal Resistance (Ohms)

Temperature Dependent Resistance (Ohms)

Universal Gas Constant equal to 82.05 (L‘atm)/(kmol"‘K)

Temperature (°C, K)

Voltage (Volts), Volume (Liters), Fluid Velocity (m/s)

Sensor Cavity Volume (Liters)

Root Mean Square Noise Voltage (Volts)

Voltage Amplitude (Volts), Nominal Sensor Cavity Volume (Liters)

Voltage Drop across Resistor (Volts)

XV

Vseg

dAVG
dOUT

dyi.

Volume of a Spherical Segment (m3)

Side Length of Square Electrode (Meters)

Mole Fraction of Air

Mole Fraction of Steam
Capacitive Reactance (Ohms)
Inductive Reactance (Ohms)

Induced Reactance (Ohms)

Impedance (Ohms)

External Circuit Impedance (Ohms)

Internal Circuit Impedance (Ohms)

Half of the Diaphragm Side Length (Meters)

Capacitor Plate Spacing (Meters), Nozzle Diameter (Meters)

Average Spiral Diameter of Inductor (um)
Outer Spiral Diameter of Inductor (um)
Silicon Recess to Inductor Spacing (Meters)
Natural Frequency (Hertz)

Inductor Self Resonant Frequency (Hertz)

Plate Spacing for Zero Deflection (Meters), Gravity ( m/sz)

Diaphragm Thickness (Meters)

xvi

Nominal Electrode Height (Meters)
Convection Coefficient (Wm-1K4)
Stagnation Point Convection Coefficient (Wm'lK-l)

Unconsu'ained Electrode Height (Meters)

Mutual Inductance Coupling Coefficient, Boltzmann’s Constant equal to
1.38E-23 (J/K), Thermal Conductivity (W/m‘K)

Air Thermal Conductivity (W/m*K)
Steam Thermal Conductivity (W/m‘K)

Fluid Mixture Thermal Conductivity (W/m‘K)

Number of Moles (Kilomoles), Number of Inductor Spiral Turns

Inductor Line Spacing (um), Spacing between Lowest Point of Hinged
Plate and Electrode (Meters)

Time (Seconds)

Diaphragm Center Deflection (Meters)
Total Flux in Coil 1

Flux from Coil l to Coil 2, Thermal Conductivity Mixture Coefficient
equal to 0.8153

Total Flux in Coil 2

Flux from Coil 2 to Coil 1, Thermal Conductivity Mixture Coefficient
equal to 0.7257

Dynamic Viscosity Mixture Coefficient equal to 0.8390

xvii

LI’21

(17740

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“R

“T

as?

“ST

141

“2

Dynamic Viscosity Mixture Coefficient equal to 0.7438

Inductor Layout Dependant Coefficient, Thermal Diffusivity (mZ/s)

Inductor Layout Dependant Coefficient, Expansion Coefficient for an
Ideal Gas (K‘l)

Linear Coefficient of Thermal Expansion for Glass equal to 3.25E-6

-1
(°C ) 1
Linear Coefficient of Thermal Expansion for Gold equal to 14.2E-6 (°C- )

Temperature Coefficient of Resistance (°C'1)
Linear Coefficient of Thermal Expansion (°C-1)

Pressure Coefficient of the Dielectric Constant of Air equal to 100E-6
-1
(°C )

Temperature Coefficient of the Dielectric Constant of Air equal to 2E-6
-1
(°C )

Skin Depth (Meters)
Dielectric Constant of Glass equal to 44.25 (pF/m)

Dielectric Constant of Free Space equal to 8.85E-12 (F/m)

Relative Dielectric Constant

Phase Angle (Radians), Relative Humidity

Permeability of a Metal (H/m), Dynamic Fluid Viscosity (Pa*s)
Air Dynamic Viscosity (Pa*s)

Steam Dynamic Viscosity (Pa* 3)

xviii

I‘m

Ilr

Fluid Mixture Dynamic Viscosity (Pa*s)
Permeability of Free Space equal to 41tE-7 (H/m)
Relative Permeability of a Material

. . . . . . 2
Porsson’s Ratio, Kinematic Viscosrty (m /s)

Sensor Phase Angle (Radians), Angle between Hinged Plate and
Horizontal (Radians)

Resistivity of a Conductor (0*m), Fluid Density (kg/m3)
Diaphragm Intrinsic Stress (Pascals)
Angular Frequency (Radians/ Second)

Natural Frequency (Radians/ Second)

xix

Chapter 1. Introduction

1.1 Glaucoma Background

Glaucoma is a group of eye diseases that slowly steals sight, often without
warning or symptoms [1]. Loss of vision results from damage to the optic nerve that
carries the images we see to the brain. Certain groups of people are at higher risk for
developing glaucoma than others. These groups include African-Americans, Asian-
Americans, persons over the age of 60, those with a family history of glaucoma, people
who have suffered blunt trauma or a penetrating injury to the eye or head, and finally
people with a history of steroid use. Although it is possible to experience vision loss
fi'om glaucoma with “normal” intraocular pressure (IOP), between 12-22 mmHg,
elevated IOP is the main risk factor associated with the disease [1]. IOP is maintained by
a balance in the production and drainage of aqueous humor from the anterior chamber of

the eye, refer to Figure 1.1.

 

Sclera
\ 9:- \n\
f: Cornea
' Macula
Pupil
Vitreous humor

 

 

 

Figure 1.1 Representation of the Eye

Elevated IOP can range from moderately high pressures over 22 mmHg to extreme levels
of 45-50 mmHg [2].

The two main types of glaucoma are primary open angle glaucoma (POAG) and
angle closure glaucoma. POAG is the most common form and affects over 3 million
Americans [1 ]. This occurs when the drainage canals for the aqueous humor become
clogged causing IOP to rise [1]. POAG develops slowly, sometimes without noticeable
sight loss for many years. If caught and treated early, POAG usually responds well to
medications. Angle closure glaucoma, also known as acute glaucoma or narrow angle
glaucoma, occurs when the drainage canals get blocked and IOP rises very rapidly [1].
Blocking results fiom the outer edge of the iris bunching up over the drainage canals [1].
This happens when the pupil enlarges too much or too quickly. Surgery to remove the
outer portion of the iris is usually successful and long lasting. Currently there is no cure
for glaucoma. It is a chronic disease that must be treated for life.

1.2 Currently Available Glaucoma Tests

Regular eye check—ups include two routine glaucoma tests, tonometry and
ophthalmoscopy [l ]. The tonometry test measures IOP. Typically drops are used to
numb the eye. The doctor then uses a tonometer to measure the pressure inside the eye.
Ophthalmoscopy examines the inside of the eye, specifically the optic nerve [1]. In a
darkened room, the doctor uses an ophthalmoscope to inspect the shape and color of the
Optic nerve [1]. If the IOP is not within the normal range, or if the optic nerve looks
unusual, two special tests may be performed. These tests are perimetry and gonioscopy.

During perimetry, the patient looks straight ahead and indicates when a light passes their

peripheral vision. Gonioscopy checks whether the angle where the iris meets the cornea
is open or closed, indicating if either open angle or closed angle glaucoma is present.
While accurate, there are several drawbacks to these tests. Only a single reading at an
instant in time is recorded in a controlled environment. Furthermore, these readings are
usually separated by long periods of time between visits to the physician’s office. A
patient’s IOP changes on a daily basis. Fluctuations in IOP around an average value
occur due to changes in activity and environment [3]. It is crucial to monitor IOP on a
continuous basis to immediately administer treatment at the onset of high IOP and
prevent permanent damage that could occur between check-ups. A research tool is
needed to better understand what affects IOP and the role it plays in developing
glaucoma.
1.3 IOP Sensor as a Superior Glaucoma Research Tool

The sensor presented in this thesis was designed by Goodall and holds many
advantages over current glaucoma tests [4]. First, the sensor will monitor IOP on a
continuous basis. This will allow for immediate treatment to prevent permanent damage
and vision loss as discussed in the previous section. This continuous monitoring will
provide valuable information to researchers regarding IOP and the development of
glaucoma. It is unknown whether peak IOP levels, cumulative IOP over a period of time,
average IOP levels, or high and low IOP differential levels have the greatest effect on the
eye. Continuous monitoring with a time record will also allow researchers to determine
how a patient’s activities, lifestyle and environment affect their IOP.

The overall dimensions of the cubic sensor are 2 mm x 2 mm x 1 mm. The sensor

will be powered by wireless telemetry, requiring no batteries. Along with the small size,

this allows for the sensor to be implanted in the patient’s eye without affecting vision or
comfort. The sensor is designed to measure pressures in the range of 0 to 60 mmHg,
covering the limits in IOP a patient may experience. However, the design of the sensor
can be altered to measure a different range of pressures for other applications.

Due to the design of the sensor, readings from the IOP monitoring system will be
sensitive to changes in temperature. This work investigates possible temperatures the
sensor may experience while implanted in the eye. Temperature fluctuations in the
sensor caused by the sensor’s environment and operation will be used to determine the

sensitivity of the pressure readings to these changes.

Chapter 2. Sensor Information

2.1 Description of Pressure Monitoring System

The pressure monitoring system discussed in this thesis consists of three
components. The first component of the system is the implantable pressure sensor. The
pressure sensor has a height of 1 mm and a width of 2 mm and represents a hollow sealed

cube as shown in Figure 2.1.

 

 

 

 

TDP UORK

 

Figure 2.1 Pressure Sensor with Overall Dimensions

The exact length of the sensor will be determined during the fabrication of the final batch
of sensors. The overall length is expected to be approximately 3 mm. The body of the
sensor will contain two holes through which sutures will be threaded during implantation.

Exact hole dimensions and positioning will also be determined during final batch

fabrication. The base of the cube consists of a square spiral inductor and an electrode, as

shown in Figure 2.2.

 

Figure 2.2 Base of the Sensor

The lid of the sealed cube is a 4 pm thick diaphragm. This diaphragm is also an
electrode, creating a capacitance with the base of the cube. The diaphragm and electrode
act as a variable capacitor, dependent upon the deflection of the diaphragm. Taking into
account the resistance in the inductor, the whole cube can be modeled as a resistor-
inductor-capacitor (RLC) circuit.

The second component of the system is the data acquisition and processing device
that will remain outside the patient’s body. This device contains a larger RL circuit. The
external device will be battery powered. When placed in close proximity to the
implanted sensor, the external inductor will induce a current in the sensor’s inductor, thus

eliminating the need for a physical connection between the two. The external inductor

will be housed in a patch to be placed on the side of the patient’s head near the eye. The
patch will be connected to a unit containing the rest of the circuitry. This unit may be
worn in the patient’s shirt pocket or attached at the waist. Unlike the sensor, the external
circuit contains an actual resistor. Information about the sensor will be obtained by
interrogating this element. The data acquisition and processing device is shown aligned

with the sensor in Figure 2.3.

 
    

Circuit Sensor
Inductive
Coupling
(Wireless)

 
 
    
 
   

Data Acquisition and
Processing Device

I
e I

Extraocular

 

Intraocular

Figure 2.3 Data Acquisition and Processing Device
The third component of the system is a central database that will maintain a time
record Of the patient’s IOP measurements. This will allow for correlations between the
patient’s lifestyle, treatment strategies and changes in IOP. This component can be
located in the patient’s home. The patient can download logged information from the
data acquisition and processing device to this component at daily or perhaps weekly
intervals. There is also the possibility for the central database to send these records to the

physician over the intemet or through phone lines.

An extensive description of the sensor design and fabrication is provided by

Goodall [4].

2.2 Overview for Determining IOP

Measuring IOP is not an easy task and must be done in several steps. The
external RL circuit is powered by an oscillating sinusoidal voltage source. This voltage
is frequency dependant and can assume a wide array of frequencies. The sinusoidal
current produced by the voltage source, when pmsing through the external inductor,
induces an equivalent current in the internal inductor all at the same frequency. The
opposition to the flow of current in the internal RLC circuit differs for the types of
components. For resistors, this opposition is independent of frequency and is called the
resistance. The opposition to current flow due to inductors and capacitors is frequency
dependant and known as reactance. The overall opposition to the flow of current in a
circuit is known as the impedance and is the sum of the resistance and the reactance. Due
to the nature of the reactance for the inductor and capacitor, they will cancel each other
out at a particular frequency known as the natural frequency. The natural frequency is
dependant on the inductor and capacitor values for the circuit. The cancellation that
occurs at the natural frequency results in a local minimum for the internal Circuit’s
impedance. When the external and internal RLC circuits are placed in close proximity,
the inductive coupling induces an additional reactance in the external circuit. This
reactance is at a local maximum for the local minimum impedance of the internal circuit

at the natural frequency.

With the internal circuit inaccessible, implanted in the body, it is therefore
necessary to interrogate components of the external circuit. There is a finite voltage drop
along the closed-loop path of any circuit. With the induced reactance in the external
circuit at a local maximum, this leaves less voltage to be dropped across the external
resistor and inductor. When the internal circuit is at the natural fi'equency, the voltage
drop across the accessible external resistor will therefore be at a local minimum.
Comparatively, the current through the external resistor, which can be determined from
the voltage drop, will also be at a local minimum. By sweeping the voltage source
through a range of frequencies and observing the voltage drop profile across the external
resistor, the natural frequency of the internal circuit can be determined.

The natural frequency of the internal circuit is dependent on the Circuit’s inductor
and capacitor values. Knowing the natural frequency and the inductor’s fixed value, it is
possible to determine the value of the capacitance at that point in time. The capacitance
created by the fixed electrode and flexible diaphragn can be modeled as a parallel plate
capacitor. The capacitance is dependent on the dielectric constant of the material
between the plates, the Spacing between the plates and the area of the plates. The sealed,
hollow cube form of the sensor contains air at atmospheric pressure, the dielectric
constant for which is known. The dimensions of the diaphragm lid and electrode plate
are also known analogous to the area of the parallel plates. Knowing the capacitance,
along with the other parameters, it is possible to determine the Spacing between the plates
in the capacitor model.

Equations governing the vertical deflection of the center of a diaphragn subject to

a uniform differential pressure are known. These equations are dependant on diaphragn

dimensions and properties. With these dimensions and properties known, along with the
center deflection of the diaphragn from the capacitor model, the differential pressure
applied to the diaphragm is known.

The differential pressure is the difference between the pressures applied at the
outer and inner surfaces of the diaphragn. Knowing the differential pressure from the
deflection equation and the pressure inside the sensor, the absolute pressure in the eye
(IOP) can be determined. The process of obtaining IOP readings from the implanted

sensor by interrogating the external device is shown in Figure 2.4.

 

Voltage Profile across Rexternal

ll

Natural Frequency of Internal Circuit

fl

Capacitance of Variable Capacitor

fl

Deflection of Sensor Diaphragn

ll

Differential Pressure across Diaphragn

fl

IOP

 

 

 

Figure 2.4 Process for Determining IOP

10

2.3 Description of how the System Works

Section 2.2 provided an overview of how the IOP monitoring system works; this
will now be covered in detail. The equivalent circuit for the data acquisition and
processing device and the implantable sensor is shown in Figure 2.5. The ovals joining

the circuits represent the inductive coupling.

Vsource ‘5 C (Diaphragm)

 

 

 

 

Figure 2.5 Equivalent Circuit

The inductor in the internal circuit, Lint, represents the square spiral inductor on the glass

substrate. The internal resistor, Rim, represents the resistance associated with the

inductor coils. The capacitor in the internal circuit, C, represents the variable capacitor
formed by the flexible silicon diaphragn and the fixed gold electrode. As mentioned in
Section 2.2, the external circuit is powered by an oscillating sinusoidal voltage source of

the form

v = Vosin((ot) (2-1)

where V0 is the amplitude of the voltage, to is the angular frequency, and t is time. This

voltage will create sinusoidal current in the external circuit of the form

11

I = losin(mt + 4)) (2.2)

where I() is the amplitude of the current, and 4) is the phase angle between the current and

the impressed voltage in radians.

When circuit elements are connected in series, as is the case for our external and
internal circuits, the current in all of the elements must be the same. However, the
voltage drop across the elements will be out of phase with the current to varying degees
depending on the type of element.

In a resistor, the opposition to the flow Of current through that element is
independent of the current frequency. This opposition is called resistance (R) and has the
unit of Ohms (Q). The instantaneous voltage required to force the alternating current
(AC) through a resistor is IR. Figure 2.6 shows the relationship between the voltage and

current through a resistor.

 

,1
l
i
l
l

 

:3 - Current-R ii
Voltage-RI};

 

 

 

 

 

 

Figure 2.6 Current, Voltage Relationship — Resistor

The maximum voltage drop across the resistor is 10R and is in phase with the current.

12

In capacitors and inductors, the opposition to the flow of current through that
element is dependent upon the current frequency and is called reactance. Reactance also

has units of Ohms. The reactance for capacitors and inductors is defined as

l
X =_ 2.3
C (0C ( )
and
XL = (0L (2.4)

where C is the capacitance in Farads (F) and L is the inductance in Henries (H). The
instantaneous voltage required to force the current through a capacitor is é—Ildt . Figure

2.7 shows the relationship between the voltage and current through a capacitor.

 

 

Voltage - C"—
- - - Current - C

 

 

 

 

Amplitude

 

 

 

 

 

 

 

Figure 2.7 Current, Voltage Relationship — Capacitor

The maximum voltage drop across a capacitor is IOXC and will occur later than the

maximum current, lagging by 90° [5]. The instantaneous voltage required to force the

13

current through an inductor is L Z—f . The relationship between the voltage and current

through an inductor is shown in Figure 2.8.

 

 

 

 

 

 

 

 

 

 

I’M—“TTHHHTWT _! ‘T 'l r VT ”7
l 15 l
l i
l 10 «A——~— 7—H“ *——-—-~ , l
‘\‘ '1' I
. 5 ~ “—1—— 4— —— a l
g \‘ l _!
,3 t - - -Current-LI'
a 0 ' mmrrr'r‘mrrrrr I‘rrr—rrr'grrrrm VoItage-L H
g 5 D '0 1- v- ‘N N 8 ('9) 8'? Ito) I?) i
- «l- ————— +.~.—___—’__._4_l_—__L_ _._____

I. “\ I"
l l
l -15 l

l

l Time I
1

Figure 2.8 Current, Voltage Relationship -— Inductor

The maximum voltage drop across an inductor is IOXL will occur before the maximum

current, leading by 90° [5]. Phasor diagams are a convenient way to illustrate the

voltage, current and resistance, reactance phase relations between components. Phasor

diagrams for RLC components are shown in Figure 2.9.

 

 

IXL IR XL
90° I 90° R
+~> >—
IXC -90° Xc -90°
Figure 2.9 RLC Phasor Diagarns

The impedance (Z) is the overall resistance to the flow of current in a circuit. The

impedance of the external circuit (Zen) can be found by adding the resistance of Rext and

14

the reactance of Lext. The resistance and reactance of the series components are out of

phase and must be added as vectors. The impedance for the external circuit is

 

2,,“ = Jsz + Xian (2.5)
The impedance for the internal circuit (Zim) can be found by adding the resistance of

Rim, along with the reactance of Lint and C. The impedance for the internal circuit is

 

Zint =T/Em2 +(XLint ‘Xclz (2-6)

Figure 2.10 shows the phasor diagam for solving Zim-

 

 

Figure 2.10 Phasor Diagam of Impedance for the Internal Circuit

 

The angle 0 is defined as
0=tan~l(XLint ”XC] (27)
Rim

and represents the phase angle between the current and the impressed voltage for the
internal circuit in radians. Substituting equations 2.3 and 2.4 into equation 2.6, the

impedance of the internal circuit is a flmction angular frequency defined as

15

 

2
z...a.=Ja+(a. g) (2.8)

It can be seen by observing equation 2.8 that the inductive and capacitive reactance will

cancel out at a particular frequency. This frequency is known as the natural frequency

 

and is defined as
a) - 1 (2 9)
r " LIDIC .
in radians/second. A more convenient form of the natural frequency is defined as
1
f r = —— (2.10)

in cycles/second or Hertz (Hz). Due to the cancellation of the inductive and capacitive

reactance at the natural frequency, the impedance of the internal circuit will be resistive

only. With a fixed amplitude impressed voltage, this local minimum in Zim will result in

a maximum current flowing through the circuit according to
1 = _ (2.11)

With the current flowing through the circuit being maximized at the natural frequency,
the corresponding voltage drops across the circuit components will be maximized as well.

Figure 2.11 shows a simulated plot of the voltage drops across the circuit elements as a

function of frequency.

16

 

 

 

on
O

 

Voltage Drop (V)

oBSS

 

 

 

 

 

 

 

 

 

I
I '96 '9’ 18% (0' N's) (19 (I? (3’ (9' <56 '99 N”? N”?
I
I

Frequency (MI-12)

m-*_fl____,______ _ __ ___ -_ _ ‘..__ _ _,- _,,I

Figure 2.1] Internal Component Voltage Drops vs. Frequency
The component values used in this simulation are arbitrary and hence, the voltage drop
values are irrelevant. However, the natural fi'equency in this simulation is 136 MHz,
which is clearly indicated by the voltage peaks. If the elements in this circuit were

accessible, the natural frequency could be determined by observing a component voltage

drop in a frequency range of interest. With a fixed inductance for Lima the present value

of the variable capacitor could be established fi'orn the natural frequency. The internal
circuit will be inaccessible once implanted in the eye. Therefore, information about the
internal circuit must be obtained in such a way that does not require direct contact.

Once the sensor is in place, a connection is needed to power that circuit and
record data. For health and safety reasons, as well as comfort, that connection must be
wireless. Inductive coupling will provide that connection. When a current is passed
through a wire, a magnetic field is generated around that wire. For a current carrying
wire wound into a coil, in the case of an inductor, the magletic field lines are

concentrated and the flux is increased. When an AC current is passed through an

17

inductor, the flux generated increases and decreases sinusoidally with time just as the
current is varying. If another inductor is placed in close proximity to the primary
inductor, some of the magnetic field lines will pass through the secondary inductor.
According to Lenz’s law, the changing flux in the secondary inductor produces a current
in that inductor in such a direction as to oppose the flux that is causing it [5]. This is
known as mutual inductance. The produced current in the secondary inductor in turn
generates a flux that also threads through the primary inductor. When the two inductors
are not physically connected and air provides a path for the flux, it is known as an air-
core transformer. In this type of transformer, the inductors are said to be loosely coupled.

The coefficient of coupling of the two coils may be expressed as

k = “’12 = 4’21 (2,12)
‘Pl 4’2

where k is the coupling coefficient, CD] is the total flux in coil 1, CD12 is the flux from coil

1 that links to coil 2, (1)2 is the total flux in coil 2, and $21 is the flux from coil 2 that

links to coil 1 [5]. The mutual inductance for the two coils can be expressed in terms of
the two inductors as

M =k LimLex, (2.13)
where M is the mutual inductance [5]. When mutual inductance occurs, an additional

reactance is induced in the external circuit coupling the impedance of both circuits. This

reactance is frequency dependent and can be expressed as

18

XM(w)=La)Z.£t-)i (2.14)

where XM is the induced reactance in the external circuit [4]. The equivalent circuit

during mutual inductance is shown in Figure 2.12.

 

:5 c (Diaphragm)

 

 

 

Figure 2.12 Equivalent Circuit During Mutual Inductance

By substituting the impedance of the internal circuit into equation 2.14, the induced

reactance becomes

X M (w) = (“My 2 (2.15)
Jain + [mam - i]

With the additional induced reactance, the impedance of the external circuit when mutual

 

 

inductance occurs is

19

 

2
(0M
Zexr(0’)= R2,“ + wLex, + ( ) 2
2 I
R. + wL- ——~
\ l/mt ( mt ("CI )

At the natural frequency, the induced reactance and hence Zext reach a local maximum.

 

(2.16)

 

 

 

 

 

According to Kirchhoffs Voltage Law, the sum of all voltages through a loop must equal

zero. Therefore, the finite amount of voltage impressed on the circuit must be dropped

across its components. With XM maximized at the natural frequency, much of the

impressed voltage is spent on this reactance leaving a minimal amount to be dropped

across Rex]. Furthermore, according to equation 2.11, with a fixed amplitude voltage and
Zext maximized, the current flowing through the external circuit will be minimized. This
reinforces the fact that the voltage drop across Rext will hit a local minimum at the

natural frequency. Figure 2.13 shows the simulated voltage drop across Rext.

 

 

 

 

 

 

 

 

 

Figure 2.13 External Voltage Drop vs. Frequency

20

Again, the voltage drop values are arbitrary, but the voltage dip clearly indicates the

natural fiequency for this simulation, 136 MHz. The current through Rext can be inferred

from the voltage drop and is shown in Figure 2.14.

 

 

 

 

 

 

 

 

 

 

 

 

0.012
001 fr= 136 MHz * 5

g 0.008 .-
E 0.006 . FREE
3 W.
o o_oo4 --.___ _. _ _ _ L a.”____ a--. a ,_ L.__.-_L_.._.,__, _.

0.002 _—————— _VVV_,_. ..........

o I I I II Tr I II III II III II fl IIIIIIIIII ET I
§§§E§§§§§§§§§

Frequency (Ml-l2)

 

 

 

Figure 2.14 External Current vs. Frequency
The inductive coupling between the two circuits allows the internal circuit to be powered
without the use of batteries, allowing its miniscule size. The wireless connection makes
the IOP monitoring system safer and more comfortable to the patient. By sweeping the
voltage source through a frequency range determined by the limits of the variable
capacitor and exploiting the phenomenon of mutual inductance, the natural frequency of
the sensor can be determined by examining an accessible component of the external
circuit. With a known, fixed value for the sensor’s inductance, the present value of the
sensor’s variable capacitor can also be determined. Upon establishing a relationship
between the sensor’s capacitance and the deflection of the sensor’s diaphragn, the

differential pressure applied to the diaphragm will be known.

21

The capacitor formed by fixed, gold electrode and flexible, silicon diaphragn of
the sensor can be modeled as a parallel plate capacitor. The capacitance of such is given

as

_ goerA
d

C (2.17)

where C is the capacitance in Farads (F), 80 is the dielectric constant of free space =
8.85E-12 F/m, er is the relative dielectric constant of the material between the plates (1

for air), A is the overlapping area of the plates in m2, and d is the spacing between the

plates in m [6]. The overlapping area of the plates is determined by the area of the

smaller, fixed electrode. The side length of the square electrode is 537 um resulting in an

overlapping area of 2.88E5 umz. The deflection of the center of the diaphragn will be

used as the spacing between the plates in this model. The distance between the plates
varies between its zero deflection and full-scale deflection of 0.5 pm. This corresponds
to a spacing of 1.5 um and 1 um respectively. The capacitance is inversely proportional
to the plate separation with the maximum capacitance of 2.55 pF occurring at the
minimum spacing of 1 um and the minimum capacitance of 1.7 pF occurring at the

maximum spacing of 1.5 pm. Once the sensor’s natural frequency is determined fiom

the voltage profile across Rext and the fixed, known inductance of 800.2 nH is used in

equation 2.10, the sensor’s capacitance is known. Since the overlapping plate area and
dielectric constants are fixed, using the capacitance in equation 2.17 reveals the present
center deflection of the diaphragn. Capacitor plate spacing, capacitance and natural

fiequency infbrmation is listed in Table 2.1.

22

Table 2.1 Plate Spacing, Capacitance and Natural Frequency

 

 

 

Plate Spacing Capacitance Natural Frequency
1.5 pm 1.7 pF 136 MHz
1.0 um 2.55 pF 111 MHz

 

 

 

 

 

Once the center deflection of the diaphragn is known, a relationship is needed
between that deflection and the differential pressure across the diaphragn. The
diaphragn thickness is much smaller than the diaphragn side length. Therefore, the
diaphragn can be modeled as a membrane. The uniform pressure required to deflect a

membrane is given by

4 3 2
AP=—E—h2—7 4.2ofi+1.58-’1§—+3‘3'5—3§— (2.18)
(l—v )a h h E h

where AP is the differential pressure across the membrane in Pascals (Pa), E is the

Young’s Modulus is Pa, h is the diaphragn thickness in m, v is the Poisson’s ratio of the
diaphragn, a is one half of the diaphragn side length in m, W6 is the center deflection of
the diaphragn in m, and o is the intrinsic stress built into the diaphragn in Pa [4]. The

sensor’s diaphragn is heavily doped with boron to make it conductive. The introduction

of the boron impurities into the silicon wafer produces considerable residual tension in

the diaphragn [7]. It is common for the intrinsic stress in p++ silicon to be around 40
Mpa [8]. The presence of the tensile stress creates an increased stiffness in the
diaphragn requiring a geater pressure differential to cause the equivalent deflection in a

stress free diaphragn. Deterrrrining the material properties of the diaphragn is a

challenge. The materials used in MEMS applications are relatively thin and can have

23

properties that differ from their bulk form [9]. In addition, silicon is an anisotropic
material whose properties are orientation dependent. Fortunately, isotropic averages can
be used. Diaphragn dimension and material property values used in this analysis are

listed in Table 2.2.

Table 2.2 Diaphragm Properties and Dimensions

 

 

 

 

 

Young’s Modulus 160 GPa
Poisson’s ratio 0.05
h 4 um
a 275.5 pm
0' 40 MPa

 

 

 

 

Using the center deflection of the diaphragn, d, solved fiom equation 2.17 and plugging

it into equation 2.18 as we, the present differential pressure across the sensor’s diaphragm

is known.

The differential pressure across the sensor’s diaphragn is the difference between

the pressure acting on the external surface, Pext: and the internal surface, Pint, given as
AP=Pm -Plnt (2'19)
When implanted in the eye, Pext will be the IOP. As a result of anodically bonding the

silicon wafer and glass substrate, the pressure inside the cavity will be atmospheric (1
atrn). Knowing the present differential pressure across the diaphragn and the constant
atmospheric pressure inside the cavity, the present IOP is finally revealed from equation
2.19. When the pressures on either side of the diaphragn are equal, no deflection will

occur. For a cavity pressure of l atrn, an external pressure of 60 mmHg above

24

atmospheric is required to achieve the maximum diaphragm deflection of 0.5 pm,
according to equation 2.18. The pressure limits designed for the sensor and

corresponding characteristics are listed in Table 2.3

Table 2.3 Pressure Limits and Characteristics

 

 

 

 

Pext (IOP) Plate Spacing Capacitance Natural Frequency
0mmHg+1atm 1.5um 1.7pF 136MHz
60mmHg+1atm 1.0um 2.55pF 111MHz

 

 

 

 

In summary, the natural frequency of the sensor is found by observing the voltage
drop versus frequency profile for the external resistor. The instantaneous capacitance is
then determined from the natural frequency using equation 2.10. The center deflection of
the diaphragn is found from the parallel plate capacitor formula equation 2.17. Plugging
the center deflection of the diaphragn into equation 2.18 then reveals the differential
pressure across the diaphragn. With the pressure in the sensor cavity sealed with 1 atrn,
the instantaneous IOP level is finally known from equation 2.19. This system allows the
constant monitoring of IOP without any inconvenience or discomfort to the patient. With
constant monitoring, the patient can be alerted at the onset of dangerous IOP levels and
seek treatment to reduce those levels, thus preventing the irreparable damage that could
occur between visits to a physician. The constant monitoring will also provide valuable

information as to what factors affect IOP.

25

 

2.4 Location of Implantation
As shown in Figure 2.15, the sensor will be implanted in the anterior chamber of
the eye where IOP is maintained. To avoid interfering with the patient’s vision, the

sensor will be anchored between the iris and the cornea at the side of the eye.

 

Sc lera

 

 

 

 

Figure 2.15 Sensor Location

Sutures threaded through the laser-drilled holes of the foot will provide that anchor. The
sutures are 9-0 Vicryl with micro needles attached to their ends. The diameter of the
sutures is 5 um, less than the diameter of a human hair. Due to the size of the sensor and
the sutures, the operation will be performed under a dissecting microscope. Once in
place, the sensor will be oriented so that the plane of the diaphragn is parallel to the
plane of the vertical and tilted slightly at an angle towards the papillary axis. The air-
core of the coupling between the internal and external inductors generally provides a
loose coupling or low coupling coefficient seen in equation 2.12.

The proposed placement for the external circuit is affixed to the side of the
patient’s head near the eye by means of a patch. In order to have a distinguishable

voltage drop across the external resistor at the natural frequency, it is desirable to

26

maximize the induced reactance, XM, and hence the mutual inductance, M. As seen in

equation 2.13, the mutual inductance is dependant upon the two inductor values and the
coupling coefficient. While the inductor values are limited by the size of the sensor and
external device, the coupling coefficient can be increased by reducing the distance
between the inductors. This allows a greater flux to link the coils. Figure 2.16 shows the

resonance curves for coupled circuits with different amounts of mutual inductance.

\\

LDC }

Current, lint

     

 

 

 

fr
Frequency

Figure 2.16 Resonance Curves for Coupled Circuits [5]
Curve a represents a coupling value below the critical level. Curve b represents a
coupling value at the critical level, while curve c represents a coupling value above the
critical level. When the coupling is below the critical value, the response will be very
sensitive to changes in frequency but the coupling will be insufficient to produce the
maximum siglal in the internal circuit. If the coupling is increased until the critical value
is reached, the maximum signal will occur at the natural fi'equency. If the coupling is
increased past the critical value, the internal circuit will have a double resonance response
[5]. The sensor will be positioned in the eye close to the surface, and its coils will be

oriented parallel to those of the external inductor, thus permitting the maximum amount

27

of flux linkage. This will allow adequate coupling to produce a sufficient current in the
internal circuit and induced reactance in the external circuit. The coupling limitations
due to the proximity of the inductors and the air medium in which the flux is linked will
ensure, however, that a double resonance response does not occur. A single resonant

response is desired for ease of determining the sensor’s natural frequency.

28

Chapter 3. Temperature and Pressure Considerations

3.1 Fabrication

The IOP sensor is designed to have a cavity pressure of 1 atrn. This will ensure
the sensor diaphragm does not deflect when placed in an equal ambient pressure. The
anodic bonding process that seals the silicon wafer to the glass substrate typically occurs
at the elevated temperature of 400°C [10]. If this bonding is performed at atmospheric
pressure, the air in the cavity will contract as it cools to room temperature creating a sub-
atrnospheric cavity pressure. The pressure at which the anodic bonding takes place must
therefore be considered. Modeling the cavity air as an ideal gas, it behaves according to
the ideal gas law
PV = nRuT (3.1)
where P is the pressure in atmospheres (atrn), V is the volume in liters (L), n is the

L-atm

number of moles in kilomoles (kmol), Ru is the universal gas constant, 82.05 km 1 K ,
0 o

 

and T is the temperature in Kelvin (K) [11]. The conditions during bonding will be
considered state 1 and the ambient conditions of body temperature (37°C = 310K) and 1
atrrr will be considered state 2 in this analysis. The universal gas constant will not change
between states. In addition, the amount of air or number of moles will not change

between states once the bonding has formed an airtight seal. The two states can then be

related by
5111 ._. "Ru = 51.2. (3.2)
T1 T 2

29

The change in cavity volume as a result of contraction during the cooling to state 2 is
2.14E-11 L. Treating the volumes as equal, the ideal gas relation between the two states

simplifies to

P
4:1: (3.3)
T1 T2

All of the conditions are known except for the ambient pressure during the bonding.
Assuming a bonding temperature of 400°C (673K), the cavity should be sealed with air at
2.243 atrn. The higher pressure in the cavity will be reduced to l atrn once the air inside

contracts as it cools to body temperature. This will ensure the correct cavity pressure that

is required to accurately determine IOP.

3.2 RLC Considerations

3.2.1 Resistor Considerations

The equivalent circuit for the sensor contains a resistive element, Rim, to model

the resistance of the inductor coils. The resistance of a conductor is given as
L
R = — 3.4
p A ( )
where R is the resistance in O, p is the resistivity in (I‘m, L is the length of the conductor
in m, and A is the cross-sectional area of the conductor in m2 [12]. Based on the

dimensions of the inductor, the length is 88720 pm. The cross-sectional area is the
product of the line height, LH, and line width, Lw, which equals 72 umz. The resistivity

of gold is dependant on its purity and processing. The value used in this analysis is

2.40E-8 0*m [6]. The nominal resistance of the inductor is therefore 29.57 (2.

30

Previously, the resistance of the internal inductor coil has been treated as a
constant value. This is not entirely valid. As the fiequency of the alternating current
increases, the generated magnetic field and thus the current is concentrated closer to the

conductor surface, as shown in Figure 3.1.

- -
I -
Frequency
Figure 3.1 Effect of Frequency on Skin Depth [13]

I.
I

’

   

Current

 

The skin depth is defined as the distance from the metal surface beyond which the current

density falls below l/e (about 37%) of its original magnitude. Mathematically, the skin

depth is expressed as
p
6 = —— (3.5)
left!

where 6 is the skin depth in m, p is the resistivity of the metal in (I‘m, f is the frequency
in Hz, and p. is the permeability of the metal in Henries/meter (film) [13]. The

permeability of a material is its ratio of magletic flux density to magletic field strength,
fl = floflr (3.6)
where #0 is the permeability of free space (no = 41rE-7 H/m) and u, is the dimensionless

relative permeability of the material [6]. The relative permeability of gold is 0.99996
[14]. The permeability of gold is therefore 1.26E-6 H/m. The skin depth as a ftmction of

frequency is plotted in Figure 3.2.

31

k .._.___L‘___A ___,#4,#__._ __..-l___,4_...__'fl

Skin Depth VS Frequency I
I

 

 

 

 

 

 

 

 

 

 

.5. 9
S 8 ":7; ,___ —— ‘- --—'-‘ _ —’
7 _._.______~ _ _ f ___
E 6 ___.,__.__ _ __ _r/_. _._’: I
; jh’*““"" ‘ “"I
Q VITVVTVT-T-TvTVTATTT-—TiTH” I
a «WWI,
c 2 I? ‘ ’— - v- A ——~ i _. ’ .— W 4_ A_ ’— —_—-!'-~' 1 7 i
: H________-_w__ —"—————————I
m 0 ‘IT‘T‘I—T—T—T"T’T'TYTT_I—Y_VTT'"'T‘T'TWI‘I—IT'TT'T"‘I‘"TT’T’T‘TT‘T‘T‘TT‘fl T—jv‘I—W‘I—T‘T—I T‘T T—TI I
@§§§&§&¢dd§$§§&$$ I
' Frequency(MHz) I
I

 

 

Figure 3.2 Skin Depth vs. Frequency
Figure 3.2 indicates that the skin depth never drops below half of the inductor line height,
4.5 um. This does not mean that the skin effect is not present. This does show, however,
that the current density in the inductor will not fall below 37% of its original magritude
anywhere in the coil.
The resistance of the inductor coil must now be revised to include the skin effect.

The reevaluated resistance for the inductor coil is given as

p cm

LL
R(f)=
Lw§\II - e_L” ”5

where R(f) is the resistance in (2, p is the resistivity in (Pm, LL is the length Of the

 

inductor in In, Lw is the line width of the inductor in m, 8 is the skin depth in m, and LH

is the line height of the inductor in m [15]. The resistance is dependant on the skin depth,

more specifically the frequency of the alternating current. As the frequency increases,

32

the skin effect reduces the effective cross-sectional area of the inductor thus increasing

the resistance. The resistance as a function of frequency is shown in Figure 3.3.

 

 

- _ __ ______.2__-I

Resistance VS Frequency I

 

 

 

 

 

 

% ‘ITT’T'T—I T‘IT‘ITI' 7—7 V'TITT' T’T I‘lTlTI—T‘ -'*l T‘ITl-I— TAT I-l TI‘T I’I I_"T T—Y” T'I'H‘T‘l

100 104 108 112 116 120 124 128 132 136 140 144 148
Frequency(MHz)

 

 

Figure 3.3 Resistance vs. Frequency
The frequency of the alternating current is not the only thing that affects the
inductor coil resistance. The resistivity of most materials changes with temperature. For
moderate temperature changes (0-100°C) and assuming only p varies significantly, the
corresponding resistance change can be approximated by

RT = R0 (1 +aRAT) (3.8)
where RT is the temperature dependant resistance in (2, R0 is the known resistance

measured at some reference temperature in (2, (IR is the temperature coefficient of

resistance (T CR) in °C'1, and AT is the difference between the actual and reference

temperatures in °C [6]. A range of TCR values for gold can be found in handbooks. The
TCR value used in this analysis is 0.0083 °C'1 [6]. Figure 3.4 demonstrates the

dependence of resistance on temperature using 20°C as the reference temperature.

33

 

I __A_Ami,r,

I Resistance VS Temperature I

/ [6] I

88

O
I
I
I

 

 

 

 

I
I
I
I

 

8N8#
\
II,
I
I
I
l
I
I
I
I
I
I
I
I I

Resistance (Ohms)

 

o 'ITTI TTT ITTT l IT" l'T'TT rr—rr TTT I‘T'T—I'T—W—l PITT—I I-TI'ITTI'ITT I TTTT’TT'I ITTI'TTT'I'TTTI I771 m EFT—Ti m TIT—IT m I'm IT‘TI T77

‘3 Secateeceeeeceeeoso
I Temperature(°C)

Lfir

 

 

 

Figure 3.4 Resistance vs. Temperature
Combining the temperature and frequency dependence, the resistance as a function of

temperature and frequency is given as

 

PLL
RT (f ) = (1+ GMAT) (3-9)
Lwé‘VI - e’l‘” /6

While it is assumed that only p varies siglificantly in the RT model, temperature

changes will also affect the cross-sectional area of the inductor. Changes in the cross-
sectional area will then affect the resistance according to equation 3.4. The change in a
dimension of the coil as it changes with temperature can be described by

AL = LoaTAT (3.10)
where AL is the change in the dimension in m, L0 is the original dimension in m, and (11"

is the linear coefficient of thermal expansion (CTE) in °C" [6]. The new dimension of

the inductor can then be found from

L = L0(1+a7-AT) (3.11)

34

where L is the new dimension in m. The vertical expansion and contraction of the
inductor coil is unrestricted by any other structures in the sensor. Therefore, the CTE of

gold will be used when solving the line height for changes in temperature

LHT =LH(1+aAuAT) (3.12)
where LHT is the new line height in In. The CTE for gold, aAu, that will be used in this

analysis is 14.2E-6 °C'1 [6]. Equation 3.1] can also be used to describe the change in line
width with temperature. While the top surface is unconstrained, the base of the thin coil
is attached to the bulk glass substrate and is therefore restricted by its motion. The width
at the top of the coil will be described by equation 3.11 using the CTE for gold. The

width at the base of the coil will be described by the same equation using the CTE for the

glass. The CTE for glass, (17740, that will be used in this analysis is 3.25E-6 °C'1 [16].

Assuming the line width varies linearly over the 9 um height between top and bottom

surfaces, the average line width is given as

L
LWT =—,1(2+ ATlaAu mm» (3.13)

where LWT is the new, average line width in m. Figure 3.5 shows how the line width

varies over the coil line height for different temperatures.

35

 

I — L3
Glass Gold Original
Dimensions

Figure 3.5 Line Width Variation of Coil for Different Temperatures
The overall length of the inductor will face the same set of constraints as the line width.
The length of the inductor as it changes with temperature follows the modified version of

equation 3.13

L
Lu =7L(2+ATIaA. +amol) (3.14)

where LLT is the new inductor length in m, and LL is the original length in m. By

incorporating equations 3.14, 3.13, and 3.12 into equation 3.4, the resistance as a function

of the CTEs for gold and glass is given as

R(CTE) = p—flL— (3.15)
LHTLWT

where R(CTE) is the new resistance in D. Figure 3.6 shows the variation of R(CTE) with

temperature.

36

 

 

 

—Rnominal
R(CTE) [6. 16]

 

 

I__ I
I

 

 

 

 

 

 

I
..I.
OOOOOOOOOOO
FNGV’IDCDNQOSP

Temperature (’0)

I 29.51 “’lllTTTTl"i-"IWIIII’TITIIIIIIIITTIIII'W'I; .i [Hill iillaIllllllmllarllill”HilllluI-llll II'I 'l

 

Figure 3.6 R(CTE) vs. Temperature
The reason for the decreasing resistance in Figure 3.6 is the increasing cross-sectional
area of the coil with temperature. However, the resistance, R(CTE), is not very sensitive
to changes in temperature. The sensitivity of R(CTE) is —4.196E-4 52/°C. The change in

resistance due to the CTE, TCR, and a combination of both can be seen in Figure 3.7.

 

 

 

- ImRnominal

I—R(CTE)[6,16] ,"

, I*--"_R('I’CR) [6] "
I R(CTE,TCR) [6, 16]_ II

 

 

 

Resistance (Oh

 

 

 

 

 

 

Temperature (’C)

 

Figure 3.7 Resistance Variations with Temperature
It is evident from Figure 3.7 that the resistance R(TCR) is much more sensitive to

changes in temperature than R(CTE). Furthermore, there is an insigrificant difference in

37

sensitivities between R(TCR) and R(CTE,TCR). The sensitivities for the different
models are listed in Table 3.1.

Table 3.1 Sensitivities of Resistor models

 

 

 

 

Model Sensitivity (Q/°C)
R(CTE) —4.l96E-4
R(TCR) 2.448E-1

R(CTE,TCR) 2.454E-1

 

 

 

 

Upon reviewing Table 3.1, the effects of thermal expansion and contraction on the coil
resistance can be neglected. The model for the inductor resistance will incorporate the

skin effect and the TCR, given in equation 3.9 as

,0

LL
Rr(f)=
Lth‘NII '- e-L" [5

It has been shown that the inductor resistance is not a constant value, as it was

 

(1+aRAT)

treated while describing how the IOP monitoring system works in section 2.3. Rather, it

is a function of frequency and temperature. When the internal circuit is at the natural

frequency, Zim will be at a minimum. According to equation 2.11, the current flowing in

the circuit will therefore be at a maximum. The maglitude of the peak current is
dependent upon the resistance so that the height and slope of the peak of the curve

increases as the resistance is reduced and vice versa [5]. This effect is illustrated in

Figure 3.8.

38

 

 

g
E 0.4 +——— kuflfi»v--v - _.__ T
0.35«_--#AAAAAA2_ ,2
3
0 0.3 —. __-
‘3‘ 0.25 as— he a-.- a ”A... “A
.g -
o
E

 

 

 

 

 

 

 

 

 

 

 

 

—l(Rint, nominal)
— l(Rint. reduced)

 

 

0,2 .»—*.—._— d #V— - __
0.15 I——- .2, — W — ~ “
0.1 I’—
0.05
0 4%7fiwrmnnmmm
100 105 110 115120 125 130135 140 145 150

Frequency (MHz)

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3.8 Resistance Change on Internal Peak Current Curve

When the current is maximized, the voltage drop across Rim will also be maximized. The

resistance affects the curve of the voltage drop in the same way. This is shown in Figure

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.9.

E 6
E 5
g4_L’_r -Afil #—
8 3 . __ # I—V(Rint, nominal)
a. —V(Rirlt.mduced)
2 2
O
- / \N
51 /
0 j
> o IIIIIIIIIIIIIIIIIIIITIITITFTTTTIIIIIIIIIITIIIIIIII

100105 110 115 120125130 135 140 145150

Frequency(MHz)

 

Figure 3.9 Resistance Change on Internal Voltage Curve

39

The effect on current and voltage curves due to changes in Rim also carries over to the

external circuit. At the natural frequency Zext will be maximized. Therefore, the current

in the external circuit will be minimized as shown in Figure 3.10.

 

A 0.012
0.01

 

 

 

 

3:2:

 

-:I(Rext, nominal)
:‘ILE’WWI

 

 

 

 

 

External Clrcult Current (A

 

 

r
i
r,

 

Figure 3.10 Resistance Change on External Peak Current Curve

With the external current minimized and the induced reactance, XM, maximized at the

natural frequency, the voltage drop across Re,“ will therefore be minimized as well. This

is illustrated in Figure 3.11.

40

 

 

._._____fi

1 -—V(Rext, reduced)
—V(Rext, nominal) .

I
I
I
I

 

 

 

 

 

 

 

 

 

Figure 3.11 Resistance Change on External Voltage Curve

Resistance changes of Rim will affect the IOP monitoring system in another way.

The changing resistance values will affect the amplitudes of the resistor vector and its
corresponding voltage drop, but the phases will not change, as can be seen in Figure 2.9.
These changing resistance values will, however, affect the phase angle between the
current and impressed voltage for the internal circuit [15]. This is apparent from the
phasor diagram in Figure 2.10. From equation 2.7 it is clear that the capacitive and
inductive reactance will cancel out at the natural frequency. This will result in a phase
lag of 0° between the current and impressed voltage for the internal circuit. Figure 3.12
shows that the current and voltage are in phase for several capacitance values and

corresponding natural frequencies.

41

 

I 138MHz

.7 I 122MHz‘I

DI", , 111MHz”
I

,,,J

 

-20 1
-40 ,
-60
-80
-100

(0997908)

Internal Circuit Phase Angel

 

 

 

 

Frequency (MHz)

Figure 3.12 Internal Circuit Phase Angle
For non-zero phase angles, changes in Rim will affect the slope of the phase curve such

that the slope of the phase curve increases as the resistance is reduced and vice versa.

This effect is illustrated in Figure 3.13.

I 100

80 .7 a
I 60. , 7
40 m , 2,
20
0":7“'1'Ir'r'Iz'vvi'i'r'w'irni I: i....,. .
.20100106 112118 1241307
-40 ~ I

 

 

     

I—TheI;(Rint, nominam
Theta(Rint. mdugd) I

 

(Degrees)

   

 

Internal Circuit Phase Angle

 

 

 

Frequency (MHz) I

L7 , “7,, 7,

Figure 3.13 Resistance Change on Internal Phase Curve
The phase angle between the current and impressed voltage in the external circuit is given

as

42

 

¢=tan—1[XLexr +XMI (3.16)
Rex!

At the natural frequency, the sum of the induced and inductive reactance is locally

maximized causing a spike in the phase curve. This can be seen in Figure 3.14.

 

 

 

 

 

 

.5 I
c .
< I
i

& I—136MHz

§ : - -122 MHz

5 - I_:—_1_111\1£
E

 

 

 

 

Frequency (MHz)

 

Figure 3.14 External Circuit Phase Angle
Changes in Rim will affect the phase curve by shifting it vertically positive and increasing

the slope of the spike as the resistance is reduced. This effect is illustrated in Figure 3.15.

43

 

 

 

 

: :rner: (Riot, nominal) I
" Thetamlmv MWE‘DI

 

 

 

 

 

External Circuit Phase Angle
(Degrees)

 

 

 

 

100106112 118124130136 142 148 I
Frequency (MHz) J

 

I, f, _- _____ __ ___ _. __.__

 

Figure 3.15 Resistance Change on External Phase Curve
This section has shown the changes that will occur to the internal inductor’s
resistance value and how those changes will manifest themselves in the system as a
whole. The system can be calibrated to account for resistance changes due to the skin

effect. Resistance changes due to the inductor coil’s TCR can be detected by observing

the voltage drop across Rext, the current through Rexta or alternatively by observing the

phase of the external circuit. If these changes are small, they may be neglected or the
system may be calibrated for accuracy. If these changes are sigrificant, the IOP sensor
will have the added ability to remotely monitor temperature as well as pressure.

An additional resistor consideration is the power in that sensor component. The

power in the components of an RLC cir‘cuit is shown in Figure 3.16.

 

 

 

 

 

 

 

Figure 3.16 Instantaneous Power in Internal Circuit

Ideal inductors and capacitors are passive components having a zero average power. The
power in those elements is 180° out of phase, and they merely exchange their electrical
energy much like the transfer of kinetic and potential energy in a mechanical system.
Resistors, however, have a positive average power. Resistors transfer electrical energy
out of the circuit in the form of heat. This is analogous to damping or fiiction in a
mechanical system. .

A more convenient way to express the heating effect of resistors is to use the
average or root mean square (rrns) power given as

V I
Pm, = R2“ (3.17)

 

where Pms is the average power in watts (W), VR is the maximum amplitude of the
voltage across the resistor in V, and IR is the maximum amplitude of the current through
the resistor in A [5]. By substituting VR = IRR and [R = 10 = go— into equation 3.17,
the rrns power can also be expressed as

45

_ V02
222

 

R (3.18)

Prms

Neglecting temperature changes and the skin effect, Prms will reach a maximum at the

natural frequency when the inductive and capacitive reactance cancels out. The changing

capacitance due to the deflection of the sensor diaphragn will therefore shift the

frequency where the maximum Pans occurs but not the maximum value itself. This is

shown in Figure 3.17.

[_____u__ A" A __ _ ____ ,_ ____ _. . A. A. A w ___ ___ I A II

 

 

 

 

 

 

 

 

 

 

 

12 I
"fr
8 ._ If _ __A
g 1 . I
_, 6 ___ ,A, a . V___4 I-————Prms-len[5]
E 7 I-Prms - Cmax [5] g
n. 4 .__ «a
Z \ / x
2 7 V/ \\
| 0 rrrrrrrrrrrrrrrrrrrrrrrrrrr

 

I 100 105 110 115 120 125 130 135 140 145 150 I
I Frequency (MHz) I

 

Figure 3.17 Pmls in Internal Circuit

A final resistor consideration is thermal noise. In any conducting material whose
temperature is above absolute zero (0 K), the random motion of charge carriers in that
conductor produces random currents and voltages. These currents and voltages produce
noise. As the temperature of the conductor increases, the random motion of the charge
carriers increases, hence increasing the noise voltage. Neglecting the skin effect, the

noise voltage in the coil windings is given by

46

= ,/4kTRTB (3.19)

where VN is the rms noise voltage in V, k is Boltzmann’s constant (13813-23 Joules/K),

T is the absolute temperature in K, RT is the temperature dependent resistance in Q, and

B is the bandwidth in Hz [17]. The estimated natural frequency range for the sensor is
Ill-136 MHz. A frequency sweep of roughly 100-150 MHz will therefore be employed
to include the complete voltage profiles produced at these fi'equencies. This corresponds
to an effective bandwidth of 50 MHz to determine the noise voltage shown in Figure

3.18.

 

 

 

 

 

 

 

‘7; 0.006 /
3 0.004 I — —« #JllL. ——_4
g

0.003 *4? «~

 

 

 

 

 

 

 

" ‘T -' IWTT’ITTTTTY- Try: TrTTn-rmr 1 Yr 1 rr

I 00"” 7 : 14 21 28 35 42 49 56W163 70 77HT84W91 98 I
I 'r (’C) I
Figure 3.18 Thermal Noise vs. Temperature
When the sensor is at the human body temperature (37°C), an rms noise voltage of
0.0054 mV will be present. This seems like a relatively small value but it must be
compared to the signal to be measured from the external circuit. In order to determine

the sensor’s natural frequency from the external circuit, the voltage drop profile across

47

Re,“ must exhibit a significant dip at that frequency. The dip will be defined as the

difference between the local maximum and minimum voltages as shown in Figure 3.19.

 

 

mQ>—3F‘O<

I
I I I - I I I ‘

- - ..................... I» .
' I I 1 I | .

 

. , . . . . . . . .1..-'_.'.--’__ .._ .' . . .
' i . I . . . . . I. IL :1. ; ; I l I.
l I 0 . V I I n f. -I, I .
. II ocathmum
I l I I I I I I I I I I I t I I n
. '..\-4-.s---4.----d--r--t..5-.-..L------.—.---.I--L.4-_L-.4-.. ______I, L n .
I * , .

I I I I n 1 -
tiaL—‘J .4 p” --_,. a , A .0- I A. .,_ . . n ‘ l

FREQUENCY

Figure 3.19 Dip Measurement from Rext Voltage Profile

The voltage dip obtained from a Pspice simulation at body temperature has a value of
160.2 mV. Comparing this to the corresponding noise voltage, a signal to noise ratio
(SNR) of $7,302 will exist. As the temperature of the sensor increases, the noise voltage
will increase and the temperature dependent resistance will increase causing a smaller dip
in the voltage profile. However, even at extreme temperatures the SNR remains
considerably >>1 to allow sensor natural frequency readings from the external circuit.

Noise must still be considered in the external circuit. If thermal noise presents a
problem outside the sensor, a tracking program may be incorporated to reduce the
required frequency sweep range and hence the bandwidth, reducing the noise.

3.2.2 Inductor Considerations

Initially the sensor was treated as a three-component RLC circuit. The capacitor

element models the capacitance between the flexible diaphragm and the fixed, gold

48

electrode. The gold coil inductor is modeled by the inductor element and its series
resistance is accounted for by the resistor element. However, additional capacitance will
be present in the circuit due to the nature of the coil and the design of the sensor. In
creating the flexible diaphragm, a 3.5 pm recess is etched in the bottom surface of the
silicon wafer. The doping process used to create the diaphragm is then applied to the 1.2
mm x 1.2 mm area of the recess. This makes the entire recess area including the
diaphragm conductive. When the silicon wafer is bonded to the glass substrate, a
capacitance will be formed between the recess area and the top face of the inductor. The
recess area outside of the diaphragm will not be flexible, creating a fixed, parallel plate
capacitor. Referring to equation 2.17, the capacitance between the inductor and the

recess can be given as

CSi—L = —— (3.20)

where dSi-L is the spacing between the recess plane and the top face of the inductor in m.
The top face of the inductor is 1 um below the top face of the glass substrate providing a
dSi-L of 4.5 um. Therefore, CSi-L has a capacitance of 1.396 pF. Additional line-to-line

capacitance will also be present between the windings of the coil. This capacitance
cannot be modeled as a parallel plate capacitor because of the continuous voltage drop
across the length of the inductor. The line-to-line capacitance for a single level, square

spiral inductor can be approximated by

49

F-

 

 

s L” +2h+0.5s LW +0.85

L” +2h 0'80“
Ly +2h+0.5s

3.542
+ 0.831 1“” I 2" I
LW + 0.8s 2h + 0.55

0.695 1.41481

 

CL—L = 5087740LL XI (321)

 

 

 

where 87740 is the dielectric constant of the substrate in F/m, s is the line spacing in m,

and h is the height of the substrate in m [18]. The dielectric constant of the glass
substrate is 44.25 pF/m [19]. The height of the glass substrate under the coils is 0.49 mm
providing a self-capacitance of 0.125 fF for the inductor. The self-capacitance of the

inductor and the inductor-recess capacitance will be in parallel with diaphragm-electrode

 

 

 

 

capacitance as shown in Figure 3.20.
Lint
-4 JL. _L_
¢\ 4\ 4M
(D‘aph’ang CSi-L CL-L
Rint

 

Figure 3.20 Sensor Equivalent Circuit Showing Additional Capacitance
The equivalent capacitance for the sensor can be found by summing all three capacitive
elements
Ceq=C+CS,-_L +CL_L (3.22)
According to equation 2.10, the increased capacitance will reduce the natural fiequency
of the sensor. This will benefit the system’s function by lowering the fi'equency

operating range and reducing the skin effect according to equations 3.5 and 3.7.

50

However, the system will have to be calibrated to obtain the correct relationship between
IOP and the sensor’s natural fi'equency. The additional capacitance values and their
effect on the natural frequency range are listed in Table 3.2

Table 3.2 Additional Capacitance Effects on Natural Frequency Range

 

 

 

 

 

fr Range
Original C ceq
Model (MHz)
1.7-2.559F 1.7—2.55 pF 111—136
C CSi-L CL-L Ceq
89.56 —
New MM“ 1.7 — 2.55 3.096 —
1.396 pF 0,125fl? 101.11
PF 3.946 pF

 

 

 

 

 

 

The inductive reactance in equation 2.4 provides the reactance of an ideal
inductor. However, the reactance of a practical inductor will increase with frequency
only to a certain point. At this point, the self-resonant frequency of the inductor, the
inductor begins to look like a capacitor and the reactance rapidly drops to zero. The self-
resonant frequency is dependent upon the resistance of the inductor coil as well as the
distributed capacitance between the windings of the coil. This fiequency can be given in
terms of the sensor as

1

= 27’1ILintCL-L

where er is the self-resonant frequency of the inductor in Hz [17]. The behavior of

er

 

(3.23)

practical inductor reactance can be illustrated by introducing a figure of merit, Q, used to

express the quality of an inductor. The Q of an inductor is the ratio of its reactance to

51

 

resistance. A high Q means that little electric energy is lost to resistive heating. The Q of

a practical inductor in terms of the sensor can be expressed as

2
("Lint f
=—— 1— —— 3.24
Q Kim [ (1’11) I ( )

where f is the frequency of interest in Hz [13]. This expression is valid for all non-zero
frequencies up to the self-resonant frequency, after which the Q is zero. This is

illustrated in Figure 3.21.

 

I

i
I I
I
I

4'”
:-

 

 

 

 

-‘ -—--

I Frequency

 

I _

 

..___4

_ Figure 3.21 The Q Variation-of an Inductor with Frequency [13]
The curve in Figure 3.21 begins by increasing with frequency, as the resistance in the coil
windings is relatively small. As the frequency is further increased, the skin effect
becomes more prominent. The increased resistance combined with the capacitance of the
windings of the coil degrade the quality of the inductor to zero at its self-resonant
fi'equency. In order to maintain a high Q of the inductor, the frequency of operation for
the sensor must be kept well below the self-resonant frequency of the inductor. More
importantly, the determination of IOP is based on the reactance of an ideal inductor. To

obtain accurate readings from the sensor, the frequency of operation must be kept well

52

below er where the behavior of a practical inductor follows that of an ideal one. The

self-resonant fiequency of the inductor is listed in Table 3.3 for comparison with

operating fiequencies of the sensor.

Table 3.3 Q, Operating Range of the Sensor

 

 

 

 

Sensor Operating Range (MHz) er (GHz)
Original 1 11 - 136
1.59
New 39.56— 101.11

 

 

 

From Table 3.3 it is evident that the original sensor operating range as well as the new
range, accounting for additional sensor capacitance, is much lower than the self-resonant
fiequency of the inductor. Therefore, the sensor coil can be modeled as an ideal inductor
to accurately determine IOP.

The expression used to determine the value of the inductor in [4] is given as
L MON = fldngwazdjfiGnaflw (3.25)
where LMON is the inductance in H, dOUT is the outer spiral diameter in urn, d AVG is the

average spiral diameter in um, n is the number of turns, sis the line spacing in urn, B and
or are layout dependent coefficients provided by [20]. Figure 3.22 and Table 3.4 provide

the inductor layout and the values used in equation 3.25, respectively.

53

 

 

dour

Figure 3.22 Layout for a Square Spiral Inductor [4]

Table 3.4 Inductance Equation Parameters

 

 

 

 

 

B a1 a2 a3 (14
0.00162 -1.21 -0.l47 2.4 1.78 -0.03
dour dm dAVG w n
1161 pm 545 um 853 pm 4 pm 26 4 pm

 

 

 

 

 

 

Some of the parameters in equation 3.25, namely dOUTa dAvg, w and s, are dependant on

the inductor dimensions that will change with temperature. Under the same assumptions

S4

 

made in section 3.2.1 regarding the behavior and constraints for the inductor, the

changing inductance with temperature is shown in Figure 3.23.

 

 

 

 

 

 

 

 

 

 

 

 

SE

5

8

§

3

u

5

799.8 —— #————-——#_ -4 _. _--__ _ __ *__z

I 799.6 IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
I °F<V®wh9r§°0$b¢ro°é°fitbq¥§ol°
L Temperaturo(°C)

 

Figure 3.23 Inductance vs. Temperature

The sensitivity of the inductance to temperature is 0.007 nH/°C and is therefore
negligible.

3.2.3 Capacitor Considerations

In designing the IOP sensor, the capacitance created by the flexible diaphragm
and fixed electrode was modeled as a parallel plate capacitor. However, this model may
not be the most accurate for determining the center deflection of the diaphragm fi'om the
capacitance. The parallel plate model treats the electrodes as two rigid plates parallel at a
distance. In the case of the sensor, the top plate is not rigid and the center deflects from
its fixed edges creating a non-uniform spacing between the plates. Other capacitor
models should be considered to determine the center diaphragm deflection from the
capacitance.

One option is to model the diaphragm as two rigid plates hinged together and at

the edges as shown in Figure 3.24.

55

 

 

 

 

 

 

A
Hinged Diaphragm
1.5 pm
V
Fixed Electrode
537 um
t >

Figure 3.24 Hinged Plate Capacitor Model
The capacitance for this model can be derived by examining one of the hinged plates.

Figure 3.25 shows the schematic for deriving the capacitance.

g=1.5 um

 

 

I

 

 

 

4 * “ >
W/2

Figure 3.25 Capacitance Derivation Schematic

Half of the hinged plate capacitance, CHP, can be derived as

56

(3.26)

£0£,W

tang

F

In

 

In.

s+—VY—tan0
2

S

1

 

I

= £05,.W

tang

P

 

L.

1+

El—tama
2

S

 

 

t‘

where W is the total side length of the square electrode in m (537 um), s is the spacing
between the lowest point of the hinged plate and the electrode in m, and 0 is the angle the
hinged plate makes with the horizontal in radians [21]. As the hinged plate becomes
parallel to the electrode or as 0 approaches zero, this model assumes the form of the
parallel plate model as ln(l + x) z x. The total hinged plate capacitance is then found by
doubling this, as equation 3.26 accounts for only one of the hinged plates.

Another option is to again model the diaphragm and electrode as a parallel plate
capacitor, modifying the spacing variable. The parallel plate model treats the spacing
between the plates as uniform and equal to the spacing between the center of the
diaphragm and the electrode. A more accurate determination of the capacitance may be

to use the average of the center and edge spacing of the diaphragm for the uniform plate

spacing given by

 

(3.27)

 

where g is the spacing when the diaphragm is at zero deflection in m (1.5 pm).

57

The capacitance for the three models from zero to full-scale deflection is shown in

Figure 3.26.

 

 

|
I
I
L I

 

 

1-5 «+Hinged Plate [21] '
1 n. —‘ ~- A r —— ~— -—————+Parallel Plate
0.5 --~—--—— — --——— ¢ __ __ _. _.. .. - Parallel Plate-Ave

 

 

Capacitance (pF)

 

 

 

 

I 1 1.1 1 .2 1 .3 1 .4 1 .5
I Center Spacing (microns)
I

I
I
I
I

 

Figure 3.26 Comparison of Capacitance Models

While all three models are equal for zero diaphragm deflection, Cpave and CHp are

approximately equal and significantly different than the parallel plate model as deflection
increases. The parallel plate model provides the only direct relationship between the
center deflection of the diaphragm and sensor capacitance. However, a more accurate
relationship may be provided through calibration of the device.

The sensor capacitance is intended to change with diaphragm deflection only.
Therefore the sensitivity of capacitance to temperature and pressure must be examined.
As discussed with the parallel plate model, among other variables, the capacitance is
dependent upon the dielectric constant of the insulating material between the plates.
Variations in the dielectric constant may produce undesirable changes in the sensor

capacitance.

58

The temperature coefficient of the dielectric constant of air, agT, at 1 atm and

20°C is 2E-6/°C [6]. The capacitance as a function of temperature is given as

_ £03,. (I + aETATM
d

 

CsT (3.28)

where A is the overlapping area of the plates (2.88E-7 m2), and d is the plate spacing in

m. Holding all other variables constant, the capacitance is plotted as a function of cavity

temperature along with the nominal capacitance in Figure 3.27.

 

 

1.7026
1.7024 ~ -
1.7022 -

1.702 -
1.7018 .
1.7016
1.7014 «
1.7012 -
1.701
1.7008
1.7006
1.7004

pacitance (pF)

 

 

 

 

 

Ca

 

 

 

 

I
I
I
I 0 714212835424956637077849198 I
I Cavity Temperature (°C) I
I I

Figure 3.27 Capacitance vs. Cavity Temperature
Figure 3.27 shows the sensitivity of the capacitance to changes in the dielectric constant

with temperature is 1.19E-5 pF/°C and is therefore negligible.

The pressure coefficient of the dielectric constant of air, (lap, at 1 atrn is a more

sizable 100E-6/°C [6]. The sensor cavity behaves according to the ideal gas law so that
the cavity pressure will vary with volume and temperature of the cavity.
The volume of the cavity will change with thermal expansion/contraction of the

sensor materials as well as the deflection of the diaphragm. The nominal volume of the

59

cavity, V0, was calculated to be 8.69E-9 L at 20°C. When subjected to an increase in

temperature of 80°C, the cavity volume was slightly decreased to 8.67E-9 L. This slight
decrease is attributed to several factors. The minor expansions caused by the relatively
low CTE for glass and silicon mostly cancel each other out producing a small increase in
cavity volume. This small increase is dominated by the expansion of the relatively high
CTE gold, filling up the cavity and reducing overall volume. To determine the volume
change of the cavity due to deflections of the diaphragm, the volume created by the

deflected diaphragm is modeled as a spherical segment according to. Figure 3.28.

 

2r

Figure 3.28 Model of a Spherical Segment [22]

The volume of the spherical segment in Figure 3.28 can be computed by
V —’"”°(32+ 2) 329
seg " —6— a we ( . )

where Vseg is the volume in m3, wc is the center deflection of the diaphragm in m, and a

is half the side length of the diaphragm (2.755E-4 m) [22]. The volume of the spherical

segment at a maximum diaphragm deflection of 0.5 um is 5.96E-ll m3. When

subtracted fi'om the nominal volume, the cavity volume is decreased to 8.63E—9 L. This

66

is a greater change in volume than that created by the expansion of the sensor materials
and will therefore be used to determine how the changing volume of the cavity affects
cavity pressure. The cavity pressure as a function of cavity volume, and hence

diaphragm center deflection can be described by

11V)... =[nRuT1’c2'v (3.30)

I"amlzmndTis fixed at

 

where P(V)cav is given in L, n is 3.42E-13 kmol, Ru is 82.05 I
o

the body temperature of 310 K. The cavity volume, Vcav, is given in L and is defined as
ch, = V0 — Vseg (3.31)
once Vseg has been converted to L. The capacitance as a function of volume dependent
pressure, C8(P.V), is given in F by

808,. (1 + agpAP)A
d

 

C£(P-V) = (3.32)
where AP is the difference between P(V)cav and the reference pressure of l atrn. P(V)cav

is a function of diaphragm deflection and C8(p.v) can therefore be plotted with the

nominal capacitance against the plate spacing in Figure 3.29.

61

 

 

 

 

 

 

 

 

 

 

 

 

 

A2.5I — f-“ I
'3 I
‘5 _.
c 15 _ - V f- _ I—Ce(P-V) [6, 22] II
i . I—Cnom I
81’“—“'#”“‘* I
0.5I——*-*___'_E_f I

I 0 I
I ‘6 NP?) "P‘ '3") "f'b (If) '0' (.3) "5 x96) \
Gap(microne) .I

 

 

Figure 3.29 C8(p-v) vs. Plate Spacing

Figure 3.29 shows that the capacitance is not affected by changes in the dielectric
constant with volume dependant pressure. Therefore, the cavity volume will be held
constant in determining how the changing temperature of the cavity affects cavity
pressure.

The cavity pressure as a function of temperature is given as

13(7)”, = [Elf—“Ire“, (3.33)

0

where P('T')cav is given in L. The capacitance as a function of temperature dependent
pressure, C8(p_-r), is given in F by

£06,.(1-i- aapAPM
d

 

Ca(P—T) = (3.34)

62

where AP is the difference between P(T)cav and the reference pressure of l atrn. C8054)

is plotted with the nominal capacitance against pressure for a corresponding temperature

range of 0-100°C in Figure 3.30.

V” _____ _._____. __ _.___ ,- _ _ -.__ ,_ __ __ _._ 4.2;, ‘LI_1

1.70142 I
1.70141 2.. —«- -— — *9 ~~——- ”flafl — ~ ..
1.7014 g 5 .. ___.-.
1.70139 .. .~ ~-———-—-~ -_M__ 52,
121813; i__fl -. L-_..__. I ' 'Ce(P-T)161I
1.70136 m ..._ . *—Cnom I
1.70135 AI , , ‘ —— .v .
1.70134 -. _—-——-—-——-——--—— —---———f—
1.70133 L—————-—--—-——
1 .70132 I”111111111111TUYUUIIIHHUHliiTiiliiH.‘IHHHIHHIYHYH'HUIHHHI‘IHIHIHIIIIIIHIHi

 

 

 

 

 

 

 

 

 

 

 

 

Capacitance (pF)

 

 

 

 

I
I
I
I
Pressure (atm) I

 

 

Figure 3.30 Cgarr) vs. Pressure

Figure 3.30 shows the sensitivity of the capacitance to changes in the dielectric constant
with temperature dependent pressure is 1.70E-4 pF/atm and is therefore negligible.
Capacitance changes as a result of dielectric constant variations with cavity
temperature and pressure are negligible for the sensor operating conditions. Capacitance
changes due to variations in overlapping plate area and spacing must therefore be
examined. The overlapping plate area will be limited by the expansion of the smaller

gold electrode. Assuming the planar expansion of the gold electrode is unconstrained at

the top surface, the overlapping plate area, AT, in m2 is given as

AT = A0 (1 + aAuAT) (3.35)

63

where A0 is the nominal plate area (2.88E-7 m2). The thermal expansion of the silicon

wafer and diaphragm, and the glass substrate will effectively cancel each other out due to
the structure of the cavity and the similar CTEs of the materials, 2.6E-6/°C and 3.25E-

6°C respectively [6]. The nominal spacing between the bottom face of the diaphragm
and the base of the 2 pm high gold electrode, go, at zero deflection is 3.5 um. The
unconstrained height of the gold electrode, hTAu, is given in m by

hTAu = 0Au(1+aAuAT) (3.36)

where h() Au is 2E-6 m. The temperature dependent capacitance due to thermal

expansions of the sensor, CT, is given in F as

CT = 32931. (337)
go - hTAu

CT is plotted with the nominal capacitance against temperature in Figure 3.31.

 

 

 

 

 

 

' ‘ 1 CT [6]
”—Cnom

 

 

 

 

 

 

 

 

 

I
I
oeeeeseeeoees I

Temperature (°C) I

Figure 3.31 CT vs. Temperature

 

Figure 3.31 shows the sensitivity of the capacitance to changes in temperature is 5.64E-5
pF/°C and is therefore negligible. The sensor capacitor will therefore perform as
designed. The capacitance will be a function of diaphragm deflection only with
insignificant changes as the temperature and pressure of the sensor cavity vary.

An important consideration when dealing with capacitors is the phenomenon of
dielectric breakdown or electrostatic discharge (ESD). This occurs when a charge
buildup or potential difference across the capacitor plates exceeds the dielectric strength
of the insulating material. The resulting breakdown permanently damages the capacitor.
The well-known Paschen curve describes the breakdown voltage of air at atmospheric
pressure as a function of the gap spacing [23]. Breakdown is attributed to the Townsend
avalanche. The excessive charge buildup pulls the negatively charged electrons in one
direction and the positively charged ions in the other. As the electrons are accelerated
towards the anode and the cations towards the cathode, they collide with other neutral
atoms in the air creating more electron/cation pairs. These then undergo the same
separating process creating an avalanche. This avalanche ionizes the air molecules
changing the air from an insulator to a conductor. The ionized air provides a path for the
current between the capacitor plates. For gaps greater than 10 um, breakdown has been
well studied and occurs when the potential difference exceeds 3 Wm [23]. Circuit
simulations indicate the sensor capacitor will experience voltage drops in the range of
7.2-3.5 V. BSD would certainly occur for the capacitor spacing of 1.5-1.0 um. However,
the electrical current can result from other mechanisms besides the Townsend avalanche
in an ionized gas, and these other mechanisms are not considered in the theory behind the

Paschen curve. For electric fields across gaps fi'om Snm to 5pm, field emission is the

65

mechanism responsible for BSD [23]. The Modified Paschen curve suggests a more
lenient field breakdown strength of 75V/um [23]. Other sub micron gap testing in
literature reports the field breakdown strength on the order of lSOV/um [23, 24]. The
greater field breakdown strengths assure that ESD will not occur in the sensor’s
capacitor.
3.3 Cavity Pressure Considerations

The differential pressure across the sensor diaphragm is determined fi'om the
diaphragm’s deflection. Once the pressure differential is known, exact IOP
measurements can be recorded only if the cavity pressure values are accurate. The
nominal cavity pressure when the sensor is at the body temperature of 37°C is l atrn.
However, this will change as the cavity temperature varies. Cavity temperature
variations will occur as the temperature of the sensor environment changes. While the
sensor is in operation, resistive heating may also elevate the cavity temperature. To
investigate the effects environmental temperature and the resistive heating of the coil will
have on cavity temperature, a FEM analysis was performed using the Ansys University
High program. To reduce the size of the program, half of the sensor cross-section was
modeled surrounded by a layer of aqueous humor. Figures 3.32 and 3.33 show the whole

model and a close-up of a portion of the sensor cavity respectively.

66

 

 

 

 

 

Figure 3.32 FEM Model

 

 

Figure 3.33 Close-up of Cavity

The mode of heat transfer in the cavity was determined by examining the cavity’s
Rayleigh number. For horizontal cavities heated from below with a width and depth

much greater than the height and Rayleigh numbers less than the critical value of 1708,

67

buoyancy forces cannot overcome the resistance imposed by viscous forces and there is

no convection in the cavity [25]. The Rayleigh number is defined as

 

3
—T L
RaL=gfl(Tl 2)
av

(3.38)

where g is gravity in m/sz, T1 and T2 are the temperatures at the bottom and top of the
cavity respectively in K, L is the cavity width in m, a is the thermal diffusivity of the

cavity fluid in mz/s and v is the kinematic viscosity of the cavity fluid in mz/s. The

expansion coefficient, [5, for an ideal gas is lsz [25]. Rayleigh numbers were calculated

using a cavity width of 1160 um. Temperatures at the top of the cavity were varied from
—23 to 127°C while increasing the temperature differential up to 20°C. Calculations
produced a maximum Rayleigh number of 2.46, several orders smaller than the critical
value of 1708 indicating no convection in the cavity. Similar calculations were
performed to determine the mode of heat transfer at the external surfaces of the sensor.
Rayleigh numbers ranging from 1.16E4 to 4.65E4 indicate that convection would occur
at the top and bottom sensor surfaces. In order to obtain a worst-case scenario of
elevated cavity temperatures, conduction was the only mode of heat transfer used in the
analysis.

A constant temperature of 37°C was applied to the outer boundary of the aqueous
humor to model body core temperature. The heat generated by the resistive components
of the sensor varies with frequency as the circuit performs a fiequency sweep. It is
estimated that it will take approximately 1 second to complete a sweep and that they will

be performed continuously. In adherence to a worst-case scenario for cavity temperature

68

 

elevations, the maximum value of 10.6 mW was used to apply a constant volumetric heat
generation of 1.5E-9 W/p.m3 to the model areas representing the gold portions of the
sensor.

The thermal conductivity of the glass, gold, silicon and aqueous humor portions

of the model were treated as properties independent of temperature. The values used in

the analysis are listed in Table 3.5.

Table 3.5 Constant Thermal Conductivities

 

 

 

 

 

Material Thermal Conductivity (W/mK)
Glass 1 .4
Gold 3 17
Silicon 148
Aqueous Humor 0.58

 

 

 

The thermal conductivity for air was entered as temperature dependent. The values used

are shown in Table 3.6.

Table 3.6 Thermal Conductivity of Air

 

 

 

 

 

 

Temperature (K) Thermal Conductivity (W/mK)
250 22.3E-3
300 26.3E-3
350 30E-3
400 33.8E-3

 

 

 

69

The elements used to mesh the model are the PLANESS four node rectangular
elements. Each node has one degree of freedom representing temperature. The model
was meshed using free triangular shapes. The triangular shapes are formed by collapsing
two nodes together. The Smart Size option was implemented using a fine mesh size of 1.
The entire meshed model and a portion of the meshed cavity are shown in Figures 3.34

and 3.35 respectively.

 

Aq‘VA‘VAYA'A‘AVA“

AVAVA AVAV‘V' v
4v, "5:31,

 

 

 

 

Figure 3.34 Entire Meshed Model

70

ultVnVMMMNi '

a VAVA‘ '1 VI'A"J"I) ’A'A

V V V V V V V 7 V V Y 7 V V V V
‘35 MA >55 “A US A MA MS ’5!
V V AV

v
9"

TA" 7" V‘V Y.
‘VA VAVL‘ KYA‘ ’

Av. E2 in! >153

 

Figure 3.35 Meshed Cavity
It is assumed the sensor will reach steady-state rapidly compared to changes in
body temperature due to its miniature size. Therefore, a steady-state analysis was
performed. Results of the analysis are presented as contour plots of the temperature
distribution throughout the sensor. Figures 3.36 and 3.37 show the contour plots of the

whole model and the cavity portion respectively. Temperatures are listed in K.

71

 

3;: :34 310.511
315 36-! 3;: 192 310.32 310/147 310.575

 

4410.330
10.32

no.4}:

Figure 3.37 Cavity Temperature Distribution
The cavity temperature under the diaphragm is maintained at the body-core temperature
of 37°C (310 K). Even with the worst-case scenario heat generation applied to the

model, the cavity temperature in the coil region is elevated a mere 0.575°C above the

72

ambient temperature. After obtaining the results, the meshing was refined at the material
interfaces in the model. Refined meshing produced identical temperature distributions
indicating the initial mesh was accurate. Additional analyses were then performed by
applying different temperatures at the outer boundary of the aqueous humor. The
ambient temperature was increased and decreased 10°C. In both cases the diaphragm
region of the cavity achieved the ambient temperature. The maximum temperature

elevation in the coil region of the cavity was 058°C. Results of the analyses are listed in

 

 

 

 

 

 

Table 3.7.
Table 3.7 FEM Analysis Results
Ambient Temperature Cavity Temperature (°C)
(°C) Diaphragm Region Coil Region
27 27 27.58
37 37 37.575
47 47 47.57

 

 

 

The results conclude that the effect of resistive heating is small and the cavity
temperature will be within 0.6°C of the ambient temperature of the sensor environment
for lO-degree deviations from body core temperature.

With negligible changes in cavity volume, the cavity pressure varies with
temperature according to the Ideal Gas Law. The temperature dependent cavity pressure

is plotted in Figure 3.38.

73

 

 

 

1000

 

 

 

 

700 IWm—_ _ -_ _ _. ,_

 

500 JH— — --— — ——<———-—-—!-—— fl.» e- ,,__ ——m— —-~—~ — -- —«

200.___.___ _ _. _ _N,,m__ _ _. _ _ 7,._,,,-_ _. m _
100-__._fi___-____._._7 H, _ _- f .-._# n W m ,

Cavity Pressure (mmHg)
I
I
I
I
I
I
I
I
I
I
I
I
I

 

 

 

Temperature (°C)

 

 

 

Figure 3.38 Cavity Pressure vs. Temperature
The cavity pressure varies with temperature with a sensitivity of 2.45 (mmHg/°C). The
0.6°C deviations caused by resistive heating would produce a mere 1.47 mmHg change in
cavity pressure. An ambient temperature swing of approximately 10°C from body core
would offset the nominal cavity pressure by 24.5 mmHg. This deviation is equivalent to
40.83% of the pressure range of interest (760 — 820 mmHg). Therefore, once implanted
in the eye, the cavity pressure of the sensor cannot be treated as a constant 1 atrn (760

mmHg). Cavity temperatures can potentially be determined from observations in the

peak height and width from the voltage profile acquired fi'om Re,“ as discussed in section

3.2.1. With known cavity temperatures, the exact cavity pressure can be used to obtain

IOP measurements accurately.

74

Chapter 4. Eye Considerations

4.1 Eye Models Available in Literature

The previous chapter has shown that the IOP sensor is temperature sensitive. It is
therefore necessary to understand what temperatures the sensor will be subjected to once
implanted in the eye. A common belief is that the temperature in the vitreous cavity is
regulated with body temperature to within a few tenths of a degree centi grade [26]. The
sensor will not be located in the vitreous cavity. Rather, it will be implanted in the
anterior chamber between the iris and cornea. A review of pertinent literature was
undertaken to investigate what sort of temperature fluctuations the sensor environment
might experience.

An article by Scott discusses a finite element model of heat transport in the human
eye [27]. The control ambient temperature is 20°C and the control body-core temperature
imposed on the sclera is 37°C. The cooling mechanisms of the model are assumed to be
at the surface of the eyeball. Heat is lost to the surrounding air from the anterior corneal
surface by evaporation, convection and radiation. The steady-state temperatures along
the pupillary axis of a wide-Open eye were calculated using the control parameters.

Scott’s results for several points along the pupillary axis are listed in Table 4.1.

75

Table 4.1 Steady-state Temperatures (Control Values) [27]

 

 

 

 

 

 

Location Temperature (°C)
Posterior Corneal Surface 33.25
35.20
Anterior Pole of the Lens
Posterior Pole of the Lens 36.01
Retina 36.89

 

 

These values indicate an uneven temperature distribution throughout the eye. The
location of the sensor would lie somewhere between the posterior corneal surface and the
anterior pole of the lens. The location of the sensor alone suggests a temperature
difference of several degrees from body-core temperature under the controlled
circumstances. Next Scott considers the effect of changing the ambient temperature.
Scott’s results of this analysis are listed in Table 4.2.

Table 4.2 Steady-state Temperatures (Increased Ambient) [27]

 

 

 

 

 

 

 

Ambient Location
Temperature Posterior Anterior Pole Posterior Pole
Retina
(°C) Corneal Surface of the Lens of the Lens
20 33.25 35.20 36.01 36.89
25 34.79 35.65 36.26 36.92
30 35.15 36.11 36.51 36.94

 

 

 

 

 

76

 

The effect of the increased ambient temperature is most severe at the corneal region and
decreases towards the retina. In the region of implantation, the values suggest an increase
of 1.9 — 0.91°C from the control values for a 10°C increase in ambient temperature. Scott
then proceeds to examine the effects of increasing the body-core temperature, which may
occur during physical activity, while holding the ambient temperature at the control
value. These results are listed in Table 4.3.

Table 4.3 Steady-state Temperatures (Increased Body-core) [27]

 

 

 

 

 

 

 

Body-core Location
Temperature Posterior Anterior Pole Posterior Pole

Retina

(°C) Corneal Surface of the Lens of the Lens
37 33.25 35.20 36.01 36.89
37.7 33.81 35.83 36.67 37.58
38 34.05 36.10 36.96 37.88
38.5 34.45 36.55 37.43 38.38

 

 

 

 

 

 

The effect of the increased body-core temperature is most severe in the retina region and
decreases towards the cornea. The values suggest an increase of 1.2 — 1.35°C fi'om the
control values in the region of implantation for a 15°C increase in body-core
temperature. However, Scott does not include an analysis for increasing both ambient
and body-core temperatures nor any experimental data

In another article Scott author considers temperature rises in the human eye
induced by infiared radiation [28]. The article focuses on glass and iron mill workers

who may be exposed to temperatures in the range of 1250 - 1500°C and experience

77

irradiation incident upon the eye up to 5000 W/mz. The effect of blinking every 283 and

holding the eyelid closed for 0.3s is incorporated in the cooling mechanisms of this finite
element model. Scott considers the case of a wide-open eye in an ambient temperature of

20°C, with a body-core temperature of 37°C exposed to the incident irradiation of 2100
W/mz. The steady-state temperature at the corneal surface reaches an elevated 44°C.

Scott then examines the effects of increased blinking, increased tear evaporation and

eyelid shielding. The author’s results are listed in Table 4.4.

Table 4.4 Corneal Surface Temperatures for 2100 W/m2 Incident Irradiation [28]

 

 

 

Increased Increased Eyelid l/2 Eyelid 3%:
Case Control
Blinking Evaporation Closed Closed
Temperature
44 43 40.6 41 .5 39
(°C)

 

 

 

 

 

 

These values show the corneal surface temperature is significantly reduced. However,
even with the most effective cooling mechanism of eyelid shielding, the temperature is

several degrees higher than body core temperature. Scott proceeds to examine the case of

a wide-open eye subject to an incident irradiation of 1250 W/m2 for a period of 30s

combined with the effect of changing the ambient temperature. The standard cooling
mechanisms are utilized with the control body-core temperature of 37°C. The Scott’s

results are listed in Table 4.5.

78

 

Table 4.5 The Effect of Ambient Temperature on Temperature Rises Experienced in the

Eye Exposed to an Incident Irradiance of 1250 W/m2 [28]

 

 

 

 

 

 

 

 

Exposure Anterior Pole Posterior Pole Sufgctfolflfris
T' Tamb (°C) of the Lens of the Lens .
rme (s) (o C) (o C) in Contact
with Lens (°C)
0 20 34.57 36.01 35.20
30 20 35.41 36.10 35.81
0 30 35.80 36.51 36.11
30 30 36.64 36.60 36.73
0 20 34.57 36.01 35.20
30 30 35.61 36.11 35.98

 

 

 

 

 

 

These values indicate that the largest temperature elevation will occur in the implantation
region for irradiation exposure combined with elevated ambient temperatures. Scott’s
calculations suggest that different levels of exposure to inflated radiation for varying
amounts of time coupled with increased ambient temperatures may significantly elevate
the temperature of the sensor’s environment.

An article by Lagendijk [29] contains a finite difference model of the human eye
along with experimental data on New Zealand rabbits. The steady-state temperature
distribution in the human eye subject to a body-core temperature of 37°C and an ambient

temperature of 20°C matches that of Scott [27]. For the experimental data, a constant

temperature water bath at 43 - 45°C transferred heat to the rabbit eyes through a thin
rubber film. A thin thermocouple was inserted in the eye of four rabbits to record

temperatures at various locations. Control values for comparison were recorded for an

79

ambient temperature of 23°C and a rectal temperature of 388°C. The Lagendijk’s results

 

 

 

 

 

are listed in Table 4.6.
Table 4.6 Experimental Rabbit Data [29]
Location Control Toe mp erature Average Temperature (°C)
4 9
Cornea 34.5 43.8
Behind Lens 37.4 40.4
Retina 38.1 39.4

 

 

 

Results show a large increase of 9.3°C from the control temperature at the cornea and a
significant increase of 3°C behind the lens. This experiment proves that the temperature
of the sensor environment can be considerable increased under certain conditions.

The review of the above articles suggests that the temperature distribution
throughout the eye varies by several degrees. Although increased cooling mechanisms
may reduce the effect, elevated body-core temperature combined with ambient and
environmental conditions have the potential to severely elevate the temperature of the
sensor’s environment. The experimental data proves that this temperature can be
significantly elevated under the right conditions.

4.2 Heat Transfer Model of the Human Eye

Upon reviewing available eye models, a two-dimensional heat transfer model of
the human eye was created to further investigate what temperature fluctuations the eye
might experience. The perimeter of the eye was modeled as a circle with a bulging at the
equator of the cornea with a diameter of 20.8 mm according to Gustrau et a] [30]. The
interior of the eye is modeled according to Amara et al and consists of seven tissues [31].

These tissues are: 1) vitreous humor; 2) aqueous humor; 3) lens; 4) iris; 5) cilliary body;

80

 

6) cornea; and 7) retina. Figure 4.1 shows the FEM model of the eye created with the

Ansys University High program.

 

 

 

 

 

Figure 4.1 FEM Human Eye Model
The thermal conductivities of the tissues are taken from Amara et a1 [31] and are
listed in Table 4.7.

Table 4.7 Tissue Thermal Conductivities [31]

k (W/mK)

 

81

The modes of heat transfer considered in the model are tear film evaporation,
radiation and convection at the anterior corneal surface with the surroundings, and
convection between the sclera and body core. The retina, permeated with blood vessels,
will be held at body core temperature. After meshing the model with PLANESS elements
as free triangular shapes, a steady-state analysis was performed to validate the model.

The retina was held at a fixed body core temperature of 37°C. Borrowing from Scott
[28], a convective coefficient, hs, of 65 Wm'lK'1 was used to apply convection fiom the

sclera to the surrounding body core temperature. Lagendijk [29] combined the
evaporation, radiation and convection heat transfer on the anterior surface of the cornea
to give a combined heat transfer coefficient, if , of 20 Wm'lK-l. This coefficient was
used for the convection between the cornea and quiescent air at 20°C. Conduction is the

mode of heat transfer within the eye. Results of the simulation are shown as a contour

plot in Figure 4.2.

82

 

ANSYS

 

—-—-—-— .sxx ll...-
306.203 307.047 307.89 308.734 309.578
306.625 307.469 308.312 309.156 310

 

 

 

Figure 4.2 Temperature Distributions in the Eye

Temperatures in Figure 4.2 are listed in Kelvin. Results of the simulation match those of
Scott [27] listed in Table 4.], thus confirming this as an acceptable heat transfer model of
the human eye.
4.3 Cat Testing

To prove temperature fluctuations can occur within eye, experimental data was
needed. Cats were used as the test subject as they were readily available and have eye
dimensions comparable to that of a human. A test rig was constructed to allow jets of air
at various wind speeds, temperatures, and with varying relative humidities to be blown on
the eye of an anesthetized cat. The rig was constructed of cylindrical aluminum duct and
a plastic funnel 40.64 cm overall in length. A fan was attached at the end of the rig and
the heating element from a hot plate was formed into a coil and housed within the 10.16
cm diameter duct. The base of the rig rested on top of a hot plate supporting a beaker

filled with water. The 2.54 cm diameter jet outlet in the funnel was placed 2.54 cm away

83

from the cat’s eye lined up dead center. The relative humidity of the jet was controlled
by boiling water on the hot plate in addition to using a common misting bottle. Along
with the steam generated by the hot plate, the jet temperature was controlled by the coil
heating element connected to a Variac variable autotransforrner. A whisper fan
connected to another Variac controlled the jet velocity. The test rig is shown in Figure

4.3.

{I ‘ 4‘:

 

Figure 4.3 Test Rig for Cat Testing
Jet velocities and temperatures were recorded using a Dwyer Instruments VT-200
flow anemometer. Jet relative humidities were recorded using an Omega RH71 digital
hygro-thermometer. Eye temperatures were recorded using an Omega HYP1-30-l/2-T-
G-60-SMPW-M type T hypodermic needle thermocouple probe. The 30 gage x 15 mm
needle was inserted in the eye between the cornea and iris near the cilliary body at the
proposed location for the sensor. The needle was inserted to a depth of approximately 3

mm. The probe leads were connected to an Omega HI~123 microprocessor thermometer,

84

converting voltage levels to temperature readings. Figure 4.4 shows the needle probe for

size comparison.

 

Figure 4.4 Hypodermic Needle Thermocouple Probe

Testing simulated conditions a person’s eye might experience in a hot or cold
environment, under dry or humid conditions, on a calm or windy day. The purpose was
to determine what temperature differences, if any, exist in the eye of a person in an
Arizona summer versus that of a person experiencing a Michigan winter. The majority of
the testing was conducted at room temperature in a lab while lower temperature testing
was performed in a cold room. In each trial, ambient temperature, jet properties, and
initial eye temperature were measured. All trials were performed at an ambient pressure
of 1 atm. Upon application of the jet, final eye temperatures were allowed to reach
steady state before being recorded. Rectal temperatures for the cat were also chronicled

intermittently. Initial conditions of the testing are listed in Table 4.8.

85

Table 4.8 Cat Testing Initial Conditions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Trial Tambient °C Teye Initial °C Trectal °C

1 23.61 34.61 39.17

2 23.61 34.61

3 23.61 34.61

4 23.61 34.61

5 27.78 36.00 39.17

6 27.78 36.28

7 27.78 36.83

8 27.78 36.28 39.22

9 27.78 36.83

10 27.78 34.50

11 27.78 36.11 38.94

12 8.50 34.00 38.44

13 8.50 34.00

14 8.50 34.00

Results of the testing are listed in Table 4.9.
Table 4.9 Cat Testing Results
Trial Tf’mal °C Tdelta °C Vjet (m/s) Tjet °C Jet %RH

1 34.22 -0.39 1.79 23 .67 13.80
2 33.06 -1 .56 3.58 23.78 13.80
3 33.17 —1.44 8.94 23.67 13.80
4 32.50 -2.11 12.52 23.67 13.80
5 35.22 -0.78 1.79 29.44 12.70
6 37.00 0.72 1.79 35.00 12.80
7 37.50 0.67 1.79 42.50 12.80
8 36.28 0.70 1.79 48.89 13.00
9 37.72 0.89 1.79 68.33 18.30
10 35.17 0.67 12.52 50.56 20.50
11 36.50 0.39 2.32 31.11 78.00
12 32.83 -1.17 3.58 8.50 42.00
13 30.78 -3.22 12.52 8.50 42.00
14 30.78 -3.22 12.52 8.50 69.00

 

86

 

Tables 4.8 and 4.9 show that the maximum temperature change caused by the
application of the jet is —3.22°C. Furthermore, the initial ocular temperatures change
slightly as the ambient temperature varies. The relative humidity of the jet does not
appear to have a significant effect on ocular temperature changes as seen by comparison

oftrials 5 to 11, and 13 to 14 in Figure 4.5.

 

._ _ ___._.____. ___. _...__. - I- - r 7,“ L1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I Trials 58:11, 138114
1.00 firial 5: %RH =12.7o.
0.50 _.. _-_... wet = 1.79 mls, net-
0 00 __ Tmitial = -6.56°C
_0 50 . __ ,_- “I ITn'al11: %RH = 78.00.
p ' ”’7 I wet = 2.32 mls, Tjet-
; -1.oo -—— Tlnitial = some
'8 .150 a. ——~~ ITrial13: %RH =42.00.
.. -L-..__-__ __ _g _ wet = 12.52 mls, 11er-
.200
2 50 Tmitul = .25.50°c
- - A ‘ M— — ” ‘7 ITrial14: %RH = 69.00. I
-3.00 k r , .. A f” "'4 Vjet = 12.52 mls, 'liet-
-3.5o Tmitial = -25.50°c II

Figure 4.5 Effect of Jet Relative Humidity on Ocular Temperature Changes
While the pairs of trials in both groups have comparable jet velocities and relative jet
temperatures, the jet relative humidities in each pair are drastically different. Even so,
the differences for temperature changes within the eye are minimal. Therefore, the
conclusion is reached that jet relative humidity does not have a significant effect on
ocular temperature changes. The absolute humidities of the jet were also investigated and
showed no significant effect as well.

The first four trials were performed with equal jet relative humidities and nearly
identical relative jet temperatures. The jet velocities were varied considerably. Ocular

temperature changes are plotted against jet velocities in Figure 4.6.

87

 

Trials 1-4

-1.00

-1.50

Tdelta ‘C

 

—2.00 *

 

 

-2. 50

 

Vjot (mls)

 

 

 

Figure 4.6 Effect of Jet Velocity on Ocular Temperature Changes
The data in Figure 4.6 shows that ocular temperature changes are sensitive to the jet
velocity, independent of the other variables.

It is also evident from Table 4.9 that the eye is more sensitive to lower
temperatures. Temperature changes for colder jets are greater at the same or lower jet
velocities than their warmer counterparts.

Results of the cat testing indicate that ambient temperatures do in fact affect
ocular temperatures. Temperature changes within the eye are increased by the
application of a jet simulating a breeze. These changes are sensitive to jet velocity and
temperature while the effect of humidity is insignificant. Furthermore, colder jets have a
greater impact on temperature changes than warm ones. The greatest temperature
fluctuations experienced during the testing suggest a deviation of i5°C from body core

would encompass all possible temperatures that may occur in the human eye.

88

4.4 Simulation Comparison to Cat Testing

The validity of the human eye model was previously established for heat transfer
to quiescent air at room temperature. Upon obtaining experimental data, it was desirable
to compare cat testing results to simulations with the model to investigate the model’s
potential for future applications. New convective heat transfer coefficients were needed
to simulate the conditions of the testing trials. A literature review uncovered an article
pertaining to round jet impingement heat transfer on a convex, hemispherical surface
[3 2]. Lee et a! developed a stagnation point Nusselt number correlation for jet Reynolds
number range from 11,000 to 50,000 and dimensionless nozzle-to-surface distance from

2 to 10
Nus, =1.68(Re)0'48(L/d)o'l(d/D)0'18 (4.1)
where Nust is the Nusselt number at the stagnation point, Re is the Reynolds number, L is

the nozzle-to-surface distance in m, d is the nozzle diameter in m, and D is the surface

diameter in m [32]. The Reynolds number is defined as

Re = L” (4.2)
,u

where p is the fluid density in kg/m3, V is the fluid velocity in m/s, d is the nozzle

diameter in m, and u is the dynamic fluid viscosity in Pa’s. The convective heat transfer
coefficient is determined from the Nusselt number correlation

hs, D
k

 

Nus, = (4.3)

where hst is the stagnation point convective coefficient, D is the diameter of the eye in m,

89

and k is the thermal conductivity of the fluid in W/mK. The values used in Eqs 4.1-3 are

listed in Table 4.10.

Table 4.10 Constants for Nust Correlation [32]

 

Constant L d D

 

 

Value (m) 0.0254 0.0254 0.0208

 

 

 

 

For all test trials, the jet fluid had a relevant relative humidity. Therefore, the
fluid properties used must be that of humid air rather than its dry air/steam constituents.
Richards et al propose two correlations for determining the dynamic viscosity and
thermal conductivity of moist air from the component properties [33]. The dynamic

viscosity can be determined using

= #1 + #2 (4.4)
1+‘1’12(X2/X1) 1+‘P21(X1/X2)

rum
where pm is the mixture viscosity in Pa*s, u] is the air viscosity in Pa*s, [.12 is the steam

viscosity in Pa*s, ‘1’12 and Wm are coefficients with values 0.8390 and 0.7438

respectively, and X1 and X2 are the mole fractions of air and steam respectively [33].

The thermal conductivity can be determined using

k1 k2
k = +
m 1’r‘1’12(X2/X1) 1+¢21(X1/X2)

 

(4.5)

90

 

where km is the mixture thermal conductivity in W/mK, k1 is the air thermal conductivity

in W/mK, k2 is the steam thermal conductivity in W/mK, (D12 and (D21 are coefficients

with values 0.8153 and 0.7257 respectively [33].
For mixtures of ideal gasses such as air and steam, each component can be treated
as an ideal gas alone at the mixture volume and temperature. Partial pressures can be

evaluated using the ideal gas equation of state

,. R'T
Zpi = g%l_ (4.6)

The mole fiactions of air and steam, X1 and X2, can therefore be determined from

X1 = £,X2 = 5V— (4.7)
Pm Pm

where P,1 is the partial pressure of the dry air, Pm is the total pressure of the mixture, and
PV is the partial pressure of the steam. The relative humidity, o, of the jet can be used to

determine Pv by

¢= (4.8)

where Pg is the saturation pressure of water at the jet temperature, readily available fi'om

steam tables. The partial pressure of the air is the difference between the atmospheric
pressure of the jet mixture and the partial pressure of the steam

Pa = Pm — Pv = Palm — Pv (4.9)
For all trials, the partial pressure of the vapor was less than the saturation pressure of

water at the jet temperature. Appropriate fluid properties for the dry air and superheated

91

vapor at partial pressures and jet temperature were then obtained from several sources
[25, 34, 35, 36]. Jet dynamic viscosity and thermal conductivity were determined using
Eqs. 4.4 and 4.5 while jet density was calculated on a mole fraction basis. The jet

properties are listed in Table 4.11.

Table 4.11 Jet Properties [33]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Trial p (kg/m’) k (W/mK) u (Pa*s)
1 1.180 1.8469E-02 1.8292E-05
2 1.180 1.8476E-02 1.8298E-05
3 1.180 1.8469E-02 1.8292E-05
4 1.180 1.8469E-02 1.8292E-05
5 1.155 1.8857E-02 1.857lE-05
6 1.130 1.9262E-02 1.8829E-05
7 1.095 1.9852E-02 191751305
8 1.064 2.040213-02 1.9467E-05
9 0.930 2.2787E-02 2.0289E-05
10 1.036 2.0784E-02 195201305
1 1 1.082 1.9654E-02 1.8577E-05
12 1.243 1.7596E-02 1.7533505
13 1.243 1.7596E-02 1.7533305
14 1.235 1.7661E-02 1.7526E-05

 

 

 

 

 

The jet properties were then used in Eqs. 4.1-2 to calculate the Reynolds and Nusselt

numbers plotted in Figure 4.7.

92

 

 

150 1m——J———’—— 4.- .4 v.-- _ _ r _-_.___.

 

Nust

100 ~9——~——— .— ~— .7 _ A 4 4* tyre—w

 

 

50 I» —————————- —_———. —.

 

I
‘ r I I I
I o 5000 10000 15000 20000 25000 '
I Re I

 

 

 

Figure 4.7 Nusselt, Reynolds Numbers From Cat Testing
It is important to note that the majority of the Reynolds numbers lie below the range used
by Lee et al [32] and may therefore provide less accurate Nusselt number correlations for
the convective heat transfer coefficient.

The coefficients obtained through Equation 4.3 were then applied to the eye
model. Convection was assumed to be the dominant form of heat transfer at the corneal
surface. The rest of the model remained the same, except that the cat rectal temperatures
were used in place of the human body core. Temperatures from the simulations were

recorded in the region of the proposed sensor location as shown in Figure 4.8.

93

  
 
  

7 Proposed
‘ fl \ Sensor
\ Location

Figure 4.8 Region for Temperature Recording fiom Simulations
This region matches the approximate location of the needle probe used in the cat testing.

Results of the simulations are compared to the testing trials in Table 4.12.

94

Table 4.12 Simulation Comparison to Cat Testing

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Trial “8 t (W/mzK) Tfinal (K) Tsimulation (K)
1 71.36 307.37 30697-30875
2 99.54 306.21 306.1 l-308.18
3 154.51 306.32 304.97-307.42
4 181.60 305.65 304.61-307. l 8
5 71.58 308.37 30896-31008
6 71.87 310.15 31088-31136
7 72.33 310.65 313.09-313.29
8 72.78 309.43 31406-31518
9 74.70 310.87 31923-32094
10 186.05 308.32 316.16-317.1 1
1 1 81.99 309.65 30920-31016
12 99.19 305.98 29954-30355
13 180.97 303.93 296.70-301.67
14 181.15 303.93 296.70—301.66

 

 

 

 

 

The data in Table 4.12 indicate that the simulations with the eye model produce results
comparable to those of the actual trials. The greatest discrepancies occurred in trials 7-
10. The simulation did not provide adequate cooling in majority of the cases where the
jet is heating the eye. The maximum difference between Tfinal and Tsimulation
observed was 8.36 K. Disparities this large discount the accuracy of the model. The

results are, however, comparable. For trials 12-14, where cold jets were used, the

95

simulation temperatures dropped a maximum of 2.6 K lower than the experimental
values. Again, while not ehtirely accurate, the results are comparable promising this

model can be improved upon for use in future applications.

96

Chapter 5. Future Work

5.1 Sensor

This thesis work has focused on temperature considerations surrounding the
sensor’s environment and operation and how they will affect its pressure readings.
However, there is still work to be done in the development of the IOP monitoring system.
To date, the Fraunhofer Institute has not yet delivered a fimctional prototype of the

sensor. Current deliveries of the sensor are shown in Figures 5.1-2.

 

Figure 5.1 Top View of Sensor

97

 

Figure 5.2 Bottom View of Sensor

These large-scale prototypes have the overall dimensions of 4 mm x 2 mm x 1 mm. A
misalignment of the wafers during bonding failed to produce a working prototype. Once
all of the fabrication issues have been worked out and the proof of concept has been
demonstrated, work can begin on scaling the sensor down to actual dimensions.
5.2 Extraocular Components

While fabrication issues of the sensor are being resolved, the extraocular
components can be developed simultaneously. While the Data Acquisition and
Processing Unit is required to complete the system, only the external coil is needed to
demonstrate a proof of concept.
5.3 Chamber Testing

Upon delivery of a firnctional sensor prototype and completion of the external

coil, testing of the sensor can begin. A cubic pressure chamber was constructed out of

98

1.78 cm thick PMMA. The sensor will be placed on the underside of the 2 mm thick
PMMA lid while the external coil will be placed outside the chamber on top of the lid.
The top of the chamber is sealed by gasket-to-gasket contact between the cube and the
lid. Two c-clamps provide adequate pressure for a watertight seal. The base of the cube
is joined to two square aluminum plates using silicone sealant. Sandwiched between the
aluminum plates is a TB Technology potted HT-127-1.4-1.15-71 thermoelectric heater.
The plates are joined by nuts and bolts at each of the four comers. The top plate is milled
out on the top and bottom surfaces to the dimensions of the heater. This provides a path
for heat flow from the heater to the interior of the chamber. Good thermal contact
between the heater and plates is ensured by tightening the bolts and the application of
thermal grease. The leads of the heater are connected to an Instek GPR-1810HD dc
power supply. By adjusting the polarity and level of current to the heater, the chamber
can be heated or cooled. A type T thermocouple leads into the interior of the chamber
through a silicone sealed hole in the side of the cube. The thermocouple wire can be
manipulated so that it records temperatures at the location of the sensor within the
chamber. A manometer tube protrudes from the other side of the cube. Once the
chamber is filled with water or saline solution to simulate the sensor environment,
adjusting the height of the manometer tube provides a means of changing the pressure
within the chamber from 0 to 60 mmHg. A meter stick attached to the side of the
chamber provides a gauge for adjusting the height of the tube. The chamber is shown in

Figures 5.3-4.

99

Iuuuuuuunu-n...

fr.

Aluminum
Plates and

Leads to Power Supply Heater

Figure 5.3 Pressure Chamber

 

100

J

I

&
1

-o
C-clamps + ‘

c-k’ka‘é r. 2"-

W

Thermocouple

t -

 

Figure 5.4 Pressure Chamber Close-up

Testing with the chamber will allow for calibration of sensor readings within the pressure
range of interest. This will also allow an investigation of how sensor-coil spacing and
orientation affect sensor readings. Using the heater to change the temperature of the
chamber will provide an experimental TCR for the sensor. This will determine whether
or not the sensor is capable of reading temperature as well as pressure.
5.4 Implantation

Once an actual scale prototype is received, the sensor may be implanted in the
eyes of cats or monkeys to investigate biocompatibility issues. Short-term and long-term
trials of up to six months can be performed to determine whether the external sensor

materials suffer from in viva etching, resulting in sensor failure. Implantation of the

101

sensor can also address the concern of sensor failure due to a fibrous encapsulation.

Should this present a problem during the period of implantation, coatings such as the

elastomer NUSIL and SiOz have shown promise at reducing cellular metabolic activity in

other research [3 7,3 8].

102

Chapter 6. Social and Ethical Considerations

In today’s society it is important to consider all the possible uses of a new
technology before it is fully explored. Particularly in the biomedical field, a technology
intended to help people could be used for harmful, if not tragic purposes. In the case of
the MEMS pressure sensor, several issues need to be considered.

The external components of the IOP monitoring system will be designed to
operate within certain limits. However, a large enough power source operating at
extremely high frequencies could conceivably melt the sensor coil unleashing the sensor
materials into the eye. All of the sensor materials themselves are biocompatible.
Although, a harmful substance could be placed within the sensor cavity. An altered
external device could then be programmed to destroy the sensor, releasing the harmful
contents in the patient’s body. While there are no issues with the sensor as designed,
there are concerns as to what destructive additions could be made during implantation.

Powerful magnets have the potential to exert large forces on metallic objects. If a
sensor is not removed from a patient, and they encounter a large magnet, serious damage
could occur. A patient undergoing an MRI, for example, with the sensor coil still
implanted, might experience severe injury to their eye. To take things a step further,
strong magnets could be used to intentionally inflict harm to sensor patients.

Although the IOP monitoring system utilizes a wireless connection between
internal and external components, surgery is still required to implant the sensor.

Furthermore, the system demands the patient wear the external components on their

103

body. This may exclude them from certain physical activities or involve some
discomfort.

The IOP monitoring system is being developed as a research tool to study the
causes of acute and chronic IOP elevations and to help physicians learn more about the
onset and progression of glaucoma. Continuous IOP monitoring will enhance the early
detection of elevated IOP and aid in determining the success of various treatment
strategies. The goal in developing this system is to ultimately reduce the number of
people who suffer fiom glaucoma related blindness.

The IOP monitoring system will not be harmful to the patients unless negligence
or bad intentions are involved. The potential for this research to improve the quality of
life for people with elevated IOP levels outweighs the possibility it could be used to do

harm.

104

Chapter 7. Conclusions

This work has produced several important pieces of information necessary for the
development of the IOP monitoring system. A model was formulated to determine the
resistance in the sensor’s inductor coil as a function of temperature and frequency. While
the resistance is not required for determining IOP, the author has demonstrated the
potential for using the changing resistance values to record temperature as well as
pressure from the sensor.

Once the sensor is implanted, a patient’s IOP levels are indirectly determined
from the voltage drop across the resistor in the external data acquisition and processing
device. An alternate means of determining IOP has been presented by measuring the
phase of the external device [15].

In order to accurately obtain IOP values from the voltage drop across the external
resistor, a dip in the profile must be easily detectable. Calculations for thermal noise
present a SNR >> 1, ensuring the required profile dip is distinguishable.

The presence of additional sensor capacitance due to the inductor coil was
investigated. Any deviations from the nominal inductance were shown to have no
detrimental effect on the sensor’s operation. The sensitivity of the inductance to changes
in temperature is 0.007 nH/°C and is therefore negligible.

The parallel plate model of the sensor’s capacitance provides the only direct
relationship between capacitance and the diaphragrn’s center spacing. However, two
additional models were presented. Calibration of the device may prove these additional

models to be more accurate as diaphragm deflection increases. The author has

105

demonstrated that the sensor capacitance will be determined from diaphragm deflection
only, with negligible changes due to variations in cavity temperature and pressure.
Furthermore, dielectric breakdown will not occur when relatively large voltages occur
across the micron level gap of the capacitor.

Investigations into the sensor cavity have shown the cavity pressure has a
significant sensitivity to temperature of 2.45 mmHg/°C. Resistive heating of the inductor
combined with a temperature increase of 10°C would produce a deviation of 40.83% of
the pressure range of interest (760 — 820 mmHg). The cavity temperature must therefore
be known to accurately determine IOP.

Testing performed on cats verified that the temperature in the eye is not constant
and will deviate from the body core temperature, as proposed by several articles [27, 28,
29]. The maximum temperature change achieved fi'om blowing a jet of air at the eye of
the subject was —3.22°C. Results suggest that a deviation of i5°C fiorn body core would
encompass all possible temperatures that may occur in the human eye. An inspection of
the testing showed that the temperature changes were a function of jet velocity and were
more significant for colder jets, while the relative and absolute humidity of the jet was
irrelevant. The author also generated a finite element heat transfer model of the eye,
producing results comparable to those fiom the cat experiment.

While implanted in the eye, the temperature of the sensor’s environment will vary
several degrees. These variations will not affect the location of the voltage dip used to
determine IOP readings from the sensor. However, temperature changes in the sensor

have the potential to manifest themselves in the height of the voltage dip, allowing the

106

sensor to record temperature as well as pressure. Recording temperature will provide the

cavity pressure values necessary to accurately determine IOP.

107

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