~1
Power Limits Influencing Retinal Prosthesis Design
by-1-1P
Russell Erich Caulfield
MASSACHUS ETTS INSTITUTE
OFTEC HNOLOGY
I APR 2 4 2001
B.S. Physics and Mathematics
Morehouse College, 1998
LIBF ARIES
Submitted to the Department of Electrical Engineering and Computer Science
in partial fulfillment of the requirements for the degree of
Master of Science in Electrical Engineering and Computer Science
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2001
© Massachusetts Institute of Technology 2000. All rights reserved.
Author................
.-......
...................
Depment of Electrical Engineering and Computer Science
October 10, 2000
Certified by......
--------I ----.
.. Q...............
John L. Wyatt, Jr.
I~ rrotessor, DeparAment of Electrical Engineering and Computer Science
Thesis Supervisor
Accepted by.................
Arthur C. Smith
Chair, Department Committee on Graduate Theses
2
Power Limits Influencing Retinal Prosthesis Design
by
Russell Erich Caulfield
Submitted to the Department of Electrical Engineering and Computer Science
on October 10, 2000 in partial fulfillment of the
requirements for the Degree of Master of Science in
Electrical Engineering and Computer Science
ABSTRACT
Ocular tolerances to light and radiofrequency radiation limit the possible designs for a
chronically implantable retinal prosthesis. The constraints imposed by these tolerances limit the
ways that power can safely be delivered to an implanted device. Two possible schemes for
powering such an implant were investigated: 1) infrared laser light and a photodiode array and 2)
a magnetically coupled coil pair.
In the first case, current safety limits for infrared lasers were obtained and ambient light levels
were determined. From these data, calculations were made which yielded the maximum power
output for this kind of arrangement. A similar method was used for the magnetically coupled
coil pair, which included a model for the two coils. The two setups were then compared, with
power output being the most salient feature.
Thesis Supervisor: John L. Wyatt, Jr.
Title: Professor
3
Acknowledgements
The work done on this thesis was supported by the Ford Foundation Predoctoral Fellowship for
Minorities and the Graduate Student Office, and I extend my heartfelt gratitude to those
organizations for supporting this stage of my graduate education.
Thanks to Shawn K. Kelly and Andrew E. Grumet, PhD. for all of their help.
Thanks to Dr. Joseph Rizzo for his generosity and knowledge.
Thanks to the summer library staff at the New England College of Optometry for all of their
assistance.
Thanks to Dean Isaac Colbert for his kindness and advice.
Thanks to my family and friends for supporting me in my efforts.
Lastly, thanks to Professor John L. Wyatt, Jr. for his invaluable mentorship, guidance and
insight.
4
Contents
1
Introduction
7
2
Implant Power Calculation
8
2.1
Assumptions.................................................................................
8
2.2
Power Derivation..........................................................................
9
2.3
Issues Requiring Further Study............................................................
3
4
14
Ambient Light
15
3 .1
Units..........................................................................................
15
3.2
Ambient Power Levels.....................................................................
16
Laser Power
18
4.1
Assumptions.................................................................................
18
4.2
Laser Power with Receiver in Posterior Region of the Eye...........................
19
4.2.1
Assumptions......................................................................
19
4.2.2
Thermal Injury/ Retinal Tolerance Levels....................................
20
4.2.3
The Thermal Model..............................................................
20
4.2.4
Damage Threshold Ranges......................................................
24
4.2.5
Posterior Placed Power Output.................................................
25
4.2.6
Theoretical Implant Performance
26
4.2.7
Issues Requiring Further Study ................................................
.............................
27
5
4.3
5
27
4.3.1
A ssumptions......................................................................
28
4.3.2
Power Calculation................................................................
28
4.3.3
Issues Requiring Further Study.................................................
31
Magnetic Coupling
5.1
U nits...........................................................................................
32
32
5.2
Damage Mechanism........................................................................
33
5.3
Threshold Standards........................................................................
33
5.4
ANSI C95.1 1982...........................................................................
33
5.5
Derivation of the ANSI Standard.........................................................
35
5.6
ANSI C95.1 1990 Proposal................................................................
38
5.7
Assumptions for Power Calculation......................................................
41
5.8
Magnetic Coupling With Receiver in the Anterior Region of the Eye............... 41
5.9
6
Laser Power with Receiver in Anterior Region of the Eye.............................
5.8.1
Assumptions.......................................................................
41
5.8.2
Coil Geometry.....................................................................
42
5.8.3
Power Calculation.................................................................
5.8.4
Power Output....................................................................... 45
Magnetic Coupling with Receiver in the Posterior Region of the Eye...............
43
46
46
5.9.1
Assumptions........................................................................
5.9.2
Power Output....................................................................... 47
5.10 Issues Requiring Further Study............................................................
48
Conclusions and Future Work
49
6.1
Biological Constraints....................................................................... 49
6
6.2g
6.3
...................................................................
Summary...--
---
- --
- - --
- -- --.. . . . . . . . . . . . . . . . ---.-
....................
..........
50
........... 51
7
Chapter 1
Introduction
The aim of this thesis is to examine parameters that would impact the design of a prosthesis that
would restore useful vision to persons suffering from degenerative conditions of the retina,
namely retinitis pigmentosa and age-related macular degeneration. In an attempt to determine an
effective method for powering this kind of implant a survey of two possible sources will be done:
1) an ambient/laser light source and 2) a magnetically coupled coil pair. First, power
requirements for an implant will be derived using measurements from short-term human
experiments. Using these power calculations, the effectiveness of the two methods will be
investigated.
To gain insight into the feasibility of using natural and artificial light sources, the following
factors will be discussed: the ambient power on the retina while exposed to daylight, the
threshold limit values (TLV) for daylight and infrared laser and the power output of a pn
converter while illuminated with the aforementioned light sources. To explore the plausibility of
using magnetic coupling, the maximum permissible magnetic field strength vs. frequency curve
will be examined and the maximized power output of a coil pair will be derived. Finally a
comparison of the two methods will be made, giving recommendations for further areas of study.
8
Chapter 2
Implant Power Calculations
2.1
Assumptions
Before any meaningful discussion can begin about the power requirements for a retinal implant,
assumptions have to be made to simplify calculations. Thus, for both powering regimes it is
assumed that: 1) the only power that is required is that needed stimulate tissue , i.e. the power
needed by the accompanying electronics will be ignored and 2) The stimulation frequency is 50
Hz. The first assumption is really an assumption that the majority of the power is dissipated in
the electrodes rather than the electronics. It is probably reasonable to ignore the power
dissipation in the logic and signal processing electronics. But, the power in the electrode drivers
might be comparable to the power lost in the electrodes themselves, in which case this
assumption would be optimistic by about a factor of two. The second is made since 50 Hz is the
"flicker fusion" frequency at which repeated electrical stimulation is perceived as continuous
illumination.
9
2.2
Power Derivation
The following power requirements are derived from human experiments conducted by the
Retinal Implant Project Group at the Massachusetts Institute of Technology. In these
experiments, volunteers who suffered from advanced stage Retinis Pigmentosa underwent acute
implantation of a micro-fabricated electrode array. A small incision was made in the eye, and
the array was then placed against the retina. The exposed area of the electrodes was connected
via leads, fabricated on a polyimide substrate, to a printed circuit board that was connected to a
stimulator box. The stimulator box generated a series of biphasic current pulses that were
delivered to the retina. After each series of pulses, the patient was asked to describe what he/she
had seen, if anything (in some instances controls were used in which no current was applied).
The values used for the power requirements represent the threshold of consistent visual
perception of the applied stimulus. Figure 2-1 shows the strength duration curves obtained.
-+-Exp#1 LE
--- Exp #1 SE
-Exp
#2 LE
1800
1600
1400
1200
1000
800 -600-400-200-0
0.25
4
1
16
Time
(Ms)
LE:Large Electrode
SE:Small Electrode
Figure 2-1: Strength vs. Durations Curves for MIT Acute Human Experiments
10
It should be noted that in experiment # 1 large electrodes (400 pm diameter) and small
electrodes (100 pm diameter) were used, while in experiment #2 only large electrodes were used.
Examination of the graph shows that measurements were taken while using 0.25ms , Ims, 4ms
and l6ms pulses, i.e. each segment of the biphasic wave form lasted the given time. Below in
Figure 2-2 is an example of a biphasic waveform with an amplitude of 200pA and a duration of
4ms:
-------- 4ms --------I = 200mA
I=0A
I=0A
I = - 200pA
------------ 4ms
-------
Figure2-2: Example of a Biphasic Waveform
The values for the 16ms pulses will be neglected since the current waveform used for those
stimuli ramped down over the pulse duration, i.e. the value of the current decreased as a function
of time. For each pulse amplitude the back voltage was measured while the electrodes were
submerged in saline, which approximates the voltage that would be seen if the device were inside
the body. In each case, there is a resistive voltage drop that occurs in the leads to the electrodes,
1
and a capacitive drop which happens at the metal/fluid boundary. Figure 2-3 shows a circuit
model which describes electrical properties of the tissue/arrayinterface.
Lead Resistance
Metal/Fluid Boundary
Figure 2-3: Circuit Model for Tissue/Array Assembly
The power equation that takes both of these voltages into account for each electrode is:
Pavg = D.C.(0.lIVres + 0.5IVcap)
(2.1)
where D.C.= duty cycle, I = the stimulating current, Vres = the resistive voltage drop and Vcap =
the capacitive voltage drop. The first term in the equation accounts for the power dissipated in
the series resistor. The 0.1 in that term is used to approximate the actual resistive contribution
seen by an implantable device, which would contain leads considerably shorter than those used
in the acute human experiments. The second term describes the power lost in the capacitor.
Analysis of the circuit model shows that power is dissipated in the resistor during both the
negative and positive parts of the input waveform. However, power is stored in the capacitor
during the negative segment and recovered during the positive portion, though the recovered
power is unused. Note, if the two terminals of the model were shorted together after the negative
part of the waveform, the passive discharging of the capacitor would be fast enough to keep up
with the input, since the time constant for the RC combination is on the order of ps and the time
12
between pulses is on the order of ms. Thus, because the goal is to minimize power, passive
discharging will be assumed, though it was not used in the acute experiments. This kind of
discharging has a power comsumption that is identical to the power used during the negative part
of the input waveform. Using this method, the duty cycle is calculated using the relation D.C.
=
(stimulation frequency) x (pulse duration). As noted, a stimulation frequency of 50 Hz will be
assumed, and the measurements for experiment # 1 used. A summary of the back voltages for
each of the pulse durations is shown in Table 2-1 below:
Table 2-1: Back Voltage Measurements for a Single Electrode Submerged in Saline
Pulse duration = 0.25ms
Pulse duration = ims
Pulse duration = 4 ms
Large Electrodes (400im)
Small Electrodes (100im)
Threshold current = 1.6 mA
Threshold current = 1.275 mA
Vres =9.6 V
Vre
Vcp =2.4 V
Vap =2.4 V
Threshold current = 800 iA
15 V
Threshold current = 450 piA
Vrs=6V
Vre=12V
Vc,= 2.4 V
Vc,= 2.4 V
Threshold current = 200 pA
Threshold current = 195 pA
Vres= 1.6 V
Vres= 6.2 V
Vcap 2.4 V
Vcap = 2 .0 V
The values found in Table 2-1 were derived from the output waveforms displayed on an
oscilloscope. A sample waveform is show below in figure 2-4
13
Vres
Vcap
Voltage
Time
Figure2-4: Sample Output Waveform for Back Voltage Measurements
This is a relatively simple waveform, and can be explained in terms of the circuit model given in
Figure 2-3. The initial vertical portion is the result of the nearly instantaneous voltage set up
across the resistor by the current step input. The ramped portion of the waveform occurs as the
now constant current removes charge from the capacitor, linearly decreasing the voltage. Thus,
Vres was determined by measuring the vertical fall of the waveform, which represents the IR
drop. Vcap was derived by simply taking the difference between the initial and final values of the
ramp.
Table 2-2, shown below, summarizes the power requirements for each of the pulse durations
described.
14
Table 2-2: Power Requirements Per Electrode
Large Electrodes (400pm)
Small Electrodes (100pm)
Pulse duration = 0.25ms
43pW
43pW
Pulse duration = ims
72gW
54pW
Pulse duration = 4 ms
54pW
63pW
2.3
Issues Requiring Further Study
Among the weaknesses of the previous derivation are the apparent inconsistencies between the
circuit model predictions and the actual measured values. The model predicts that Vres should
scale linearly with stimulation current and Vap should scale with charge. However, Table 2-1
shows that neither is the case. Furthermore, for a 4 ms pulse duration, the lead resistance should
be equal to Vres / Threshold current = 1.6V / 200pm= 8k Q2. But, the array has a resistance per
square of 0.276 0 /0L.
With 2400 squares between the pc board and a 400pm electrode, the
series resistance should be 2440 El x 0.276Q/ = 660 Q, which is an order of magnitude smaller
than what was measured. Similar discrepancies occur for the other stimuli. Development of a
more comprehensive model should give results closer to the measured values. However, since
the power calculations serve only as an estimate of the power needed, the model is adequate for
the purposes of comparing the two methods under consideration.
15
Chapter 3
Ambient Light
3.1
Units
There are numerous systems of units that have been used to describe the various aspects of
radiant spectral energy, e.g. the photometric, radiometric and heat transfer regimes, among
others. For the purpose of minimizing the confusion that could arise while attempting to
compare values, the radiometric system of units will be used. This scheme is used by several
disciplines, and readily lends itself to easy conversion among quantities [1]. One unit of
particular interest is the illuminance, which describes the power incident on a surface per unit
area (W/cm 2). This unit will serve as the standard for comparison of retinal power levels when
exposed to light of any kind. When discussing retinal tolerance to different kinds of light,
figures often give the maximum radiant fluence (J/cm2 ) allowed for a given exposure time (sec).
In these cases, one can easily calculate the illuminance by dividing the radiant fluence by the
exposure time.
16
3.2
Ambient Power Levels
The sun emits a tremendous amount of electromagnetic radiation in all direction as a result of
fusion reactions. However, only a tiny fraction, 0.1380 W/cm 2 , actually reaches the earth's
atmosphere [2]. The amount of power that reaches the surface of the earth is smaller still, and
varies greatly depending on weather conditions, time of year and location. A figure commonly
used is 0.100 W/cm 2 [3]. The amount of power incident on the retina is also variable, and is
influenced not only by the aforementioned factors, but also by age, pupil size and eye position.
Figure 3-1 illustrates a variety of irradiances the retina might encounter.
Some irrandiances of note are:
a) Ambient daylight looking away from the sun
b) In daylight looking towards the sun
-10-
W/cm2 [4]
~10 W/cm2 [4]
It should be noted that for a) the sun's energy is not directly incident on the eye, and so the
power on the retina is less than 0.1 W/cm2 . In b) the lens focuses the sun's image, raising the
power at the retina by a factor 100 over the surface irrandiance.
17
le'
I
i
LASER
(I
I
W INTO EYE I
10" I
102
0
XENON SHORT-ARC SEARCi,..GHT
20 kA
-LASE
2
-E10,
8000"N
WELECT
OR CARBON
40
< L
RC
FO
ARC
'
.
AB"N 1
I%40
K
0.15 s. ExPKS.RE
3007K
BLACKBCOY
4r
T_0
-
-j
4Ij
N SE
BLUE
LIGHT
FILAMENT
zL~
a:
RO
TECHNIC
0w0
0
(.
HAZARDS
FLARE
FROSTEV
INCANOESCENT
LAMP
o S.
1,
CD
FLUORESCTNLAMP
"S
OUTOOOR
OAYLUGoT
C ANOL E
E
10 -
w
ELECTROLUMINESCENT
PANEL
INTERIOR
(DAY)
5-j-
-J
S10 MIN.
Jr
IdolI9,Um
- I 11:1,111109
ANGLE
iIlIltll
m
6-1
I
SOURCE
1,11,1111ll
Imm
Icnm
TYPICAL RETINAL IMAGE SIZE
0-
7-
Figure 3-1: Retinal Irradiances [4]
-
18
Chapter 4
Laser Power
4.1
Assumptions for Laser Power
Numerous issues arise from using an infrared laser to deliver power to an implanted device,
among them the focusing effects of the lens. Because a laser is collimated light source, it's
intensity will magnified several orders of magnitude before it reaches the retina [8,9,10]. As a
result, the part of the retina that is actually illuminated will be very small. In addition, the size of
the pupil is highly variable, and depends on the light level. To avoid the problems associated
with a small area and the variability of the pupil, two assumptions will be made about the laser
set up, 1 ) the lens has been removed and 2) the size of the pupil is fixed. The third assumption is
that the receiver is a pn diode array with 15% efficiency and that the size of the accompanying
circuitry is negligible. It should be noted that the engineering goal is to spread the laser beam
over the area of the photodiode array. Focusing by the lens is contrary to that aim, and as such,
the lens is removed from the model.
19
The aforementioned assumptions simplify the comparisons between not only laser and
magnetic coupling, but also between anterior and posterior placement of the receiver in the laser
powered arrangement. When the effects of the lens and the pupil are ignored, easier use is made
of safety standards developed for the retina itself. In addition, neglecting the lens allows simpler
calculation of the illuminated area of receiving device.
4.2
Laser Power With Receiver in Posterior Region of the Eye
When discussing the possibility of placing a receiver in the posterior region of eye, it is
necessary to describe where that region lies. Figure 4-1 below is a cross-section of the eye, and
illustrates the placement of the receiver:
Iris
Vitreous
Receiver
Retina
Cornea
Aqueous
Figure 4-1: Posterior Placement of the Receiver
4.2.1
Assumptions
As previously stated, neglecting the magnifying effects of the lens allows for simpler calculation
of the illuminated area. To facilitate comparison between laser and magnetic coupling, the
20
following assumptions will be made about the laser/receiver arrangement 1) The largest device
that could be implanted is a circular disc with area 1cm 2 and thickness 1 Opm 2) a lens has been
implanted which spreads incoming light such that 1 cm 2 is illuminated on the retina 3) the
limiting factor for incoming light is the amount the could that could safely continuously fall on
the retina and 4) the safety standards for a non-laser optical source that yields a large retinal
image are comparable to those for a laser whose beam has been spread by a lens with negative
curvature. The first assumption comes from surgical constraints that would limit the size of an
incision that could be made in the eye, as well as the restrictions on how flexible the device
would have to be. The device has to be thin (-10 pm), to be flexible enough not to harm the
retina when placed against it. The second removes the need to calculate the effects of the lens.
The third assumption takes into account the worst case, in which the receiver is misaligned and
the incoming power falls directly onto the retina. The fourth assumption results from the lack of
safety standards for the laser setup being considered. Since this arrangement is somewhat novel,
it is not unexpected that such an absence should arise. However, without the focusing power of
the lens, it is reasonable to treat the power delivered by the laser the same as any other light
source. In this case, the safety standards assume a broadband light source, which includes
contributions by shorter wavelengths [34]. Since shorter wavelengths have less of an effect on
temperature than infrared, the standards may actually be conservative for a pure infrared source.
With these assumptions an investigation of posterior placement can now begin.
4.2.2
Thermal Injury/Retinal Tolerance Levels
A number of studies have been done on the damaging effects of light on the retina, and
mechanisms responsible for them. Most conclude that there are three processes by which light
21
damages the retina: photochemical, thermal, and mechanical [5]. Photochemical damage often
results from excessive exposure to ultraviolet (UV) radiation that can be found in sunlight as
well as other industrial sources [5]. Thermal effects are often linked to infrared light, which,
when incident on the retina, can cause significant temperature rises. Mechanical damage can be
caused by short bursts of UV light produced by pulsed lasers.
Of the retinal injuries that occur, problems caused by sunlight are among the most common. The
harm associated with sunlight results mostly from the photochemical effects of the shorter
wavelengths of the spectrum. The retina sustains burns after only 90 seconds of looking directly
into the sun [6].
In addition to the connection between wavelength and retinal injury, there is
also a correlation between retinal image size and the damage threshold: as the image diameter
increases, the threshold for damage decreases [11]. This inverse relationship is illustrated in
Figure 4-2, which shows threshold levels for durations of Is to lOs [27].
It should be noted that
the curves shown in Figure 4-2 are for non-laser sources. However, as stated, it is assumed that
these values are reasonable approximations for the laser arrangement being discussed.
The inverse curve results from the retina's inability to dissipate heat as effectively for large
images. This fact is especially salient in this context since, for longer durations in the infrared
region, the primary mechanism for damage is thermal. As the retinal temperature increases, the
probability of coagulation also rises. It is generally accepted that temperature rises greater than
9-100 C for several minutes constitute a danger to retinal tissue [5,14]. The above statements are
derived from the work of Clark, Ham and others who have developed thermal models of the
retina based on heat conduction.
22
1000'
3-mm
pupil
E
7-mm
Threshold from data of Ham
et al.
pupil
w
100
z
z
USAEHA MPE
c
10-
IO1m
1OOJm
1000pjm
RETINAL IMAGE SIZE
Figure 4-2: Safety Thresholds for Retinal Irradiances vs. Image Size
for Broadband Light Sources [27]
4.2.3
The Thermal Model
Though a number of models have been developed which describe heat flow in the retina, the one
proposed by Clarke, Geeraets and Ham most lends itself to use in designing a chronically
implantable device [13]. The reason this model is more useful lies in the fact that it predicts the
steady state values of the temperature rise, which is a main criterion for a retinal implant.
23
In this derivation, it is assumed that the pigment epithelium and the choroid act as uniform
absorbers, with differing absorption coefficients [13]. It is also assumed that the beam has a
uniform power distribution in its cross-sectional area [13]. Inserting this model in the steady
state heat equation:
V2 (T) = -A(r,O,x)/K
(4.1)
where r, 0, and x are cylindrical coordinates, T = temperature above ambient; K = thermal
conductivity; A = a heat generator function = A(r,0,x) = Ace'
= aaye'
(0<=x<=-c,O<=r<=b,O<=<=27) and is 0 elsewhere; and a = an absorption coefficient and c0 =
surface power density, we find the axial temperature to be:
T(xa) = (aaJ/2K)e'c x I
eax'[b 2 + (x
-
x') 2] 1
2
-
Ix-x'l dx'.
(4.2)
The numerical integration was performed by Clarke, Geereats, and Ham using a modified
trapezoidal rule technique [14]. The spatial parameters of the above equations are shown below
in Figure 4-3:
INCISENT
BEAM
C
-
-
Figure 4-3: Spatial Parameters for Heat Conduction Based Retinal Model [14]
24
In this case K = 1.5 x 10-3 cal/*C cm-s, which is the thermal conductivity of water. The results
for images with the diameters ranging from 5 pm to 1 mm are shown below in Table 4-1.
Table 4-1: Retinal Temperature Rise Due to Optical Irradiances for the Rabbit [151
Radius (p)
1000
800
500
400
250
200
150
100
75
50
25
12.5
10.0
5.0
Temperature rise6
[*C(WI/cmi)]
Position. of
hottest point
(JA)
4.15
3.30
2.03
1.60
0.96S
.
0.758
0.550
0.345
0.247
0.152
0.0648
0.0269
0.0201
0.0078
10109+
9+
9
98+
87+
76
5+
5
5-
Power density
at the retina for
10'C temperature
rise (W/cm 2)
Power entering
eye for 10*C
temperature rise
(mW)
2.41
3.03
4.93
6.25
10.3
13.2
18.2
29.0
40.5
65.S
154
372
498
1282
82.3
66.2
42.1
34.1
20.0
18.0
14.0
9.90
7.78
5.62
3.29
1.98
1.70
1.09
Spectral and spatial similarities between the human and rabbit retina make these calculations applicable to the hunan.
bAs measured at the hottest point.
Behind the anterior boundary of the pigment epithelium.
The table features the temperature rise that results from an illuminance of 1 mW/cm2 (column 2)
and the amount of power needed to raise the temperature 10*C, among other properties. The
featured results use the spectral characteristics of rabbits from the chinchilla gray and Dutch
strain [14]. These results are similar enough to human values that they may be substituted for
human results [15].
4.2.4
Damage Threshold Ranges
It has been suggested that a temperature increase of as little as 1 to 3 0 C may make the retina
more susceptible to UV photochemical damage. However, when a pure infrared source is used,
25
the effects are thermal, and temperature elevation in this range can be tolerated for extended
periods (several minutes) [5,14,17]. There is no clear line separating the wavelengths of light
that cause thermal and photochemical damage. However, it has been shown that a retina
illuminated for extended periods with wavelengths below 550 nm show damage with
temperature rises which are too low to be attributed to thermal effects. [181. In addition, with
wavelengths above 550 nm, significant heating can take place, and thermal damage is likely if
the incident power is sufficiently high [18].
4.2.5
Posterior Placed Receiver Power Output
Most simple pn photodiodes are made of silicon and have efficiencies ranging from 10% to 25%.
If one has a circular disc device with an active area of 1cm 2 , this corresponds to a diameter of
1.12cm. Assuming that the trend shown in Figure 4-2 continues, extrapolation gives a maximum
retinal irradiance of approximately 0.1 W/cm2 . With a 1cm2 device operating with 15%
efficiency, one would expect a power output of 0.15 x 1cm 2 x 0.1 W/cm2 = 15mW when
illuminated with an infrared laser at the TLV. Similar calculations were done for direct sunlight
and ambient daylight. The results are summarized below:
Light Source
Theoretical Electrical Power Available
Infrared laser (-820nm)
15 mW
Ambient daylight
15 ptW
Direct sunlight
11 8p.W (only for 90 seconds)
26
The 118 LW obtained for direct sunlight results from calculating the area based on a retinal
image diameter of 0.01cm, and an exposure of 10 W/cm2 (see figure 3-1 for these values).
4.2.6
Theoretical Implant Performance
To access the viability of using light as a source of power for a retinal prosthesis, a survey of the
power requirements for such a device was done. For simplicity, the assumption will be made
that all of the power produced by the photodiodes is available for use in stimulating tissue.
Using the values above, the number of electrodes that could be powered for each combination of
light source and stimulation value is shown below in Table 4-2:
Table 4-2: Number of Electrodes Powered for Various Light Sources
Large Electrodes (400 jm)
Pulse Duration = 0.25ms
Pulse Duration = tms
Pulse Duration = 4 ms
Small Electrodes (100pjm)
Power needed/elec. = 43ptW
Power needed/elec. =43jiW
# via laser = 348
# via laser = 348
# via direct sunlight = 2*
# via direct sunlight = 2*
# via ambient daylight = 0
# via ambient daylight = 0
Power needed/elec = 72 ptW
Power needed/elec = 54 tW
# via laser = 208
# via laser = 277
# via direct sunlight = 1*
# via direct sunlight = 2*
# via ambient daylight = 0
# via ambient daylight = 0
Power needed/elec = 54 ptW
Power needed/elec = 63 ptW
# via laser = 277
# via laser = 238
# via direct sunlight = 2*
# via direct sunlight = 1*
# via ambient daylight = 0
# via ambient daylight = 0
*Direct sunlight is safe for only 90 seconds of continuous exposure
27
4.2.7
Issues Requiring Further Study
There are three items that require additional attention before a more precise assessment can be
made of using a laser powered implant with the receiver placed in the posterior region: 1) there
are no safety standards for lasers with large beam cross-sections 2) the non-laser standards used
in the power calculations only cover retinal areas up to 2mm in diameter and 3) very little of the
literature addresses long term temperature elevation. The first two issues are related, and
highlight problems associated with designing devices to operate outside of the body's normal
experiences. The third issue is a concern because, although temperature rises of 100 C might be
tolerable for timescales on the order of minutes, it might be unwise to attempt to extrapolate the
effects for levels that are maintained for days or weeks.
4.3
Laser Power With Receiver in the Anterior Region of the Eye
Figure 4-4 shown below illustrates a receiver place in the anterior region of the eye:
Iris
Vitreous
Receiver
Retina
Cornea
Aqueous
Figure 4-4: Anterior Placement of the Receiver
28
4.3.1 Assumptions
Numerous issues immediately arise when attempting to design a receiver that sits in the anterior
region of the eye. Foremost is the problem of modeling such a system. Because the notion of
placing a heat-generating object in the front of the eye has not received serious study, no thermal
limits have been developed for the acceptable power output of such a device. However, one is
able to place an upper bound on the amount of power that can be delivered if the following
assumptions are made about the configuration: 1) the incident power is generated uniformly
throughout the volume of the eye 2) the thermal properties of the vitreous are approximately the
same as for water 3) the eye is surrounded by an infinite bath of water which is separated from
the vitreous by an infinitely thin membrane and 4) the highest temperature rise that can be
tolerated occurs in the center of the eye and is 1" C. The first three assumptions are made so that
the maximum power is dissipated in the illuminated region. The fourth assumption is based on
the safety standards for the retina, which allows a 100 C rise in temperature. A factor of 10 was
added to account for the unknown properties of the other structures in the eye that are less
vascularized than the retina. The aforementioned assumptions do not agree fully with ocular
properties, e.g. the membrane at the boundary is not perfectly conducting, and the tissue around
the eye is not uniform enough to behave like an infinite bath. However, as a first pass, the values
that will be obtained should provide an estimate of the upper bound on the incident power that
could safely be delivered to the eye.
4.3.2
Power Calculation
The calculation is begun with the relation:
29
p(4/3)nr3 = J47r
2
(4.3)
Where p = the power density [W/cm3 ] , r = radius, and J = heat flux density [W/cm2 ] directed
outward in the radial direction. This relation implies:
p(4/3)ir 3 = C V T47rr 2
(4.4)
where C is the thermal conductivity and T is temperature. Simplifying gives:
pr/3C
=
-8T/8r
(4.5)
which implies
T(r) = -pr 2/6C + T,
(4.6)
Where T. is a constant. The assumption that the membrane is infinitely thin yields
T(R)
=
Text
(4.7)
where Text is the external temperature and R is the radius of the eye. Note, by the assumption
that the highest temperature occurs in the center:
T(O)
=
Text + pR2 /6C
(4.8)
Thus the following relationship is obtained for the temperature as a function of distance from the
center of the eye:
T(r) = Text + p(R 2 -r2)/6C
(4.9)
To find the power needed to cause a 10 C rise in the center (above Text = normal body
temperature), first, rearrange equation 4.9, which gives:
30
p = 6CAT / R 2
(4.10)
where C = 6.29x10 3 J/oC s-cm is the thermal conductivity of water and AT = T(0)- Text is the
temperature change and R = 1.25cm. Substitution yields p = 0.024 W/cm 3 , which for an eye of
radius R = 1.25cm gives 200 mW of total power entering the eye. Assuming that a photodiode
array with 15% efficiency is used, then the maximum power available becomes 30mW.
Table 4-3: summarizes the numbers of electrodes that could be powered using this value
Table 4-3: Number of Electrodes Powered With
Receiver in the Anterior (an upper bound)
Pulse Duration = 0.25ms
Pulse Duration = ims
Pulse Duration = 4 ms
Large Electrodes (400pm)
Small Electrodes (100pm)
Power needed/elec. = 43pW
Power needed/elec. = 43pW
# via laser = 697
# via laser = 697
# via direct sunlight = 2*
# via direct sunlight = 2*
# via ambient daylight = 0
# via ambient daylight = 0
Power needed/elec = 72 pW
Power needed/elec = 54pW
# via laser = 416
# via laser = 555
# via direct sunlight = 1*
# via direct sunlight = 2*
# via ambient daylight = 0
# via ambient daylight = 0
Power needed/elec = 54 pW
Power needed/elec = 63 pW
# via laser = 555
# via laser = 476
# via direct sunlight = 2*
# via direct sunlight = 1*
# via ambient daylight = 0
# via ambient daylight = 0
*Direct sunlight is safe for only 90 seconds of continuous exposure
4.3.3
Issue Requiring Further Study
31
The main issues that should be resolved before a more precise description of this assembly can
be done are: 1) An accurate model for heat conduction in the anterior configuration should be
developed and 2) safety thresholds for relevant ocular structures need to be obtained. Again, due
to the nature of this set up, established standards do not totally account for the subtleties that may
arise from this design, e.g. the effect of having a large percent of the incoming power locally
dissipated into the vitreous and surrounding tissue, and the fact that the eye wall is not perfectly
conducting.
32
Chapter 5
Magnetic Coupling
5. 1
Units
As in examining the effects of light on tissue, when studying the interactions of radiofrequency
(RF) radiation with biological systems, units that will serve as the basis for comparison must be
adopted. In this case, the standard units that will be used are the average specific absorption rate
(SAR), i.e. the time rate of change of the total energy transferred to the absorber, divided by the
total body mass, given in W/kg, and the intensity of the magnetic field H, measured in
Amperes/meter. Thus, when a threshold curve is given in terms of magnetic field strength as a
function of frequency, it is based on a particular SAR, i.e. the magnetic field strength is the field
magnitude necessary for the whole human body to absorb the power described by the SAR.
This set of units is chosen since the most relevant results given in the literature adopt this scheme
[19,20,21,22].
33
5.2
Damage Mechanisms
The majority of the data relating to damage caused by frequencies from 0.5 MHz to 100GHz
suggest that injury is the result of thermal insult [25]. According to work published by S. M.
Michaelson, RF tissue heating in the 10kHz - 100MHz range is caused by the free rotation of
proteins and other bipolymers [26]. Since absorption in this mode does not result in structural
changes in the molecule, the resulting collisions with neighboring molecules only result in an
increase in kinetic energy [26]. With the biological molecules unchanged, this increase in energy
causes an increase in temperature, which can lead to the denaturation of proteins and other
adverse effects.
5.3
Threshold Standards
A brief survey of the literature on the subject reveals large disparities in the safety standards
between counties, and even within countries, depending on the agency setting the guidelines.
The main reason for the variations lies in differences in philosophy among various countries
about the factors that warrant consideration in setting standards, e.g. whether it is sufficient to
consider radiation levels that induce changes in biological functions or whether adverse effects
are needed for exposure to be deemed excessive [20].
5.4
ANSI C95.1 1982
A series of standards have been developed in the West which have been useful in determining
safe limits for exposure to magnetic and electric fields. The first of the most recent set of
guidelines was the American National Standard Institute (ANSI) C95.1, published in 1982. This
34
document was the result of a selection process which involved several hundred papers, 32 of
which were chosen for compilation [21]. The selection criteria included: relevance, positive
findings, reproducibility, and docimetric quantifiability, for which they used the SAR [21]. The
committee developing the ANSI C95.1 took a conservative approach, and used data that gave the
lowest thresholds when two or more reports yielded the same biological endpoint [21]. The
committee determined that the limiting factor for many of the standards was the behavioral
disruption observed in test animals while exposed to radiation of varying frequencies [21]
(though not specifically mentioned in the ANSI C95. 1, a recommended figure for the SAR
averaging time, i.e. the exposure time, is six minutes, which is an estimate of the thermal
equilibrium time [19]). Behavioral disruption included: convulsion activity, work stoppage,
work decrement, decreased endurance, perception of the exposing field and aversion behavior
[22].
The results yielded an SAR of 4 W/kg, below which there were no observable adverse effects as
a result of the applied radiation [23,25].
To take into account biological uncertainties, a factor
often was introduced, giving a threshold of 0.4 W/kg [19,23].
In agreement with other studies,
this value serves as the basis for the threshold curve shown in Figure 5-1 [23]. It should be noted
that, for frequencies between 0.3 and 3 MHz, the values given in the Figure 5-1 reflect, not the
limiting SAR of 0.4 W/kg, but instead the limits imposed by currents induced by the applied
electric field and "surface effects". These surface effects include perception and electric shock
[23].
106
102
F-
35
E - f ieid
E
N
E
101
N
-c
H - f ield
C
0)
-0
U,
(V,
V
0)
-c
'4-
Ci
103
/
/
-ii
I
I.
'----/
10
2
10-2
I
10-
1
I
|I
1
101
102 103
Frequency (MHz)
I
104
a)
C
0'
0
_ 10-2
105
Figure 5-1: ANSI C95.1-1982 RFPGs for Continuous Exposure
5.5
C.)
[35]
Derivation of the ANSI Standards
The standards derived in the previous section are largely the result of work done by Durney and
others who developed a model for power absorption based on ohmic heating [28]. In this model
the SAR at a specific point is given by:
SAR
=
P/pm = aIE12 /pm =
OE6'E1 2 /pm
(5.1)
where P = absorbed power, a = conductivity, E = rms electric field magnitude, o = angular
frequency, pm = the mass density of the object at that point, sF, = permittivity of free space, E
=
the unitless imaginary part of the complex permittivity (which describes the frictional effects
induced by an electric field, where the complex permittivity e* = so(s' - js") and s' = the
dielectric constant) [29,33]. From the aIE
2
form of the SAR the ohmic nature of the heating
36
can be deduced. Thus, if the electric field and conductivity are known at a point, then the
absorbed power can be derived. Implicit in the model is the assumption that biological tissue
has properties which 'behave' like conductivity and permittivity. These properties result from
the reactions of various biological molecules with incident electromagnetic fields. Since these
reactions are functions frequency, a and s" also have strong frequency dependences. Figure 5-2
below shows the frequency dependence of "
10
2
1C
3
10
1o4
FREQUENCY (M-zh
Figure 5-2: Average Permittivity vs Frequency [32]
From this dependence comes the SAR reliance on frequency.
In order to extrapolate the SAR at a point to that for person, a boundary value problem was
solved in which the body was approximated as a prolate spheroid. The incident field was a plane
wave with the electric field oriented such that it's plane was parallel the major axis of the
37
spheroid (in this configuration the electric field couples most strongly the object). Using
different values for the height and weight of the spheroid, the average SAR could be calculated
by integrating over the entire volume and dividing by the mass of the body. Shown below in
Figure 5-3 are the normalized SARs for several body sizes:
100-
ci.0
-
2
o
o
----
--- de 1. 75
-- H t 1. 38 m
----Hi-0.74m
---Mon an G.
W t 70 kg
W t-32kg Wt-10qg
Plano
102
103
FREQUENCY (MHz)
Figure 5-3: Normalized SAR vs. Frequency [28]
Normalizing the curves to the ANSI recommended SAR of 0.4 W/kg gives basic guidelines for
the safety standards adopted in 1982. The relationship is shown in Figure 5-4:
38
E
200 --100
N :.
......
--
--20
10
5
-A
NSI (Sipp 82)
H f - I.75
Wi -70kg
H - 1.38rn
Wr-32k g
Wt -10 kg
H -0.74 m
Mon on Gd Plane
1
2
0
D. 5
Uj
0.1 100U0NCY2
(
0}
A
FREQUENCY (MHz)
Figure 5-4: 0.4 W/kg SAR and ANSI 1982 Safety Recommendation [28]
5.6
ANSI C95.1 1990 Proposal
In an effort to correct some of the shortcomings of the ANSI C95.1 1982 and a subsequent report
published by the National Council on Radiation Protection and Measurements (NCRP) in 1986, a
new draft of the ANSI C95.1 was composed. The results contained in the final draft of the ANSI
C95.1 1990 were similar to its predecessors, using 0.4 W/kg as the limiting SAR [24].
However, the new report differs in that it differentiates between controlled and
uncontrolled environments. Controlled environments are defined as areas in which persons
exposed are likely to be aware of the possibilities for exposure, e.g. employees in certain work
places. Uncontrolled environments are locations where there is no expectation of exposure [24].
Other differences include accounting for the effects of pulsed radiation and partial body
exposure. In the case of partial body exposure, the maximum total body averaged SAR can be
39
allowed to reach as high as 20 W/kg in some instances. The exceptions to this limit are the
eyes and testes, which were mentioned, but, for which no further explanation was given [25].
The most useful difference is the relaxation of the magnetic field standards below 3 MHz, which
better captures the actual effects of the magnetic field on the whole body SAR. This is
important since it yields 16.3/f dependency for the maximum safe magnetic field. Because it
represents a comprehensive survey of the relevant literature on the subject, the ANSI C95.1 1990
proposal will serve as the basis for the calculations used in assessing the feasibility of powering a
retinal implant using magnetic coupling. The maximum permissible exposures given in the
paper are summarized in Figures 5-5 and 5-6:
1,000
614 Vm- 1
EE
~>100
Electric
field
strength
---
1842-f-1
163 A -m -n
C
E
614 V-m1
Magnetic
field
-
c'J
-
strength
10
C/
Wm-2
163f100
+ --
16.3I~
- ~Power
100
density
CV
13)
iow-m-2
13 4-
cy
CU
10
02)
f
(MHz)
O.63 A-m-i
0.003 0.1
1
10
100
1000
Frequency (MHz)
10,000 100,000
300,000
Figure 5-5: Proposed ANSI C95.1 Standards for Continuous Exposure in Controlled
Environments [30]
0
a-
40
1,000
6 14
E
<
£E
100
E Iect ric
Mfield
strength
-2
V-m-
+-823
8
f
1,000
-
1631
Mogne ticN
field
-
,
strength
10
)
E
27,5 V- me
density
,,e
C:CPower
100
10
m2
f - 150
1
10
3 - f -1.688
-158
000
C
U2W-m-2'
(' -*
0.1
1
0. 7o3A-m-2-
LL
f
(MHz)
I
0.003 0.1
I
1
10
100
1,000
1
[]ill
I
10,000 100,000
111,11
300,000
Frequency (MHz)
Figure 5-6: Proposed ANSI C95 Standards for Continuous Exposure in Uncontrolled
Environments [30]
It is important to keep in mind that the above safety standards are derived for whole body SARs
in which the object is exposed to plane waves. This will be an important point to consider when
deriving the output power in the following section.
41
5. 7
Assumptions for Power Calculations
In order to proceed with power calculations, a number of assumptions must be made about the
coil pair arrangement. It is assumed that 1) the primary coil is sufficiently large relative to the
secondary such that the magnetic field seen by the secondary is uniform 2) the incident field is
perpendicular to secondary coil 3) the two discs are perfectly co-axial 4) the imposed magnetic
field is of the form H(t) = Hcos(2nft), where Ho is the peak amplitude and f is the coupling
frequency 5) the secondary coil is optimally loaded such that the load resistance equals the
source resistance of the secondary itself 6) in the case where there are multiple layers, each layer
will be separated by insulation and 7) each winding within a given layer will be separated by
insulation. The first three assumptions simplify calculations by creating the optimum coupling
arrangement for the two coils. This will allow use to be made of the ANSI safety standards,
which were derived from this kind of incident power. The fourth and fifth assumptions place
constraints on the power calculations, and the last two take into account how an actual coil might
be fabricated.
5.8
Magnetic Coupling with Receiver in the Anterior Region of
the Eye
5.8.1 Assumptions
It is assumed that the receiver is placed in the same position shown in Figure 4-4. In addition, it
is assumed that 1) the field strength seen at the secondary is equal to H., i.e. the field strength
decay is negligible and 2) the secondary is a circular disc of diameter 6.5mm and thickness 2mm.
Assumption 1) is made to simplify the power calculation, since for short distances away from the
42
primary, the field strength is essentially unchanged. Assumption 2) is based on surgical
constraints, since the largest device that could be placed in the front of the eye would have a
diameter of 6.5 mm, and a thickness of 2mm.
5.8.2
Coil Geometry
Based on the surgical constraints described in the section 5.8.1, the coil shown in figure 5-7
could be constructed:
rMx - rmin
au
thickness
awire
rmax
rmin
Figure 5-7: Secondary Coil Geometry
thickness
43
In the figure 5-7 it is important to note that awire is the actual cross-sectional area of a turn
(wire) itself and ausej is the cross-sectional area taken up by a turn and it's accompanying
insulation. Thus:
awire =
(5.2)
kfracause
where kfrac is a constant that describes the relationship between the cross-sectional area of the
insulation and the wire. The total cross-sectional area A occupied by a group of turns is the
number of turns N times ause, ie.:
A = Nausew
(5.3)
Combining equations 5.2 and 5.3 gives:
awire
5.8.3
=
kfracA/N
(5.4)
Power Calculation [31]
From the assumption that the coil is optimally loaded, i.e. when the load resistance equals the
source resistance of the coil, the following power relationship can be derived:
Pavg -
1v2
RS
(5.5)
8 R,
where Pavg is the average power output obtained for a sinusoidal input, VOC, is the peak open
circuit voltage and R, is the source resistance of the coil. It is known that the voltage in a single
turn of wire is given by:
44
d
VOCP fJto H-n da
dt
(5.6)
Where pt,= 47Ex 10-7 H/m is the magnetic permeability, H is the magnetic field, and n is the
vector normal to the area enclosed by the turn. Substituting the magnetic field
H(t) = Hcos(2nft) into equation 5.6 gives:
V,,/turn = -(2.7nc2)(Hof)r 2
(5.7)
where f is the frequency of the magnetic field (coupling frequency) and H0 is the peak magnetic
field strength.
To calculate the total voltage of coil is to sum the voltages of all the turns. To avoid having to
calculate Vop for each turn individually (r2 changes as r goes from rnin to rmax), use the average of
r2 which is roughly equal to the square of the average of r , i.e.
(r2)avg &ravg2 . Thus, the total
open circuit voltage for a coil with N turns is given by:
Vtoep= -N(2pon 2)(Hof)ravg 2
(5.8)
The total resistance of the coil is given by:
R, = (27ravg)Np / awire
(5.9)
45
where p is the resistivity of the coil metal. Note, since the circumference of each turn scales
linearly with r, it is sufficient to use ravg N in place of the radii which range from rmin to rmax.
Lastly, substituting equations 5.8 and 5.9 into equation 5.5 gives:
)r3 pi4(H, f)
Pavg,ant
5.8.4
2
kfracA(.
=
(5.10)
Power Output
In the subsequent calculations, the following values will be used: f= 1MHz, p 0 = 1.26x10 H/m,
p = 2.2x10-8
0.25,
Qm
(gold), ravg
=
2.28 mm (from rmax = 3.25mm and rmin = 0. 4 rmax =1.3mm), kfrac
A = 3.9x106 m 2 (from (rmax-rin)
x
2mm where 2mm is the thickness of the coil) H, = 23
A/m (ANSI standard for 1MHz). It should be noted that the ANSI standard given in Figure 5-5
was derived using the root-mean square magnitude of the electric field. To get the standard in
terms of the peak H field strength, which was used in section 5.8.2, the ANSI value was
multiplied by V2, which gives H0 = 23 A/m. Substituting these values into equation 5.10 gives
Pavg = 3.4 mW. Using this value in conjunction with those given in Table 2-2, the number of
electrodes that could be powered can be derived, and is shown below in Table 5-1:
46
Table 5-1: Possible Numbers of Electrodes Powered
By a Magnetically Coupled Coil Pair (Ant. Receiver)
Large Electrodes (400pm)
Pulse Duration = 0.25ms
Pulse Duration = ims
Pulse Duration = 4 ms
5.9
Power needed/elec.
43pW
Small Electrodes (100pm)
Power needed/elec.
=
43pW
# electrodes = 79
# electrodes = 79
Power needed/elec = 72 pW
Power needed/elec = 54pW
# electrodes = 47
# electrodes = 62
Power needed/elec = 54 pW
Power needed/elec = 63 pW
# electrodes = 62
# electrodes = 53
Magnetic Coupling With Receiver in the Posterior Region
of the Eye
5.9.1 Assumptions
It is assumed that the receiver is oriented the same way as shown in Figure 4-1. It is also
assumed that 1) the secondary is a circular disc with a diameter of 1.12 cm and a thickness of
10pm and 2) the field seen at the secondary = 0.84H.
Assumption 1) is the result of surgical
constraints, as in the posterior case for the laser. Assumption 2) takes into account the decay of
the field as the secondary is now farther away from the primary. The constant comes from
assuming that the field at distance = 0 from the primary is Ho, and solving the expression:
H(d) = 2(d
2
Nir
2
2(d 2 + r )
(5.7)
Y
47
where at 1 MHz Ni = const = 228A, rp = 7 cm = radius of the primary coil, and d = 2.5cm
(approximately 1 eye diameter) = the distance between the primary and secondary [31]. The
1 0ptm thickness is an estimate of how thin the receiver would have to be to remain flexible
enough not to harm the retina when placed against it.
5.9.2
Power Output
Using the above assumption the power is given by:
Pavg,post =
Ir /1p0 (0.84 Hof) r,kf,., A
4
4p
(5.8)
As in the previous section, the following values will be used: f= 1 MHz, po = 1.26x10- H/m,
p = 2.2x10-8
0
m, kfrac = 0.25, and H. = 23 A/m (ANSI standard at 1MHz using the peak H field
magnitude-see section 5.8.3). However, in this case r.ax= 5.6mm and rmin = 0. 4 rmax = 2.25mm.
Thus, A = I pm x (r.ax - rmin)= 3.35 x 10-8 m2 and ravg = 3.93mm. Substituting these values
into equation 5.8 gives Pavgp
=
106 p.W of output power. The numbers of electrodes that could
be powered are shown below in Table 5-2:
Table 5-2: Possible Numbers of Electrodes Powered
By a Magnetically Coupled Coil Pair (Post. Receiver)
Large Electrodes (400pm)
Pulse Duration = 0.25ms
Pulse Duration = tms
Small Electrodes (100pm)
Power needed/elec. = 43pW
Power needed/elec. = 43pW
# electrodes = 2
# electrodes = 2
Power needed/elec =72 pW
Power needed/elec = 54pW
# electrodes = 1
# electrodes = 1
48
Pulse Duration = 4 ms
5.10
Power needed/elec = 54 [tW
Power needed/elec
# electrodes = 1
# electrodes = 1
63 ptW
Issues That Require Further Study
The main issue that need to be resolved for both posterior and anterior placement is the best way
to make use of the limited field strength afforded by the ANSI standards. The non-uniform
nature of the magnetic field presents another problem. Because the field generated by the coil is
not a plane wave, the ANSI standards do not apply exactly. However, since the SAR of 0.4 is
the limiting factor and not the form of the incident field, it is possible perform a more precise
analysis. This would involve solving the boundary value problem subject to the constraints that
the absorbed power is 0.4 W/kg and the incident field resembles the one coming from the
primary. In this case a more accurate model of the interactions between the primary coil and the
eye would need to be developed.
49
Chapter 6
Conclusions/Future Work
6.1
Biological Constraints
It was found that whether a chronically implantable retinal prosthesis is powered via infrared
laser or using a magnetically coupled pair, the primary limiting factor would be the injury that
results from heating. In the case of the laser, photons at the wavelengths of interest transfer
energy to tissue, resulting in temperature elevation that causes denaturation of proteins. The
threshold for damage corresponds to a 10*C rise above ambient body temperature that lasts for
several minutes. Presumably, this value would be lower for chronic use. When magnetic
coupling is used with coupling frequencies between 1 MHz and 10MHz, free rotation of
biological molecules results in increased kinetic energy, which causes a temperature rise, which
may also result in the denaturation of proteins.
50
6.2
Insights
When the diameter of the active area of the device is constrained to be 1.1cm, which corresponds
to an area of 1cm2, it was found that for the three stimulus lengths measured, interfacing via laser
offered a greater possibility of powering electrodes in the posterior regime. The flexibility that
has to be maintained with posterior placement of the receiver prevents the coil pair from being a
feasible option in this arrangement. However, when the receiver is placed in the front of the eye
the coil pair offers an improved opportunity for extracting power. The feasibility increases by a
factor of 8 if a 2mm thick receiver with 1.1 cm diameter could be placed inside the vitreous,
since the gain in area outweighs the loss in field strength. In this arrangement however, the
power dissipated in the receiver itself and its load is a factor of 16 greater than the power
delivered to the vitreous by the field (the power delivered to the vitreous = (mass of the eye) x
(safe SAR) = 0.008 kg x 0.4 W/kg = 3mW). The prospects for an anterior receiver for the laser
case are undetermined. An upper bound of 30mW was found, however, without an accurate
model of the heat flow in this kind of configuration, the problem will remain unsolved.
An additional point of interest is that the total power allowed to enter the eye for the laser regime
is a approximately 100mW, but in the case of the coil pair the ANSI standards limit the RF
power dissipated in Ohmic heating in the vitreous to 3mW. This difference may result from the
fact that the laser standards were derived with tissue damage as the threshold, whereas the RF
standards were determined using behavioral disruption as the metric.
51
6.3
Summary
The main task that needs to be completed before more a conclusive assessment can be made is
that more precise models for the posterior coil regime and the anterior laser setup need to be
developed . Among the configurations considered in this thesis, an implant powered via infrared
laser with a posterior receiver offers the best prospects for success. However, if a magnetically
coupled coil receiver with a diameter of 1.1cm could be placed 1cm from the front of the eye, it
would give an even higher ouput power.
52
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55
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