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Prosthetic visual perception: retinal electrical stimulation in blind human patients
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Prosthetic visual perception: retinal electrical stimulation in blind human patients
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PROSTHETIC VISUAL PERCEPTION: RETINAL ELECTRICAL STIMULATION
IN BLIND HUMAN PATIENTS
by
Alan Matthew Horsager
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(NEUROSCIENCE)
MAY 2009
Copyright 2009 Alan Matthew Horsager
ii
Acknowledgments
First and foremost, I must thank my thesis advisor, Dr. Ione Fine, who taught me
to think critically about a problem without sacrificing creativity and intuition. The
majority of the work in this thesis was focused on fundamental questions about a new
technology; Ione provided clear insight into seemingly intractable questions. Secondly, I
want to thank Dr. Geoff Boynton for his substantial contributions to the modeling work.
Seeing Geoff and Ione working together is truly a sight to behold. Equally as important
as these two are the retinal prosthesis subjects I worked with, Linda Morfoot and Terry
Byland. They are two of the most exceptional people I have ever met. They have given
without expectation of gain, and both have decidedly made the world a better place.
Outside the lab, Sarah Hughes provided me with constant love and support, and
knew just what it took to get the “whos” out of my head. My family, particularly my
mom and dad, suffered through my extended youth and exploration. I’m sure they are
happy I’ve finally settled on something – at least for the time being. I thank my BBQ
group including Dr. Doug Scofield, Steven Denlinger, Chip Dornell, Lucy and Lilly
Napolskykh, Chuck Harlander, and Julien Benassaya for keeping me full of good food
and wine.
My committee members consistently provided feedback and criticism that
ultimately made this work what it is. I particularly want to thank Dr. Gerald Loeb for his
thoughts, and Alapakkam Sampath and James Weiland for their support.
Second Sight Medical Products, Inc. made this possible. Without them, there
would be no retinal prosthesis. Specifically, I want to thank Dr. Rob Greenberg, Dr.
iii
Matthew McMahon, Kelly McClure, Scott Greenwald (now at UW), Dr. Allen Zhou, Arup
Roy, Dr. Brian Mech, and Dr. Ashish Ahuja for all their kind and intellectual support.
As with every endeavor, collaboration and discussion is what helps develop a
student into a scientist. The University of Southern California was an excellent
environment in which to train. Particularly, I would like to thank Cyrus Arman, Matthew
Behrend, Devyani Nanduri, Dr. Mark Humayun, Dr. Norberto Grzywacz, and Dr. Bartlett
Mel.
iv
Table of Contents
Acknowledgements ..............................................................................................................ii
List of Figures ..................................................................................................................... vii
List of Tables ........................................................................................................................ x
List of Abbreviations ........................................................................................................... xi
Abstract ........................................................................................................................... xiii
Chapter 1 ‐ Introduction ..................................................................................................... 1
1.1 The structure and computation of the retina ...................................................... 4
1.1.1 Basic cellular makeup and structure of the vertebrate retina ..................... 4
1.1.2 Timing and computation of the retina .......................................................... 6
1.2 Retinal degeneration and neural reorganization ................................................. 8
1.2.1 Structural and functional changes in the diseased retina ............................ 9
1.2.2 Cortical changes as a function of retinal disease ........................................ 11
1.3 In vitro electrical stimulation of retinal tissue ................................................... 13
1.3.1 Response thresholds to single pulse retinal electrical stimulation ............ 14
1.3.2 Preferential cellular activation .................................................................... 16
1.3.3 The site of activation in retinal ganglion cells ............................................ 17
1.3.4 Methods for modeling the response to electrical stimulation ................... 18
1.4 A Back‐to‐Front History of Visual Prostheses .................................................... 20
1.4.1 Stimulating Primary Visual Cortex ............................................................. 21
1.4.2 Stimulating LGN .......................................................................................... 23
1.4.3 Stimulating the Optic Nerve ....................................................................... 24
1.4.4 Extraocular, Subretinal, Epiretinal Prostheses ........................................... 24
1.5 The outline of this thesis .................................................................................... 27
Chapter 2 – Predicting temporal sensitivity in retinal prosthesis patients ...................... 29
2.1 Introduction ........................................................................................................ 29
v
2.2 Materials & Methods ......................................................................................... 30
2.2.1 Subjects ....................................................................................................... 30
2.2.2 Psychophysical Methods ............................................................................. 31
2.2.3 A model of temporal sensitivity .................................................................. 35
2.2.4 Determining the optimal parameters of the model ................................... 37
2.3 Results ................................................................................................................ 38
2.3.1 Predicting visual sensitivity for novel temporal patterns ........................... 39
2.3.2 Model Power ............................................................................................... 45
2.4 Discussion ........................................................................................................... 46
Chapter 3 – Spatiotemporal interactions in retinal prosthesis subjects .......................... 53
3.1 Introduction ........................................................................................................ 53
3.2 Materials & Methods ......................................................................................... 55
3.1.1 Subjects ....................................................................................................... 55
3.2.2 Psychophysical methods ............................................................................. 56
3.3 Results ................................................................................................................ 58
3.3.1 Experiment 1 – Synchronous vs. asynchronous stimulation ...................... 58
3.3.2 Experiment 2 – Pseudo‐synchronous vs. asynchronous stimulation ......... 60
3.3.3 Experiment 3 – The effects of inter‐electrode distance ............................. 63
3.3.4 Experiment 4 – Pulse timing effects for a single electrode ........................ 65
3.3.5 Experiment 5 – Clockwise vs. counterclockwise stimulation ..................... 67
3.3.6 Experiment 6 – Electrode order and brightness ......................................... 70
3.4 Discussion ........................................................................................................... 73
Chapter 4 ‐ Interactions during multi‐electrode suprathreshold stimulation .................. 75
4.1 Introduction ........................................................................................................... 75
4.2 Materials & Methods ............................................................................................. 76
4.2.1 Subjects ....................................................................................................... 76
4.2.2 The Retinal Prosthesis ................................................................................. 77
4.2.3 Psychophysical Methods ............................................................................. 78
4.2.4 Model of spatiotemporal integration ......................................................... 81
4.3 Results ................................................................................................................ 84
vi
4.3.1 Subjective brightness and pulse timing across electrodes ......................... 85
4.4 Discussion ........................................................................................................... 89
Chapter 5 ‐ Conclusions .................................................................................................... 92
5.1 Coding for brightness within an electrode ......................................................... 93
5.1.1 Stimulation protocols that satisfy multiple constraints ............................. 95
5.2 Spatiotemporal interactions, integration, and correlations .............................. 98
5.2.1 Decoding and perceptual grouping ............................................................ 99
5.2.2 Spatiotemporal stimulation – synchronous vs. phase‐shifted ................. 102
References ...................................................................................................................... 107
Appendices ..................................................................................................................... 127
Appendix A – Linear and nonlinear transformations in neurons ............................... 127
A1. Rules of linearity: superposition and time invariance ..................................... 128
A2. The impulse and impulse response .................................................................. 128
A3. Linear filters: The leaky integrator ................................................................... 129
A4. Nonlinear mechanisms: threshold and static transforms ................................ 130
Appendix B ‐ Supplemental materials to Chapter 2 ................................................... 132
B1. Example Weibull fits for threshold and suprathreshold data .......................... 132
B2. Systematic changes in brightness due to adaptation ...................................... 133
B3. Threshold and suprathreshold fits for data used to optimize model .............. 135
B4. Parameter values for model predictions of various data sets ......................... 141
B5. Additional model predictions of various data sets .......................................... 142
B6. Model statistics – F‐test ................................................................................... 147
B8. Alternative models ........................................................................................... 150
Appendix C ‐ Supplemental materials to Chapter 3 ................................................... 153
Appendix D ‐ Supplementary materials to Chapter 4 ................................................ 154
D1. Example fits from brightness matching task .................................................... 154
D2. Subjective equibrightness at different amplitudes ......................................... 155
D3. Additional model fits for neighboring electrodes ............................................ 156
D4. Additional model fits for 1600 and 2400 μm separated electrodes ............... 157
vii
List of Figures
Fig. 1.1. Patient Percepts .................................................................................................... 3
Fig. 1.2. The retina .............................................................................................................. 6
Fig. 1.3. Reorganization of the retina during degeneration ............................................. 10
Fig. 1.4. Cartoon schematic of the retina being stimulated by a single electrode ........... 14
Fig. 1.5. Strength‐duration curves .................................................................................... 15
Fig. 1.6. Schematic of the retinal prosthesis ..................................................................... 27
Fig. 2.1. Model schematic ................................................................................................. 36
Fig. 2.2. Single pulse threshold ......................................................................................... 40
Fig. 2.3. Fixed‐duration pulse train threshold................................................................... 41
Fig. 2.4. Variable‐duration pulse train threshold .............................................................. 42
Fig. 2.5. Fixed‐duration pulse train suprathreshold ......................................................... 43
Fig. 2.6. Bursting pulse triplets, suprathreshold ............................................................... 44
Fig. 3.1. Synchronous vs. asychronous stimulation .......................................................... 59
Fig. 3.2. Discriminating between pseudo‐synchronous and asynchronous stimuli ......... 61
Fig. 3.3. Subject performance, experiment 3 ................................................................... 64
Fig. 3.4. Subject performance, experiment 4 ................................................................... 67
Fig. 3.5. Clockwise vs. counterclockwise stimulation ....................................................... 69
viii
Fig. 3.6. Brightness matching as a function of electrode order ........................................ 72
Fig. 4.1. Retinal prosthesis schematics and experimental design .................................... 77
Fig. 4.2. Theoretical model outputs .................................................................................. 82
Fig. 4.3. Normalized charge to match the brightness of the standard stimulus .............. 85
Fig. 4.4. Spatially‐separated electrode pairs ..................................................................... 89
Fig. 5.1. Efficiency predictions for a 500 ms pulse train ................................................... 97
Fig. 5.2. Perceptual differences and electrode order .................................................... 103
Fig. A1. Static Nonlinearity .............................................................................................. 131
Fig. B1. Example Weibull fits for threshold detection and brightness matching ........... 132
Fig. B2. Fits for single pulse thresholds ........................................................................... 135
Fig. B3. Fits for latent addition threshold ....................................................................... 136
Fig. B4. Fits for 0.075 ms fixed‐duration pulse train thresholds ..................................... 136
Fig. B5. Fits for 0.975 ms fixed‐duration pulse train thresholds ..................................... 137
Fig. B6. Fits for 2‐pulse variable duration pulse trains ................................................... 137
Fig. B7. Fits for 3‐pulse variable duration pulse trains ................................................... 138
Fig. B8. Fits for 15‐pulse variable duration pulse trains ................................................. 138
Fig. B9. Fits for 0.075 ms fixed‐duration pulse train, suprathreshold ............................ 139
Fig. B10. Fits for 0.975 ms fixed‐duration pulse train, 2X suprathreshold ..................... 139
Fig. B11. Fits for 0.975 ms fixed‐duration pulse train, 3X suprathreshold ..................... 140
ix
Fig. B12. Additional predictions for single pulse thresholds .......................................... 142
Fig. B13. Predictions for latent addition thresholds ....................................................... 143
Fig. B14. Predictions for 0.075 ms pulse train thresholds .............................................. 143
Fig. B15. Predictions for 0.975 ms pulse train thresholds .............................................. 144
Fig. B16. Predictions for 2‐pulse variable duration pulse train thresholds .................... 144
Fig. B17. Predictions for bursting 15, 30, and 60 pulse trains ........................................ 145
Fig. B18. Predictions for fixed duration pulse trains, suprathreshold ............................ 145
Fig. C1. 0.225 ms phase‐shifted pulses across electrode pairs ....................................... 153
Fig. D1. Example fits from brightness matching task...................................................... 154
Fig. D2. Subjective equibrightness at different amplitudes ........................................... 155
Fig. D3. Additional model fits for neighboring electrodes .............................................. 156
Fig. D4. Additional model fits for 1600 and 2400 μm separated electrodes ................. 157
x
List of Tables
Table 3.1. Performance and d‐prime ................................................................................ 61
Table 4.1. Parameter values for model fits for all electrode pairs ................................... 88
Table 4.2. Parameter values for 1600 and 2400 μm separated electrode pairs .............. 90
Table B1. Fit threshold parameter values ....................................................................... 136
Table B2. Fit suprathreshold parameter values .............................................................. 137
Table B3. Predicted threshold parameter values ........................................................... 142
Table B4. Predicted suprathreshold parameter values .................................................. 143
xi
List of Abbreviations
AMD Age‐related macular degeneration
ANOVA Analysis of variance
BLP Bare light perception
CFF Critical flicker fusion limit
ChR2 Channelrhodopsin‐2
CIS Continuous interleaved stimulus
FDA Food and Drug Administration
fMRI Functional magnetic resonance imaging
GABA
A
Gamma‐aminobutyric acid, A
Goα G‐protein, α subunit
Hz Hertz, unit of frequency
iGluR Ionotropic glutamate receptor
IPL Inner plexiform layer
LGN Lateral geniculate nulceus
LPZ Lesion projection zone
mGluR6 Metabotropic glutamate receptor, 6
μA microampere
ms Millisecond
μm Micron; micrometer
NLP No light perception
OPL Outer plexiform layer
xii
PC Personal computer
rd1 retinal degeneration, type 1 (mouse model of photoreceptor disease)
RP Retinitis pigmentosa
V1 Primary visual cortex
VPU Visual processing unit
xiii
Abstract
Can functional vision be restored in blind human subjects using a microelectronic retinal
prosthesis? The initial indications suggest that, yes, it is possible. However, the visual
experience of these subjects is nothing like a digital scoreboard‐like movie, with each
electrode acting as an independent pixel. The work described here suggests that there
are interactions between pulses and across electrodes, at the electrical, retinal, or even
cortical level that influence the quality of the percept. In particular, this work addresses
the question , “how does the percept change as a function of pulse timing on single and
multiple electrodes”? The motivation for the work described here is that these
interactions must be understood and predictable if we are to develop a functional tool
for blind human patients.
1
Chapter 1
Introduction
Visual impairment is one of the most common disabilities. At the most recent
estimate, 110 million people worldwide have low vision and 40 million are blind
(Thylefors et al., 1995). Photoreceptor diseases such as retinitis pigmentosa (RP) and
age‐related macular degeneration (AMD) are responsible for blindness in 15 million of
those people (Chader, 2002), a number that continues to increase with the aging
population (Congdon et al., 2004). Currently, there are no FDA approved treatments for
photoreceptor disease‐related blindness.
Although a number of highly promising treatments are being developed, each
contains its own unique set of constraints. For example, gene replacement therapy
efforts are on track to treat one form of Leber’s Congenital Amaurosis (i.e., an RPE65
mutation) in humans (Acland et al., 2001; Acland et al., 2005; Batten et al., 2005; Pawlyk
et al., 2005; Aguirre et al., 2007; Bainbridge et al., 2008); however, this form of RP is
relatively rare, and photoreceptor diseases are genetically heterogeneous, with single
and multi‐gene mutations occurring in over 180 different genes responsible for
photoreceptor function (Daiger et al., 2007). If gene replacement therapy were to cure
photoreceptor disease, it would need as many (and, most likely, many more) treatments
2
as there are mutations. Optical neuromodulators such as channelrhodopsin (ChR2) can
be genetically targeted to retinal bipolar (Lagali et al., 2008) or ganglion cells (Bi et al.,
2006; Lin et al., 2008) to restore visual responsiveness in a mouse model of blindness
(rd1). Still, ChR2 activation requires light stimulation levels that are 5 orders of
magnitude greater than the threshold of cone photoreceptors (Schnapf et al., 1987) and
has a substantially limited dynamic range (2 log units) (Wang et al., 2007a). An ideal
therapy would be able to treat blindness independently of the genetic mutation, in the
absence of photoreceptors, and with reasonable response sensitivity.
Therapies employing direct electrical stimulation of the retina fulfill the
constraints described above. However, they contain their own set of limitations. There
are a number of engineering concerns such as charge density safety limits (i.e., requiring
the use of large electrodes), placement of the electrode array relative to the target
retinal cells, and power that make prosthesis design extremely challenging. Electric
current fields from these relatively large electrodes indiscriminately drive local retinal
circuits in an unnatural way, leading to complex retinal responses. Although electrically‐
driven retinal activation produces phosphenes in blind human subjects, these percepts
are complex and cannot be simply thought of as a one to one, electrode to pixel,
scoreboard‐like experience with punctate individual phosphenes (Fig. 1.1).
There is a substantial history evaluating the use of electrical stimulation to
generate visual percepts in both sighted and blind human subjects (LeRoy, 1755;
Lowenstein, 1918; Foerster, 1929; Penfield and Rasmussen, 1952; Brindley and Lewin,
1968; Dobelle, 1974; Humayun et al., 1996; Schmidt et al., 1996; Weiland et al., 1999;
3
Humayun et al., 2003; Rizzo et al., 2003; Mahadevappa et al., 2005; Murphey and
Maunsell, 2007; Pezaris and Reid, 2007; Yanai et al., 2007). However, there has not yet
been a been a systematic analysis of how these pulsing stimuli interact, sum, and
integrate over the network of neurons in time and space to form the visual image the
subject sees.
The goal of thesis is to start a quantitative understanding of the relationship
between electrical stimulation and percept generation using a retinal prosthesis.
Specifically, the association between the brightness of the percept and pulse timing
within single electrodes and across multiple electrodes is evaluated and modeled.
Fig. 1.1. Patient Percepts. Example percepts generated by retinal
electrical pulse train stimulation in 2 blind subjects, S05 and S06,
respectively. Percepts (top) were hand drawn by experimenter
based upon patient report. Stimulating electrodes over the 4x4
array, in each condition, are noted with blue dots.
4
1.1 The structure and computation of the retina
The retina is an intricate system of cells that pools and filters the visual image
into at least a dozen different channels of information. These channels “inform” cortex
about the luminance, contrast, motion, and color of the image. Although a retinal
prosthesis involves interfacing with neurons in a highly unnatural way, it is nevertheless
essential to understand how the retina performs its transformation of light stimuli into
electrochemical signaling under normal conditions. This knowledge will help guide
device design considerations (i.e., resolution of the array and electrode size) and
stimulation protocols (i.e., amplitude versus frequency modulated signals, pulse width,
and spatially patterned stimulation).
1.1.1 Basic cellular makeup and structure of the vertebrate retina
The vertebrate retina is structurally divided into 5 main types of neural cells:
photoreceptors and horizontal cells (outer nuclear layer), bipolar and amacrine cells
(inner nuclear layer), and ganglion cells (Rodieck, 1998). These main types of cells are
then further divided into at least 54 different subtypes based upon a combination of
morphology and physiology (Masland, 2001). There are 4 different photoreceptors (rods
and L, M, and S cones), 2 types of horizontal cells, 9 to 11 bipolar cells (Ghosh et al.,
2004; MacNeil et al., 2004), at least 29 different amacrine cells (Masland, 1988), and 10
to 15 ganglion cells (Dacey, 1994; Peterson and Dacey, 1998). Additionally, there are 2
major layers of synaptic connections, the outer and inner plexiform layer (Fig. 1.2). As I
will be discussing electrical stimulation of the diseased or photoreceptor‐less retina,
only processing of the inner plexiform layer will be discussed here.
5
The laminar structure of the inner plexiform layer (IPL) is a highly intricate
network where the bipolar, amacrine, and ganglion cells synapse. The dendritic and
axonal spread of each cell can vary from highly localized (1‐2 μm) to diffuse (30 μm), the
entire width of the IPL (MacNeil et al., 1999). The stratification of the IPL is thought to
contain at least 10 distinct layers (Roska and Werblin, 2001). Evidence suggests that
these different strata are involved in different functional pathways (Famiglietti and Kolb,
1976; Amthor et al., 1984; Wu et al., 2000; Pang et al., 2004). The dendritic integration
of excitatory and inhibitory currents within each separate strata leads to unique
patterns of spiking in ganglion cells (Roska and Werblin, 2001). In other words, the
ganglion cell response to a stimulus is dependent on IPL strata in which its dendritic tree
resides. In addition to the two‐dimensional spatial mapping of the visual scene on the
retina, the fact that different strata have such unique response kinetics suggests that
temporal processing also plays an important role (Baccus, 2007).
6
1.1.2 Timing and computation of the retina
The retina encodes the incoming visual signal captured by the photoreceptors
into a spatiotemporal series of ganglion cell spikes through the outer and inner
plexiform layer networks. Within the outer plexiform layer (OPL), chemical signals from
rods and cones are received by the bipolar cells and are modified by the network of
horizontal cells. The responses of bipolar cells are of 2 main types: ON and OFF. ON
bipolar cells depolarize to increments of light, where OFF bipolar cells depolarize to
decrements of light (Rodieck, 1998). Bipolar cells then pass this signal on to the retinal
ganglion cells through graded potentials that are modified and filtered by amacrine cells
within the inner plexiform layer (IPL).
Fig. 1.2. The retina. (Left) Cross‐sectioned immuno‐stained mature mouse retina (courtesy of
Rachel Wong and Josh Morgan, University of Washington). (Right) Retinal schematic, from top to
bottom, of the rod and cone photoreceptors (R & C), outer plexiform layer (OPL), horizontal cells
(H), rod and cone bipolar cells (RB & RC), amacrine cells (A & AII), and ganglion cells (G).
7
The classic view of the ganglion cell receptive field is that it responds with an
excitatory center and inhibitory surround (Kuffler, 1953). As with bipolar cells, ganglion
cells can either have a ON center of OFF center response behavior, where light intensity
increments in the center of the receptive field generate an increase or decrease in firing
rate in each cell type, respectively (Rodieck, 1998). Early models of these receptive fields
can be simply and mathematically represented by a difference of Gaussians (Rodieck,
1965; Rodieck and Stone, 1965). However, the ganglion cell response is reasonably
complex and cannot fully be explained or predicted by this simple linear model.
Photoreceptors have been shown to adapt to ambient light levels, adjusting their
sensitivity, so as to maximize the dynamic range of response (Burns and Baylor, 2001).
Contrast adaptation, on the other hand, consists of changes in response kinetics and
sensitivity to fluctuations in light intensity rather than overall luminance, and is a
function of the inner retina (Smirnakis et al., 1997; Chander and Chichilnisky, 2001; Kim
and Rieke, 2001; Baccus and Meister, 2002). The timescale of adaptation can be fast
(less than 100 ms) or much slower (on the order of tens of seconds) (Baccus and
Meister, 2002). The mechanism for this slow contrast adaptation is partially at the
bipolar‐ganglion cell synapse, and partially intrinsic to the ganglion cell (Zaghloul et al.,
2005; Manookin and Demb, 2006).
In addition to adapting to temporal changes in contrast, the retina has been
found to adapt to spatiotemporal patterns (Hosoya et al., 2005). The receptive field of
ganglion cells change, or adapt, within a few seconds to reduce sensitivity to temporally‐
correlated stimuli along a spatial dimension. In other words, the receptive field will
8
become less sensitive along the vertical axis, in response to a vertically aligned, static,
stimulus. This change in sensitivity as the result of spatiotemporal correlations has been
described as “predictive coding”, and is thought to be a function of the wide inhibitory
network of amacrine cells (Srinivasan et al., 1982).
Finally, retinal ganglion cells do not behave independently; their firing behavior
is dependent on the activity on the cells around them. Direct evidence of this comes
from the fact that neighboring ganglion cells of the same class fire synchronously more
frequently than would be expected by chance (Mastronarde, 1983a, b, c; Meister et al.,
1995; Meister, 1996; Amthor et al., 2005). This concerted firing behavior is spatially
constrained (~600 μm) and is most likely the result of ganglion‐to‐ganglion cell gap
junctions and common synaptic input (Brivanlou et al., 1998).
1.2 Retinal degeneration and neural reorganization
Although the visual consequence of retinitis pigmentosa (RP) is generally the
same across different diseases, the complexity and breadth of underlying gene
mutations and biological progression is substantial. There are dominant, recessive, and
X‐linked forms of retinitis pigmentosa, and a variety of multi‐gene forms. Currently,
there are 181 mapped genes known to be responsible for retinal disease, and this
number will most likely double as we learn more about the genetics of RP (Daiger et al.,
2007). The same gene mutations can lead to unique disease progression across
individuals, suggesting that environmental factors also play a role. In addition to this
genetic complexity, the progression of retinal degeneration has widespread implications
on structure and function that extends as far downstream as visual cortex.
9
1.2.1 Structural and functional changes in the diseased retina
The loss of photoreceptors as a function of retinal disease leads to substantial
reorganization and morphological changes to the remaining cells of the retina (Fig. 1.3).
The inner nuclear layer, consisting of bipolar and amacrine cells, is significantly thinned
with a loss of approximately 20‐60% of these cells (Santos et al., 1997; Humayun et al.,
1999; Strettoi and Pignatelli, 2000; Marc and Jones, 2003; Gargini et al., 2007). The
structure of bipolar cell dendritic arbors changes as well, with the formation of
recurrent bipolar‐bipolar synapses (Marc and Jones, 2003), the sprouting of neurites (Li
et al., 1998; Peng et al., 2000; Sullivan et al., 2007), and the complete retraction of
dendrites in later stages of the disease process (Furukawa et al., 1999; Strettoi and
Pignatelli, 2000; Chang et al., 2002; Strettoi et al., 2002; Strettoi et al., 2003).
Interestingly, glycinergic amacrine cells appear to maintain their normal connections to
ON bipolar cells, suggesting that amacrine‐bipolar cell circuitry is preserved during
disease (Marc and Jones, 2003). There is evidence of substantial cell loss (25‐80%) in the
ganglion cell layer as well (Stone et al., 1992; Santos et al., 1997; Humayun et al., 1999).
However, the morphology, including the stratification of the ON and OFF ganglion cell
dendrites, is preserved (Margolis et al., 2008).
10
In addition to structural alterations, there are a host of functional changes,
particularly in bipolar cells. ON bipolar cells decrease their responsiveness to glutamate,
while enhancing their GABA
A
receptor mediated signaling (Varela et al., 2003; Marc et
al., 2007). This could be the result of diminished expression of mGluR6 and Goα, two
glutamate receptors found in ON bipolar cells (Dhingra et al., 2002; Strettoi et al., 2002;
Gargini et al., 2007). Taken together, these data suggest there is a shift of ON bipolar
cells behaving more like OFF bipolar cells. Indeed, OFF responses in diseased retina are
preferentially preserved (Stasheff, 2008). Additionally, the formation of bipolar‐bipolar
recurrent connections is thought to corrupt the signaling from inner retinal circuits
(Marc et al., 2003).
Fig. 1.3. Reorganization of the retina during degeneration. Not only is there a substantial thinning
of the retinal layers, there is potentially massive reorganization, including cell migration. Adapted
from (Jones et al., 2003).
11
Ganglion cells have a higher spontaneous activity during disease and produce
rhythmic bursts or waves of activity (Ye and Goo, 2007; Margolis et al., 2008; Stasheff,
2008). However, there are a number of interesting data that suggest that the inner
retinal circuitry is well conserved. First, both ON and OFF ganglion cells maintain their
intrinsic firing properties (Margolis et al., 2008). In the presence of synaptic blockers,
the intrinsic firing behavior of ON, OFF‐transient, and OFF‐sustained ganglion cells in
response to electrical current injection was indistinguishable between wild‐type and rd1
retinal ganglion cells. Indeed, OFF transient cells showed rebound firing to negative
current injections, whereas this behavior was absent in ON ganglion cells. Second, the
balance of excitatory and inhibitory currents to the ganglion cell response is conserved
in rd1 retinae (Lagali et al., 2008; Margolis et al., 2008). Third, selectively stimulating ON
bipolar cells using channelrhodopsin leads to naturalistic ganglion cells responses
including transient spiking and center‐surround organization (Lagali et al., 2008).
In summary, the inner layers of the retina change substantially as a result of
photoreceptor loss. However, it appears that bipolar‐amacrine‐ganglion cell circuitry is
well maintained and may even function similar to normal retina.
1.2.2 Cortical changes as a function of retinal disease
With the occurrence of localized retinal lesions as a result of retinal
degeneration, there is a perceptual filling‐in effect. In other words, small local damage
to the retina does not lead to the percept of a blind spot. Instead, the “blind” retinal
region in filled in based on the surrounding visual scene. This suggests that there is a
certain amount of plasticity within the visual system to compensate for the retinal loss.
12
Indeed, it is found in animal studies of retinal lesions that there was an immediate
increase in receptive field size for cortical cells within the lesion projection zone (LPZ),
and months later the cells within the LPZ were responsive to retinal stimuli outside of
this lesion area (Gilbert et al., 1990; Kaas et al., 1990; Heinen and Skavenski, 1991; Chino
et al., 1992; Gilbert and Wiesel, 1992; Darian‐Smith and Gilbert, 1995; Gilbert, 1998). It
is thought that this filling in is the result of modifications of lateral connections within
V1 (Gilbert et al., 1990; Gilbert and Wiesel, 1992; Gilbert, 1998) but see (Murakami et
al., 1997; Horton and Hocking, 1998; Smirnakis et al., 2005). To further support cortical
reorganization, the responsiveness of the LPZ in LGN was silent (Gilbert and Wiesel,
1992; Darian‐Smith and Gilbert, 1995).
Studies of cortical cellular functionality in the LPZ show that these cells maintain
sensitivity to orientation, spatial frequency, and direction (Chino et al., 1995; Zur and
Ullman, 2003; Giannikopoulos and Eysel, 2006) but a decrease in sensitivity to contrast
(Chino et al., 1995). Human studies evaluating patients with macular degeneration using
fMRI show conflicting results regarding cortical plasticity (Sunness et al., 2004; Baker et
al., 2005; Horsager et al., 2008; Masuda et al., 2008).
There are also likely to be more complex changes within cortex as a result of very
long term blindness. Studies of sight recovery in human subjects after long‐term
blindness (upwards of 40 years) show the ability to recognize simple shapes and
perceive motion like normal sighted subjects, however, there appears to be a
substantial limitations in spatial and binocular vision (Gregory and Wallace, 1963; Fine
et al., 2003; Gregory, 2003).
13
Taken together, these data suggest that even if there is perfect restoration of
retinal function, it may not be possible to restore certain qualities of vision in subjects
that have been blind for many years. As sight recovery cases are rare, whether visual
performance is affected by the number of years blind still remains unknown.
1.3 In vitro electrical stimulation of retinal tissue
Our understanding of retinal responses to extracellular current stimulation is still
relatively limited. Little is known about the response properties of individual retinal
cells, much less how the population of cells under a large disc electrode responds to
stimulation (Fig. 1.4). However, in recent years there has been a growing body of work
examining retinal electrical stimulation. We are beginning to understand how much
current is required to initiate a neural response in the retina. Additionally, modeling
efforts and stimulation techniques have demonstrated that it might be possible, albeit
in a limited way, to preferentially stimulate certain retinal neurons. We are beginning to
understand the underlying neural mechanisms involved in retinal electrical stimulation.
These are important findings when thinking about the eventual perceptual response.
14
1.3.1 Response thresholds to single pulse retinal electrical stimulation
The most basic measurement of neural response to a stimulus, whether it is
photonic or electrical, is threshold. Threshold is defined as the stimulus quantity (e.g.,
number of photons, charge, or current amplitude) that is necessary to result in a
measureable response (e.g., graded potential change, spike, or percept). When
developing a neural prosthesis, it is necessary to know how much current or charge is
necessary to reach threshold. Indeed, threshold defines the lower limit of the dynamic
range.
Fig. 1.4. Cartoon schematic of the retina being stimulated by a single disc electrode. Although the
current fields produced by each electrode cannot be simply represented by an oval area, the area
of stimulation is certainly broad and indiscriminant. Retinal schematic courtesy of Cyrus Arman.
15
In figure 1.5, the amount of current necessary to reach neural threshold in
retinal ganglion cells in monkey, guinea pig, and rat is plotted as a function of pulse
duration using single pulse stimuli (Sekirnjak et al., 2006). Similar values (in the sub 10
μA range) were found when stimulating rabbit retina with large disc electrodes (Jensen
et al., 2003; Jensen et al., 2005b). The ganglion cell thresholds appear to increase
approximately an order of magnitude in degenerated (i.e., rd1 mice) retina (Jensen and
Rizzo, 2008). Using biphasic pulses, cathodic‐first epiretinal (Sekirnjak et al., 2008) and
anodic‐first subretinal (Jensen et al., 2005a; Jensen and Rizzo, 2006) stimulation lead to
similar threshold measurements in ON and OFF ganglion cells. However, it appears that
it may be possible to bias or preferentially stimulate ON ganglion cells using cathodic‐
Fig. 1.5. Strength Duration Curves. The current amplitude necessary to reach threshold response in
retinal ganglion cells is plotted as a function of pulse duration. Data is taken from monkey, guinea pig,
and rat. Graph adapted from (Sekirnjak et al., 2006).
16
first subretinal stimulation (i.e., OFF cells had thresholds that were double that of ON
cells using cathodic‐first stimulation).
1.3.2 Preferential cellular activation
In addition to preferentially stimulating ON ganglion cells using cathodic‐first
subretinal stimulation, it is certainly of interest to exclusively stimulate other
subpopulations of cells (e.g., bipolar or ganglion cells). It is thought that using longer
pulse widths may lead to selective activation of bipolar cells as the membrane time
constant and integration period of these cells is much longer than ganglion cells
(Greenberg, 1998; Jensen et al., 2005b; Shah et al., 2006). Additionally, it is thought that
using shorter pulse widths (< 0.15 ms) may selectively stimulate retinal ganglion cells
(Fried et al., 2006).
Pulse train stimulation, particularly while using shorter pulse widths, may lead to
ganglion cell spiking that is exclusively the result of direct ganglion cell activation. In
other words, bipolar cell activation in pulse train stimulation does not result in spiking
behavior in the downstream ganglion cells. It has been found in rabbit retina that
temporally precise single ganglion cell spikes were elicited using shorter pulse widths,
and spike rates could be generated at frequencies up to 250 Hz, using a large range of
stimulus amplitudes (Fried et al., 2006; Sekirnjak et al., 2006). In addition, bipolar cell
contribution to retinal ganglion cell spiking diminishes with repetitive pulse train
stimulation (Fried et al., 2006; Jensen and Rizzo, 2007). Although the mechanism for this
is unknown, it is thought that there may be inhibitory feedback from amacrine cells as
the result of repetitive stimulation that silences the bipolar input to ganglion cells.
17
Overall, the data suggests that it is possible to finely control the spiking behavior of
ganglion cells (i.e., retinal output) using pulse trains of electrical stimulation.
1.3.3 The site of activation in retinal ganglion cells
The literature examining the site of activation in retinal ganglion cells is mixed.
As mentioned above, it may be possible to selectively activate ON ganglion cells using
cathodic‐first subretinal stimulation (Jensen et al., 2005a; Jensen and Rizzo, 2006).
However, there is no evidence that epiretinal stimulation has the ability to selectively
stimulate ON versus OFF retinal ganglion cells (Sekirnjak et al., 2008). Compartmental
models of ganglion cell activation suggest that thresholds for spiking are lower for cell
bodies and the axon hillock than for fibers of passage (i.e., axons) (Greenberg et al.,
1999; Schiefer and Grill, 2006). However, recent calcium imaging data mapping the
spatial activation of ganglion cells and cellular components suggests that axons have
thresholds that are just as low as cell bodies when using large disc electrodes (Behrend,
2008). Additionally, electrophysiology results show that the two most sensitive regions
of the ganglion cell are on the axon, 40 μm and ~200 μm from the soma (Fried, 2008).
Using smaller electrodes (e.g., 9‐15 μm electrodes), it may be possible to spatially
isolate activation to a single ganglion cell and avoid axonal stimulation (Sekirnjak et al.,
2008).
Taken together, these data and models suggest that it is possible to selectively
activate certain subpopulations of cells and localize activation to a single cell when using
very small electrodes. However, using larger electrodes complicates the spatial accuracy
of stimulation. Thus, given current engineering and safety constraints, it is possible to
18
control the timing of retinal output but the ability to create highly spatially localized
retinal activation is still significantly limited.
1.3.4 Methods for modeling the response to electrical stimulation
Quoting the statistician George Box from 30 years ago, “All models are wrong,
but some are useful.” Models, when useful, provide insight into the underlying function
or mechanism of a much more complicated system. In many ways, the brain is a vast
black box, where making predictions about visual perception necessitates
computational modeling, as the neural mechanisms between photon and percept are
far from understood. Indeed, a full account of how visual stimuli are encoded within the
retina and interpreted by the rest of the visual brain is well beyond the scope of this
thesis. However, models of visual processing are useful and potentially allow for us to
predict certain qualities of the resulting percept as a function of changes in the stimulus
(whether it is electrical or photonic).
The response of individual neurons to spatial stimuli is generally modeled using
center‐surround receptive fields as described in the beginning of this section (Rodieck,
1965; Rodieck and Stone, 1965). However, when thinking about retinal electrical
stimulation using large disc electrodes (where inputs are not coming via photoreceptors
with excitatory and inhibitory connections), these difference‐of‐Gaussian models
become less useful. It is more useful to think about how the population of cells, under
each electrode, responds to the stimulus.
Electrical field modeling. One way to start thinking about this is by using an
electric field model, and determining which cells within a given region are activated. The
19
effect of extracellular current stimulation on the excitation of a neuron is, at best, highly
complex. Excitation depends on the extracellular potential created by the stimulus and
on properties of the cell, such as morphology and membrane conductance. Assuming a
homogenous medium and a return electrode at infinity, the extracellular potential for
any given distance from the electrode center can be modeled as (Wiley and Webster,
1982b; Cottaris and Elfar, 2005):
V
e
(x,y,z) =
2V
0
π
arcsin
2α
(r + α)
2
+d
2
+ (r −α)
2
+d
2
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
(1.1)
where r is the radius of the electrode, d is the distance of the cell from the center of the
electrode, and V
0
is the electrode current times the resistance of the cell. Using this
model, you can estimate the spatial population of retinal cells that are activated by
electrical stimulation from the electrode. However, the response of these cells to
electrical stimulation (and light) is not, of course, linear. One useful technique for
describing these population responses is the class of models known as linear‐nonlinear.
Linear nonlinear models. Generally, a stimulus will result in a neural (or
perceptual) response, and this response is temporally sensitive. Additionally, the
response typically increases with increasing intensity in the stimulus. The models used in
this thesis are variants of linear‐nonlinear (LN) models. Please see Appendix A for a basic
review of linear and nonlinear tools for modeling biological systems.
The stimulus intensity that varies with time, s(t), is passed through a linear filter,
F(t). The convolution of the stimulus with this linear filter represents the time course of
20
the response. The output of this convolution is then transformed by a static
nonlinearity, N. This can be represented as:
∫
− = ) ) ( ) ( ( ) ( ' τ τ τ d t F s N t r . (1.2)
Here, the linear filter, F, can be thought of as the impulse response of the
system, summing stimuli linearly in time. The nonlinearity, N, accounts for the
threshold, sensitivity, and saturation of single neurons or neural systems as a function f
stimulus intensity.
Models such as these have been used to predict the response of retinal ganglion
cells to certain types of stimuli, such as a white noise (Chander and Chichilnisky, 2001;
Kim and Rieke, 2001; Baccus and Meister, 2002). Interestingly, this same model, with
only slight modifications, can be used to predict the threshold brightness of a visual
stimulus in human subjects (Watson, 1986). As we will show in Chapter 2, we can use a
very similar model to predict the perceptual brightness of electrical stimuli in retinal
prosthesis subjects. Combining the above modeling techniques, it may be possible to
determine the perceptual response to spatiotemporal, multi‐electrode stimulation.
1.4 A Back‐to‐Front History of Visual Prostheses
Restoring functional vision using electrical stimulation has been a goal of
ophthalmologists and vision scientists for more than a century. The inspiration for these
studies comes from very early (and probably inadvertent) electrical activation of visual
cortex during neurosurgery. The earliest documented electrically generated percept in a
blind human patient occured in 1755, when Charles LeRoy, a French chemist and
21
physician, discharged a Layden jar and supplied electrical current to a brass coil that
wrapped around the head of a blind man (LeRoy, 1755). In addition to “provoking
terrible cries (Marg, 1991)”, the young patient perceived a flame that rapidly descended
before his eyes. This is, more than likely, the first documented visual phosphene
perceived by a blind subject via electrical stimulation. It wasn’t until the middle of the
20
th
century that scientists and clinicians began to investigate, more deliberately and
rigorously, the relationship between electrical stimulation of neural tissue and visual
perception.
The early visual system of humans and nonhuman primates contain 4 main
stages: the retina, the optic nerve leading to the subcortical lateral geniculate nucleus
(LGN) of the thalamus, and primary visual cortex (V1). All these sites have been targeted
in the attempt to build a visual prosthesis. Here we provide a brief overview, beginning
in the cortex.
1.4.1 Stimulating Primary Visual Cortex
During his studies of the cerebral cortex and the neural origins of epilepsy,
Penfield found subjects experienced visual percepts described as stars, wheels, discs,
spots, streaks, and lines during electrical stimulation (Penfield and Rasmussen, 1952;
Penfield and Jasper, 1954). About a decade later, Button and Putnam implanted semi‐
chronic devices with 4 occipital‐lobe electrodes with percutaneous wires into 3 subjects,
where electrical current amplitude and frequency could be modulated using a cadmium‐
sulfide photocell. The subjects could carry this “stimulator” around with them while
22
attempting to navigate and localize objects in their environment using this crude device
(Button and Putnam, 1962).
The first attempt at true chronic stimulation in visual cortex was by Brindley and
Lewin (Brindley and Lewin, 1968). They implanted, in a 52‐year‐old woman, an array of
80 platinum disc electrodes that was placed on the surface of the occipital pole.
Through electrical stimulation, the subject was able to see 32 independent visual
percepts, allowing Brindley to conduct mapping and threshold experiments. Brindley
implanted another subject in 1972 with an 80‐electrode array, 79 of which generated
percepts of varying size (Brindley et al., 1972). Although an attempt was made to
combine the phosphenes into crude letters and shapes, these implants did not
ultimately prove to be functionally useful to the subjects.
Perhaps the most famous vision scientist that implanted electrode arrays
chronically in visual cortex is Dr. William Dobelle. Dobelle began experiments in 1974,
when he implanted to two blind subjects with 64 platinum disc electrodes (each
electrode was approximately 1 mm
2
) in a hexagonal array (Dobelle et al., 1974). Like
Brindley, Dobelle carefully evaluated how changes in the parameters of stimulation lead
to changes in the quality of the percept (Henderson et al., 1979). His most important
findings were in relation to spatial vision. Evaluation of the phosphenes maps generated
with the electrode arrays indicated that stimulation that was progressively farther from
the occipital pole led to phosphenes further and further into the periphery. Just as
importantly, stimulation of points clustered on the surface of the visual cortex produced
phosphenes clustered in visual space (Dobelle et al., 1979). However, later studies found
23
that simultaneous and interleaved pulse stimuli on pairs of electrodes resulted in fused
percepts (either dumbbell‐shaped or elongated lines) even when separated by as much
as 1 mm apart (Bak et al., 1990). This suggests that generating grids of punctate
phosphenes using multi‐electrode stimulation may be complicated by electrode‐
electrode and lateral neural interactions.
Although efforts to develop a cortical prosthesis continue (Schmidt et al., 1996;
Normann et al., 1999; Bradley et al., 2005; Fernandez et al., 2005), the technology faces
a number of surgical and safety hurdles before this approach will reach clinical
acceptance (Kotler, 2002; de Balthasar et al., 2008; Horsager et al., 2008; Girvin, 1988
#3965).
1.4.2 Stimulating LGN
Although V1 and the retina have been the primary targets of interface with
visual prostheses, it is also possible to target the LGN with electrical stimulation to
generate visual percepts. Pezaris and Reid have recently performed groundbreaking
scientific work in this area, establishing that either visually or electrically stimulating
specific receptive fields of the LGN results in highly localized and repeatable eye
movements to the percept in nonhuman primates (Pezaris and Reid, 2007).
While targeting the LGN may appear to be highly invasive, Deep Brain
Stimulation (DBS) of the thalamus in human patients for the treatment of Parkinson’s
disease and depression is becoming more commonplace and the safety of using this
technology is well established (Pena et al., 2007). Additionally, the projections from the
retina to V1 maintain their retinotopy within the LGN, suggesting that it may be possible
24
to provide stimulation patterns using an array of electrodes that produce spatially
arranged percepts (Schneider et al., 2004). This technology is in early days but the
recent results of Pezaris and Reid have certainly established feasibility.
1.4.3 Stimulating the Optic Nerve
Between the retina and the LGN is the optic nerve, the collection of ganglion cell
axons projecting back to the rest of the visual brain. With the development of cuff
electrodes for nerve fiber recordings (Hoffer et al., 1981), and stimulation of both
muscle fibers (Baratta et al., 1989; Fang and Mortimer, 1991) and the vagus nerve
(Woodbury and Woodbury, 1991), it became possible to apply this technology optic
nerve stimulation. One group has shown in a single blind volunteer that optic nerve
stimulation using a cuff electrode is effective for generating visual percepts (Veraart et
al., 1998; Brelen et al., 2005). A major concern with this approach is that the optic nerve
does not maintain retinotopy (Fitzgibbon and Reese, 1996), making spatial mapping of
the stimuli difficult. However, this same group has shown evidence that the variations in
the parameters of the stimulus (e.g., frequency and pulse width) lead to changes in the
perceived location of the percept.
1.4.4 Extraocular, Subretinal, Epiretinal Prostheses
The majority of effort in developing visual prostheses for the blind has focused
on electrical stimulation of the retina. Indeed, there is a substantial amount of neural
processing within the LGN (Dan et al., 1996; Wang et al., 2007b; Alitto and Usrey, 2008)
and V1 (Hubel and Wiesel, 1962) that shape the visual signal. Thus, targeting stimulation
as early as possible in the visual pathway allows one to maximize the computational
25
processing of the visual system. Even with this in mind, there has been a diversity of
technologies developed to target the retina with electrical stimulation.
Extraocular electrical stimulation has a long history. Perhaps the primary reason
for this is that it is, relatively speaking, noninvasive. Brindley’s work established the
feasibility of using this type of stimulation when he applied stimulating pulse trains to
his own eye using a makeshift corneal electrode, showing that these pulses could
systematically interfere with visual light stimuli (Brindley, 1962). More recently, groups
have focused on developing extraocular stimulating devices as a potential clinical
treatment for vision loss (Chowdhury et al., 2005; Fujikado et al., 2007). However, it
remains a major hurdle to develop a high‐resolution extraocular device when the
distance between the electrodes and retina is so great.
There is a wide assortment of subretinal techniques, ranging from passive
photosensitive diode arrays (Chow and Chow, 1997; Peyman et al., 1998; Chow et al.,
2004), to neurotransmitter‐based stimulation methods (Peterman et al., 2003), to more
active stimulation, using photo‐to‐electrical signal amplification (Palanker et al., 2005;
Zrenner et al., 2006; Zrenner, 2007) or subretinal electrical stimulation (Jensen and
Rizzo, 2006, 2008). The goal of subretinal stimulation is to maximize the computational
processing of the retinal circuitry by targeting the retinal bipolar cells. However, there is
conflicting evidence of the fidelity of the bipolar‐ganglion cell synapse (Marc and Jones,
2003; Jones et al., 2005; Lagali et al., 2008). Additionally, there is data suggestive of
substantial subretinal gliosis (Marc and Jones, 2003; Jones et al., 2005), making effective
26
placement of the subretinal array and efficient stimulation of the retinal bipolar cells,
challenging at best.
Although there are a variety of other groups developing epiretinal stimulation
arrays (Wyatt and Rizzo, 1996; Rizzo and Wyatt, 1997; Hornig et al., 2006), I will focus
here on the array developed as part of a collaborative effort between Second Sight
Medical Products, Inc. and the Doheny Eye Institute (Humayun et al., 1996; Humayun et
al., 2003; de Balthasar et al., 2008). This device is currently the only array that that has
been chronically implanted in human patients, and the data in this thesis were collected
in patients implanted with this device.
The Second Sight Medical Products, Inc. epiretinal prosthesis contains both
intraocular (electrode array) and extraocular (e.g., glasses, Visual Processing Unit)
components. As previously described, the intraocular array consisted of 16 platinum
electrodes in a 4 x 4 arrangement, held in place within a clear silicone rubber platform
(Humayun et al., 2003; Mahadevappa et al., 2005). Electrodes are either 260 or 520 μm
in diameter (subtending 0.9° and 1.8° of visual angle, respectively). Electrodes are
spaced 800 μm apart, center‐to‐center. The electrode array is implanted epiretinally in
the macular region and held in place using a retinal tack. Pulse train signals are
generated and sent to an external Visual Processing Unit (VPU) using custom software
run on a PC laptop. Power and signal information are sent from this processor through a
wire to an external transmitter coil that attached magnetically, and communicated
inductively, to a secondary coil that is implanted subdermally in the patient’s temporal
skull. From this secondary coil, power and signal information are sent through a
27
subdermally implanted wire that traversed the sclera to the array of electrodes (Fig.
1.6.). Stimulation can be presented using two different protocols: 1) camera mode –
real‐time video captured by a miniature video camera mounted on the subject’s glasses
is continuously sampled by the VPU to match the stimulation current amplitude in each
electrode to the brightness at the corresponding area of the scene and 2) direct
stimulation mode ‐ the stimulation signal sent to each electrode is independently
controlled by the VPU.
1.5 The outline of this thesis
This thesis is focused on understanding the visual response to electrical
stimulation in retinal prosthesis patients. More specifically, this thesis evaluates the
relationship between pulse timing during single and multi‐electrode stimulation and the
Fig. 1.6. Schematic of the retinal prosthesis. (A) Electrode array. The electrode array consisted of 260
or 520 micrometers (μm) electrodes arranged in a checkerboard pattern, with center‐to‐center
separation of 800 μm. The entire array covered ~2.9 mm by 2.9 mm of retinal space, subtending ~10°
of visual angle. (B) Prosthesis system schematic. The stimulus sets were programmed using Matlab
®
on
a PC, which then communicated the stimulus parameters to an external Visual Processing Unit (not
shown). Signal and power information was then passed through an external inductive coupling device
(not shown) that attaches magnetically to a subdermal coil implanted in the patient’s temporal skull.
This signal is then sent through a parallel system of wires to the epiretinally implanted electrode array.
Note that the power and signal information can be independently controlled for each electrode.
28
brightness of the percept, both from a qualitative and quantitative perspective. A full
discussion of size, shape, and color of the percepts, and how they change as a function
of stimulation parameters, is beyond the scope of this thesis.
Chapter 2 presents data and a model of temporal sensitivity. The data show that
perceptual brightness changes as function of pulse width and timing and the model
allows for the prediction of perceptual brightness for any given stimulation pattern on a
single electrode.
Chapter 3 focuses on understanding how systematic changes in pulse timing lead
to changes in the quality of the percept. More specifically, the data presented in
Chapter 3 evaluates the limits of sensitivity to pulse timing on single and multiple
electrodes. These data show that changing pulse timing across electrodes leads to
qualitative changes in the percept. Although psychophysics has limitations on
determining the mechanisms of action, these data clearly show that underlying
interactions with multi‐electrode stimulation and the sensitivity to pulse timing across
electrodes is, at least partly, neural in nature.
Chapter 4 expands upon Chapter 3 by describing data and a model of perceptual
brightness for multi‐electrode stimulation. This chapter expands upon Chapter 3 by
quantifying the interactions across electrodes. Finally, a model is presented that shows
the brightness of multi‐electrode stimulation can be described through a fairly simple
equation.
Chapter 5 presents concluding remarks regarding the data and modeling work
presented in Chapters 2 through 4. Suggestions for future work will also be presented.
29
Chapter 2
Predicting temporal sensitivity in retinal prosthesis
patients
2.1 Introduction
To create perceptually meaningful images it is necessary to predictably generate
a range of brightness levels over both space and time. Although the literature examining
the perceptual consequences of electrical stimulation has a long history (LeRoy, 1755;
Lowenstein, 1918; Foerster, 1929; Penfield and Rasmussen, 1952; Brindley and Lewin,
1968; Dobelle, 1974; Humayun et al., 1996; Schmidt et al., 1996; Weiland et al., 1999;
Humayun et al., 2003; Rizzo et al., 2003; Mahadevappa et al., 2005; Murphey and
Maunsell, 2007; Pezaris and Reid, 2007; Yanai et al., 2007), there is still relatively little
data in humans systematically quantifying the effects of retinal electrical stimulation as
a function of stimulation current levels and the temporal stimulation pattern.
We show here that, at the single electrode level, retinal electrical stimulation
results in predictable visual qualia that can be described using a relatively simple linear‐
nonlinear model. This model predicts the relationship between electrical stimulation
and sensitivity for a wide variety of temporally‐varying stimulation patterns. This model
30
can not only be used to determine the “optimal” pattern of stimulation given a variety
of engineering constraints (such as stimulating at safe levels of charge density and
minimizing overall charge), but it may also provide some insight into the neural
pathways that underlie the perceptual effects of electrical stimulation.
2.2 Materials & Methods
2.2.1 Subjects
We examined two patients chronically implanted with 16‐electrode retinal
prostheses (Second Sight
®
Medical Products, Inc.). (See section 1.4.3 and Fig. 1.6 for an
in depth description of the device). Pre‐operatively, subject S05 had bare Light
Perception (BLP) in the implanted eye, was blind for 8 years before implantation, and
was 59 years of age when implanted. Subject S06 had no Light Perception (NLP), was
blind for 10.5 years before implantation, and was 55 years of age when implanted.
These tests were carried out during a period of approximately 90 to 1170 days after
implantation in the case of S05, and 30 to 1110 days after implantation in the case of
S06.
These two patients were a subset of six patients implanted since February 2002.
The other four patients were excluded for a variety of reasons: one patient was
excluded because of geographic location, two patients were excluded due to unrelated
medical conditions, and in one patient the array cable became exposed. Because the
cardiac status of this patient precluded general anesthesia, the multi‐wire cable
connecting the array to the external stimulator was cut and the intraocular portion of
the array was left in place.
31
All tests were performed after obtaining informed consent under a protocol
approved by the Institutional Review Board at the Keck School of Medicine at the
University of Southern California and under the principles of the Declaration of Helsinki.
2.2.2 Psychophysical Methods
All pulse waveforms consisted of biphasic, cathodic‐first, charge‐balanced square
wave pulses, presented either in isolation or as a train of pulses. All individual pulses
within a pulse train were charge‐balanced in order to maximize tissue safety and
electrode integrity. Here, we used cathodic and anodic pulses of equal width and
amplitude. We tested subjects under standardized photopic conditions (so as to match
the conditions under which a prosthetic implant might be used).
Perceptual threshold measurements. Thresholds were measured on single
electrodes using a single interval, yes‐no procedure. On each trial, subjects were asked
to judge whether or not they had been stimulated on that trial. The time between each
trial varied depending on the subject's response time, but generally ranged between 3‐5
seconds. This reporting procedure meant that subjects would report stimulation for
either a light or dark spot; subjects were explicitly instructed to include either type of
percept in making their decision.
During the first few weeks after implantation thresholds and matching
judgments tended to be fairly variable (de Balthasar et al., 2008). The gradual increase
in the stability of thresholds (and probably a slight reduction in threshold) is likely to be
partially due to subjects becoming increasingly expert observers – similar effects can be
noted for traditional psychophysical experiments. These experiments were begun
32
several sessions after implantation, at a point where additional learning effects were
likely to be fairly minimal. It should be noted that we used a large number of catch trials,
and monitored and compensated for false‐positive responses to prevent changes in
subjects' criteria over time affecting thresholds. Half of the trials were stimulus‐absent
catch trials, and these stimulus‐absent catch trials were interleaved randomly with the
stimulus‐present trials. These catch trials were used to compensate for any change in
criterion with time or practice. Current amplitude was varied using a three‐up‐one‐
down staircase procedure to find the threshold current amplitude needed for the
subjects to see the stimulus on 50% of stimulus‐present trials, corrected for the false
alarm rate. If the subject responded correctly three times in a row, the task was made
more difficult by decreasing the current amplitude. If the subject answered incorrectly
on any trial, the task was made easier by increasing the current amplitude. During each
staircase, only amplitude varied. All other parameters (frequency, pulse width, pulse
train duration, and the number of pulses) were held constant. Each threshold was based
on fitting a Weibull function to a minimum of 125 trials and error bars were estimated
using Monte‐Carlo simulation (Wichmann and Hill, 2001). See Appendix B1 for examples
of Weibull fits of the data collected for both threshold and suprathreshold data. Weibull
functions generally provided good fits to threshold data (de Balthasar et al., 2008) and
failures to find a good fit appeared to be non‐systematic and due to noise. We did not
observe any systematic variation of slope across the experimental conditions tested.
Suprathreshold brightness matching judgments. Suprathreshold brightness‐
matching was carried out on single electrodes using a two‐interval, forced‐choice
33
procedure. Each trial contained two intervals (separated by approximately 1 second),
with each interval containing a pulse train of a different frequency. For example, interval
1 might contain a 15 Hz pulse train and interval 2 might contain a 45 Hz pulse train.
Subjects were asked to report which interval contained the brighter stimulus. The order
of the intervals was randomized on each trial in order to minimize potential
presentation order biases or adaptive effects (see Appendix B2). The time between each
trial varied depending on the subject's response time, but generally ranged between 3‐5
seconds. A one‐up, one‐down staircase method was used to adjust the amplitude of the
higher frequency pulse train based on the observer’s response. Occasionally
(approximately 1/10 of cases), a dark phosphene rather than a white or yellow
phosphene was elicited for a particular electrode. Because all comparisons were carried
out within a single electrode, subjects were never asked to brightness match a bright to
a dark phosphene. When brightness matching a dark phosphene, subjects reported
which interval contained the darker phosphene.
The first brightness match was made by fixing the amplitude of a “standard” 5 Hz
pulse train (a single pulse within a 200 ms window) to be 2 or 3 times threshold
amplitude, and finding the amplitude needed for a 15 Hz “test” pulse train to match the
brightness of the standard pulse train. Using the measured brightness‐matched value of
the 15 Hz pulse train, the 15 Hz pulse train then became the “standard” pulse train and
was compared in brightness to a 45 Hz “test” pulse train and so on. It should be noted
that this technique led to the accumulation of small errors as the standard changed, but
unfortunately software limitations made it impossible to either use a fixed standard or
34
perform all‐pair wise comparisons. On a few electrodes we collected data "backwards",
beginning with a 225 Hz stimulus as the standard, and results were qualitatively similar.
Each brightness match was based on a minimum of 80 trials. A cumulative
normal was used to find the point of equibrightness, and error bars were again
estimated using an adaptive sampling Monte‐Carlo simulation (Wichmann and Hill,
2001). Each individual psychometric function was inspected to make sure that an
adequate fit was obtained, and data was recollected if fits were inadequate (based
either on the estimated error or visual inspection). A cumulative normal appeared to
provide a good fit to the data (Appendix B1). Using this method, we were able to obtain
an isobrightness curve that represented the current amplitude needed to maintain the
same subjective brightness across a wide range of frequencies.
Stimulus set. In each of our two subjects, we measured detection thresholds for
10 different categories of stimulation pattern and suprathreshold perceived brightness
for 6 different categories of stimulation pattern. Data were collected from 12 electrodes
across the two subjects. Across these 12 electrodes, we collected 534 threshold and 116
suprathreshold measurements in total.
Due to the limited availability of our subjects, we were unable to collect data on
all electrodes. The only criterion used to choose the six electrodes used in these
experiments was that single pulse thresholds were relatively low. This allowed us to
collect suprathreshold data across a range of brightness levels while remaining within
charge safety limits. Given this constraint, electrodes were then chosen that were
dispersed as evenly as possible across the array. The data presented here represent
35
testing sessions that occurred on roughly a weekly basis (~3 hours per session) over the
course of 2 years.
2.2.3 A model of temporal sensitivity
Data were modeled using a linear‐nonlinear model (Fig. 2.1) similar to models of
auditory stimulation in cochlear implant users (Shannon, 1989), retinal ganglion cell
spiking behavior during temporal contrast adaptation (Chander and Chichilnisky, 2001;
Rieke, 2001; Baccus and Meister, 2002), and human psychophysical temporal sensitivity
in normal vision (Watson, 1986). We began by convolving the stimulus with a temporal
low‐pass filter, or “leaky integrator” using a 1‐stage gamma function as its impulse
response:
) , 1 , ( ) ( ) (
1 1
τ δ t t f t r ∗ = (2.1)
where f (t) is the electrical stimulation input pattern, t is time (ms), and δ is the
impulse response function with time constant τ
1
. We report here time constants
(τ
1
rather than chronaxie values (c), which are also commonly reported in the literature:
τ
1
= c/ln(2). The gamma function used to model the impulse response can be generally
described as:
1
1
1
1
) (
)! 1 (
) , , (
1
−
−
−
=
n
t
t
n
e
n t
τ
τ
τ δ
τ
, (2.2)
where t = time, n = the number of identical, cascading stages, and τ
1
is the time constant
of the filter (the 1‐stage gamma function in Eq. 1 is simply an exponential function).
We assumed that the system became less sensitive as a function of accumulated
charge. This was implemented by calculating the amount of accumulated cathodic
36
charge at each point of time in the stimulus, c(t), and convolving this accumulation with
a second 1‐stage gamma function having a time constant τ
2
. The output of this
convolution was scaled by a factor ε, and then subtracted from r
1
(Eq. 1),
)) , 1 , ( * ) ( ( ) ( ) (
2 1 2
τ δ ε t t c t r t r − = . (2.3)
r
2
was then half‐rectified, passed through a power nonlinearity,
( )
β
| ) ( | ) (
2 3
t r t r = (2.4)
and convolved with a low‐pass filter described as a 3‐stage gamma function with time
constant τ
3
,
) , 3 , ( * ) (
3 3 4
τ δ t r t r = . (2.5)
We assumed that the response reached threshold (or the point of equibrightness during
suprathreshold experiments) when
θ >= ) ( max
4
r
t
(2.6)
where θ is a fixed constant.
Fig. 2.1. Model schematic. The time varying stimulus, f(t), is convolved with a linear filter, δ
1
(t). The result of this
convolution is passed through a static nonlinearity, N(r
2
), and convolved with a secondary linear filter, δ
2
(t). We
assumed that a stimulus was at visual threshold (or a given brightness level) when r
3
(t) reached a threshold value,
θ(r
3
).
37
2.2.4 Determining the optimal parameters of the model
Optimization was carried out using a subset of the full set of data ‐ 2 electrodes
for each of the two patients (S05 – B3 & C2, S06 – B1 & C2). Threshold and
suprathreshold fits and parameter values for these electrodes are shown in Appendices
B3 and B4 (Figs. B2‐B11 and Tables B1 and B2).
The parameter values
2 1
,τ τ and
3
τ were optimized across the 7 threshold and 3
suprathreshold experiments using a standard least‐squared error minimization
technique. The parameters ε (linear shift as a function of charge) and β (power
nonlinearity) were fit separately for threshold and suprathreshold levels of stimulation.
When fitting suprathreshold data, ε and β were allowed to vary across different levels
of apparent brightness.
The parameter that represented the model output at threshold, θ, was allowed
to vary across each experiment on a given electrode. Variation in θ accounts for
differences in mean sensitivity between the two patients, differences in sensitivity
across electrodes, and slight changes in electrode sensitivity over time. The set of data
in this paper were collected over slightly more than a two year period. During this
period of time we observed gradual changes in sensitivity which appeared to be mainly
due to slight changes in the position of the electrode array over time (de Balthasar et al.,
2008). We also saw some variation in threshold within individuals across different
testing sessions. Similar variability (of roughly the same magnitude) has been reported
for sensitivity (perimetry) data in visually normal control subjects, and appears to
38
increase with age (Heijl et al., 1987; Katz and Sommer, 1987). Because each experiment
on a given electrode was collected over a relatively short time period (usually within the
same testing session) we assumed that electrode sensitivity did not vary within an
experiment.
2.3 Results
Patients typically reported that phosphenes appeared white or yellow in color,
and were round or oval in shape. At suprathreshold, percepts were reported as brighter
and the shape occasionally became more complex than a simple round or oval shape.
The shapes were reported as being approximately 0.5‐2 inches in diameter at arm's
length, corresponding to roughly 1‐3 degrees of visual angle. When the percept was
reported as oval in shape, the longer axis was generally 2‐3 times the length of the
shorter axis. As described above, a small proportion of electrodes elicited a dark rather
than bright phosphene. We did not see any systematic differences in threshold or slope
of the psychometric functions between light and dark phosphene measurements.
Occasionally, during brightness matching tasks, phosphenes generated by two different
frequencies differed in their shape and/or color, though these differences were fairly
small near the point of equal brightness. Subjects were told to base responses on
changes in brightness and ignore other qualitative changes. Subjects reported that this
was easily done.
39
2.3.1 Predicting visual sensitivity for novel temporal patterns
After optimizing the model using a subset of the full set of data, we averaged
the best‐fitting parameters values for ε τ τ τ , , ,
3 2 1
and β across all the four electrodes
used for optimization and used these mean values to predict threshold and
suprathreshold data for novel electrodes. For these novel electrodes, the only
parameter allowed to vary across each experiment was the threshold parameter,θ.
Values of θ for these novel electrodes, as well as other parameter values, are shown in
Appendix B6 (tables B3 and B4).
Figure 2.2 shows subject thresholds (gray squares) and model predictions (solid
line) for a single biphasic pulse presented on a novel electrode for both subjects. Note
the logarithmic horizontal axis. Figure 2.3 shows threshold data and predictions on a
novel electrode for 200 ms pulse trains whose frequency varied between 5 Hz and 225
Hz. Pulse trains consisted of either 0.075 ms (B) or 0.975 ms (C) charge‐balanced
biphasic pulses. Figure 2.4 shows threshold data and predictions for pulse trains
containing either 2 (B) or 15 (C) pulses, whose frequency was varied between 3 Hz and
3333 Hz. Figure 2.5 shows suprathreshold data and model predictions for 200 ms pulse
trains consisting of either 0.075 ms (B) or 0.975 ms (C) pulses, whose frequency varied
between 5 Hz and 135 Hz. Additional threshold and suprathreshold data and predictions
are shown in Appendix B5. The model and parameter values generalized to successfully
predict data on novel electrodes.
40
Fig. 2.2 Single pulse threshold. These data are from electrodes C3 and A1,
from patient S05 and S06, respectively. Stimuli (A) were single, biphasic,
charge‐balanced square pulses, whose pulse width (dashed arrow) varied in
duration from 0.075 ms to 4 ms. For each pulse width, the amplitude was
varied (solid arrow) to determine perceptual threshold. In the data plots (B),
the x‐axis represents pulse width (plotted logarithmically) and the y‐axis
represents the current amplitude (μA) needed to reach threshold. The solid
black line represents the prediction of our model.
41
Fig. 2.3 Fixed duration pulse train threshold. These data are from electrodes
C3 and A1, from patient S05 and S06, respectively. Stimuli (A) were 200 ms
pulse trains, consisting of charge‐balanced biphasic pulses, whose frequency
varied between 5 Hz and 225 Hz. Pulse trains using 0.075 ms (B) and 0.975 ms
(C) pulse widths (red arrows) were evaluated. The amplitude (solid black
arrows) of all pulses within the train was varied simultaneously to determine
threshold (see Methods for a full description of the threshold detection task).
The x‐axis represents pulse train frequency (Hz) (plotted logarithmically) and
the y‐axis represents the current amplitude (μA), per pulse, needed to reach
threshold. The black line represents the prediction of our model.
42
Fig. 2.4 Variable duration pulse train threshold. These data are from
electrodes C3 and A1, from patient S05 and S06, respectively. Stimuli (A) were
pulse trains whose frequency was varied between 3 Hz and 3333 Hz. Pulse
trains contained either 2 (B) or 15 (C) pulses (see Supplemental Data 2 for data
with trains of 3 pulses). The amplitude of all pulses within the train was varied
simultaneously to determine threshold (see Methods for a full description of
the threshold detection task). The x‐axis represents pulse train frequency (Hz)
(plotted logarithmically) and the y‐axis represents the current amplitude (μA),
per pulse, needed to reach threshold. The black line represents the prediction
of our model.
43
Fig. 2.5 (A) Fixed Duration Pulse Train Suprathreshold. These data are from
electrodes C4 and B2, from patient S05 and S06, respectively. Stimuli (A) were
200 ms pulse trains consisting of either 0.075 ms (B) or 0.975 ms (C) pulses,
whose frequency varied between 5 Hz and 135 Hz, plotted logarithmically on
the x‐axis. The amplitude value for the 5 Hz train was set at 2 times threshold
and the amplitude of the 15, 45, and 135 Hz pulse trains was modulated to
find the amplitude that was equally bright to that of the 5 Hz pulse train (see
methods for the description of the brightness matching task). Thus, we then
obtained an isobrightness curve for frequencies from 5 Hz to 135 Hz. The x‐
axis represents pulse train frequency (Hz) (plotted logarithmically) and the y‐
axis represents the current amplitude (μA), per pulse, needed to reach
equibrightness. The black line represents the prediction of our model.
We then examined the ability of the model to predict responses to novel pulse
train waveforms not used to optimize model parameters (Fig. 2.5). We again used the
same fixed values for ε τ τ τ , , ,
3 2 1
and β based on the electrodes and stimulus patterns
used for optimization, and the only parameter allowed to vary across each experiment
44
was the threshold parameter,θ. The novel waveforms consisted of repeated bursts of 3
pulses with a variable inter‐burst delay. Data for this novel waveform was collected at
both threshold and suprathreshold levels of stimulation on novel electrodes not used
for the original model fits. The model and parameter values generalized to successfully
predict these data from a novel stimulation pattern on a novel electrode.
Fig. 2.6 Bursting Pulse Triplets, Suprathreshold. (A) Pulse train stimuli were
15 (B), 30 (C), or 60 (D) pulse trains, 500 ms in duration. Bursts consisted of
0.45 ms biphasic pulses with no inter‐phase delay. The x‐axis is the inter‐
pulse delay between the set of 3 bursting pulses (plotted logarithmically),
and the y‐axis is current amplitude (μA), per pulse, needed to reach
equibrightness. The black line represents the prediction of our model.
45
2.3.2 Model Power
The power of this model was significantly higher than that of a less constrained
model where ε τ τ τ , , ,
3 2 1
, β and θ were all allowed to vary across each experiment and
electrode (F test, F
ratio
= 0.6483, α < 0.01). The power of the model was also significantly
better than that of a variety of simplified versions of the model as well as slight variants
of this model. There is of course an infinite supply of alternative models of the same or
greater complexity, however none of the alternative models that we examined
performed as well as the model described above.
This model is also highly constrained compared to analogous models that have
been used to model human responses to temporally varying light patterns e.g. (Watson,
1986; Foley, 1994). In these psychophysical models a similar number of parameters are
required, a smaller range of temporal patterns are generally modeled, and parameters
are typically allowed to vary across subjects. This model is also constrained relative to a
similar model of temporal sensitivity in cochlear implants (Shannon, 1989) where once
again, a similar number of parameters were required, a smaller range of temporal
patterns was modeled, and parameters were allowed to vary across subjects. Finally,
this model is constrained compared to similar models that have been used to describe
the spike timing response of retinal ganglion cells (Chander and Chichilnisky, 2001;
Rieke, 2001; Baccus and Meister, 2002). In these models a similar number of parameters
are required to describe cell responses, a smaller range of temporal patterns are
modeled, and parameters of the model are allowed to vary across each individual cell.
46
It is, of course, unlikely that our model is the best of all possible models and it is
to be hoped that more powerful models will be developed in the future (either by
finding a model that is less complex, or by finding a model of equal complexity that fits
our data more closely). Moreover, as more a wider range of temporal data is collected
in humans (for example, we could not collect data for pulse durations longer than 4ms
because of charge safety limits) it should be possible to develop models of greater
complexity that are not under‐constrained.
2.4 Discussion
We find that perceptual responses to retinal electrical stimulation could be
predicted with a surprisingly simple model that resembles models of ganglion cell firing
behavior during contrast adaptation (Chander and Chichilnisky, 2001; Rieke, 2001;
Baccus and Meister, 2002), human temporal integration of light stimuli (Watson, 1986),
and auditory processing in cochlear implant users (Shannon, 1989).
Our model, like those describing the perception of light stimuli, presumably
approximates the responses of neuronal populations. Observed thresholds were
comparable to in vitro thresholds in primates for equivalent pulse widths and electrode
size (Sekirnjak et al., 2006). Also see deBalthasar et al. (de Balthasar et al., 2008), for a
direct comparison of thresholds in our patients to those obtained within in vitro animal
models. Subjects with normal vision can reliably detect flashes of 100 photons (Hecht et
al., 1942); a very small increase in the firing rate of ganglion cells is sufficient to mediate
detection. It is possible that thresholds in our subjects are mediated by a relatively small
number of spikes. These spikes might, of course, occur either in a single cell or across
47
several cells. At suprathreshold our model presumably approximates the population
response of a larger number of cells each producing one or multiple spikes.
Quantitative models, as well as providing a description of behavioral
performance, can also sometimes provide insight into neural organization (Campbell
and Robson, 1968; Henning et al., 1975; Albrecht and De Valois, 1981; Mandler and
Makous, 1984). In the case of retinal stimulation, neurophysiological interpretations are
necessarily highly speculative given the current body of knowledge describing
membrane and synapse properties of degenerate retina and the scarcity of
neurophysiological data regarding the effects of retinal stimulation.
Histological evidence shows that bipolar cells of degenerated retinae have a
general decrease and redistribution of glutamate receptors, leading to a decrease of
mGluR6‐ and iGluR‐mediated currents (Strettoi et al., 2003; Marc et al., 2007). However,
retinal ganglion cells continue to show iGluR currents (Marc et al., 2007). The ganglion
cells of retinal degenerated retinae have a much higher spontaneous firing frequency
than wild‐type, which sometimes produces rhythmic bursts of activity as a result of self‐
signaling (Marc et al., 2007; Stasheff, 2008). However, expressing and activating
channelrhodopsin (ChR2), a light‐activated cation channel, in ON bipolar cells of rd1
mice results in excitatory responses in retinal ganglion cells of rd1 retinae similar to
those of wild‐type (Lagali et al., 2008). These findings suggests that the circuitry
between bipolar and ganglion cells is not entirely disrupted, and that this circuitry, when
presented with stimuli, has some functional similarities to normal retina. Given this, we
48
find it interesting that many of the stages in our model are quite similar to those used to
describe in vitro models of the normal retina.
In our model, the parameter
1
τ (Eq. 2.1) represents the time course of the first
stage of current integration and was constrained by the shape of the functions for single
pulse thresholds (Fig. 2.4.1B). Estimates varied between 0.24‐0.65 ms, with a mean of
0.42 ms, a value very similar to electrophysiology estimates of the integration of current
by ganglion cells in rodent and primate models (Jensen et al., 2005a; Fried et al., 2006;
Sekirnjak et al., 2006) It should be noted that intracellular current injection results in
slower time constants, ranging from 3.9 to 94.6 ms (O'Brien et al., 2002). Lipton and
Tauck (Lipton and Tauck, 1987) have found the time constant of sodium channel
activation in ganglion cells is approximately 0.1 ms: our
1
τ parameter is therefore closer
to the time constant of sodium channel activation than the time constant of the entire
membrane (Lipton and Tauck, 1987). In contrast, the time constant associated with
spikes originating from mammalian bipolar cells seems to be much longer. Long‐latency
spiking in ganglion cells, occurring > 8‐60 ms after the beginning of electrical stimulation
(Greenberg, 1998; Jensen et al., 2005a; Fried et al., 2006), is thought to originate from
bipolar cells since it is suppressed by a cocktail of synaptic blockers. The measured time
constant associated with these longer latency spikes varies between 20‐26 ms,
depending on electrode size (time constants for amphibian bipolar cells may be shorter
(Greenberg, 1998)). The time constant associated with the inhibitory input from
amacrine cells is also much longer, on the order of 100‐200 ms (Fried et al., 2006). The
49
fast integration time course of the first stage of our model therefore suggests that direct
stimulation of ganglion cells may be the primary source of percepts in our subjects for
the pulse durations and amplitudes that we used.
ε and τ
2
(Eq. 2.3) represent desensitization as a consequence of accumulated
charge: ε represents the strength of desensitization and τ
2
represents the time constant
over which charge was integrated. These values were determined by the difference in
the data curve slopes between the fixed duration 0.075 and 0.975 ms pulse trains for
both threshold and suprathreshold data (Fig. 2.4.2 & 2.4.4). Slopes were steeper for
0.075 than for 0.975 ms pulses, consistent with desensitization as a function of
accumulated charge. ε ranged from 2 to 3 with a mean of 2.25 for threshold stimulation,
and between 8 to 10 with a mean of 8.73 for suprathreshold stimulation. Estimates of τ
2
ranged between 38 and 57 ms with a mean of 45.25 ms. Our need to include
desensitization as a function of charge to adequately fit our data is consistent with the
finding that shifts in resting potentials can be produced in ganglion cells by injection of
hyperpolarizing current (Baccus and Meister, 2002). Interestingly, it is possible that
these shifts in resting potential as a result of injection of hyperpolarizing current may be
analogous to at least some of the processes that underlie slow contrast gain control for
light stimuli (Chander and Chichilnisky, 2001; Rieke, 2001; Baccus and Meister, 2002). Of
course, inhibition from presynaptic cells is also likely to play a role in the desensitization
that we observed: inhibitory presynaptic influences on spiking in response to electrical
stimulation have been described by Fried et al. (Fried et al., 2006), particularly for longer
pulses. It seems likely that the desensitization stage of our model approximates a series
50
of complex adaptive processes, with time courses varying between milliseconds to tens
of seconds (Chander and Chichilnisky, 2001; Rieke, 2001; Baccus and Meister, 2002).
β (Eq. 2.4) describes a power input‐output nonlinearity which presumably
describes the input‐output nonlinearity across a population of cells. β was constrained
by the slopes of the threshold and suprathreshold pulse train stimuli (Figs. 2.4.2 &
2.4.4). An increase in the brightness of the percept to be matched led to a decrease in
the slope of the response nonlinearity. β varied between 3.0‐4.2, with a mean of 3.43
for threshold stimulation, and ranged between 0.6‐1.0, with a mean of 0.83 for
suprathreshold data. One possibility is that as the intensity of stimulation increases,
neurons with shallower input‐output nonlinearities are recruited. Alternatively, this
change in the power function may be driven by changes in the input‐output nonlinearity
within individual cells. While it is necessary to be cautious in generalizing from
responses to light stimuli to the effects of electrical stimulation, similar nonlinearities,
including changes in slope as a function of increased contrast or injected hyperpolarizing
current (Rieke, 2001; Baccus and Meister, 2002), are found in linear‐nonlinear models
describing spiking behavior in ganglion cells (Chander and Chichilnisky, 2001; Baccus and
Meister, 2002) and human behavioral data for light stimuli (Watson, 1986).
τ
3
(Eq. 2.5) represents the integration period of the final low pass filter. τ
3
was
primarily determined by the shapes of the curves of Fig. 2.4.3. Thresholds decrease as a
function of frequency for a fixed number of pulses, with an asymptote at around 100‐
200 Hz. τ
3
ranged between 24‐33 ms, with a mean of 26.25 ms. This time constant is
consistent with the slow temporal integration that occurs in cortex (Watson, 1986; Reid
51
et al., 1992), though of course there are many stages (or combination of stages) along
the visual pathway that might mediate this slow integration.
A successful retinal prosthesis will need to produce percepts consisting of
regions of constant brightness across a range of brightness levels, while satisfying a
complex set of engineering constraints: charge densities must remain relatively low, it is
technically difficult to produce very high current amplitudes, and absolute charge must
be minimized to maximize battery life. Models of the perceptual effects of electrical
stimulation over time, such as that described here, will be critical in allowing stimulation
protocols to be selected that best satisfy these many constraints.
Of course, a wide variety of challenges remain. For example, apparent brightness
is not the only perceptual quality that needs to be considered. It is likely that different
temporal patterns stimulate slightly different subpopulations of neurons, resulting in
distinct percepts. Another constraint is that stimulation should ideally be at a rate that is
high enough to avoid perceptual flicker. Moreover, our experiments described in
Chapter 2 only considered pulse trains of a few seconds. Longer periods of continuous
stimulation (minutes or hours) may result in long‐term adaptation, sensitization, and/or
retinal rewiring (Marc et al., 2003).
Possible interactions with the extent of retinal degeneration are another
important consideration, especially given that this model is based on only two subjects.
It is not currently known whether implanting the electrode array shortly after the onset
of blindness would improve performance or result in different temporal dynamics.
Given the changes that occur within the diseased retina (Marc and Jones, 2003; Marc et
52
al., 2003), timing of implantation may well be an important consideration. As more
patients are implanted and tested, this will be an interesting question to address.
Finally, the model described here is limited in its scope – it simply predicts
sensitivity over time at the single electrode level. The extension of models such as ours
to the spatial domain is an obvious next step (these data are described in Chapters 3
and 4). Finally, a successful prosthesis will involve designing arrays which are stable on
the retina, map to predictable locations in space, and are of high enough resolution to
provide the quality of visual information needed to perform useful real world tasks.
53
Chapter 3
Spatiotemporal interactions in retinal prosthesis
subjects
3.1 Introduction
To date, only limited data have been reported about how electrodes interact
during spatiotemporal stimulation in the retina. It is well known that for cochlear
implants the precise timing of stimulation across electrodes has perceptual
consequences as a result of both electrical field (Boex et al., 2003; Stickney et al., 2006)
and neuronal interactions (de Balthasar et al., 2003). One technique that has been used
in the cochlear implant field to reduce channel interactions (or cross‐talk between
electrodes) has been phase‐shifting stimuli across electrodes. This technique is also
referred to as continuous interleaved sampling (CIS) (Wilson et al., 1993). In the case of
cochlear implants, interleaved patterns of electrical pulses result in more independent
channels. This reduces electrical and neural nonlinearities generated by channel
interactions and makes the resulting electrical fields and percepts easier to
computationally model.
Besides reducing interactions, phase‐shifting stimulation across electrodes also
provides the technical advantage of allowing multiple electrodes to share the same
54
driver. The devices implanted in the subjects tested here used shared drivers across
pairs of electrodes (i.e., 8 drivers for the 16 electrode implant), and the ability to share
drivers across multiple electrodes may be even more critical in future implants with
many hundreds or even many thousands of electrodes.
The experiments described here measure the ability of subjects to discriminate
between pulse patterns across groups of electrodes in which the stimulation on any
individual electrode was identical across the two pulse patterns, but the temporal
relationship (phase‐shifting) between electrodes varied. For example, in Experiment 1
we tested the ability of subjects to discriminate between stimuli where 4 electrodes
were stimulated simultaneously, or the pulse trains were temporally phase‐shifted with
respect to each other (see Figure 3.1).
It should be noted that in the experiments described here, most results were
obtained using pulse patterns that were well above the critical flicker fusion (CFF) limit ‐
the rate at which there is no conscious awareness of flicker. It is known for light stimuli
that as the intensity and size of stimuli increase, sensitivity to flicker also increases to a
maximum of approximately 60 Hz in the periphery (Hecht and Verrijp, 1933). Given that
the size of our electrodes on the retina represented approximately 1‐2° of visual angle
(Oyster, 1999) and the brightness was relatively modest (current levels of 2‐3 times
threshold), we might expect CFF sensitivity lower than 60 Hz in our prosthesis subjects.
Indeed if we assumed that the percepts elicited by a given electrode were twice the size
of the electrode on the retina (an upper limit of 4° of visual angle) then this would result
in CFF limits of approximately 45 Hz at asymptotic brightness levels. While our subjects
55
did report seeing flicker for 20 Hz stimuli, they did not report flicker for any stimuli of 40
Hz or greater. However, it is also worth noting that there is some evidence of cortical
sensitivity to rates of flicker above the perceivable limit (Shady et al., 2004).
3.2 Materials & Methods
3.1.1 Subjects
Results reported here are based on data from two subjects, S05 and S06,
chronically implanted with 16‐electrode retinal prostheses (Second Sight Medical
Products
©
, Inc.). See section 1.4.3 and Fig. 1.6 for an in depth description of the device.
Subjects were 59 and 55 years old at implantation (2004), respectively. Pre‐operatively,
subject S05 had Bare Light Perception (BLP) in the implanted eye and was blind for 8
years before implantation, and subject S06 had No Light Perception (NLP) and was blind
for 10 years before implantation. Data collection within these subjects for these data
reported here began several months after they were implanted.
These two subjects (S05 and S06) were a subset of six subjects implanted since
February 2002. In some experiments, data was only collected in subject S06. This was
because subject S05 became unavailable after a surgical procedure in 2008 to adjust the
extraocular cable component. This adjustment resulted in the slight lifting of the array
from the retina. This lifting of the array resulted in a substantial increase in perceptual
thresholds, making it impossible to continue data collection using the paradigms used in
this paper. The retinal prosthesis device is the same as described in Chapter 1.
56
All tests were performed after obtaining informed consent under a protocol
approved by the Institutional Review Board at the Keck School of Medicine at the
University of Southern California and under the principles of the Declaration of Helsinki.
3.2.2 Psychophysical methods
Stimulation paradigm. All pulse waveforms on each electrode consisted of
biphasic, cathodic‐first, charge‐balanced square wave pulses, presented as trains of
pulses. For safety reasons, all individual pulses within a pulse train were charge‐
balanced. Here, we used cathodic and anodic pulses of equal width (0.075 ms). Each
biphasic pulse within the pulse train contained a 0.075 ms interphase delay. Pulse trains
were 500 ms in duration. All stimuli were presented in photopic conditions so as to
mimic conditions when the device would be used in the home. All pulse train stimuli
were set to be approximately 2‐3X the measured threshold (de Balthasar et al., 2008) of
each electrode.
Same‐different discrimination task. Performance was measured using a two
temporal interval, same‐different paradigm. In each trial subjects were presented with
two temporal intervals of stimulation. Each interval contained one of two pulse trains (A
or B). The stimuli in the 2 intervals could be A and A, B and B, A and B, or B and A. The
order of the A and B stimuli across the 2 intervals was randomized across trials, and
each possible combination was presented with equal frequency. Subjects were asked to
judge if the two temporal intervals contained stimuli that were the same or different,
via a button press response.
57
A and B stimuli consisted of suprathreshold pulse train stimulation across groups
of 4 electrodes in a square configuration (Fig 3.1). The temporal properties of the pulse
train presented on each electrode were identical in every way (pulse train frequency,
and pulse width) except for the phase‐shift between pulses across electrodes. On any
individual electrode, the pulse train presented was identical across synchronous and
asynchronous stimuli.
Subjects were instructed to use any visual cue to discriminate between the two
stimulation patterns. Phosphenes on single electrodes were generally reported as being
round or oval shaped and were white or yellowish in color. When stimulation was
presented on the 2x2 sets of electrodes, the percept was generally of a larger spot of
relatively uniform brightness which was reported to appear to be approximately 2‐4
inches in diameter at arm’s length, corresponding to roughly 3‐6° of visual angle.
Pseudo‐synchronous and asynchronous stimuli were only reported to differ in perceived
temporal properties (such as flicker) for pulse frequencies of 20Hz.
Brightness matching task. To match the brightness of different stimuli, we used
a two‐interval, forced‐choice procedure. One interval contained the “standard”
stimulus, and the other contained the “test” stimulus (Fig. 3.5). The order of the two
intervals was randomized across trials. On each trial, subjects were asked to report
which interval contained the brighter stimulus. A one‐up, one‐down staircase method
was used to adjust the amplitude of the test stimulus based on the observer’s response.
Each brightness match was based on a minimum of 100 trials. A cumulative normal was
then used to find the point of subjective equibrightness, and error bars were estimated
58
using an adaptive sampling Monte‐Carlo simulation (Wichmann and Hill, 2001). Each
individual psychometric function was inspected to make sure that an adequate fit was
obtained, and data was recollected if fits were inadequate (based either on the
estimated error or visual inspection).
3.3 Results
3.3.1 Experiment 1 – Synchronous vs. asynchronous stimulation
The goal of this experiment was to measure the perceptual impact of a
combination of electrical field and neuronal spatiotemporal interactions. The
synchronous stimulus (A) consisted of pulse train stimuli that were time‐synched across
all four electrodes. In the asynchronous stimulus (B) the pulse train was phase‐shifted
across each electrode by 12, 6, 3, or 1.5 ms (Fig. 3.1), depending of the frequency being
used (20, 40, 80, and 160 Hz, respectively). These phase‐shifts were chosen to maximize
the temporal separation between stimulation on each electrode.
For each of the 2 subjects, 5 different 4‐electrode groups were evaluated for
each of the 4 different frequencies. Electrodes were always spatially separated by 800
μm center‐to‐center. 100 trials were run for each frequency, and data were averaged
across all 5 electrode groups: each bar in the graph represents 500 trials (Fig. 3.1B).
Standard errors across percent correct for all five electrode groups were calculated for
each frequency tested.
59
Fig. 3.1. (A) Synchronous versus asynchronous stimulation. Subjects
discriminated between two synchronous and asynchronous pulse train stimuli
across groups of 4 electrodes using a same‐different task. (B) Subject
performance Experiment 1. Percent correct is shown for frequencies of 20,
40, 80, and 160 Hz (corresponding to phase‐shifts of 12, 6, 3, and 1.5 ms). 50%
is chance performance.
As seen in Fig. 3.1B, both subjects easily discriminated between synchronous and
asynchronous stimuli, with performance consistently above 80%. Performance was
significantly above chance for every frequency (1‐tailed t‐test, p<0.01). An ANOVA
analysis found no effect of subject, condition, or frequency (3 factor ANOVA, subject x
condition x frequency; p>0.05). Performance (both percent correct and d’) is reported
for all experiments in Table 3.1.
60
Generally, subjects described the synchronous stimulus as being brighter and
having a different shape than the asynchronous stimulus. In Experiment 6 we measured
the charge needed to brightness match synchronous vs. asynchronous stimulation
patterns, and found that almost twice as much current was needed in the asynchronous
patterns to match the brightness of a synchronous standard, consistent with subjects’
subjective verbal reports in this experiment.
Subject 20 Hz 40 Hz 80 Hz 160 Hz
Experiment 1
S05 83%/2.65d’ 94%/3.74d’ 95%/3.90d’ 93%/3.59d’
S06 92%/3.46d’ 95%/3.90d’ 94%/3.74d’ 89%/3.14d’
Experiment 2
S05 58%/1.04d’ 64%/1.45d’ 62%/1.31d’ 55%/0.80d’
S06 61%/1.24d’ 53%/0.60d’ 58%/1.04d’ 53%/0.60d’
Experiment 5
S05 NA 66%/1.57d’ 68%/1.67d’ NA
S06 NA 63%/1.38d’ 64%/1.45d’ NA
Table 3.1. Performance and d‐prime. Performance values for each subject in each of the same/different tasks for
experiments 1, 2, and 5. Values of percent correct and d‐prime (d’) are presented for each frequency tested.
3.3.2 Experiment 2 – Pseudo‐synchronous vs. asynchronous stimulation
Here we measured performance after having eliminated electric field
interactions by very small phase‐shifts. We modified the synchronous stimulus used in
Experiment 1 by introducing a 0.225 ms phase‐shift across each of the four electrodes,
creating a pseudo‐synchronous stimulation pattern (Fig. 3.2A). The entire set of four
pulses across all four electrodes occurred within a 1 ms time window. This phase shift
was adequate to eliminate electric field interactions (see Appendix C) but is still
relatively short compared to the integration period of bipolar (approximately 100 ms)
61
(Mao et al., 1998), amacrine (49 – 69 ms) (Coleman and Miller, 1989), or ganglion cells
(4.5 – 81.6 ms) (O'Brien et al., 2002).
Fig. 3.2 (A) Discriminating between pseudo‐synchronous and asynchronous stimuli.
Subjects discriminated between pseudo‐synchronous and asynchronous pulse train stimuli
on groups of 4 electrodes using a same‐different task. All electrodes were neighboring (i.e.,
800 μm center‐to‐center separation). (B) Subject performance in task. Subjects
discriminated between pseudo‐synchronous and asynchronous stimuli that were
presented at frequencies of 20, 40, 80, and 160 Hz (corresponding to phase‐shifts of 12, 6,
3, and 1.5 ms). The x‐axis represents frequency and the y‐axis represents the % correct.
For both subjects, the five 4‐electrode groups that were evaluated for each of
the 4 different frequencies were the same as in Experiment 1. 100 or 200 trials were run
62
for each condition, and once again data were averaged across electrodes and standard
errors were calculated across the 5 repetitions. For S05, each bar in the graph (Fig. 3.2B)
represents approximately 500 trials. For S06, each bar represents approximately 900
trials. Other methodological details were identical to Experiment 1.
Performance was significantly worse than in Experiment 1 (Fig. 3.2B, Table 3.1).
The difference in performance at each frequency between Experiment 1 and
Experiment 2 was significant for every frequency (3 factor ANOVA, subject x condition x
frequency; p< 0.001). However, performance was still significantly above chance for
intermediate frequencies (single‐tailed t‐test, p<0.05 for 40 and 80Hhz for both subjects,
S05 p<0.05 for all frequencies), indicating that pulse timing across electrodes affected
percepts even after electric field interactions were eliminated. This ANOVA analysis did
not find a significant difference between different electrode groups or frequencies but
did find a significant difference in performance between the two subjects (p < 0.05).
The drop in performance (and d’) compared to Experiment 1 suggests that
stimulation using the prosthesis configuration tested did result in overlapping electrical
fields, and that these interactions between electric fields had a significant effect on
subjects percepts. However, despite a drop in performance, pseudo‐synchronous and
asynchronous stimulation remained perceptually distinct, even at frequencies well
above the CFF limit.
One parsimonious explanation of these results is that differentiation between
these two stimuli is mediated by neurons in between, and receiving stimulation from,
more than one electrode. Any individual neuron sitting intermediate two electrodes will
63
receive a different pattern of stimulation from pseudo‐synchronous and asynchronous
stimulation patterns. If individual neurons are sensitive to these small differences in
timing, as is suggested by earlier work measuring threshold sensitivity to different
temporal patterns of stimulation (Horsager et al., 2008), then these neurons would have
the potential to mediate the ability of subjects to differentiate the two stimulus
conditions. If this were the case we would expect differences between pseudo‐
synchronous and asynchronous stimulation patterns to decrease as a function of
electrode separation.
3.3.3 Experiment 3 – The effects of inter‐electrode distance
Here we evaluated subjects’ ability to discriminate between pseudo‐synchronous
and asynchronous stimuli as a function of electrode spacing. A and B stimuli were
identical to those described in Experiment 2, but we measured discrimination
performance for electrodes groups that were separated by 1131, 1600, and 2400 μm
(Fig. 3.3). Only stimuli at 80 Hz were evaluated. For the 800, 1131, 1600, and 2400 μm
distances, 5, 4, 4, and 1 (there is only one possible configuration for the 2400 μm
separation condition) different electrode groups were evaluated respectively, for each
subject. A minimum of 300 trials was run for each electrode separation.
64
Fig. 3.3. Subject performance, Experiment 3. Subjects discriminated between pseudo‐
synchronous and asynchronous pulse train stimuli (80 Hz) on groups of 4 electrodes using a
same‐different task. Electrodes were separated by center‐to‐center distances of 800, 1131,
1600, and 2400 μm. Example schematics of these electrode distances are presented on the y‐
axis.
Subjects' ability to discriminate pseudo‐synchronous from asynchronous
stimulation decreased as a function of increasing electrode separation, to the point
where they were performing at chance (1‐tailed t‐test, p>0.05) for electrodes separated
by 2400 μm (Fig. 3.3). For both subjects performance was significantly above chance for
electrode separations of 800 and 1131 μm (single tailed t‐test, p<0.05), and for subject
SO5 performance was also above chance for electrode separations of 1600 μm.
Although there seems to be a decrease in performance as a function of increasing
electrode distance, we did not see a significant drop in performance as a function of
electrode spacing when evaluated with a 3 factor ANOVA (subject x condition x
frequency).
65
3.3.4 Experiment 4 – Pulse timing effects for a single electrode
As described above, one possibility is that discrimination between pseudo‐
synchronous and asynchronous stimulation might be mediated by differences in the
response to the two stimulation patterns within individual neurons lying between two
electrodes that receive direct stimulation from two (or more) electrodes. It is known
that the intensity of electric fields decrease as a function of distance from the electrode
(Wiley and Webster, 1982a; Cottaris and Elfar, 2005). Take the case where stimulation
occurred in a pattern where electrode 1 was stimulated before electrode 2. A neuron
lying closer to the electrode 1 would be stimulated by a high amplitude pulse followed
by a low amplitude pulse, whereas a neuron lying closer to electrode 2 than to electrode
1 would be stimulated by a low amplitude pulse followed by a high amplitude pulse.
If low‐high vs. high‐low pulse pair relationships have a differential effect on
driving cell activity then these differences within individual cell responses might result in
perceptually distinguishable response patterns based on temporal differences in
stimulation even at rates well above the CFF. Take, for example the case of clockwise
versus counter‐clockwise stimulation, as illustrated in Figure 3.5. In the clockwise
pattern, electrode 1 is stimulated before electrode 2 whereas in the counter‐clockwise
pattern electrode 2 is stimulated before electrode 1. Neurons lying closer to electrode 1
are therefore stimulated by high followed by a low amplitude pulses in the case of the
clockwise pattern, and low followed by high amplitude pulses in the counterclockwise
pattern. If neurons were less sensitive to low‐high than to high‐low patterns of
66
stimulation (for example) then this would lead to local differences in brightness across
the two patterns in regions where electric fields overlap significantly. While the spatially
averaged mean brightness of clockwise and counterclockwise patterns would be
identical, local patterns of brightness would differ, resulting in what might be a
distinguishably different percept.
Experiments 4‐6 were designed as a further test of this hypothesis. In
Experiment 4 we tested whether high‐low vs. low‐high amplitude patterns have a
differential effect on cell responses when presented on a single electrode. In Experiment
5 we tested whether clockwise and counterclockwise patterns were perceptually
discriminable, and in Experiment 6 we tested whether there was a global difference in
brightness between clockwise and counterclockwise patterns.
Subjective brightness matching was carried out within a single electrode
between a standard which consisted of pulse pairs of equal amplitude and test stimuli
consisting of either low‐high vs. high‐low pulse pairs. The standard pulse pair (Fig. 3.4)
consisted of a pair of biphasic pulses of equal amplitude (304.8 μA for every electrode).
This standard was brightness matched to two test stimuli: (1) a low followed by high
amplitude biphasic pulse pair or (2) a high followed by a low amplitude biphasic pulse
pair. All pulses had 0.075 ms pulse width, and a 0.075 inter‐pulse interval. At the start of
the experiment, these test pulse pairs were set to have the same total charge as the
standard stimulus. The low amplitude pulse had ½ the amplitude of the standard
stimulus (approximately 150 μA) and the high amplitude pulse had 1½ times the charge
of the standard stimulus (approximately 450 μA). We used the two‐interval, forced‐
67
choice procedure described above. Staircase logarithmic increases or decreases in test
stimuli amplitude as a function of subjects’ responses were applied to both pulse trains
on the electrode pair. Data were collected on 3 electrode pairs in S06.
As predicted, we found a difference in the charge needed to obtain a brightness
match between high‐low vs. low‐high pulse pairs. There was no significant difference in
the amount of charge needed to match low‐high pulse pairs to the standard containing
pulse pairs of equal amplitude (2‐tailed t‐test, p>0.05). In contrast high amplitude
followed by low amplitude pulses required significantly less charge (~10% less) to
appear as bright as the standard (2‐tailed t‐test, p<0.05).
Fig. 3.4. Subject performance, experiment 4. Subjects compared
the brightness of a standard (2 pulses of equal amplitude) to two
test stimuli (a low followed by high amplitude pulse pair, or a high
followed by low amplitude pulse pair). Plotted is the cathodic
charge required to reach the point of equibrightness between
standard and test stimuli.
3.3.5 Experiment 5 – Clockwise vs. counterclockwise stimulation
If performance in Experiments 2 and 3 is mediated by differences in responses
within individual neurons lying between two electrodes that receive direct stimulation
from two (or more) electrodes then, as described above, we might predict that subjects
68
would be able to differentiate between clockwise and counterclockwise stimulation
patterns even at rates well above the critical fusion frequency.
We asked subjects to discriminate between clockwise and counter clockwise
stimulation patterns, presented on groups of four electrodes. In the clockwise stimulus,
phase‐shifts across pulses were presented across electrodes in a sequentially clockwise
order, while in the counterclockwise stimulus identical pulses were presented in the
reverse order. Pulse train frequencies were 40 or 80 Hz, corresponding to phase‐shifts
of 6 or 3 ms between electrodes (Fig. 3.5A).
As previously described for Experiments 1‐3, stimulation on each individual
electrode was suprathreshold, with current levels adjusted so that the percept across
each individual electrode of the group of four was roughly brightness‐matched.
Performance was measured using a two‐interval same‐different paradigm where
subjects were asked to say whether the two stimulation patterns presented in the two
intervals were the same or different. For the 2 subjects, both 40 and 80 Hz stimuli were
evaluated on five 4‐electrode groups. 300 trials were run for each of these conditions,
for each group of electrodes. Thus, each bar in the graph of Fig. 3.5 consists of 1500
trials.
69
Fig. 3.5. (A) Clockwise and counterclockwise stimulation. Pulse train stimuli were
presented on groups of 4 electrodes in either clockwise or counterclockwise rotating
order and subjects were asked to differentiate between the two patterns using a
same‐different task. All electrodes had 800 μm center‐to‐center separation. (B)
Subject performance Experiment 5. Subjects successfully discriminated between
clockwise and counter clockwise stimuli.
Subjects were able to reliably discriminate between clockwise and
counterclockwise stimulation (Fig. 3.5B; 1‐tailed t‐test, p<0.05 for all frequencies and
subjects). A three factor ANOVA (subject x electrode group x frequency) found no
difference between subjects or frequencies. However, there was a significant difference
in performance across electrode groups (p < 0.01). Percent correct and d’ values are
reported in Table 1.
70
3.3.6 Experiment 6 – Electrode order and brightness
If performance in Experiments 2‐5 is mediated by differences in response within
individual neurons lying between two electrodes that receive direct stimulation from
two (or more) electrodes, then performance differentiating clockwise and
counterclockwise patterns should not be based on any change in mean brightness. We
therefore measured the amount of current required to brightness match stimulation
patterns on electrode pairs that differed presentation order.
We use our standard two‐interval, forced‐choice brightness matching procedure.
All pulse train stimuli were 500 ms pulse trains at 50 Hz, using biphasic pulses of 0.45 ms
per phase. Each trial contained two intervals containing either time‐synched pulse trains
on each electrode, or phase‐shifted pulse trains on each electrode (Fig. 3.6A). The
phase‐shift was 0.075, 0.375, 1.8, or 9 ms. Subjects were asked to report which interval
contained the brighter stimulus. A one‐up, one‐down staircase method was used to
adjust the amplitude of the phase‐shifted pulse train based on the observer’s response.
Increases or decreases in amplitude as a function of the staircase were applied to both
pulse trains on the electrode pair.
We measured perceived brightness for E1 first, and E2 first stimulation to
evaluate whether electrode stimulation order had an effect on perceived brightness
(Fig. 3.6B). Each brightness match was based on a minimum of 100 trials. A cumulative
normal was used to find the point of subjective equibrightness, and error bars were
again estimated using an adaptive sampling Monte‐Carlo simulation (Wichmann and
Hill, 2001). Each individual psychometric function was inspected to make sure that an
71
adequate fit was obtained, and data was recollected if fits were inadequate (based
either on the estimated error or visual inspection). Data was collected on 3 electrode
pairs in S05 and 2 electrode pair in subject S06.
As expected given subjects’ subjective reports in Experiment 1, we found that
the brightness of electrode pair stimuli was substantially brighter when pulses were
presented synchronously than when pulses were phase shifted across electrodes (Fig.
3.6B). The amount of charge necessary to maintain equal brightness to the synchronous
stimulus increased as a function of the phase‐shift across electrodes, with a 9 ms phase
shift 20% more charge was required to match the synchronous stimulus.
Consistent with our notion that performance mediating differentiation between
clockwise and counterclockwise stimulation patterns is not based on any mean change
in brightness, we found that there was no significant difference in the amount of current
required to match the standard between E1‐first and E2‐first stimuli (Fig. 8C, p>0.05, 1‐
tailed t‐test).
72
Fig. 3.6 (A) Brightness matching as a function of electrode order. Subjects compared the brightness of
a standard (500 ms pulse trains, 50 Hz, 0.45 ms pulse width) where pulse trains were synchronous
across the electrode pair to test stimuli (identical to the standard except for a phase‐shift across the
electrode pair. Either E1 or E2 was stimulated first. (B‐C) Normalized charge required to match
brightness between synchronous and asynchronous stimuli in S05 and S06. The x‐axis represents the
phase‐shift when either E1 or E2 was stimulated first and the y‐axis represents normalized (based on
the synchronous stimulus) charge necessary to maintain equibrightness. S06 was unavailable for
testing in the E2 – E1 condition due to limited experimental time.
73
3.4 Discussion
We show here that changes in spatiotemporal stimulation patterns well above
the critical flicker fusion limit do affect perception: subjects can discriminate stimuli that
are differentiated by phase shifts of ~12 ms or less (corresponding to frequencies of 80
Hz or higher), even once electric field interactions were removed.
Experiment 1 showed that subjects could differentiate between synchronous
and asynchronous stimulation patterns with high accuracy. In Experiment 2 we found
that subjects could still differentiate between pseudo‐synchronous and asynchronous
stimulation, but there was a significant drop in performance. This drop in performance
between Experiment 1 and 2 suggests that there were significant electrical field
interactions under the condition of simultaneous stimulation used in Experiment 1.
Experiment 6 further confirmed this result by demonstrating that synchronous
stimulation results in brighter percepts than asynchronous stimulation: in our
experiment the asynchronous pulse pattern required nearly 20% more charge than the
synchronous pattern to appear matched in brightness.
In Experiments 2‐6 we examined spatiotemporal interactions across electrodes
once electric field interactions had been eliminated. Experiment 2 demonstrated that
subjects could differentiate between pseudo‐synchronous and asynchronous
stimulation, demonstrating that removing electrical field interactions was not sufficient
to cause the percept elicited by a given electrode to be independent of stimulation of
other electrodes.
74
One explanation is that different interleaving pulse patterns vary in the
effectiveness with which they stimulate individual neurons that lie intermediate
between electrodes. We carried out four experiments to further test this hypothesis.
Consistent with this hypothesis, spatiotemporal interactions decreased with electrode
separation (Experiment 3). Analogous timing differences to those tested in Experiments
1‐3 were perceptually distinguishable on a single electrode with a high‐low pattern of
stimulation resulting in a brighter percept than a low‐high pattern of stimulation
(Experiment 4). In Experiment 5 we demonstrated that subjects were able to distinguish
clockwise from counterclockwise stimulation, and Experiment 6 demonstrated that
these judgments were unlikely to be based on overall (rather than local) differences in
brightness between the two stimuli.
75
Chapter 4
Interactions during multi‐electrode suprathreshold
stimulation
4.1 Introduction
In Chapter 4, we examine how systematic variations in spatiotemporal patterns
of multi‐electrode retinal stimulation influence the perceived brightness in our
prosthesis patients. It is well known that for cochlear implants the precise timing of
stimulation across electrodes has perceptual consequences as a result of both electrical
field (Wilson et al., 1993; Boex et al., 2003; Stickney et al., 2006) and neuronal
interactions (de Balthasar et al., 2003). However, to date, only limited data have been
reported examining how electrodes interact during spatiotemporal stimulation in the
retina. Earlier work (Chapter 3) of ours demonstrated significant interactions between
pairs of electrodes, even when they are stimulated non‐simultaneously. Here we
systematically examined how these interactions affect perceived brightness and we
present a simple computational model that describes the behavior of these data.
76
4.2 Materials & Methods
4.2.1 Subjects
Data reported here were collected on two patients chronically implanted with
16‐electrode retinal prostheses (Second Sight
®
Medical Products, Inc.). These two
patients, S05 and S06, were 59 and 55 years old at implantation (2004), respectively.
Pre‐operatively, subject S05 had Bare Light Perception (BLP) in the implanted eye and
subject S06 had No Light Perception (NLP). These two patients were a subset of six
patients implanted since February 2002. The other four patients were excluded from
this particular study for a variety of reasons: one patient was excluded because of
geographic location, two patients were excluded due to unrelated medical conditions,
and in one patient the array cable became exposed. Because the cardiac status of this
patient precluded general anesthesia, the multi‐wire cable connecting the array to the
external stimulator was cut and the intraocular portion of the array was left in place.
All tests were performed after obtaining informed consent under a protocol
approved by the Institutional Review Board at the Keck School of Medicine at the
University of Southern California and under the principles of the Declaration of Helsinki.
77
Figure 4.1 Retinal prosthesis schematics and experimental design. (A) Electrode array.
The electrode array consisted of 260 or 520 micrometers (μm) electrodes arranged in a
checkerboard pattern, with center‐to‐center separation of 800 μm. (B) Prosthesis
schematic. Stimuli were programmed using Matlab® on a PC, which then communicated
parameters to an external Visual Processing Unit (not shown). Power and signal
information could be independently controlled for each electrode. (C) Pulse train.
Stimulation on each electrode was a 50 Hz pulse train that was 500 ms in duration.
Unless otherwise noted, the cathodic and anodic phases or each biphasic pulse was 0.45
ms in duration, with a 0.45 ms interphase delay. (D) Brightness matching task. Subjects
compared the brightness of a standard (1) and test (2) stimulus. The timing of pulses
across the two electrodes was time‐synched (phase‐shifted by 0 ms) in the case of the
standard. The test stimulus was identical to the standard except there was a phase‐shift
between pulses across electrodes.
4.2.2 The Retinal Prosthesis
Subjects were implanted, epiretinally, with a four by four array of disk electrodes
in the macular region (4.1A). Electrodes were either 260 or 520 micrometers (μm) in
diameter, arranged in an alternating checkerboard pattern with 800 μm center‐to‐
center separation between each electrode. As described elsewhere (Humayun et al.,
78
2003; Mahadevappa et al., 2005; Horsager et al., 2008), pulse train signals were
generated and sent to an external signal processor using custom software run on a PC
laptop. Power and signal information were sent from this processor through a wire to an
external transmitter coil that attached magnetically, and communicated inductively, to a
secondary coil that was implanted subdermally in the subject’s temporal skull (4.1B).
From this secondary coil, power and signal information were sent through a
subdermally implanted wire that traversed the sclera to the array of electrodes. The
timing and current of electrical pulses on each electrode could be controlled
independently.
4.2.3 Psychophysical Methods
All pulse waveforms consisted of biphasic, cathodic‐first, charge‐balanced square
wave pulses, presented as trains of pulses (Fig. 4.1C). For safety reasons, all individual
pulses within a pulse train were charge‐balanced. Here, we used cathodic and anodic
pulses of equal width (0.45 ms, unless otherwise noted), with the cathodic phase
presented first (Loeb et al., 1983; Jensen et al., 2005a). Each biphasic pulse within the
pulse train contained a 0.45 ms interphase delay between cathodic and anodic phases.
Pulse trains were 500 ms in duration at a rate of 50 Hz. All stimuli were presented in
photopic conditions.
Subjective brightness matching during paired‐electrode stimulation. Subjective
brightness matching was carried out within a given electrode pair using a two‐interval,
forced‐choice procedure. Each trial contained two temporal intervals. One interval
always contained synchronized pulse trains across the pair of electrode. The amplitudes
79
of these synchronized pulse trains were set to 1.5, 2, 2.5, or 3 times the perceptual
threshold of each electrode in the pair (see (de Balthasar et al., 2008) for a detailed
description of threshold measurement methods).
The other interval contained pulse trains that were phase‐shifted by 0.075,
0.375, 1.8, or 9 ms. At our stimulation frequency (50 Hz), a 9 ms phase‐shift resulted in
perfectly interleaved pulses across a pair electrodes, as shown in Fig. 4.1D). The order
of presentation of the two temporal intervals was randomized, and subjects were asked
to report which interval contained the brighter stimulus. In most conditions pulse trains
were presented on both electrodes in the pair. A one‐up, one‐down staircase method
was used to adjust the amplitude of the phase‐shifted pulse trains based on the
observer’s response. For example, if the observer responded that the test phase‐shifted
stimulus was brighter than the standard time‐synched stimulus, the amplitude of the
phase‐shifted pulse trains was decreased by a fixed amount of charge. Depending on
the condition, the increase or decrease in charge was applied to both electrodes in the
pair or to only one of the two electrodes. We also compared the brightness of the
standard time‐synched electrode pair to test stimuli consisting of just one of the two
electrodes in the pair.
Each brightness match was based on a minimum of 100 trials. A cumulative
normal was used to find the point of subjective equibrightness, and error bars were
estimated using an adaptive sampling Monte‐Carlo simulation (Wichmann and Hill,
2001). Each individual psychometric function was inspected to make sure that an
adequate fit was obtained, and data was recollected if fits were inadequate (based
80
either on the estimated error or visual inspection). Example fits of these data can be
seen in the Supplementary Materials (Appendix D, Fig. D1).
Stimulus set. A total of 3 different electrode pair combinations were evaluated
across all experimental conditions for subject S05, and 13 were evaluated in subject S06.
Data for electrodes separated by 800 μm (Fig. 3) was collected on a total of 13 electrode
pairs across both subjects. 4 and 3 electrode pairs were evaluated for electrodes
separated by 1600 and 2400 μm distances, respectively, for subject S06 (Fig. 4).
The only criterion used to choose the electrode pairs used in these experiments
was that single pulse thresholds were relatively low. This allowed us to collect
suprathreshold data across a range of brightness levels while remaining within charge
safety limits. Given this constraint, electrodes were then chosen that were dispersed as
evenly as possible across the array.
For each phase‐shift, we measured the current necessary to match the
brightness of a standard pulse consisting of pulses presented simultaneously on E1‐E2.
Five different test stimuli were used: 1) E1 only, 2) E2 held fixed and E1 adjusted, 3) E1
and E2 adjusted simultaneously, 4) E1 held fixed and E2 adjusted, and 5) E2 only. The
obtained amplitude values for electrodes E1 and E2 at the point of brightness match
were normalized by amplitude required to match the brightness of the test stimulus
using only the E1 or E2 electrode, respectively. Example data sets are shown in Figure 3,
further data sets and models fits are shown in Supplementary Materials.
The data presented here represent testing sessions that occurred on roughly a
weekly basis (~3 hours per session) over the course of 2 years. Data for the model
81
collected on subject S05 (3 pairs) was limited due to lifting and translating of the array
during a recent (June 2008) surgical procedure. This lifting and translating of the array
lead to a sharp increase in thresholds (in many cases, too high to measure), that made it
impossible to continue data collection with this subject.
4.2.4 Model of spatiotemporal integration
Data were fit using the following model:
(4.1)
where B
τ
is the brightness of the percept generated by stimulation for the given
stimulation pattern on the electrode pair. τ represents the delay in stimulation between
the two pulses, E
1
and E
2
are the normalized current amplitudes on each of the two
electrodes in the pair (charge needed to match the brightness of the standard divided
by the charge needed to match the brightness of the standard using E
1
or E
2
alone). The
free parameter γ
τ
can be thought of as representing the mutual interaction between E
1
and E
2
. β can be thought of as representing the nonlinear increase in brightness as a
function of the amount of current for electrodes E
1
and E
2
.
82
Fig. 4.2 (A) Theoretical model outputs. The data above is theoretical and is an example
of how the model output varied as a function of the parameters γ and β. The lines
represent model fits using a range of parameters.
Figure 4.2 illustrates example model fits. The x and y axes represents normalized
charge, and each line represents model fits for six different parameter values of γ and β.
The solid black curve represents the simplest case, linear integration, or perfect
summation (β = 1 and γ = 0). In this case apparent brightness sums linearly across both
electrodes in the pair. The gray dashed‐dot curve is an example of perfect independence
where brightness is essentially determined by whichever of the two electrodes appears
brightest. Note that, since and are always less than or equal to 1, the interaction
83
terms have very little effect on the final output when β
is large. The red, green and blue
lines represent three intermediate conditions. The red line represents β = 3.5, γ = 0, the
green line represents β = 2, γ = 0, and the blue line represents β = 3.5, γ = 1. Note that
the effect of increasing the facilitatory interaction between the two electrodes is very
similar to reducing the value of β. The dashed gray curve represents an example of
suppression between electrodes (β = 3.5, γ = −1.0), resulting in a bowing out of the
curve beyond the boundary of x<=1, y<=1. In other words the amount of current needed
to match the brightness of the standard in this case is greater than is required for either
electrode stimulated in isolation.
When fitting data we treated the all four delays as part of the same data set. For
each delay we generally collected three data points. With the end‐points (which were
constrained to fall on x=1, y=0 and y=0, x=1, this meant that there were in total 12 data
points within each data set.
Our assumption was that β can be thought of as representing the nonlinear
increase in brightness as a function of the amount of current and γ represents mutual
interaction between electrodes. As described above, changes in γ and β
trade off
against each other in “bowing” the curves. This meant that, if γ and β
were fit
simultaneously the model was under‐constrained ‐ while we obtained a fairly well‐
defined curve representing changes in γ as a function of delay for each electrode pair,
our function minimization procedure tended to converge on a fairly arbitrary value of
beta which was compensated for by an absolute shift across all the obtained γ values.
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We therefore held β fixed at a value of 3.5 for all delays. This fitting process resulted in a
model with 5 free parameters (β,γ
0.075
,γ
0.375,
γ
1.8,
γ
9.0
).
4.3 Results
Subjects typically reported that phosphenes appeared white or yellow in color,
and were round or oval in shape. At suprathreshold, percepts were reported as brighter
and the shape occasionally became more complex than a simple round or oval shape.
Shapes were reported as being approximately 0.5‐2 inches in diameter at arm's length,
corresponding to roughly 1‐3 degrees of visual angle. When stimulation was presented
on the electrode pairs, the percept was generally of a larger area of relatively uniform
brightness which was reported to appear to be approximately 2‐4 inches in length or
width at arm’s length, corresponding to roughly 3‐6° of visual angle. Occasionally, a dark
percept rather than a white or yellow percept was reported. In this case, the patient
would use the relative contrast of the percept for subjective brightness comparison. We
did not see any systematic differences in threshold or slopes of the brightness matching
psychometric functions between light or dark percepts.
In the brightness matching task, subjects were asked to ignore all components of
the percept other than brightness/contrast. As described above, percepts could either
be single or multi‐phosphene percepts. In multi‐phosphene percepts, subjects were
asked to average the brightness across all phosphenes. The obtained psychometric
functions for these brightness matches (see Appendix D, Fig. D1) suggest that subjects
were able to perform the task quite easily.
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4.3.1 Subjective brightness and pulse timing across electrodes
Fig. 4.3. Normalized charge required to match the brightness of the standard stimulus.
Each curve represents a different phase‐shift in the test stimuli. All electrodes shown
here are separated by 800 μm. The data points plotted for 0.075, 0.375, 1.8, and 9.0 ms
phase‐shifts are represented by black, dark gray, medium gray, and light gray circles,
respectively. Model fits for each of the different phase‐shifts are solid, dash‐dotted,
dashed, and dotted lines of the same color. (A‐B) Two electrode pairs are shown for both
subject S05 and S06. (C) The parameter γ as a function of the phase‐shift.
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As shown in Figure 4.3, the amount of charge required to match the brightness
of the standard increased as a function of phase‐shift, as represented by the curves
“bowing out” further from the line x=y as a function of phase‐shift in Panels A and B.
Panel C represents γ as a function of the phase‐shift. As described above, γ and
β
trade off against each other in “bowing” the curves. With β fixed at a value of 3.5, we
found that values of γ decreased as a function of delay (See Figs. 4.3C and 4.4C), though
curves shifted up or down the y‐axis depending on the electrode pair. The drop in γ as a
function of delay, suggesting a general progression from facilitatory to suppressive
interactions as a function of delay.
The curve for the 0.075 ms phase‐shift generally overlapped the data point
representing the standard stimulus (where the pulses were presented simultaneously).
There was also little difference in the curves representing 1.8 and 9 ms phase shifts,
suggesting that the interactions between electrodes within this dataset begin to
asymptote by 1.8 ms.
It might be expected that, since the current fields’ size increases as a function of
increasing current amplitude, there might be an increase in the spatiotemporal
interactions at higher amplitudes (or for stimuli which were further above threshold).
An increase in spatiotemporal integration would be though to result in higher values of
γ. However, we found no effect of pulse amplitude on spatiotemporal integration.
Similar integration values were found for stimuli at threshold, 1.5X threshold, and 2‐3X
threshold (Appendix D, Fig. D2). There was no statistical difference between these 3
different conditions using a two‐way ANOVA (electrode x condition, p>0.05). On 4 pairs
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of electrodes, we tested threshold, 1.5X, 2X, and 3X threshold. When we limited our
statistical analysis to those electrodes (paired single tailed t‐test, p>0.05) we still found
that interactions were no larger for stimuli that were further above threshold.
Subject Experiment E1 E2 phase‐shift (ms) β γ error
S05 800 C1 D1 0.075 3.5 ‐0.14 1.033
S05 800 C1 D1 0.375 3.5 ‐0.12 1.033
S05 800 C1 D1 1.8 3.5 0.22 1.033
S05 800 C1 D1 9.0 3.5 0.00 1.033
S05 800 A1 A2 0.075 3.5 0.54 0.089
S05 800 A1 A2 0.375 3.5 0.54 0.089
S05 800 A1 A2 1.8 3.5 0.29 0.089
S05 800 A1 A2 9.0 3.5 0.29 0.089
S05 800 C3 C2 0.075 3.5 1.81 0.377
S05 800 C3 C2 0.375 3.5 0.57 0.377
S05 800 C3 C2 1.8 3.5 ‐0.30 0.377
S05 800 C3 C2 9.0 3.5 0.13 0.377
S06 800 C1 B1 0.075 3.5 0.73 0.118
S06 800 C1 B1 0.375 3.5 0.26 0.118
S06 800 C1 B1 1.8 3.5 ‐0.66 0.118
S06 800 C1 B1 9.0 3.5 ‐0.18 0.118
S06 800 C3 B2 0.075 3.5 0.18 0.962
S06 800 C3 B2 0.375 3.5 ‐0.29 0.962
S06 800 C3 B2 1.8 3.5 ‐0.52 0.962
S06 800 C3 B2 9.0 3.5 ‐0.64 0.962
S06 800 C2 B2 0.075 3.5 ‐0.18 0.856
S06 800 C2 B2 0.375 3.5 ‐0.14 0.856
S06 800 C2 B2 1.8 3.5 ‐0.47 0.856
S06 800 C2 B2 9.0 3.5 ‐0.48 0.856
S06 800 B3 B2 0.075 3.5 0.12 0.351
S06 800 B3 B2 0.375 3.5 ‐0.32 0.351
S06 800 B3 B2 1.8 3.5 ‐0.82 0.351
S06 800 B3 B2 9.0 3.5 ‐0.71 0.351
S06 800 A4 B4 0.075 3.5 0.04 0.425
S06 800 A4 B4 0.375 3.5 ‐0.32 0.425
S06 800 A4 B4 1.8 3.5 ‐0.56 0.425
S06 800 A4 B4 9.0 3.5 ‐0.75 0.425
S06 800 A1 A2 0.075 3.5 0.80 0.476
S06 800 A1 A2 0.375 3.5 0.55 0.476
S06 800 A1 A2 1.8 3.5 0.20 0.476
S06 800 A1 A2 9.0 3.5 ‐0.64 0.476
Table 4.1. Parameter values for model fits for all electrode pairs. Column 1 is the subject
being evaluated, Column 2 shows the brightness of the standard and the electrode
distance. Column 3 lists the electrodes being evaluated. Column 4 lists the phase‐shift.
Column 5 and 6 are the β and γ parameter values. Column 8 shows the error values of the
model fits.
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Fig. 4.4. Spatially‐separated electrode pairs. Normalized charge to maintain
equibrightness as a function of phase‐shift between pulses across 1600 and 2400 μm
separated electrodes. The data points plotted for 0.075, 0.375, 1.8, and 9.0 ms phase‐
shifts are represented by black, dark gray, medium gray, and light gray circles,
respectively. The model fits for each of the different phase‐shifts are solid, dash‐dotted,
dashed, and dotted lines of the same color. (A) One electrode pair for subject S06 at 1600
μm. (B) One electrode pair for subject S06 at 2400 μm separation. (C) The parameter γ as
a function of the phase‐shift. Subject S05 was unavailable for this experiment.
Figure 4 shows data and model fits for electrode pairs separated by 1600 and
2400 μm for S06. We fit these data with same model as was used for the 800 μm
separated data. Two example electrode pairs (one at 1600 and the other at 2400 μm
separation) (Fig. 4.4A & 4.4B) are presented for subject S06. S05 was unavailable for
testing in these conditions (see the Subjects section in the Methods). The values of the
parameter γ are plotted in Fig. 4.4C as a function of phase‐shift for the 800, 1600, and
2400 μm separation conditions. Additional data sets for 1600 and 2400 μm separated
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electrode pairs with the associated model fits can be found in the supplementary data
(Fig. S4). The parameter values for the 1600 and 2400 μm separated electrodes can be
found in Table 4.2.
Subject Experiment E1 E2 phase‐shift (ms) β γ error
S06 1600 B2 B4 0.075 3.5 2.16 0.286
S06 1600 B2 B4 0.375 3.5 1.10 0.286
S06 1600 B2 B4 1.8 3.5 0.84 0.286
S06 1600 B2 B4 9.0 3.5 0.52 0.286
S06 1600 A2 C2 0.075 3.5 0.25 0.341
S06 1600 A2 C2 0.375 3.5 0.16 0.341
S06 1600 A2 C2 1.8 3.5 0.22 0.341
S06 1600 A2 C2 9.0 3.5 0.25 0.341
S06 1600 B3 B1 0.075 3.5 0.88 0.079
S06 1600 B3 B1 0.375 3.5 0.54 0.079
S06 1600 B3 B1 1.8 3.5 0.19 0.079
S06 1600 B3 B1 9.0 3.5 0.31 0.079
S06 1600 A1 C1 0.075 3.5 1.30 0.411
S06 1600 A1 C1 0.375 3.5 0.79 0.411
S06 1600 A1 C1 1.8 3.5 0.05 0.411
S06 1600 A1 C1 9.0 3.5 ‐0.09 0.411
S06 2400 A1 A4 0.075 3.5 0.99 0.269
S06 2400 A1 A4 0.375 3.5 0.32 0.269
S06 2400 A1 A4 1.8 3.5 0.28 0.269
S06 2400 A1 A4 9.0 3.5 0.21 0.269
S06 2400 C4 C1 0.075 3.5 ‐0.88 7.212
S06 2400 C4 C1 0.375 3.5 0.13 7.212
S06 2400 C4 C1 1.8 3.5 ‐0.76 7.212
S06 2400 C4 C1 9.0 3.5 ‐0.19 7.212
Table 4.2. Parameter values for 1600 and 2400 μm separated electrode pairs. Column 1
is the subject being evaluated, including the theoretical data plotted in Fig. 2. Column 2 is
the distance between the electrode pairs being evaluated. Column 3 & 4 are the
electrodes being evaluated. Column 5 is the phase‐shift. Column 6 and 7 are the β and γ
parameter values. Column 8 is the error value of the model fits.
4.4 Discussion
Earlier work of ours (Chapter3) demonstrated significant interactions between
pairs of electrodes, even when they are stimulated non‐simultaneously. Here we
examined how these interactions affect perceived brightness. We measured the
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perceptual change in brightness as a function of the temporal separation between
suprathreshold electrical pulses across pairs of electrodes. We found that interactions
between electrodes moved from facilitatory towards suppressive interactions as a
function of the phase‐shift. Similar interactions were found, even when electrodes were
separated by as much as 2400 μm. A relatively simple model could be used to describe
these data with reasonable accuracy, suggesting that it may be relatively simple to
predict the effect of these interactions on perceived brightness.
These data demonstrate that when more than one electrode is stimulated over
time, the percept that is generated is not independent from neighboring electrodes.
Even when electric fields are not overlapping in time, there are still mechanisms of
integration (Chapter 3). In this data set the effects of these interactions seem to begin to
asymptote when pulses are separated by approx 1.8 ms. The time course of these
interactions is compatible with a number of physiological substrates.
One possibility is that local differences in brightness are mediated by neural
populations that are between electrodes. In Chapter 3, we carried out multiple
experiments to test this hypothesis. As with the data presented here, we found that
spatiotemporal interactions decreased with electrode separation, consistent with the
idea of intermediate neural populations mediating differences in brightness.
We also found that electrodes separated by more than 2 mm on the retina still
interact in a way that affects the overall perceived brightness. One possibility is that
these interactions are mediated by neurons lying in between, and receiving stimulation
from, more than one electrode. The electrodes in our display differ in their height from
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the retinal surface, which presumably means that the extent of current spread on the
retinal surface is different across electrodes. A second possibility is that these long‐
range interactions are mediated by lateral connections in the retina. Recent evidence
suggests very fine temporal sensitivity within lateral connections mediated by wide‐field
amacrine cells. These connections can span up to many millimeters within the retina
(Amthor et al., 2005; Baccus, 2007). These connections therefore have the qualities that
would be required to influence our subjects' ability to discriminate between patterns
differentiated by extremely fine temporal information across relatively wide regions of
space within the retina. Finally, it is possible that these interactions may be mediated by
cortical sensitivity to precise timing patterns across space.
Finally, it is possible that the perceived differences in brightness are mediated by
cortical mechanisms rather than retinal. Stimulation using extremely short pulses (~0.1
ms) results in precise single spikes within ganglion cells that are phase‐locked to the
pulses with a precision of <0.7 ms (Fried et al., 2006; Sekirnjak et al., 2008), and
presynaptic‐driven spiking is abolished with stimulation frequencies above 10 Hz
(Sekirnjak et al., 2006; Ahuja et al., 2008). If this precise timing information is passed
from retina to cortex, it is possible that the sensitivity to pulse timing across electrodes
is the result of a cortical mechanism sensitive to spatiotemporal firing patterns
originating in the retina.
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Chapter 5
Conclusions
The possibility of restoring sight through electrical stimulation has captured the
interest of laymen and scientists for many years (LeRoy, 1755; Lowenstein, 1918;
Foerster, 1929; Penfield and Rasmussen, 1952; Brindley and Lewin, 1968; Dobelle, 1974;
Humayun et al., 1996; Schmidt et al., 1996; Weiland et al., 1999; Humayun et al., 2003;
Rizzo et al., 2003; Mahadevappa et al., 2005; Murphey and Maunsell, 2007; Pezaris and
Reid, 2007; Yanai et al., 2007). As we make progress, the goals associated with restoring
sight in blind patients have become more sophisticated and we are now looking to
create images that are predictable over both space and time.
The ultimate goal of most implants is to generate useful vision in blind patients
by transforming visual information into a spatial and temporal sequence of electrical
pulses. Visual percepts generated by direct retinal electrical stimulation can be
controlled by varying the amplitude (amplitude encoding) (Greenwald, 2009), the pulse
timing within an electrode (frequency encoding), and the timing across electrodes
(spatiotemporal coding). In this thesis, I have shown that pulse timing within an
electrode and across electrodes have an effect not just on percept brightness, but also
on overall appearance.
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To create a two‐dimensional image that changes in time (i.e., a representative
movie of visual space) using a two‐dimensional array of electrodes requires an
understanding of how pulses across electrodes interact and integrate current over time.
It is possible that each electrode behaves as an independent channel of information,
where each electrode represents a ‘pixel’ such as on a computer monitor. However, the
data I present in Chapters 3 and 4 suggests that this is not the case. Electrodes that are
separated by distances as great as 2400 μm still interact with one another and the
resulting brightness and appearance generated by these two electrodes is dependent on
the pulse timing across them. These data, and our ability to model these data, suggests
that it may be possible to control spatiotemporal stimulation such that the resulting
percept behaves in a predictable way.
5.1 Coding for brightness within an electrode
In the retinal prosthesis patients implanted with the Second Sight Medical
Products, Inc. device, coding regions of brightness in a two‐dimensional image is
currently controlled by amplitude modulation. Our group has shown that the apparent
brightness of a percept, when stimulating within a single electrode, systematically
changes as a function of current amplitude in patients implanted with a retinal
prosthesis (Greenwald, 2009). We found that the amplitude‐brightness relationship can
be easily described by a power function with a single scaling factor as a parameter.
Although this is a reasonably efficacious methodology, the output of the retina is
in the form of brief impulse responses or spikes and it would be potentially beneficial to
encode the light signal using short pulse sequences that trigger specific patterns of
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activity in these cells. Indeed, it has been shown that using short electrical pulses results
in phase‐locked spikes in ganglion cells up to 250 Hz (Fried et al., 2006; Sekirnjak et al.,
2006). Directly controlling the timing of spikes through the timing of stimulation (rather
than through the amplitude of the stimulation current) may also be more “natural” and
powerful. The retina delivers information about the visual scene to higher visual centers
through its time‐varying spike signal (Adrian and Matthews, 1928; Field and Chichilnisky,
2007). Until recently, the general assumption has been that the rate of ganglion cell
firing is simply monotonically related to the “intensity” of the stimulus. However, this
idea of ‘simple rate coding’ has recently come into question as it has been shown that
visual system is sensitive to spike timing on a much finer scale ( < 10 ms) (Rieke, 1997)
and spike train variability cannot simply be described by a Poisson distribution (Berry et
al., 1997; Uzzell and Chichilnisky, 2004). Indeed, in Chapter 2 we show that the human
visual system is not only highly sensitive to changes in overall pulse train frequency (Fig.
2.4), but to the distribution of the pulses within a given window of time (Fig. 2.6).
Although we can only speculate as to the underlying physiological mechanism that is
involved in integrating these pulse signals, it clearly shows that being able to control the
precise timing of spikes may prove to be as important as controlling their absolute rate.
In the data described in Chapter 2, I show that brightness can also be controlled
by frequency modulation or pulse timing. Additionally, we find that this frequency‐
brightness relationship is predictable and can be described by a simple linear‐nonlinear
model. As well as predicting brightness for a given temporal pattern of stimulation, the
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model can be used as a tool to find the most energy efficient stimulation pattern to
obtain a given brightness level.
5.1.1 Stimulation protocols that satisfy multiple constraints
Achieving useful percepts via electrical stimulation requires satisfying a variety of
safety and engineering constraints. First, we assume that useful percepts will require
stimulation at frequencies higher than subjects’ perception of visible flicker (frequencies
above the “critical flicker frequency”). Second, safety concerns dictate relatively
stringent charge density limits, since high charge densities have the potential to
compromise the integrity of electrode material (Brummer and Turner, 1975; Brummer
et al., 1983) and cause damage to stimulated neural cells (McCreery et al., 1988;
McCreery et al., 1990; Shannon, 1992). Third, the maximum current amplitude that can
be produced may in some cases be limited by the compliance voltage of the stimulator.
A final set of constraints include limits in the amount of power available to the implant
given the need for a long battery life, and power limits inherent in transmitting power
inductively, resulting in a need to minimize overall charge.
Our model described in Chapter 2 provides an example of how the optimal
stimulation pattern needed to produce a percept of a given brightness level can be
determined given a set of constraints. Figure 5.1 shows example predictions of
threshold current amplitude (Fig. 5.1A), charge density (Fig. 5.1B), and overall charge
(Fig. 5.1C) for a 500 ms pulse train presented on an electrode of typical sensitivity across
a range of pulse widths and frequencies. The dashed lines represent examples of safety
and engineering constraints that might restrict the potential set of stimulation patterns.
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One constraint is that stimulation should ideally be at a rate that is high enough
to avoid perceptual flicker. There seems to be little difference between the CFF of early
stage RP patients and visually normal controls (Graham, 1965), though in later stages of
the disease temporal sensitivity declines sharply (Dagnelie, 1992; Felius and Swanson,
1999). If it is the photoreceptor stage that limits temporal sensitivity then prosthetic
devices may require stimulation rates far higher than 50 Hz to avoid visible flicker.
However the ability to produce behavioral adaptation effects using "invisible" rates of
flicker above the CFF suggest that stages of processing beyond the retina may mediate
the ability to consciously perceive flicker (Shady et al., 2004). We therefore assume here
that stimulation must be at a rate higher than a critical flicker frequency (CFF) of 50 Hz.
In the example shown here, we further assume a current amplitude limit of 200
μA, and a charge density limit of 0.35 mC/cm
2
. Given these example constraints, our
model predicts that the most charge efficient stimulation pattern, for the conditions and
prosthetic device tested here, is a 50 Hz pulse train consisting of 0.089 ms pulses. Our
hope is that this model (or similar models) will generalize to other devices. Of course
this ability to evaluate engineering and safety trade‐offs across different pulse patterns
need not be restricted to the simple stimulation patterns used in this example, though
any generalization of these predictions should, of course, be treated with caution.
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Fig. 5.1 Efficiency predictions for a 500 ms pulse train. In each panel the x‐axis represents pulse
width on a logarithmic axis, and the y‐axis represents frequency. Red dashed lines represent a
current amplitude limit of 200 μΑ, yellow dashed lines represent the constraint that stimulation
must occur above the critical flicker frequency of 50Hz, and blue dashed lines represent the
constraint of a charge density limit of 0.35mC/cm
2
. Light shading represents pulse widths and
frequencies that fall outside these constraints. The z‐axis represents current (A), charge density
(B), and overall charge across the entire pulse train (C). Given these example constraints, our
model predicts that the most charge efficient stimulation pattern is a 50 Hz pulse train consisting
of 0.089 ms pulses, as shown by a * in Panel (C).
However, charge efficiency is not equivalent to energy efficiency. All other things
being equal, evaluating a strength‐duration curve leads to the conclusion that charge is
minimized with the shortest pulse width. However, there is a point where the energy to
create these amplitudes (voltage) begins to reach levels of energy consumption that do
not justify the use of these shorter pulse widths (and minimized charge). That is because
a higher compliance voltage is required to push a higher peak current through a given
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electrode impedance; the total energy dissipated is the product of the compliance
voltage of the stimulator times the current delivered. For a given compliance voltage,
the most efficient operation (in terms of energy delivered to the electrodes vs. energy
dissipated in the current regulator) is when the voltage drop across the electrodes is
near this compliance voltage. This is thus the largest current that can be supplied and
the shortest pulse width that will be required to obtain the desired stimulation. It has
been found that the most energy efficient pulse width is at the point of the chronaxie
(Coates and Thwaites, 2000; Geddes, 2004). Assuming this to be true, we calculated an
average chronaxie value from our strength‐duration data (0.29 ms). Our model suggests
that the behavior of our strength‐duration curves can be described by a single chronaxie
value, which says that a 0.29 ms pulse width would be the most energy efficient pulse
width under any condition. Depending on the necessary constraints of the stimulation
protocol, this pulse width value can be used to constrain the efficiency prediction
derived by the model.
5.2 Spatiotemporal interactions, integration, and correlations
Synchronous or correlated activity in retinal ganglion cells has been shown to
occur across great distances (Schnitzer and Meister, 2003). In Chapters 3 and 4 we show
that pulse timing across electrodes, not just on a single electrode, can influence the
overall brightness and quality of a percept. Each electrode clearly does not behave as an
independent channel of information. Although it is difficult to pinpoint the exact
mechanism underlying these perceptual responses, and electric field interactions do
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play a major role, our data from Chapters 3 and 4 suggest that there is at least some
neural component that is responsible for these differences in brightness and shape.
5.2.1 Decoding and perceptual grouping
The normal early visual system integrates and represents the visual image using
a 2‐dimensional array of spatiotemporal filters or receptive fields (Hubel and Wiesel,
1962; Movshon et al., 1978). Additionally, the visual system is capable of grouping
diverse image properties such as color, shape, and luminance into meaningful objects
and contours. It has been suggested that the representation of objects and contours
across the visual field is at least partially mediated by synchronous neuronal activity
within those neurons representing the contour (Milner, 1974; Reitboeck, 1983; von der
Malsburg and Schneider, 1986; Gray et al., 1989; Konig et al., 1995; Brosch et al., 1997;
Fries et al., 1997; Roelfsema et al., 1997; Singer, 1999). Synchronous firing at high
temporal frequencies has been recorded for contour stimuli within the retina
(Mastronarde, 1983a, b, c; Meister et al., 1995; Amthor et al., 2005) and visual cortex
(Kreiter and Singer, 1996; Singer et al., 1996; Brosch et al., 1997; Fries et al., 2001b; Fries
et al., 2001a; Gabriel and Eckhorn, 2003).
Psychophysically, there is evidence that grouping of visual stimuli occurs based
on temporal structure at frequencies up to approximately 35 Hz (Usher and Donnelly,
1998; Lee and Blake, 1999), but it is possible that such stimuli still contain visible flicker
(Graham, 1965) or motion information (Fahle and Poggio, 1981; Heeger, 1987; Grzywacz
et al., 1990; Grzywacz and Yuille, 1990; Nowlan and Sejnowski, 1995; Simoncelli and
Heeger, 1998; Bair and Movshon, 2004). Although it has not yet been clearly shown that
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frequencies beyond the CFF mediate grouping performance, there is some evidence of
orientation specific (implying a cortical substrate) adaptation to temporal frequencies
above the CFF (Shady et al., 2004).
Conversely, it is possible that sensitivity to spatiotemporal changes in activity is a
function of the well known filtering properties of the visual system (Farid and Adelson,
2001). Here, regions can be represented as low‐pass or band‐pass filters that integrate
input within some window of time. Low‐pass filtering would represent static structure
through mechanisms of persistence and band‐pass filtering would emphasize flickering
or moving stimuli.
It is possible that the ability to differentiate the retinal stimulation patterns
described in Chapter 3 is mediated by cortical sensitivity to precise timing information. It
is likely that our stimulation patterns created very precise spatiotemporal patterns of
spiking activity in the retina. Stimulation using extremely short pulses (~0.1 ms) results
in precise single spikes within ganglion cells that are phase‐locked to the pulses with a
precision of <0.7 ms (Fried et al., 2006; Sekirnjak et al., 2008), and that presynaptic‐
driven spiking is abolished with stimulation frequencies above 10 Hz (Sekirnjak et al.,
2006; Ahuja et al., 2008). If precise timing information is passed from retina to cortex, it
is possible that the sensitivity to pulse timing across electrodes is the result of a cortical
mechanism sensitive to spatiotemporal firing patterns originating in the retina.
However, it is still not known whether these synchronous firing patterns have functional
importance.
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This sensitivity to precise timing in visual cortex is thought to originate from long
distance lateral connections between cortical neurons (Kreiter and Singer, 1996;
Castelo‐Branco et al., 2000; Biederlack et al., 2006) but see (Lamme and Spekreijse,
1998; Shadlen and Movshon, 1999; Roelfsema et al., 2004). Not surprisingly, the
incidence of synchronous activity between pairs of neurons drops off dramatically as a
function of distance (Roelfsema et al., 2004). Nevertheless, it is still possible that the
subjects’ ability to discriminate synchronous and asynchronous patterns of stimulation
may be mediated by cortical mechanisms. It is also important to keep in mind that, in
addition to reorganization of the retina during photoreceptor degeneration, there is
strong evidence of cortical reorganization (Gilbert et al., 1990; Gilbert and Wiesel, 1992;
Gilbert, 1998). This reorganization is thought to include an increased diameter of lateral
connections. This last point suggests that correlated activity between cortical neurons
may occur at much greater distances in visually impaired or blind subjects.
Generating percepts would be much more computationally simple if it were
possible to create spatiotemporally independent electrodes. However, the interactions
described in Chapters 3 and 4 (both between synchronous and non‐synchronous
stimulation, and between different patterns of non‐simultaneous stimulation) do offer
the potential for significant perceptual flexibility. Simply by altering the order of
stimulation, it is potentially possible to create distinct percepts. It should be noted that
very similar interactions have been explored in cochlear implants as a means of creating
“virtual electrodes” that can produce shifts in pitch intermediate between two
stimulated electrodes (Donaldson et al., 2005).
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5.2.2 Spatiotemporal stimulation – synchronous vs. phase‐shifted
One parsimonious explanation of the results in Chapter 3 is that differentiation
between these two stimuli is mediated by neurons in between, and receiving
stimulation from, more than one electrode. Any individual neuron sitting intermediate
two electrodes will receive a different pattern of stimulation from pseudo synchronous
and asynchronous stimulation patterns. If individual neurons are sensitive to these small
differences in timing, as is suggested by earlier work measuring threshold sensitivity to
different temporal patterns of stimulation (Horsager et al., 2008), then these neurons
would have the potential to mediate the ability of subjects to differentiate the two
stimulus conditions. If this were the case we would expect differences between pseudo‐
synchronous and asynchronous stimulation patterns to decrease as a function of
electrode separation.
103
Figure 5.2. Perceptual differences and electrode order. An illustration
of how the expected percept might differ for clockwise (A) vs.
counterclockwise (B) stimulation if the response of a neuron at a given
point in time is suppressed by previous stimulation. Here we used the
simple model:
, where B is apparent
brightness across the retina, C
and
are the current fields at each
point in time and c is a constant. We assumed equal electrode sizes
unlike the checkerboard array implanted in the subjects tested here.
This model is simply used as an intuitive illustration since actual
interactions over time are demonstrably more complex (Horsager et
al., 2008).
As described above, one possibility is that discrimination between pseudo‐
synchronous and asynchronous stimulation might be mediated by differences in the
response to the two stimulation patterns within individual neurons lying between two
electrodes that receive direct stimulation from two (or more) electrodes. It is known
that the intensity of electric fields decrease as a function of distance from the electrode
(Wiley and Webster, 1982a; Cottaris and Elfar, 2005). Take the case where stimulation
occurred in a pattern where electrode 1 was stimulated before electrode 2 (Fig. 5.2). A
neuron lying closer to the electrode 1 would be stimulated by a high amplitude pulse
followed by a low amplitude pulse, whereas a neuron lying closer to electrode 2 than to
electrode 1 would be stimulated by a low amplitude pulse followed by a high amplitude
pulse.
104
If low‐high vs. high‐low pulse pair relationships have a differential effect on
driving cell activity then these differences within individual cell responses might result in
perceptually distinguishable response patterns based on temporal differences in
stimulation even at rates well above the CFF. Take, for example the case of clockwise
versus counter‐clockwise stimulation, as illustrated in Figure 5.2. In the clockwise
pattern, electrode 1 is stimulated before electrode 2 whereas in the counter‐clockwise
pattern electrode 2 is stimulated before electrode 1. Neurons lying closer to electrode 1
are therefore stimulated by high followed by a low amplitude pulses in the case of the
clockwise pattern, and low followed by high amplitude pulses in the counterclockwise
pattern. If neurons were less sensitive to low‐high than to high‐low patterns of
stimulation (for example) then this would lead to local differences in brightness across
the two patterns in regions where electric fields overlap significantly. While the spatially
averaged mean brightness of clockwise and counterclockwise patterns would be
identical, local patterns of brightness would differ, resulting in what might be a
distinguishably different percept.
However, it is possible that neuronal lateral connections or cortical sensitivity to
precise timing patterns across space may also play a role. Recent evidence suggests very
fine temporal sensitivity within lateral connections mediated by wide‐field amacrine
cells. These connections can span up to many millimeters within the retina (Amthor et
al., 2005; Baccus, 2007). These connections therefore have the qualities that would be
required to influence our subjects' ability to discriminate between patterns
differentiated by extremely fine temporal information across relatively wide regions of
105
space. The sensitivity to clockwise versus counterclockwise stimulation demonstrated in
Experiment 5 is harder to explain in terms of retinal lateral connections. However, it
should be noted that while current levels were chosen so as to roughly brightness‐
match the percepts across each of the four electrodes in the group this brightness
matching was not perfect. Moreover, electrodes differ in their height from the retinal
surface, which presumably means that the extent of current spread on the retinal
surface is different across electrodes. Finally, it is likely that there are inhomogeneities
in retinal wiring across the 3 mm covered by the electrode array. These inhomogeneities
across electrodes and the retinal surface might conceivably produce perceptually
distinguishable patterns for clockwise vs. counter‐clockwise stimulation.
In Chapter 4, we found that these complex interactions could be
approximated, though not perfectly, with a reasonably simple model. Although it is
certainly the case that the model could be improved, the simplicity of the model
described here has the advantage that it would require a relatively small amount of data
to be collected to estimate the 2 parameters. As a result, such a simple model might be
of practical use when designing stimulation protocols that involve multi‐electrode
arrays.
We have previously been able to model perceived brightness as a function of
electrical stimulation on a single electrode for a number of different timing
configurations (Chapter 2). Coupled with a model that is capable of describing
spatiotemporal interactions our data suggest that it should be possible to predict the
perceived brightness for different regions of an array of percepts generated by a two‐
106
dimensional electrode array. Such a model will of course be necessary to accurately
represent a visual scene is that is constantly changing both in space and time.
107
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APPENDICES
Appendix A
Linear and nonlinear transformations in neurons
Analyzing the function of a particular system generally involves the
measurement of some response (output) as a function of changes in the stimulus
(input). These stimuli change in amplitude (i.e., luminance or current) as a function of
time, s(t). The response, which could be either neural or psychophysical, can also
change as a function of time, r(t). When measuring retinal ganglion cell spiking
responses, the system being evaluated is the retina. However, when evaluating
perceptual responses to light stimuli, the system being analyzed extends from the retina
to visual cortex. Thus, the system can be defined as the collection of physical processes
that are between the stimulus and the response. It is important to keep in mind that
defining the system is not always straightforward, particularly in psychophysics.
The purpose of this section is to provide basic concepts in linear systems theory
and nonlinear mechanisms, and how these concepts apply to models of visual function.
128
A1. Rules of linearity: superposition and time invariance
For a system to be linear, it must obey the principles of superposition and time
invariance. Superposition states that the response caused by two or more stimuli is
equal to the sum of responses to each of those stimuli, individually. In other words, the
action of the system, A, on the stimulus function, s(t), maps directly on the output
function, r(t). Mathematically, this can be represented by
A[s(t)] = r(t). eq. A.1
Additionally, the system is considered time invariant if
A[s(t − τ)] = r(t − τ) eq. A.2
Delaying the input by some duration τ, leads to a delay in the response by the same τ,
but leaves the response otherwise unaltered. Taken together, a system is linear if there
is a point response for every point stimulus, and the properties of the system do not
change over time.
A2. The impulse and impulse response
An impulse, δ(t), is defined as a stimulus pulse with infinite height, and
infinitesimal width and area. Using this definition, the time varying stimulus can be
represented by a series of impulses
s(t) = s(τ)δ(t − τ)dτ =s(t)*δ(t)
t
∞
t
0
∫
, eq. A.3
where the original s(t) becomes the convolution of s(t) and δ(t). The impulse response,
γ(t), is simply the system transformation of the impulse at time t. We can replace δ with
γ and the response of the system to s(t) can now be defined as
129
r(t) = s(τ)γ(t − τ)dτ =s(t)* γ(t)
t
∞
t
0
∫
. eq. A.4
If the impulse response is known, it is simple to calculate the response to a given
stimulus in a linear system. In other words, the impulse response function characterizes
the system transformation on the stimulus that leads to the response.
A3. Linear filters: The leaky integrator
Integration can be thought of in terms of the integral, where the response is the
sum of the area under the function. However, most systems integrate the stimulus over
time, s(t), and leak the stimulus at a rate that is proportional to the original input. This
is defined as a leaky integrator and can represented mathematically as
h(t) =s(t)
τ
n−1
(n −1)!
(
t
τ
)
n−1
e
1
τ
eq. A.5
where t is time, τ is the time constant, and n is the number of identical cascading leaky
integrators. The system behaves like a low‐pass filter that is dependent on τ and repeats
n number of times.
Although a mathematical derivation cannot be done, h(t) can be related to the
membrane time constant, or filter of a cell, which is defined as τ
m
= R
m
C
m
, where R
m
and
C
m
are the resistance and capacitance of the cell membrane, respectively. Furthermore,
both h(t) and τ
m
can be related to the strength‐duration curve, or chronaxie (T
ch
), that is
frequently measured when electrically stimulating neural tissue.
If the amount of current to reach threshold is I
th
and the system is linear, then
the lowest value of I
th
will be reached when the stimulating pulse is infinitely long. The
130
amount of current to reach threshold when using this infinitely long pulse is called the
rheobase, I
rh
. If we know the rheobase value, membrane time constant, and the pulse
width, we can determine the amount of current necessary to reach threshold for that
pulse width using the equation
I
th
=
I
rh
1−e
−T /τ
m
. eq. A.6
I
th
plotted as a function of pulse width, T, is called the strength‐duration curve. The
chronaxie, T
ch
, is defined as the minimum pulse duration needed to reach threshold if I
th
is twice I
rh
. Thus,
T
ch
= τ
m
ln2, eq. A.7
or
τ
m
=
T
ch
ln2
. eq. A.8
A4. Nonlinear mechanisms: threshold and static transforms
The threshold is the measurable point where some level is reached, whether it is
the point a neuron accelerates into a full action potential or the point a visual stimulus is
just barely perceptible. Threshold is the simplest transformation between the filtered
output of the system, and the response of the system to that output. In psychophysics,
reaching perceptual threshold leads to a “yes, I see it” response. See Chapter 2 for a
discussion on measuring detection at threshold and suprathreshold using
psychophysics. Depending on the model being used, threshold can be a fixed property
of the system, or a variable value that changes as a function of some criterion.
131
Threshold can be used for detection of overall stimulus intensity as well as excursions
from a baseline (decrements and increments).
Static transformations are independent of time. In common examples of this
transformation, the input is raised to a power, which can be an accelerating,
decelerating, or a sigmoidal response relationship.
This static nonlinear transformation can also be thought of in terms of
probability summation, which is the probability that each point within a stimulus
exceeds the threshold limit. Again, threshold can be either neural or perceptual. r
i
is the
response of the internal system within a given interval i and, if it is linear, it is
proportional to the stimulus strength. Assume that the probability that this response
exceeds threshold within i is defined as p
i
and is independent of all other intervals. The
probability of detection for all intervals (probability summation) will be
p =1−e
∑ r
i
β
. eq. A.9
Fig. A1. Static Nonlinearity. The input output relationship and how it can be transformed
depending on the transform function. The red curve is an example of a sigmoid transformation,
and the blue line is an expanding transformation.
132
Appendix B
Supplemental materials to Chapter 2
B1. Example Weibull fits for threshold and suprathreshold data
Fig. B1. Example Weibull fits for threshold detection and brightness matching.
(A) Row A contains two examples (one from each subject, S05 and S06) of the
psychometric functions generated during a threshold detection task (see main
text for the description of methods). (B) Row B contains two examples (one from
each subject, S05 and S06) of the psychometric function generated during a
brightness matching task between two pulse trains of different frequencies. The
lower frequency pulse train had fixed amplitude and the pulses in the higher
frequency pulse train was adjusted until it was perceptually equal in brightness.
133
B2. Systematic changes in brightness due to adaptation
To determine if there was any systematic change in brightness throughout the testing
session, we evaluated inter‐trial, intra‐run, and intra‐session adaptation. To do this, we
compared brightness matching data on 4 separate electrodes for two identical pulse
trains (pulse width = 0.975, frequency = 100 Hz, duration = 500 ms, 200 trials). The
"standard" pulse train was fixed at an amplitude of 77.5 μA and the "test" pulse train
was allowed to vary in amplitude to find the point of equal brightness. The interval
order for presentation of the standard and test pulse was randomized across trials, as in
the main data set. If changes in sensitivity occurred between the two intervals of each
matching trial we would expect that, at the point of equal brightness, the stimulus
presented in the second interval would require higher or lower current amplitudes than
the stimulus in the first interval. We found that the pulse in the second interval required
more current to obtain a brightness match (2‐tailed t‐test p<0.005), consistent with a
loss of sensitivity between the two intervals of the trial. On average the pulse required
presented in the second interval required 13% more current than the standard (10.2+/‐
2.5 μA).
Fortunately in our brightness matching task the presentation order of the
intervals was randomized, thereby minimizing interval order effects. Nonetheless, this
desensitization may have biased our results slightly. If the standard resulted in greater
desensitization than the test stimulus at the point of equal brightness, then our
estimate of the amount of current required in the test stimulus would be a slight
134
overestimate. Similarly, if the standard resulted in less desensitization than the test
stimulus at the point of equal brightness, then our estimate of the amount of current
required in the test stimulus would be a slight underestimate. One advantage of our use
of a shifting standard (whereby brightness was matched between stimuli that were
reasonably close in temporal frequency) is that differences in the effectiveness of
desensitization across stimuli were minimized. Based on the results of the control
experiment described above, conservative calculations estimate that any resulting bias
never exceeded 3% of the estimated brightness match, and was generally much smaller
(less than 1 μA for almost all data points). Given the small size of these biases, for
simplicity sake, we did not include inter‐interval interactions in our model.
We measured thresholds on 10 electrodes using one of our more charge
intensive pulse trains (pulse width = 0.975, frequency = 100 Hz, duration = 500 ms, 150
trials total). We then divided the data into two halves ‐ the first 75 vs. the last 75 trials
and fit psychometric functions separately to each half. We found no systematic increase
(or decrease) in measured threshold between these two halves of the data. The mean
threshold based on trials in the first half of the run was 25.7+/‐3.0 μA (standard error),
and the mean threshold based on the second half of trials in the run was 26.9+/‐2.9 μA.
Paired t‐tests (both 1 and 2 tailed) were below significance (p>0.05).
We also compiled previously collected data (the data reported in the main
paper) that included a wide range of pulse widths and frequency, and found no
significant differences between the first and second half of trials in a run across this data
135
set. These results therefore suggest that desensitization within a run did not significantly
affect our data.
We measured thresholds (pulse width = 0.975 ms, frequency = 100 Hz, duration
= 500 ms, 200 trials) on 5 electrodes before and after high intensity stimulation
(collecting suprathreshold brightness matching for high frequency pulse trains) on the
same electrode. We found no systematic increase (or decrease) between these two
thresholds. The mean threshold before high intensity stimulation was 28+/‐ 4.6 μA
(standard error), and the mean threshold after high intensity stimulation was 25+/‐3.9
μA. Paired t‐tests (both 1 and 2 tailed) were below significance (p>0.05). These results
suggest that desensitization within a testing session did not significantly affect our data.
B3. Threshold and suprathreshold fits for data used to optimize model
Fig. B2. Fits for single pulse thresholds (see main text for description of methods).
136
Fig. B3. Fits for latent addition thresholds. Stimuli were 0.075
ms pseudo‐monophasic pulse pairs (the anodic phases were
presented 20 ms after the end of the second cathodic pulse). The
initial cathodic pulse always had fixed amplitude of 50% of the
single pulse threshold. The delay between the start of the
conditioning pulse and the start of the test pulse was varied
between 0.15 ms and 12 ms (dotted arrow). The amplitude of
this test pulse was varied to determine threshold (solid arrow).
Fig. B4. Fits for fixed duration pulse trains thresholds using
0.075 ms pulse widths (see paper for description of methods).
137
Fig. B5. Fits for fixed duration pulse trains thresholds using 0.975
ms pulse widths (see paper for description of methods).
Fig. B6. Fits for variable duration pulse trains using 2 pulses (see
paper for description of methods).
138
Fig. B7. Fits for variable duration pulse trains using 3 pulses (see
paper for description of methods).
Fig. B8. Fits for variable duration pulse trains using 15 pulses
(see paper for description of methods).
139
Fig. B9. Fits for fixed duration pulse trains (0.075 ms pulse width at
2X threshold (see paper for description of methods).
Fig. B10. Fits for fixed duration pulse trains (0.975 ms pulse
width at 2X threshold (see paper for description of methods).
140
Fig. B11. Fits for fixed duration pulse trains (0.975 ms pulse width
at 3X threshold (see paper for description of methods).
141
B4. Parameter values for model predictions of various data sets
Table B1: Fit Threshold Parameter Values
Subject Electrode Experiment
τ
1
τ
2
β τ
3
σ θ
error
S05 B3 Single Pulse 0.24 38 3.1 33 3 143.0 326.2
S05 B3 Latent Addition 0.24 38 3.1 33 3 113.8 3701.1
S05 B3 Fixed Duration ‐ Short Pulse 0.24 38 3.1 33 3 21.1 280.4
S05 B3 Fixed Duration ‐ Long Pulse 0.24 38 3.1 33 3 147.0 30.5
S05 B3 Variable Duration ‐ 2 Pulse 0.24 38 3.1 33 3 104.2 1444.8
S05 B3 Variable Duration ‐ 3 Pulse 0.24 38 3.1 33 3 143.0 2887.6
S05 B3 Variable Duration ‐ 15 Pulse 0.24 38 3.1 33 3 159.3 11455.3
S05 C2 Single Pulse 0.65 48 3.0 24 2 14.0 164.0
S05 C2 Latent Addition 0.65 48 3.0 24 2 11.9 133.7
S05 C2 Fixed Duration ‐ Short Pulse 0.65 48 3.0 24 2 10.5 646.4
S05 C2 Fixed Duration ‐ Long Pulse 0.65 48 3.0 24 2 54.0 50.1
S05 C2 Variable Duration ‐ 2 Pulse 0.65 48 3.0 24 2 7.0 3496.1
S05 C2 Variable Duration ‐ 3 Pulse 0.65 48 3.0 24 2 15.3 9192.5
S05 C2 Variable Duration ‐ 15 Pulse 0.65 48 3.0 24 2 6.7 1701.4
S06 B1 Single Pulse 0.38 38 4.2 24 2 505.5 505.3
S06 B1 Latent Addition 0.38 38 4.2 24 2 415.0 848.8
S06 B1 Fixed Duration ‐ Short Pulse 0.38 38 4.2 24 2 2500.0 138.6
S06 B1 Fixed Duration ‐ Long Pulse 0.38 38 4.2 24 2 2900.0 76.3
S06 B1 Variable Duration ‐ 2 Pulse 0.38 38 4.2 24 2 333.0 1105.8
S06 B1 Variable Duration ‐ 3 Pulse 0.38 38 4.2 24 2 383.9 1672.4
S06 B1 Variable Duration ‐ 15 Pulse 0.38 38 4.2 24 2 396.8 3798.4
S06 C2 Single Pulse 0.40 57 3.4 24 2 1612.5 1967.8
S06 C2 Latent Addition 0.40 57 3.4 24 2 1620.0 3727.0
S06 C2 Fixed Duration ‐ Short Pulse 0.40 57 3.4 24 2 230.0 2651.1
S06 C2 Fixed Duration ‐ Long Pulse 0.40 57 3.4 24 2 900.0 55.7
S06 C2 Variable Duration ‐ 2 Pulse 0.40 57 3.4 24 2 1230.0 5412.3
S06 C2 Variable Duration ‐ 3 Pulse 0.40 57 3.4 24 2 990.0 5027.9
S06 C2 Variable Duration ‐ 15 Pulse 0.40 57 3.4 24 2 810.0 11727.3
Average 0.42 45.25 3.43 26.25 2.25 563.48 2650.9
Range
0.25
‐
0.40
61.4
‐
76.7
3.12‐
3.31
4.6‐
24.6
6.5‐
8.2
4.9‐
771.2
10.7‐
12087.5
142
Table B2: Fit Suprathreshold Parameter Values
subject Electrode Experiment
τ
1
τ
2
β τ
3
σ θ
error
S05 B3 Short Pulse (2X threshold) 0.24 38 0.60 33 8 0.200 2387.8
S05 B3 Long Pulse (2X threshold) 0.24 38 0.60 33 8 0.105 28.7
S06 B3 Long Pulse (3X threshold) 0.24 38 0.60 33 8 0.124 302.9
S05 C2 Short Pulse (2X threshold) 0.65 48 0.90 24 8 2.100 2046.4
S05 C2 Long Pulse (2X threshold) 0.65 48 0.90 24 8 0.360 342.2
S05 C2 Long Pulse (3X threshold) 0.65 48 0.90 24 8 0.440 83.6
S06 B1 Short Pulse (2X threshold) 0.38 38 0.80 24 9 1.000 888.6
S06 B1 Long Pulse (2X threshold) 0.38 38 0.80 24 9 0.205 481.2
S06 C2 Short Pulse (2X threshold) 0.40 57 1.00 24 10 4.560 1581.3
S06 C2 Long Pulse (2X threshold) 0.40 57 1.00 24 10 0.606 515.1
S06 C2 Long Pulse (3X threshold) 0.40 57 1.00 24 10 0.865 163.1
Average 0.42 45.91 0.83 26.45 8.73 0.96 801.90
Range
0.25‐
0.40
61.4‐
76.7
0.59‐
0.72
4.6‐
24.6
25.5‐
29.5
0.031‐
0.754
26.5‐
8218.1
Tables B1 & B2. Threshold and suprathreshold model parameter values and squared error for model fits used during
the optimization of the model (figures B2‐B11).
B5. Additional model predictions of various data sets
Fig. B12. Additional predictions for single pulse thresholds.
143
Fig. B13. Predictions for latent addition thresholds.
Fig. B14. Predictions for fixed duration pulse train thresholds using 0.075 ms
pulse width.
144
Fig. B15. Predictions for fixed duration pulse train thresholds using 0.975 ms
pulse width.
Fig. B16. Predictions for variable duration pulse trains using 2 pulses.
145
Fig. B17. Predictions for Bursting 15, 30, and 60 pulse trains.
Fig. B18. Predictions for fixed duration surprathreshold pulse trains at 2X (top
row) and 3X (bottom row) threshold using 0.975 ms pulse width.
146
Table B3: Predicted Threshold Parameters
Subject Electrode Experiment
τ
1
τ
2
β τ
3
σ θ
error
S05 A1 Single Pulse 0.42 45.25 3.43 26.25 2.25 11.2 1151.8
S05 A1 Fixed Duration ‐ Short Pulse 0.42 45.25 3.43 26.25 2.25 10.5 111.5
S05 A1 Fixed Duration ‐ Long Pulse 0.42 45.25 3.43 26.25 2.25 154.0 2.5
S05 A1 Burst Threshold ‐ 15 pulse 0.42 45.25 3.43 26.25 2.25 720.0 108.4
S05 A1 Burst Threshold ‐ 30 pulse 0.42 45.25 3.43 26.25 2.25 390.0 32.6
S05 A1 Burst Threshold ‐ 60 pulse 0.42 45.25 3.43 26.25 2.25 420.0 46.2
S05 C3 Single Pulse 0.42 45.25 3.43 26.25 2.25 110.3 186.9
S05 C3 Latent Addition 0.42 45.25 3.43 26.25 2.25 48.1 67.2
S05 C3 Fixed Duration ‐ Short Pulse 0.42 45.25 3.43 26.25 2.25 36.3 37.7
S05 C3 Fixed Duration ‐ Long Pulse 0.42 45.25 3.43 26.25 2.25 307.5 90.8
S05 C3 Variable Duration ‐ 2 Pulse 0.42 45.25 3.43 26.25 2.25 65.0 529.6
S05 C3 Variable Duration ‐ 3 Pulse 0.42 45.25 3.43 26.25 2.25 95.0 3392.9
S05 C3 Variable Duration ‐ 15 Pulse 0.42 45.25 3.43 26.25 2.25 51.3 5856.9
S05 C4 Single Pulse 0.42 45.25 3.43 26.25 2.25 140.0 39.5
S05 C4 Fixed Duration ‐ Short Pulse 0.42 45.25 3.43 26.25 2.25 49.5 899.2
S05 C4 Fixed Duration ‐ Long Pulse 0.42 45.25 3.43 26.25 2.25 141.8 58.9
S06 A1 Single Pulse 0.42 45.25 3.43 26.25 2.25 10.0 592.5
S06 A1 Latent Addition 0.42 45.25 3.43 26.25 2.25 10.6 39.5
S06 A1 Fixed Duration ‐ Short Pulse 0.42 45.25 3.43 26.25 2.25 6.1 119.9
S06 A1 Fixed Duration ‐ Long Pulse 0.42 45.25 3.43 26.25 2.25 94.5 4.0
S06 A1 Variable Duration ‐ 2 Pulse 0.42 45.25 3.43 26.25 2.25 7.5 158.8
S06 A1 Variable Duration ‐ 3 Pulse 0.42 45.25 3.43 26.25 2.25 6.3 233.4
S06 A1 Variable Duration ‐ 15 Pulse 0.42 45.25 3.43 26.25 2.25 5.1 932.4
S06 A2 Burst Threshold ‐ 15 pulse 0.42 45.25 3.43 26.25 2.25 252.0 12.7
S06 A2 Burst Threshold ‐ 30 pulse 0.42 45.25 3.43 26.25 2.25 299.0 28.1
S06 A2 Burst Threshold ‐ 60 pulse 0.42 45.25 3.43 26.25 2.25 390.0 38.3
S06 B2 Single Pulse 0.42 45.25 3.43 26.25 2.25 132.0 1802.4
S06 B2 Latent Addition 0.42 45.25 3.43 26.25 2.25 123.5 2960.5
S06 B2 Fixed Duration ‐ Short Pulse 0.42 45.25 3.43 26.25 2.25 216.0 384.5
S06 B2 Fixed Duration ‐ Long Pulse 0.42 45.25 3.43 26.25 2.25 546.0 83.9
S06 D1 Single Pulse 0.42 45.25 3.43 26.25 2.25 132.0 1802.4
S06 D1 Latent Addition 0.42 45.25 3.43 26.25 2.25 147.0 2306.2
S06 D1 Fixed Duration ‐ Short Pulse 0.42 45.25 3.43 26.25 2.25 188.0 696.1
S06 D1 Fixed Duration ‐ Long Pulse 0.42 45.25 3.43 26.25 2.25 588.0 80.6
Average 173.65 732.0
147
Table B4: Predicted Suprathreshold Parameters
subject Electrode Experiment
τ
1
τ
2
β τ
3
σ θ
error
S05 A1 Burst Equibrightness ‐ 15 pulse 0.42 45.91 0.83 26.45 8.73 0.229 812.9
S05 A1 Burst Equibrightness ‐ 30 pulse 0.42 45.91 0.83 26.45 8.73 0.206 673.5
S05 A1 Burst Equibrightness ‐ 60 pulse 0.42 45.91 0.83 26.45 8.73 0.205 185.2
S05 A1 Short Pulse (2X threshold) 0.42 45.91 0.83 26.45 8.73 0.630 1336.1
S05 A1 Long Pulse (2X threshold) 0.42 45.91 0.83 26.45 8.73 0.170 35.1
S05 A1 Long Pulse (3X threshold) 0.42 45.91 0.83 26.45 8.73 0.208 258.8
S05 C4 Short Pulse (2X threshold) 0.42 45.91 0.83 26.45 8.73 0.848 672.9
S05 C4 Long Pulse (2X threshold) 0.42 45.91 0.83 26.45 8.73 0.180 220.2
S05 C4 Long Pulse (3X threshold) 0.42 45.91 0.83 26.45 8.73 0.236 208.8
S06 B2 Short Pulse (2X threshold) 0.42 45.91 0.83 26.45 8.73 1.485 4592.5
S06 B2 Long Pulse (2X threshold) 0.42 45.91 0.83 26.45 8.73 0.271 430.8
S06 B2 Long Pulse (3X threshold) 0.42 45.91 0.83 26.45 8.73 0.341 276.9
S06 A2 Burst Equibrightness ‐ 15 pulse 0.42 45.91 0.83 26.45 8.73 0.161 45.8
S06 A2 Burst Equibrightness ‐ 30 pulse 0.42 45.91 0.83 26.45 8.73 0.256 373.2
S06 A2 Burst Equibrightness ‐ 60 pulse 0.42 45.91 0.83 26.45 8.73 0.337 468.1
Average 0.457 706.1
Tables B3 & B4. Threshold and suprathreshold estimates of θ for novel electrodes not used to develop the model.
Other parameter values were fixed to be the mean values from Tables 2.1 and 2.2.
B6. Model statistics – F‐test
When fitting data for novel electrodes, only was allowed to vary across each
threshold and suprathreshold experiment. We compared this constrained model to an
unconstrained version where all 6 parameters were allowed to vary for novel
electrodes. Using the data contained in figures from S2, we compared the power of the
constrained (simpler) and unconstrained (more complex) models using an F test
(parameter and error values are shown in Table B5).
The total number of data points for the threshold and suprathreshold data
across the 4 electrodes, across the two subjects was 158, producing 38 degrees of
freedom for the unconstrained model (DF
U
) and 133 degrees of freedom for the
constrained model (DF
P
). Here, the degrees of freedom are defined as the difference
148
between the number of data points and number of free variables. For the constrained
model, the number of free variables was defined as θ for each data set that we fit (20
total across both subjects) and 5 for all the fixed parameters, for a total of 25 free
parameters to fit the 158 data points across the 20 data sets.
The sum of squared errors for the unconstrained (RSS
U
) and predictive (RSS
P
)
model were 7023.0 μA and 18644.6 μA, respectively. The F
ratio
was calculated as
U
U
U P
U P
ratio
DF
RSS
DF DF
RSS RSS
F
−
−
= ,
To establish the constrained model is the better of the two, you should get an
F
ratio
that is close to 1. If the value is above 1, this suggests the constrained model is
worse. We found the F
ratio
= 0.6483 with an α < 0.01, suggesting that the constrained, or
simpler, model provided a fit of greater power than the unconstrained version.
As described in Chapter 2, the power of the model described in the paper was
significantly higher than that of a less constrained model where ε τ τ τ , , ,
3 2 1
, β and θ
were all allowed to vary across each experiment and electrode, see Tables 5 & 6. The
constrained and unconstrained versions of the full model were compared across the full
data set.
149
Table B5: Threshold ‐ Constrained vs. Unconstrained
Subject Electrode Experiment
τ
1
τ
2
β τ
3
ε θ
Error
S05 C3 Single Pulse 0.42 45.25 3.43 26.25 2.25 110.3 186.9
S05 C3 Latent Addition 0.42 45.25 3.43 26.25 2.25 48.1 67.2
S05 C3 Fixed Duration ‐ Short Pulse 0.42 45.25 3.43 26.25 2.25 36.3 37.7
S05 C3 Fixed Duration ‐ Long Pulse 0.42 45.25 3.43 26.25 2.25 307.5 90.8
S05 C3 Variable Duration ‐ 2 Pulse 0.42 45.25 3.43 26.25 2.25 65.0 529.6
S05 C3 Variable Duration ‐ 3 Pulse 0.42 45.25 3.43 26.25 2.25 95.0 3392.9
S05 C3 Variable Duration ‐ 15 Pulse 0.42 45.25 3.43 26.25 2.25 51.3 5856.9
S06 A1 Single Pulse 0.42 45.25 3.43 26.25 2.25 10.0 592.5
S06 A1 Latent Addition 0.42 45.25 3.43 26.25 2.25 10.6 39.5
S06 A1 Fixed Duration ‐ Short Pulse 0.42 45.25 3.43 26.25 2.25 6.1 119.9
S06 A1 Fixed Duration ‐ Long Pulse 0.42 45.25 3.43 26.25 2.25 94.5 4.0
S06 A1 Variable Duration ‐ 2 Pulse 0.42 45.25 3.43 26.25 2.25 7.5 158.8
S06 A1 Variable Duration ‐ 3 Pulse 0.42 45.25 3.43 26.25 2.25 6.3 233.4
S06 A1 Variable Duration ‐ 15 Pulse 0.42 45.25 3.43 26.25 2.25 5.1 932.4
S05 C3 Single Pulse 0.63 45.3 4.20 35.3 10.30 173.60 129.0
S05 C3 Latent Addition 0.34 35.3 3.30 26.3 2.10 50.00 21.2
S05 C3 Fixed Duration ‐ Short Pulse 0.42 45.3 3.43 26.3 2.25 48.10 37.7
S05 C3 Fixed Duration ‐ Long Pulse 0.32 18.6 4.18 16.8 15.25 7.60 18.6
S05 C3 Variable Duration ‐ 2 Pulse 0.17 49.1 3.10 28.6 2.52 73.40 345.1
S05 C3 Variable Duration ‐ 3 Pulse 0.41 46.1 3.47 26.4 2.28 94.70 3082.0
S05 C3 Variable Duration ‐ 15 Pulse 0.23 45.3 2.92 26.3 2.28 53.80 1436.7
S06 A1 Single Pulse 0.43 44.9 3.79 27.0 25.25 10.27 40.1
S06 A1 Latent Addition 0.41 45.3 3.40 26.3 2.10 10.52 39.5
S06 A1 Fixed Duration ‐ Short Pulse 0.43 43.4 3.55 26.3 4.37 6.27 10.2
S06 A1 Fixed Duration ‐ Long Pulse 0.42 45.3 3.55 36.3 2.25 94.50 3.5
S06 A1 Variable Duration ‐ 2 Pulse 0.42 45.3 3.43 26.3 2.25 7.50 158.8
S06 A1 Variable Duration ‐ 3 Pulse 0.44 48.0 3.53 29.6 3.30 6.33 170.8
S06 A1 Variable Duration ‐ 15 Pulse 0.13 45.3 3.80 15.4 0.50 573.63 683.4
Unconstrained Fit Average 0.37 43.00 3.55 26.63 5.50 86.44 441.19
Unconstrained Fit Range
0.13‐
0.63
18.6‐
49.1
2.92‐
4.20
15.4‐
36.3
0.5‐
25.25
6.33‐
173.6
3.5‐
3082.0
Predicted Total Error 12242.5
Unconstrained Total Error 6176.6
150
Table B6: Suprathreshold‐Constrained vs. Unconstrained
subject Electrode Experiment
τ
1
τ
2
β τ
3
ε θ
Error
S05 C4 Short Pulse (2X threshold) 0.42 45.91 0.83 26.45 8.73 0.848 672.9
S05 C4 Long Pulse (2X threshold) 0.42 45.91 0.83 26.45 8.73 0.180 220.2
S05 C4 Long Pulse (3X threshold) 0.42 45.91 0.83 26.45 8.73 0.236 208.8
S06 B2 Short Pulse (2X threshold) 0.42 45.91 0.83 26.45 8.73 1.485 4592.5
S06 B2 Long Pulse (2X threshold) 0.42 45.91 0.83 26.45 8.73 0.271 430.8
S06 B2 Long Pulse (3X threshold) 0.42 45.91 0.83 26.45 8.73 0.341 276.9
S05 C4 Short Pulse (2X threshold) 0.40 50.9 1.25 27.44 4.73 7.920 257.5
S05 C4 Long Pulse (2X threshold) 0.42 45.9 2.79 26.45 3.73 70.620 4.6
S05 C4 Long Pulse (3X threshold) 0.44 45.9 2.50 26.45 2.00 80.740 10.6
S06 B2 Short Pulse (2X threshold) 0.46 45.9 1.32 26.45 3.04 26.616 481.0
S06 B2 Long Pulse (2X threshold) 0.41 45.9 2.30 26.45 3.73 51.800 5.8
S06 B2 Long Pulse (3X threshold) 0.42 47.6 2.15 26.45 2.73 60.490 86.9
Unconstrained Fit Average 0.43 47.03 2.05 26.62 3.33 49.70 141.07
Unconstrained Fit Range
0.41‐
0.46
45.9‐
50.9
1.25‐
2.79
26.45‐
27.44
2.00‐
4.73
7.92‐
80.74
4.6‐
481.0
Predicted Total Error 6402.1
Unconstrained Total Error 846.4
Tables B5 & B6. Parameter values and errors for the constrained versus unconstrained model comparison using the F
test. Unconstrained values are in blue.
B8. Alternative models
We compared our model to a variety of other models, across a reduced data set
(1 electrode for each of the two subjects). In all cases, the cumulative error of the fits of
our constrained model were clearly lower than those of the unconstrained alternative
models, despite these alternative models having a larger number of free parameters.
These alternative models included a variety of simplified versions of the model, as well
as a slight variant of our model (a variety of other versions of our model were also
tested informally). The table below describes fit error across these various models.
We did not compare constrained versions of the simpler, alternative models to
our model. This is because fit errors were such that, even if constrained versions of
151
these alternative models showed the same cumulative fit error as the unconstrained
versions (i.e., showed the best possible performance), our model would still have
outperformed all these alternative models using an F‐test.
Model components Total
error
% increase in error
relative to the Full
model (A‐D)
Total Degrees
of Freedom
F
ratio
relative
to Full Model
Full model (A‐D) constrained 1031.8 11
A, D unconstrained 11140.7 980 18 NA
A, D constrained 11140.7 980 8 94.7
A, B, D unconstrained 5161 400 24 NA
A, B, D constrained 5161 400 10 116.1
A, C, D unconstrained 1484 41 30 NA
A, C, D constrained 1484 41 9 5.9
A, B, D with a nonlinearity added to B (i.e.,
Eq. 3 becomes
β
τ δ ε )) , 1 , ( * ) ( ( ) ( ) (
2 1 2
t t c t r t r − =
constrained
14965 1350 NA
A, B, D with a nonlinearity added to B (i.e.,
Eq. 3 becomes
β
τ δ ε )) , 1 , ( * ) ( ( ) ( ) (
2 1 2
t t c t r t r − =
unconstrained
14965 1350 NA*
Table B7. Comparison of Alternative models. Our original model can be thought of as consisting of four components:
(A) Integration and rectification (Eq. 2.1 & 2.2), (B) Desensitization (Eq. 2.3) (C) Power non‐linearity (Eq. 2.4), and (D)
Low pass filter (Eq. 2.5). We could not conduct an F‐test on the constrained version of the final model as it contained
the same number of Degrees of Freedom as the Full Model.
While there were some small deviations between the model and the data, these
deviations were relatively small compared to comparable models of psychophysical
performance for temporal light stimuli e.g. (Watson, 1986; Foley and Boynton, 1994).
There were some systematic deviations between the model and performance for long
pulses at suprathreshold levels of stimulation. It is perhaps not surprising that our
model did not generalize completely to suprathreshold levels of stimulation with long
pulses given that neurophysiological data on the effects of electrical stimulation
suggests that presynaptic cells will have a much larger influence on neuronal responses
152
to such stimuli (Fried et al., 2006). Models of greater complexity were capable of better
capturing the long pulse data, but led to "over‐fitting" across the full data set.
Table B8: Alternative Model Values
Subject Electrode Experiment
τ
1
τ
2
β τ
3
σ θ
error
S05 C3 Single Pulse 0.42 45.25 3.43 26.25 2.25 110.3 186.9
S05 C3 Fixed Duration ‐ Short Pulse 0.42 45.25 3.43 26.25 2.25 36.3 37.7
S05 C3 Fixed Duration ‐ Long Pulse 0.42 45.25 3.43 26.25 2.25 307.5 90.8
S06 A1 Single Pulse 0.42 45.25 3.43 26.25 2.25 10.0 592.5
S06 A1 Fixed Duration ‐ Short Pulse 0.42 45.25 3.43 26.25 2.25 6.1 119.9
S06 A1 Fixed Duration ‐ Long Pulse 0.42 45.25 3.43 26.25 2.25 94.5 4.0
S05 C3 Single Pulse 0.26 NA NA 0.26 NA 4.0 5152.3
S05 C3 Fixed Duration ‐ Short Pulse 0.32 NA NA 0.13 NA 4.0 2466.1
S05 C3 Fixed Duration ‐ Long Pulse 0.32 NA NA 0.32 NA 13.3 18.6
S06 A1 Single Pulse 0.48 NA NA 0.47 NA 0.6 2974.0
S06 A1 Fixed Duration ‐ Short Pulse 0.51 NA NA 0.39 NA 0.5 492.6
S06 A1 Fixed Duration ‐ Long Pulse 0.50 NA NA 0.49 NA 6.4 37.1
S05 C3 Single Pulse 0.43 73.5 NA 0.39 71.1 2.0 418.3
S05 C3 Fixed Duration ‐ Short Pulse 0.43 73.5 NA 0.39 78.7 1.0 3938.5
S05 C3 Fixed Duration ‐ Long Pulse 0.43 73.5 NA 0.41 67.0 2.0 18.6
S06 A1 Single Pulse 0.42 76.1 NA 0.35 88.1 0.9 113.3
S06 A1 Fixed Duration ‐ Short Pulse 0.48 73.5 NA 0.39 75.8 0.6 635.6
S06 A1 Fixed Duration ‐ Long Pulse 0.42 73.5 NA 0.39 55.3 2.2 37.1
S05 C3 Single Pulse 0.47 NA 2.61 11.7 NA 11.8 565.1
S05 C3 Fixed Duration ‐ Short Pulse 0.44 NA 2.84 11.7 NA 11.6 194.2
S05 C3 Fixed Duration ‐ Long Pulse 0.44 NA 2.90 9.4 NA 23.2 85.7
S06 A1 Single Pulse 0.40 NA 3.30 11.7 NA 18.9 365.3
S06 A1 Fixed Duration ‐ Short Pulse 0.48 NA 2.95 11.7 NA 10.5 209.4
S06 A1 Fixed Duration ‐ Long Pulse 0.51 NA 2.52 11.7 NA 18.9 34.0
S05 C3 Single Pulse 0.27 24.7 2.81 12.7 41.61 0.1 3332.8
S05 C3 Fixed Duration ‐ Short Pulse 0.29 24.6 2.89 12.7 41.60 0.1 5349.2
S05 C3 Fixed Duration ‐ Long Pulse 0.10 24.8 2.40 9.9 41.30 0.3 18.6
S06 A1 Single Pulse 0.23 24.8 4.19 12.8 41.60 0.1 2000.6
S06 A1 Fixed Duration ‐ Short Pulse 0.28 24.9 3.48 12.0 43.53 0.1 4215.3
S06 A1 Fixed Duration ‐ Long Pulse 0.32 24.8 2.10 13.0 42.00 0.1 48.9
Table B8. Parameters for Alternative models. The parameter values for the different fits of each of the
compared models.
153
Appendix C
Supplemental materials to Chapter 3
Fig. C1. (A) 0.225 ms phase‐shifted pulses across electrode pairs. Voltage recordings were
measured on two different electrodes that were separated by 800 μm. Electrode 1 is
shown in black, electrode 2 is shown in blue. The phase shift across electrode 1 and 2 was
set at 0.225 ms. While the amplitude of the pulses was not affected by the timing of pulses
from neighboring electrodes we did find a small overlap between the anodic phase of the
first pulse with the cathodic phase of the second pulse. B) 0.3 ms phase‐shifted pulses
across electrode pairs. Phase‐shifting the pulses by 0.3 ms removed any overlap of the
pulses. (C) The slight overlap of the 0.225 ms phase‐shift has no perceptual consequence.
S05 and S06 could not discriminate between 0.225 ms and 0.3 ms stimuli using the same‐
different task described in the main paper.
154
Appendix D
Supplementary materials to Chapter 4
D1. Example fits from brightness matching task
Fig. D1 – Example fits from brightness matching task. The data shown here are example
fits from a brightness matching task from subject S05. These data were collected on the
electrode pair of B2 (left column) and B3 (right column). See Fig. 1 for a schematic of the
electrode array. Each row shows the brightness matching fits for each delay (0.075, 0.375,
1.8, and 9.0 ms). These fits show the absolute current value inA. The values presented
in figures 3 and 4 in the manuscript have been normalized by the amplitude of the
amplitude of the single electrode (end‐point) measurements.
155
D2. Subjective equibrightness at different amplitudes
Fig. D2 – Subjective equibrightness at different amplitudes. Subjective equibrightness curves as a
function of phase‐shift (0, 0.075, 0.375, 1.8, and 9 ms) were generated at 3 different brightness
levels: threshold, 1.5X threshold, and 2‐3X threshold. 4, 8, and 5 electrode pairs were averaged for
each curve, respectively. Error bars represent standard error. The electrode distance for all pairs was
800 μm, as schematically depicted by the electrode array in the top left corner.
156
D3. Additional model fits for neighboring electrodes
Fig. D3 Normalized charge to maintain equibrightness as a function of phase‐shift between
pulses across 800 μm separated electrodes. The data points plotted for 0.075, 0.375, 1.8, and 9.0
ms phase‐shifts are represented by black, dark gray, medium gray, and light gray circles,
respectively. The model fits for each of the different phase‐shifts are solid, dash‐dotted, dashed,
and dotted lines of the same color. The beta (β) value was fixed at 3.5 and the i parameter was
allowed to vary for each phase‐shift. The average γ values are plotted for each phase‐shift, for
each subject in Fig. 4.3 in the manuscript. Note the increasing value of γ as a function of phase‐
shift.
157
D4. Additional model fits for 1600 and 2400 μm separated electrodes
Fig. D4 Normalized charge to maintain equibrightness as a function of phase‐shift between pulses
across 1600 and 2400 μm separated electrodes. The data points plotted for 0.075, 0.375, 1.8, and 9.0
ms phase‐shifts are represented by black, dark gray, medium gray, and light gray circles, respectively.
The model fits for each of the different phase‐shifts are solid, dash‐dotted, dashed, and dotted lines of
the same color. The beta (β) value was fixed at 3.5 and the i parameter was allowed to vary for each
phase‐shift. The average i values for 800, 1600, and 2400 μm separations are plotted for each phase‐
shift for subject S06 in Fig. 4.4C in the main text. Subject S05 was unavailable for this experiment.
Abstract (if available)
Abstract
Can functional vision be restored in blind human subjects using a microelectronic retinal prosthesis? The initial indications suggest that, yes, it is possible. However, the visual experience of these subjects is nothing like a digital scoreboard-like movie, with each electrode acting as an independent pixel. The work described here suggests that there are interactions between pulses and across electrodes, at the electrical, retinal, or even cortical level that influence the quality of the percept. In particular, this work addresses the question, "how does the percept change as a function of pulse timing on single and multiple electrodes"? The motivation for the work described here is that these interactions must be understood and predictable if we are to develop a functional tool for blind human patients.
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Asset Metadata
Creator
Horsager, Alan Matthew
(author)
Core Title
Prosthetic visual perception: retinal electrical stimulation in blind human patients
School
College of Letters, Arts and Sciences
Degree
Doctor of Philosophy
Degree Program
Neuroscience
Publication Date
04/29/2009
Defense Date
03/11/2009
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
blindness,computational model,medical device,OAI-PMH Harvest,retinal prosthesis,vision,visual psychophysics
Language
English
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Fine, Ione (
committee chair
), Sampath, Alapakkam P. (
committee chair
), Loeb, Gerald E. (
committee member
), Weiland, James D. (
committee member
)
Creator Email
horsager@gmail.com,horsager@usc.edu
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https://doi.org/10.25549/usctheses-m2151
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Tags
computational model
medical device
retinal prosthesis
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