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Viewing the picture we paint

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Viewing the picture we paint

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VIEWING THE PICTURE WE PAINT

by

Matthew R Behrend

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
(ELECTRICAL ENGINEERING)

May 2009

Copyright 2009 Matthew R Behrend
ii
Epigraph

For as far as I know, there is no proof whatever of the existence of an objective reality
apart from our senses, and I do not see why we should accept the outside world as such
solely by virtue of our senses.

- M.C. Escher
‘On Being A Graphic Artist’ in MC Escher 29 Master Prints, Abrams, New York

iii
Acknowledgements

I am grateful to my friends who have supported me through these recent years. Wynee
Hu, Scott Callaghan and Zeeshan Ahmed have often helped me make sense of things
during the learning process of getting the experiments to work and they have kept me
balanced. Ashish Ahuja has been a good friend throughout. My advisors made my
graduate studies a rewarding experience by proving materials and the belief that I could
succeed. Jim Weiland’s persistence in starting an imaging project and inviting me to
participate turned out to make all the difference in the course of my research. Cheryl
Craft has had a special influence on my career as I delve deeper into the molecular basis
of disease. I truly enjoyed working with Bob Chow, with whom I share a love for physics
and the tinkering mindset to build gadgets and repair lab equipment. I received valuable
technical training from AP Sampath, Chris Sekirnjak, EJ Chichilnisky’s lab, Bruce
Brown, and Jack Turman.

I am forever thankful to the Hertz Foundation for providing not merely funding, but
fostering a network among fellows that encouraged us to enjoy life and science together.

iv
Table of Contents

Epigraph ii

Acknowledgements iii

List of Tables vi

List of Figures vii

Abbreviations xi

Abstract xiii

Chapter 1. Introduction 1
1.1 Retinal degeneration and treatment 1
1.2 Visual prosthesis background 3
1.3 Overview of retinal anatomy 8
1.4 Electrophysiology of the retina 10
1.5 Electrical stimulation of neurons 12
1.6 Experiment design and aims 16

Chapter 2. Electrostatics and Electrodynamics of the Tissue Interface 20
2.1 Predictions of spatial resolution 21
2.2 Charging the double layer capacitor 26

Chapter 3. Experiment Design and Methods 47
3.1 Probing the interface from electrodes to tissue 48
3.2 Probing activity in excitable cells 54
3.3 Calcium imaging in neurons 58
3.4 Retrograde loading of calcium indicators into retinal ganglion cells 66

Chapter 4. Apparatus Design 88
4.1 Electrophysiology rig overview 88
4.2 Microscope 90
4.3 Current sources 92
4.4 Potentiostat 94
4.5 Gel Spinner 95
4.6 Retrograde loading tools 98
4.7 Fabrication of microelectrode arrays 98
4.8 Recording chamber 104
4.9 Interface board 106

v

Chapter 5. Data processing 107
5.1 Image data reduction 109
5.2 Response detection and threshold 110
5.3 Rejection of false responses 111
5.4 Measuring stimulation threshold 112
5.5 Plotting threshold maps 113

Chapter 6. A Conversation with the Retina 118
6.1 Correlation of calcium signals with electrical activity of the cell 118
6.2 Repeatability of the threshold measurement 119
6.3 Single electrode stimulation of somata and axons 121
6.4 Short pulses preferentially stimulate RGCs instead of the inner retina 127
6.5 Separation from the array raises threshold 129
6.6 Bipolar stimulation is advantageous only for small electrodes 132
6.7 Line pattern stimulation 136
6.8 Stimulation under pressure 138
6.9 Estimating the effective spatial resolution of prosthetic vision 140

Chapter 7. Conclusions and Future Work 145

References 152

vi
List of Tables

1. Retina model specifications 23

2. Error metrics for disk model 42

3. Measurement repeatability 119

4. Threshold change for antidromic stimulation after kynurenic acid 126

5. Change in threshold after kynurenic acid 127

6. Soma thresholds increase for phased bipolar stimulation 135

7. Compression thresholds 140

8. Effective diameter of responding area 141

9. Center positions of responding regions 142

10. Low threshold value 143

vii
List of Figures

1. The first chronic cortical prosthesis 4
2. Conceptual drawing of retinal prosthesis 4
3. Axon tracks in the human retina 7
4. Anatomy of the eye and the retina 8
5. Structure of the retina 9
6. Diversity of cell morphology in the retina 10
7. Glutamate immunoreactivity in the retina 11
8. Stimulation of a cell in a uniform electric field 12
9. Cable model of an axon 13
10. Depolarization and hyperpolarization of an axon 14
11. Strength-duration relationship for stimulation of a neuron 15
12. Layout of the retina finite element model 23
13. Finite element model predictions for relative threshold profiles 24
14. Model fit to experimental thresholds 25
15. Schematic of capacitive charge on an electrode 31
16. Schematic of model construction for capacitive charging 32
17. Mesh of the finite element model for the double layer 33
18. Dynamic current desnsity as a function of radial position 36
19. Current nonuniformity as a function of time 37
20. Accumulated charge density 38
21. Local time constants as a function of radial position 40
viii
22. Local time constants as a function of time 40
23. Fundus image of retinal stimulation 47
24. Literature review of threshold charge 50
25. Longitudinal versus transverse axonal stimulation 52
26. Agarose chemical structure 54
27. Machined barrel for the biolistic gun 65
28. Photo of the biolistic gun 66
29. Retrograde dye loading assembly 70
30. Density of labeled retinal ganglion cells 75
31. Double staining of ganglion cells with calcium indicator and tracer dyes 76
32. Correlation of calcium signal with spiking activity 77
33. Calcium signals were sensitive to TTX and cadmium 78
34. Threshold map of stimulated ganglion cells 80
35. Threshold map with a streak of responding cells 81
36. Panel of staining quality in rat and salamander 82
37. Whole mount image of salamander stained with calcium indicator 84
38. Diagram of the in vitro imaging setup 89
39. Photo of the electrophysiology rig 90
40. Fluorescence spectra of Oregon-Grenn-488 91
41. Fluorescence spectra of Alexafluor-594 91
42. Circuit schematic of a light flash detector 92
43. Circuit schematic of a voltage to current converter 93
ix
44. Schematics of voltage and current sense circuits 93
45. Printed circuit board layout of the 16-channel current source 94
46. Circuit schematic of a potentiostat for electroplating 95
47. Photo of the agarose gel spin coater 96
48. Circuit schematic of the motor control for the spinner 97
49. Mask layout for microelectrode arrays 100
50. Layout of the hexagonal close pack array 101
51. Layout of the quad electrode array 102
52. Layout of the spiral and small hexagonal grid array 103
53. Layout for the carrier circuit board for microelectrode arrays 104
54. Photo of the interface board and recording chamber 105
55. Photo of the interface board 106
56. Stimulation protocol for threshold measurements 109
57. Regions boundaries for fluorescence measurements 110
58. Response detection from fluorescence signals 111
59. Response latency histograms and subtraction of false responses 112
60. Stimulation threshold map 115
61. High resolution composite threshold map 117
62. Calcium signals are correlated with a long burst of spontaneous activity 118
63. Calcium signals correlated with long burst of evoked spikes 119
64. Repeatability of the threshold measurement 120
65. Threshold maps for single electrodes in contact with the retina 123
x
66. Thresholds for anodic first pulses 125
67. Kynurenic acid does not block axonal stimulation 126
68. Kynurenic acid raises threshold for long pulses 128
69. The center of the response shifts in the presence of kynurenic acid 129
70. Threshold maps for stimulation with a 30-µm spacer 130
71. Threshold maps for stimulation with a 50-µm spacer 131
72. Threshold maps for transverse bipolar stimulation 133
73. Bipolar stimulation with and without array separation 135
74. Line pattern stimulation 137
75. Threshold profile with compression of the retina 139
76. Size of the responding area with separation of the array 144
77. Optimal electrode array designs 151

xi
Abbreviations

APB - 2-amino-4-phosphonobutyric acid, selective blocker of metabotropic glutamate
receptors, blocks the on-pathway

APV -2-amino-5-phosphovaleric acid, a competitive NMDA receptor antagonist

CAD – computer aided drafting

CNQX – 6-cyano-7-nitroquinoxaline, a competitive AMPA/kinate receptor antagonist

DNA – deoxyribonucleic acid

INL – inner nuclear layer (contains cell bodies of dipolar cells, Müller cells, horizontal
cells, and amacrine cells)

IPL – inner plexiform layer

IS – inner segments (of the photoreceptors; contains photosensitive membrane disks)

LED – light emitting diode

MCS - Multichannel Systems, GmbH

MEA – microelectrode array

OAT – organic anion transporter

OGB-1 – Oregon Green-BAPTA-1, a fluorescence calcium indicator

ONL – outer nuclear layer (contains the cell bodies of photoreceptors)

OPL – outer plexiform layer

OS – outer segments (of the photoreceptors)

PVP – polyvinylpyrolidone, used as an adhesion promoter for biolistic particles

RGC – retinal ganglion cell

RMS – root mean square

RPE – retinal pigmented epithelium

xii
SD – standard deviation

SEM – standard error of the mean

SHG – second harmonic generation; a frequency doubling effect that reports
transmembrane potential in some voltage sensitive dyes.

TIFF – tagged image file format

TTX – tetrodotoxin, a sodium channel blocker

xiii
Abstract

The aim of this study is to provide guidelines for the design of a retinal prosthesis with
specific emphasis on spatial resolution. Optical recordings from retinal ganglion cells
(RGCs) using novel methods provide the first clear picture of how the retina sees
electrical stimuli. Analysis of the spatial properties of the response show that the site of
action potential initiation is not in the soma, but in the initial segment of the axon, ~ 40
µm from the soma. Furthermore, 60-µs pulses directly stimulate RGCs, while longer
pulses target inner retinal neurons. Short pulse widths have a more focal response area
than long pulses. The smallest response area was about 100 µm, even for electrodes as
small as 30 µm.

Separation of the electrode array from the retina by a saline gel increases the area of the
response and raises stimulation threshold. Spacers with thickness less than 25% of the
electrode diameter have little effect on the response size. Therefore, attachment of the
array in vivo should have a gap less than 25% of the electrode diameter in order to
preserve resolution.

Axonal stimulation remains a problem that threatens to severely limit the perception of
pattern stimulation. Recordings at 400−µs and 1000-µs pulse widths from distant
peripheral somata indicate that axons are stimulated at roughly 160% of the threshold for
local RGCs, but 60-µs pulses avoid axons to at least 200% of the local RGC threshold.
Data suggest a means to selectively stimulate RGCs proximal to the electrode at short
xiv
pulse widths. Bipolar configurations, directing electric field lines transverse to axon
bundles, avoided stimulation of those bundles, but could not avoid axons that pass over
the cathodic electrode, except for the smallest (10-µm) electrodes. Pulse width appears to
be the best means of control at the present time. The optimal array configurations are
either a grid of electrodes spaced by 100 µm, or a conformal array of 10-µm bipolar pairs
oriented with field lines transverse to the axon bundles. We can expect a resolution of 0.4
degrees of visual field corresponding to Snellen acuity of 20/480.
1

Chapter 1. Introduction

1.1 Retinal degeneration and treatment

Retinal degeneration is a group of diseases that results in the death of photoreceptors in
the retina. The loss of vision is gradual, spreading from the center or the periphery
depending upon the disease.

Based on the 2000 U.S. census data, it is estimated that age-related macular degeneration
(AMD) affects 1.75 million people over 40, and that by the year 2020 this population will
grow to 3 million people (Friedman et al., 2004; Klein et al., 1997). Of the two varieties
of AMD, the dry form (constituting about 90% of all cases) has no available therapy. Wet
AMD is associated with choroidal neovascularization, and causes rapid vision loss due to
the leakage and rupture of vessels near the macula (Elizabeth Rakoczy et al., 2006).
Lucentis, an anti-neovascularization drug (Genentech; (Rosenfeld et al., 2006)), can be
injected on a monthly basis to slow the progression of wet AMD.

Retinitis pigmentosa (RP) is a family of genetic disorders with a prevalence of 100,000 in
the United States and about 1.5 million worldwide (Research to Prevent Blindness).
Combined, AMD and RP are the leading causes of retinal blindness. More than 120 genes
causing various forms of RP have been identified (RetNet database;
http://www.sph.uth.tmc.edu/retnet/disease.htm), 53 of which are responsible for
nonsyndromic RP (Daiger et al., 2007). Transfer of a single therapeutic gene can
2
theoretically rescue function; >120 unique treatments are required. Gene therapy has
shown success in rapidly restoring vision in animal models of Leber congenital
amaurosis, by AAV2-mediated delivery of hRPE65 (Bennicelli et al., 2008), but is
limited to treating less than 1% of RP cases.

A broadly applicable gene therapy with great promise uses channelrhodopsin-2 (ChR2), a
bacterial cation channel that is photo-gated with blue light in the presence of the
endogenous chromophore, retinal (Boyden et al., 2005; Nagel et al., 2003).
Photosensitivity can be conferred upon ganglion cells or bipolar cells to circumvent lost
rods and cones. Visually evoked potentials in response to a high-intensity light flash were
recorded from homozygous rd1 mice that were intravitreally injected with an AAV2
vector carrying a cassette encoding ChR2 (Bi et al., 2006). Stable expression was
observed for at least 6 months. Most people are seropositive for AAV2, and the
prevalence of neutralizing antibodies is about 20 to 40% (Erles et al., 1999; Hildinger et
al., 2001; Moskalenko et al., 2000), thus, limiting the usefulness of AAV2. A number of
problems can plague viral vector approaches if the antigenic load is too high. More work
remains to be done in proving the safety in humans with respect to the immune response
to AAV vectors and the gene products.

3
When photoreceptors die, other cells follow in their wake to some extent. However, the
inner nuclear layer retains 80% of its nuclei and the ganglion cell layer retains 30% of its
nuclei in histology of postmortem human retinas in advanced stages of degeneration
(Santos et al., 1997; Stone et al., 1992). Electrical stimulation of these surviving neurons
may provide functional vision, but it will be critical to have control over which cells are
stimulated. Additionally, electrical stimulation appears to provide some protective effect
for retinal ganglion cells (Morimoto et al., 2002).

1.2 Visual prosthesis background

The first attempts to electrically stimulate the visual system targeted the primary visual
cortex (Foester, 1929), and evoked the perception of phosphenes similar to spots of light.
This portion of the brain (posterior pole of the occipital cortex) is accessible and has a
visuotopic mapping that corresponds to space in the visual field. Phosphenes are usually
white or yellow and vary in shape (Margalit et al., 2002). When it was observed that
corneal stimulation in blind patients could evoke phosphenes (Potts and Inoue, 1969),
interest was generated in a retinal prosthesis. Temporary implantation of an electrode
array in patients with end-stage RP could evoke distinct percepts from adjacent electrodes
(Humayun et al., 1999), corresponding to an acuity of 20/1000.

4

Figure 1. The first chronic cortical prosthesis. From Margalit, 2002.

Figure 2. Conceptual drawing of a retinal prosthesis with most electronics self contained within the eye.

A German group (Retina Implant, AG, Reutlingen, Germany) is producing a subretinal
implant with an active photodiode array (Gekeler et al., 2007). The device was safely
5
implanted in pig, but leaks in device encapsulation, which is supposed to protect it from
water, caused the photodiode array to fail when powered in vivo (ARVO 2008,
unpublished data). The primary advantage to using a photodiode array to gate stimulus
pulses to electrodes is that the cable to the device need only carry wires for power. The
array is easily scaled without the problem of routing hundreds of traces through a cable to
a separate pulse generator chip. Secondarily, the imager is on the retina, so gaze-tracking
hardware is unnecessary. Similarly, our group is working on an intraocular camera to this
end. If the imager is internal to the eye, then eye motion is properly integrated with image
motion.

Simulations of prosthetic vision in normally sighted subjects found that 256 pixels are
needed to read size 36 point font, corresponding to a visual acuity of 20/600 (Hayes et al.,
2003). At 16 pixels, subjects could distinguish between some object forms, but
functionality was limited. The grid arrangement of the electrodes may influence visual
acuity, but the difference is likely to be small. Hexagonal close pack had a 4%
improvement in acuity versus a square grid (Chen et al., 2005) in simulated artificial
vision with normally sighted subjects. These simulations are highly idealized and serve as
an estimate of the best-case limits of acuity.

Because the information in artificial images is so crude (few pixels and few brightness
levels), we rely upon some plasticity in the brain to interpret the artificial images. In
rhesus monkey (Bradley et al., 2005), an implant of 150 microelectrodes in primary
6
visual cortex (V1) initially produced receptive fields 2.5 times larger than visual
receptive fields, but with training over several months the electrically evoked receptive
fields approached unity. One might also ask if a person blind from birth would be a
viable candidate for a retinal prosthesis. The developmental window for visual processing
would have passed without training by natural vision. In one case of severe congenital
cataracts (Ostrovsky et al., 2006), a woman was able to perform well on face recognition
tasks twenty years following removal of the blinding cataracts at age 12. However,
spatial resolution was degraded 30-fold by long term deprivation of visual information in
a man whose blindness was later reversed by corneal transplant (Fine et al., 2003).

On an array of identical electrodes, the ones with higher impedance (de Balthasar et al.,
2008; Mahadevappa et al., 2005) had lower perceptual thresholds. For this reason I
studied separation as a parameter affecting threshold and response area. Impedance
increases with proximity of the electrode to the retina.

The orientation of a line of electrodes relative to the path of RGC axons (Fig 3) was
found to affect the percept shape, changing from focal spots to an oblong spot (Rizzo et
al., 2003). The size of percepts measured in humans from that study was 2.25° to 4.5°
using 400-µm electrodes on an array. Percept size and shape are probably affected by the
stimulation of axons passing over the electrode that originate from distant RGCs. The
brain cannot tell from where the action potential initiated, whether from the soma or a
7
point along the axon. Stimulation of axon bundles could lead to a characteristic streak
percept.

Figure 3. Left: Axon tracks from RGCs in the nerve fiber layer of the human retina. RGC axons converge
at the optic disk (hole). A small pole of axon origination, next to the horizontal raphe, lies at the fovea.
From (Oyster, 1999). Right: Fundus image of the human retina. From webvision.med.utah.edu.

A 16-electrode device implanted in blind RP patients significantly improved their ability
to detect objects, count them, and discriminate between object forms (Yanai et al., 2007).
Although subjects could discriminate between electrodes in paired-pulse testing, their
performance with single-electrode activation was not significantly different from multi-
electrode stimulation at most tasks, with the aid of head scanning. If sixteen electrodes
are not better than a single electrode, it underscores the importance of investigating
percepts when multiple electrodes are activated.

8
1.3 Overview of retinal anatomy

The retina is a thin, layered tissue lining the interior of the eye. Light passes through all
layers in the retina before reaching the photoreceptors on the rear surface of the retina
(Fig 4).

Figure 4. Anatomy of the eye and the retina. From webvision.med.utah.edu.

On the photoreceptor side, the retinal pigmented epithelium (RPE) interdigitates with
photoreceptor outer segments to consume used disks and provide nutrients. The retina is
the most metabolically active tissue in the body, largely due to the high turnover of
phototransduction machinery.

Of the five major layers in the retina, three contain cell bodies and two are plexiform
layers containing synaptic connections. The outer nuclear layer contains the cell bodies of
9
photoreceptors. The outer plexiform layer contains synapses from rod and cone terminals
to bipolar cells and horizontal cells. In the inner nuclear layer, somata reside for
horizontal cells, bipolar cells, and amacrine cells. The inner plexiform layer is the thicker
of the two plexiform layers. This layer is subdivided into lamina for the on-pathway, the
off-pathway, and other specialized visual information such as directionality.

Retinal ganglion cells form their own layer, but half of the cells here are displaced
amacrine cells. All RGCs are spiking neurons, while other cell type in the retina are
graded potential neurons. However, some amacrine cells do spike.

Figure 5. Retina in cross section. From webvision.med.utah.edu.

10
Within the classes of retinal cells (photoreceptors, horizontal cells, bipolar cells, amacrine
cells, RGCs, and glia) there is a great diversity of types that are distinct in morphology
and function (Masland, 2001).

Figure 6. Diversity of cell morphology in each retinal cell type. From (Masland, 2001).

1.4 Electrophysiology of the retina

The excitatory neurotransmitter, glutamate, mediates essentially all vertical signal
transmission from photoreceptors, to bipolar cells, to retinal ganglion cells (RGCs). Since
11
photoreceptors are inverting (reduce glutamate release in the presence of light), the on-
pathways employs an inverting synapse to the on-bipolar cell. On-bipolar cells express
metabotropic glutamate receptors (mGluR6) that hyperpolarize the cell in response to
glutamate. The off-bipolar cells express ionotropic glutamate receptors that depolarize
the cell in response to glutamate. The on-pathway can be selectively blocked with APB,
which antagonizes mGluR6. Other blockers of glutamatergic transmission (Kynurenic
acid, CNQX) are effective against various ionotropic receptors. To pharmacologically
isolate RGCs from the retinal network, kynurenic acid (a broad spectrum glutamate
antagonist that acts on the glycine site of NMDA receptors) was applied in some
experiments.

Figure 7. From webvision.med.utah.edu.

Bipolar cells axon terminals contain receptors for the inhibitor neurotransmitters GABA
and glycine, to receive input from amacrine cells.

12
1.5 Electrical stimulation of neurons

Neurons are electrically excitable cells, meaning they posses voltage-gated ion channels
that are activated during events that perturb the resting membrane potential. This
differentiates them from passive cells, which also have capacitive membranes and a
resting potential of about -60 mV (inside of the cell is more negative than the outside).
Neurons can be stimulated to spike by applying a current source near the cell. The second
spatial derivative of extracellular potential along the surface of the cell is the driving
force for altering transmembrane potential. On the macro scale, it is current density that
scales the threshold for stimulation.

For a spherical cell in the presence of a uniform electric field, the transmembrane voltage
is given by (Horch and Dhillon, 2004),

!
V
m
=
3
2
E"rcos# (1)

Figure 8. Stimulation of a cell in a uniform electric field. The cell is hyperpolarized on the left side and
depolarized on the right side. From (Horch and Dhillon, 2004).

13
The spherical cell solution is valid for cases in which the membrane is much less
conducting than the internal medium. The time scale where the membrane capacitance
becomes as conductive as physiological saline is on the order of 100 ns. Therefore, the
model above is applicable for all relevant stimuli, which are typically greater than 50 µs.

Considering the case of axon stimulation, the axon can be broken in compartments and
modeled as a transmission line (Fig 9). Solving the node equations toward the limit of
infinitely small compartments yields (3) the relationship of transmembrane potential, V
m
,
to the propagation length constant, λ, and the potential on the extracellular surface of the
axon, V
e
. The length constant is,

!
" =
R
m
R
i
. (2)

Figure 9. Cable model of an axon (discretization of the distributed network). The passive axon model
contains the membrane conductance, membrane capacitance, and the internal volume conductance. From
(Horch and Dhillon, 2004).

14
(3)
Simplifying for short pulses and assuming that the internal potential is initially uniform,
the transmembrane voltage is approximately,
(4)

Once again, the driving force for membrane perturbation is the second derivative of
potential. If we consider a point source electrode near an axon, it can be shown that a
region of depolarization exists beneath the electrode with flanking regions of
hyperpolarization. It is the strong central depolarization that opens voltage-gated sodium
channels to trigger an action potential.

Figure 10. Stimulation of an axon with a cathodic electrode depolarizes the axon near the tip of the
electrode and slightly hyperpolarizes the axon at distant position. The spike will initiate beneath the
electrode. From (Ranck 1975).

15
Assuming a passive model for the cell (axon or soma) membrane, the relationship of
pulse width to threshold current is given by the strength-duration equation,

!
I
s,th
=
I
rh
1"e
"T /#m
(5)

For a cell membrane with transmembrane resistance and capacitance giving a time
constant τ
m
there are two parameters that characterize the response of the neuron:
rheobase and chronaxie. The rheobase current is the minimum amplitude for a very long
pulse to stimulate the neuron. Chronaxie is the minimum pulse width at which twice the
rheobase current will stimulate the neuron. The strength-duration curve is a plot of
threshold values, widely used in psychophysics and single unit recording. It is important
to bear in mind that the neuron will also be stimulated with a longer pulse or a larger
current.

Figure 11. The strength-duration relationship for electrical stimulation of a neuron. Threshold
asymptotically approaches rheobase current for long pulses. More current, but less charge is used for short
pulses. From (Horch and Dhillon, 2004).
16

1.6 Experiment design and aims

In our phase I clinical trials of the Argus I and the Argus II retinal prostheses, end point
measures included stimulation threshold and visual discrimination tasks (e.g. identifying
a plate or knife or cup in a high contrast environment, or reporting direction of motion).
Only recently have we begun to ask the question to patients, what does an electrically-
evoked percept look like (Nanduri et al., 2008)? My work systematically measures
percepts in a controlled in vitro model of the retinal prosthesis. Both lines of work
indicate that electrodes are not selectively stimulating cells in their vicinity, and that
stimulation of axon bundles may be determining the limits to spatial resolution of the
prosthesis.

I originally set out to understand the spatial extents of RGC stimulation as a function of
electrode size and separation from the epiretinal surface. Immediately, the data revealed
that bundles of RGC axons passing over the electrode also responded. Stimulation of
axon bundles presents a significant problem to the faithful representation of visual
information to the retina: a streak would be seen instead of a focal spot-like phosphene
over the electrode. Based on the physiology of axonal stimulation, I hypothesized that
axons could be avoided by directing field lines perpendicular to the nerve fiber layer.
Several stimulation configurations were tested in an attempt to selectively stimulate RGC
somata. In the case of bipolar stimulation, the location of stimulated axons could be
17
moved, but axon bundles were still stimulated at amplitudes near the soma threshold over
the cathodic electrode.

A finite element model was constructed to aid the design of future experiments and to
design new electrodes that could be more effective in directing field lines to avoid axon
bundle stimulation. The model was fit to empirical data from the isolated salamander
retina. Two important pieces of information can be extracted from the model. First, the
threshold to stimulate a retinal ganglion cell was determined in terms of absolute current
density, so any type of electrode and interface may be evaluated. Second, the model
provides a prediction for the size of a phosphene. The profile of current density away
from the electrode reveals the point at which current density drops below some critical
value to stimulate neurons.

Several interesting phenomena were observed that improve our understanding of how
electrodes interact with the retina. The site of action potential initiation has been
suspected to be at the axon hillock or at the initial segment of the axon. My data are
consistent with the initial segment hypothesis, in that the central point of stimulated
somata lies consistently about 40 µm toward the peripheral side of the electrode.
Stimulation pulse width also affected which elements in the retina were the target of
stimulation, with short pulses driving the RGCs directly, and long pulses stimulating the
bipolar cells, which synaptically drive the RGCs. Over the electrode surface, the
threshold was somewhat uniform, in agreement with my finite element model.
18
Stimulation thresholds do not indicate that current density is concentrated on the edge of
the electrode, as has been expected by many investigators from naïve assumptions of
stimulation in isotropic medium. My finite element modeling work has explained that
current density is quite uniform as a consequence of a high conductivity saline layer and
a low conductivity retina.

To find an engineering solution to the problem of axon bundle stimulation the following
specific aims were formulated to test the hypothesis that redirection of field lines could
alter the relative threshold for RGC somata and axon bundles. A satisfactory solution has
not yet emerged to control field lines, but pulse width may provide selectivity for somata.

1. Separate the retina from the electrode array by a saline agarose gel to mimic
the in vivo conditions and then map the stimulation thresholds. Surgical
implantation of the stimulating array leaves a gap of 0 to 200 µm between the
electrodes and the retina, although not a uniform gap over that surface. With
separation, stimulation current is broadly spread over a larger area of retina since
the vitreous saline is about 20-fold more conductive than the retina. The spreading
of current may permit field lines to enter the retina more perpendicular to its
surface.

2. Selectively stimulate RGC somas over axons by using a combination of
anodic block and bipolar stimulation. Our preliminary experiments found a
19
statistically significant difference between the thresholds to stimulate RGC somas
and their axon bundles from a single electrode. However, it was too small to be
physiologically relevant. Bipolar stimulation can more than double the amount of
current required to stimulate an axon if the current passes perpendicular to the
path of the axon. It may also be possible to block stimulation of axons passing
directly over the electrodes by an anodic prepulse to hyperpolarize the axon.

3. Evaluate mechanical pressure as a modulator of threshold. Data from
implanted blind patients show a correlation between low thresholds and array-to-
retina proximity, even to the point of compression. Mechanical pressure of the
array against the retina may reduce thresholds lower than for a simple apposition
of the array on the retinal surface. Weight was applied onto the retina to press it
firmly against the electrode array. Threshold profile for a 200-µm electrode will
be compared to the baseline of minimal pressure.

20
Chapter 2. Electrostatics and Electrodynamics of the Tissue Interface

Two finite-element modeling tools were built to study the interaction of electrodes with
retinal tissue. The first is a layered model of the retina in near contact with an electrode
via a thin layer of saline. The retina is more resistive than the saline interface layer and
thus the current density entering the retina is influenced by the electrode diameter and
saline thickness. The second model considers the dynamics of charge accumulation on
the electrode surface from the electrochemical perspective. It can be used to design
electrodes for high capacitive charge transfer. This dynamic model can also be combined
with the retina model to create new stimulation protocols where the pulse shape affects
the spatial properties of stimulation in retinal ganglion cells.

The electrostatic retina model was constructed for the purpose of predicting spatial
resolution limits of electrical stimulation. To this end the modeling results were fit to
experimental data from the salamander retina so that absolute magnitudes of stimulation
can be predicted under any variety of modeling conditions. The model’s prediction of
percept size is in agreement with the experimentally determined responses for long pulse
widths. At short pulse widths, the responding region was smaller than the model
prediction. At any pulse width the model is consistent with the experimental observation
that adding a saline spacer increases the size of the responding region by only a small
amount.

21
Experimentally, short pulses had a smaller responding region and these were found to
stimulate RGC directly. Longer pulses preferentially stimulate the inner retina (bipolar
cells), and these had a larger responding region. Therefore, the cutoff amplitude that
defines the spatial extents of a percept may be different for RGCs and bipolar cells. It
may be possible that current density in one direction is more effective for stimulation
than in another direction for RGCs, but that absolute current density stimulates bipolar
cells without preference for directionality. The model will be further investigated to fit it
to experimental data with consideration for separate spatial components of the current
density.

2.1 Predictions of spatial resolution

Relative stimulation thresholds were predicted from electrostatic analysis of an electrode
interfaced to a multilayered retina model. Electrode sizes were 10-, 60-, and 200-µm in
diameter. For each electrode, the model was solved for a range of vitreous gel spacers
under the retina, [0.0001 1 2 3 5 7 10 15 20 30 50 100 200] µm. Stimulation of a
spherical cell in the ganglion cell layer is assumed, where the tissue structure is
considered homogeneous within each layer. Areas in which current density is
concentrated require less electrode current to stimulate a cell. Therefore, threshold was
taken to be the inverse of the current density magnitude in the midsection of the ganglion
cell layer. Normalizing to the threshold of a cell above the center of the electrode with 10
µm of vitreous gel spacer gave the relative thresholds.
22

The model was constructed in 2 dimensions with axial symmetry about the line passing
normal to the center of the electrode. A metal electrode with a constant current boundary
condition of 1 µA was placed at the origin near the ganglion cells. The apical surface of
the retina (photoreceptor side) was held at zero potential. All other perimeter boundaries
were set to electrical insulation. A layer of vitreous gel (1% hyaluronic acid in saline)
with 10 µm thickness separated the electrode from the epiretinal surface. The thickness of
this layer was controlled by using anisotropic conductance to represent varying thickness
of the isotropic medium. For example, without re-meshing the model (Fig 12), the saline
thickness could be doubled by halving its conductivity in the z-direction and doubling its
conductivity in the r-direction. The model extended 5 mm in the radial direction.
Doubling the radial extents changed the value of current density in the ganglion cell layer
over the electrode by less than 12%, for the worst-case sensitivity scenario of a 200-µm
vitreous gel.

The finite element model solver COMSOL Multiphysics, ver 3.3 was used to solve the
system of equations. The parametric solver mode ran the simulation for the range of gel
thicknesses. Each individual run was solved by the linear direct solver SPOOLES.

Conductivities of retinal layers are given in (Karwoski et al., 1985) for the frog retina.
Assuming that the density of cell bodies in perikarya layers and the density of processes
23
in the plexiform layers are the same for other species, these conductivity values can be
used.

Table 1. Retina model specifications

Layer thickness (µm) conductivity (S/m)
IS/OS 40 0.077
ONL 75 0.017
OPL 5 0.056
INL 40 0.017
IPL 45 0.056
RGC 20 0.014
total 225 µm
ringers saline 1.28

Figure 12. Layout of the retina model to scale.
/Electrode Modeling/FEMLAB Simulations/spacers/

24

Figure 13. Electrostatic model predictions of relative threshold profiles for an electrode near the epiretinal
surface. Left column: Threshold profiles for a range of vitreous gel thickness. The x-axis is the lateral
distance of a ganglion cell from the electrode center. Each trace is the relative threshold profile for a
different vitreous gel thickness (trace labels). Red segments of the curve mark the spatial extents of
stimulated cells, where threshold has increased by 50%. Right column: Threshold increases as the vitreous
gel thickness is increased. Model Prediction of relative threshold (points), second order fit to model (blue
trace), linear fit to model (dark red short trace). Note differing scales.
/Electrode Modeling/FEMLAB Simulations/spacers/

10-µm electrode
60-µm electrode
200-µm electrode
25
The model was fit to thresholds measured from the salamander retina (section 6), to
provide a prediction of absolute stimulation thresholds in the isolated salamander retina.
These thresholds can be used as a rough guide to stimulation in other species. This
model, and corresponding measurements, takes into account the size of the electrode on a
planar array and the gap from the array to the retina. The absolute threshold was
calculated from the model as k/J_total, where k is the scaling coefficient (A/m
2
) and
J_total is the current density magnitude in the ganglion cell layer normalized to the
electrode current. The value of k was 9.6 pA/m
2
.

Figure 14. Stimulation thresholds predicted by finite element modeling (traces) and measured in the
isolated salamander retina (points, 400-µs pulse width). Electrode size 200 µm (blue squares), 60 µm (red
circles), 10 µm (green triangle).
/Electrode Modeling/FEMLAB Simulations/spacers/

26
2.2 Charging the double layer capacitor

Charging dynamics on the electrode surface are relevant in two aspects to the prosthesis.
First, the distribution of charge determines the polarization of the double layer, which
affects corrosion of the electrode and hydrolysis. Second, it could affect the pattern of
cells that are stimulated in close proximity to the electrode. The second case is not very
significant except for large electrodes > 200 µm in direct contact with the retina. The
capacitive charge double layer was studied under transient conditions to understand how
current is distributed in contact with isotropic medium. The metal electrode is one plate
of the capacitor with electrons as charge carriers, separated by a monolayer of water from
the distributed second plate of saline, having ionic charge carriers. The study should be
extended to include electrochemical reactions and diffusion of ions, with the electrode in
contact with the isolated retina model in order to apply the results to the design of new
electrodes. The following article (Behrend et al., 2008) is the basis for this future work.

ABSTRACT

With applied potential, the current distribution at the surface of a disk electrode is
spatially nonuniform and time dependent. This distribution is important to control in
applications that desire a uniform current density profile or minimal corrosion. We
examine the current density profile of a capacitive disk electrode subjected to a voltage-
step using finite element analysis software to solve the system of partial differential
27
equations. In detailed analyses we show quantitatively that the current density shifts from
peripheral enhancement to near-uniformity following ½ of the lumped element time
constant. As charging continues, the current density is slightly enhanced in the central
region. We present curves for the evolution of local “time constants” as time progresses
and calculate their effective values. The model is intended to be the basis of future work
to control the corrosion profile of biologically implantable electrodes of arbitrary shape.
Data suggest a means to control corrosion by retarding the edges of a stimulus pulse.
Additionally, smaller electrodes may be more effective in fully utilizing surface area for
charge transfer due to their shorter time constants.

BACKGROUND

Electrostatic solutions for current density of a disk electrode system have established that
the electric field (and thus current density) is sharply enhanced at the periphery of the
electrode immediately following application of a potential step (Kim et al., 1986;
Ksienski, 1992; Newman, 1966; Overmyer et al., 1979; Rubinstein et al., 1987; Wiley
and Webster, 1982). These assume no capacitive layer in series with the resistive liquid
medium. In reality, capacitance of the electrochemical double-layer profoundly affects
the current density on the time scale of the electrode time constant. The disk electrode
time constant represents charging behavior of the electrode on a macro scale, i.e. a
lumped element model consisting of a single capacitor and single resistor in series. The
28
potential of the double-layer is necessarily assumed uniform, expressed by the
exponential decay function
) 1 ( ) (
/! t
e E t V
"
" # = (6)

where V(t) is the potential of the double-layer at time t, E ! is the applied step potential to
the uncharged network, and τ is the charging time constant. The total current I(t) into the
electrode is similarly,
! /
) (
t
s
e
R
E
t I
"
#
= . (7)
Access resistance (of the aqueous medium) to an inlaid disk of radius a in medium of
conductivity κ is given as (Newman, 1966),
a
R
s
! 4
1
= (8)
and the total capacitance of the double-layer is,
2
a C ! " = (9)
where γ is the capacitance per unit area. The time constant τ is given by the product R
s
⋅C.
This RC circuit model is useful for designing electronic circuits connected to electrodes
but, ignores spatial distribution of current. Closed-form analytical methods (Newman,
1966; Wiley and Webster, 1982), analytical-numerical methods (Ksienski, 1992;
Rubinstein et al., 1987), and finite element analysis (Hung et al., 2003, 2005), have been
applied to solving Maxwell’s equations for the case of a disk electrode contacting
resistive medium. These electrostatic models predict current density sharply enhanced at
the periphery. From this primary current distribution the initial charging rate of the
29
double layer (indicated by local time constant) can be calculated (Oldham, 2004) as a
function of radial position on the disk. However it is expected that nonuniform charging
of the electrochemical double-layer will cause the current density profile to shift as time
elapses, thus altering the overall and the local “time constants.” For this reason, the
concept of a charging time constant does not apply here in a strict sense; it is a function
of time. We will define and plot the local time constants to indicate how rapidly the
current density is changing at any time and position on the electrode surface.

Two different approaches have been taken previously to model the electrochemical
double-layer in the time domain. Both involved numerical solvers after translating the
physical system to an equivalent electrical circuit. Numerical calculations by Hung (Hung
et al., 2003, 2005) simulated an unconventional structure with a double layer and
Faradaic processes. These predicted that current nonuniformity at the edge of an
electrode diminishes with time concurrently with a shift to tangential current near the
charged surface. The model had very low spatial resolution and the presentation of results
was largely qualitative. Hung’s system of the electrode in saline medium was broken up
into finite elements of resistors and capacitors by a C++ program and exported as a
SPICE circuit netlist. HSPICE (Synopsis Inc., Mountain View, CA) circuit simulation
software takes the netlist and solves the node voltage equations for the resistor-capacitor
network representing the physical system. Another approach by Myland (Myland and
Oldham, 2005) solved the classical disk electrode beneath an infinite hemisphere of
conductive medium using somewhat similar methods. The model was constructed in
30
oblate spheroidal coordinates to the advantage of reducing the electrostatic equations to a
more approachable form and reducing computational demands. While this change in
coordinate system provides a convenient analytical solution at time t=0, it still requires
numerical techniques for time greater than zero. As the double-layer charges electric field
lines bend away from the zeta unit vector of oblate spheroidal coordinates and do not
yield a closed form solution. Thus, the geometry was broken up into a network of
discrete resistors and capacitors, and subsequently solved for node voltages using a
numerical solver.

We take the approach of finite element analysis using the partial differential equation
solver COMSOL Multiphysics ver. 3.2 (COMSOL, Burlington, MA) to overcome the
following limitations in the above methods of Hung and Myland. Modeling with HSPICE
is confined to electric circuit elements without the diffusion of charge carriers in the
electrolyte. Alternatively, changing coordinate systems (e.g. oblate spheroidal) constrains
the electrode structure to a small set of stereotype geometries. Either approach is a
complicated two-stage process to model the electrode. However, finite element analysis
can mesh arbitrary structures and solve any system of equations including
reduction/oxidation and diffusion. Here we provide a thorough treatment of capacitive
charging dynamics as a building block for future models incorporating multiple physical
processes.

31

Figure 15. Capacitance is distributed in the electrochemical double-layer with each incremental capacitor
free to hold a unique potential, φ, on its aqueous terminal. Current density J(r,t) (arrows) at the surface is
shown broken into orthogonal components r ˆ and z ˆ for a point in time greater than zero (edge
enhancement is diminished). Not to scale.

The double layer is not a typical parallel plate capacitor. On the metal side of the
interface the equipotential surface constitutes a “capacitor plate,” however, on the
aqueous side of the interface there is no metal to force an equipotential condition. Our
model is for position-dependent values of electric potential on the aqueous side of the
double layer. A direct consequence of this physical arrangement (Fig. 15) is that
components of the current may exist tangential as well as normal to the surface of the
interface.

FINITE ELEMENT MODEL SYSTEM
A. Geometry
The disk electrode model (Fig. 16) is constructed in cylindrical coordinates, reduced to
two dimensions by the axis of symmetry normal to the disk at its center. A flat metal disk
of radius a is inlaid with an insulating basal surface, above which is located a
hemispherical region of radius 15a and conductivity κ. The potential of the disk is
stepped from 0 to ΔE at time t=0, while the counter electrode positioned effectively at
infinity is held at zero-potential (ground). All data presented are normalized to the
32
appropriate system parameters of radius a, applied potential ΔE, conductivity of the
aqueous medium κ, and capacitance per unit area of the double-layer γ.

Figure 16. The metal (perfectly conducting) disk electrode of radius a, is centrally positioned beneath the
base of a hemispherical region of resistive medium. The equipotential boundary and remaining series
resistance replicate an infinitely large volume in the half space above the electrode.

Access resistance is broken into two portions: distributed and lumped. The distributed
domain extends from the electrode surface to some chosen limit where equipotential lines
are approximately hemispherical. Beyond this radius any hemispherical surface is
assumed equipotential; the medium from here to infinity amounts to a single resistive
element to ground. For example, if one assumes an equipotential hemisphere of radius
11.6a, the error in electric field magnitude over the surface is +/- 0.19% of its mean
magnitude, as follows from analysis in oblate spheroidal coordinates (Myland and
Oldham, 2005), under electrostatic conditions. Our model extents are 15 times the disk
radius, yielding an error of +/- 0.11% in electric field magnitude on this surface. The
remaining lumped series resistance is found by the formula for two concentric
hemispheres,
!
!
"
#
$
$
%
&
' =
max min
1 1
2
1
r r
R
rem
()
. (10)
33
For our system, r
min
is 15a and r
max
is infinity, giving the remaining resistance R
rem
=
1/(30πκa).
B. Mesh Element Design
Mesh element size is constrained to a/30,000 on the disk edge point, as described in the
discussion, with the intention of accurately resolving the radial position 0.999a. Mesh
elements (Fig. 17) are expanded toward the disk center and away from the disk edge by a
growth factor of 1.1, meaning that the longest edge of adjacent elements may not differ in
length by more than this factor. The graded mesh maintains spatial resolution while
minimizing the degrees of freedom in the system.

Figure 17. Display of the graded mesh density. Inset: close-up of the disk edge point, where the mesh is
constrained to a minimum size.

C. System of Equations and Boundary Conditions
In the resistive medium domain of the model, Laplace’s equation is applied in cylindrical
coordinates (11).
0 ) , , (
0
= ! " !
> z
t z r # $ (11)
Current density is given by,
) , , ( ) , , ( t z r t z r J ! "# =
v
. (12)
34
At the insulating basal surface no current crosses the interface, thus
0 ) , ( ˆ
, 0
= !
> = a r z
t r J n
v
(13)
where n ˆ is the local unit vector normal to the surface pointing outward from the solid
region and J
v
is the current density vector. The hemispherical boundary of radius 15a
defines the extents of model space. As discussed, this hemisphere constitutes an
equipotential surface. The value of its potential φ given by Ohm’s law is
rem
a z r
R t I t z r ) ( ) , , (
15
2 2
=
= +
! (14)
where R
rem
is the remaining resistance to the remote ground and I(t) is the total current
crossing the hemispherical boundary,
dS t z r J n t I
a z r ! = +
" =
15
2 2
) , , ( ˆ ) (
v
. (15)
Assuming an infinitely thin electrode-electrolyte interface, current passes through the
capacitive double-layer with a current density such that,
( )
metal
a r z
a r z
t r
t
t r J n ! ! " #
$
$
= %
& =
& =
, 0
, 0
) , ( ) , ( ˆ
v
. (16)
Since
metal
! is held constant at ΔE for time t>0, this reduces to the nonuniform boundary,
a r z
a r z
t r
t
t r J n
! =
! =
"
"
= #
, 0
, 0
) , ( ) , ( ˆ $ %
v
. (17)
Initial conditions are found by solving the system at time t=0
+
, at which point the
potential ΔE is applied to the metal disk but no charge has accumulated on the aqueous
side of the double-layer. Potential is equal on both sides of the interface and the boundary
condition for the disk surface becomes
E r
t a r z
! =
= " = 0 , , 0
) ( # . (18)
35
The solution for this initial boundary condition is saved as a data file containing the
electric potential at every mesh node. These data are enforced as the initial value set in
the time-dependent system with a capacitive boundary at the disk. Conditioning the
system of equations in this manner ensures proper convergence.
D. Solving the System
Time steps are chosen based on the spatial resolution desired at the disk edge, where the
initial time constant (22) at r=0.999a is 0.09τ. Increments in time are about 1/30
th
or less
of the smallest local time constant. The solver records time steps from 0 to τ/3 in
increments of τ/300 and from τ/3 to 3τ in increments of τ/30, whereas the computer is
free to take smaller internal time steps without outputting the data. At each time step the
system of equations (11)-(15), (17) is solved using the direct solver UMFPACK.
COMSOL Multiphysics ver. 3.2 is run on a computer with AMD Athlon™ 64X2 4400+
dual processor, 2 GB RAM, and 200 GB hard disk. Node point data is exported via text
file to Matlab 7.0 (The MathWorks; Natick, MA) for postprocessing.
E. Electrode Size
For generality, the data are presented in terms of dimensionless parameters, e.g. time /R
s
C
and radius /a. The validity of this normalization is explicit at t=0 in (22) where τ(r) /τ is a
function of r/a, and in (23) where J
z
(r) /(ΔE /R
s
πa
2
) is a function of r/a, regardless of
electrode size, a. The same normalizations were used for time greater than zero,
implicitly in the model construction of Myland (Myland and Oldham, 2005). To verify
that current density profiles and local time constants can be expressed as functions of r/a
and t/τ, our model was reevaluated for the three following cases: increase γ tenfold,
36
increase a tenfold, increase both κ and a tenfold. The values of τ and disk radius are thus
altered independently and concomitantly in this test. All normalized data plots are found
to be identical, for all time, to those obtained without increasing the above parameters.

RESULTS
A. Charge and Current Profiles

Figure 18. Normalized current density normal to the disk surface versus radial position for several time
points 0.15τ to 3τ.

Current density normal to the disk at its surface, J
z
(r), has a time-varying profile, in
which, the local maximum moves inward to the center of the disk (Fig. 18) as time
progresses. After a time of about ½ τ, current density near the perimeter is less than the
spatial average. Looking closer at current distribution, we can plot a measure of
nonuniformity for each point in time. Geometric current density is given by J
geom
(t) =
I(t)/πa
2
. Taking the standard deviation (19) of J
z
(r) from the geometric current density
(summation weighted by surface area) gives a measure of the magnitude of current
37
density departing from J
geom
(t). We define nonuniformity as the relative proportion of
current density departing from J
geom
(t), given by the normalized standard deviation σ
J
(t) /
J
geom
(t). Fig. 19 reveals that the nonuniformity associated with the electrostatic current
distribution is extremely short-lived. While both σ
J
(t) and J
geom
(t) approach zero toward
the steady state, their ratio indicates that a nonuniform distribution of current persists
(Figs. 18, 19).
( )
2 / 1
0
2
2
2
) 2 ( ) ( ) , (
1
) (
!
!
"
#
$
$
%
&
' =
(
=
a
r
z J
dr r a t I t r J
a
t ) )
)
* (19)

Figure 19. Nonuniformity measured as the normalized standard deviation in current density, σ
J
(t) / J
geom
(t),
falls rapidly from 1.44 at t=0 to a minimum of 0.052 at t=0.47τ, then levels out to 0.153. The calculation
indicates the relative imbalance of current density over the surface of the electrode overall.

Accumulated charge density, Q
dens
(r, t), on the surface of the disk is calculated by
temporal integration of J
z
(r, T)dT from 0 to t. Charge markedly collects near the edge
early in time (Fig. 20), after which the central region gradually catches up.

38

Figure 20. Normalized accumulated charge density on the disk surface, versus radial position for time
points 0.15τ to 3τ.

B. Time Constants
Total charge transfer, Q(t) (given by temporal integration of I(t) in (15) from 0 to t),
resembles the lumped RC model, in which the effective time constant τ
eff
is found to be
8.03% larger than the lumped element prediction. The instantaneous value τ(t) increases
from τ to 1.10τ with time (data not shown, but see Fig. 22). The effective time constant of
the electrode overall is found by taking the average of τ(t) in (20), weighted by the
incremental charge transferred as Q(t) goes from 0 to CΔE. For time beyond the model
domain of t=0 to 3τ, τ(t) has reached a steady state to transfer the remaining charge (CΔE
- Q(3τ)). Thus, the calculation of τ
eff
accounts for charging the electrode to completion.
!
!
"
#
$
$
%
&
' ' + (
' (
' =
E C t t Q
E C t Q
Ln t t
/ ) ( 1
/ ) ( 1
/ ) ( ) (20)
It is important to calculate τ(t) from the charge curve rather than the current curve in
order to set the asymptote to the maximum charge value CΔE. The exponential decay
approximation becomes
39
)
/
1 ( ) (
eff
t
e E C t Q
! "
" # = , (21)
where τ
eff
= 1.0803R
s
C, which is consistent with the effective time constant of Myland
(Myland and Oldham, 2005). Despite local dynamics, the electrode as a whole charges
according to this exponential decay. If taking (21) as a fit to the simulation data, R
2
=
0.9998.
Since the disk charges at different rates as a function of radial position, the concept of a
local time constant was created to indicate the rate of charge transfer. Oldham’s
calculation of initial local time constants (Oldham, 2004) is given by (22), in which τ is
the lumped element time constant (R
s
·C) and r is radial position on the surface of the disk
electrode of radius a.
2
2
0
1 2 ) (
a
r
r
t
! =
=
" " (22)
Following the same method as with (20), but using charge density instead of charge, the
local time constants as a function of time τ(r, t) are calculated (Figs. 21, 22). Their
influence is apparent in the accumulated charge of Figure 20.

40

Figure 21. Local time constants initially range from 0 to 2τ settle toward a uniform value of 1.10τ. Dotted
curve represents the effective local time constant given by the charge density-weighted average of local
time constant from zero to full charge density.

Figure 22. Local time constants alternatively plotted versus time at several radial positions.

C. Verifying the Solution
Finite element models readily produce solutions to complex problems without the
security of rigorous analytical derivations. We therefore make multiple checks against
what is known analytically. The primary current distribution at t=0 on the surface of the
41
disk is a convenient point in this model to verify because it is very sensitive to mesh
resolution. Primary current distribution is given by (Newman, 1966),
) (
1 2
) (
2 2
r a
E
r J
z
!
"
=
#
$
. (23)
The root-mean-squared error (RMSE) of our finite element solution relative to (23) for
various mesh densities is given in table 2. Radial position was limited to the range 0 -
0.999a since the singularity at r = a cannot be captured numerically. To eliminate any
bias due to the distribution of sample points the squared-error is weighted by surface
area. Similarly, the RMSE of the electric potential at t=0 over the region r
2
+ z
2
<
(11.6a)
2
, weighted by volume and normalized to ΔE, is shown. In cylindrical coordinates
the analytical electrostatic solution for potential in the half space above the electrode is
found in (Wiley and Webster, 1982). Observed current, I
0
, normalized to the theoretical
value of 4κaΔE yields results comparable to the accuracy of a semi-analytical solution
(Myland and Oldham, 2005). Additionally, we have agreement with current density plots
in that study for time greater than zero, although their temporal error was not estimated.

Accuracy of the time-dependent solver is evaluated by increasing the temporal resolution
3 to 30-fold, using uniform time steps from t=0 to 3τ in increments of τ/1000. The
effective time constant is changed by less than 0.04%, current density values are changed
by less than 0.1%, and local time constants are changed by less than 0.5%.

42

Table 2. Error metrics for disk model

Edge
Mesh
Size
Growth
Factor E a
I
! " 4
0

RMSE
J
z
(r)/J
0

RMSE
E
z r
!
) , ( "

Mesh
Elements
a/10 1.1
1.04
1.0089
1.0079
0.52
0.47
0.00084
0.00074
1.8k
4.8k
a/100 1.1
1.04
1.00090
1.00080
0.19
0.21
0.000084
0.000075
4.3k
17k
a/1000 1.1
1.04
1.000094
1.000071
0.017
0.014
0.000013
0.000012
7.3k
33k
a/10000 1.1
1.04
1.0000075
1.0000071
0.0034
0.0014
0.000011
0.000010
10k
50k
a/30000 1.1
1.04
1.00000045
1.0000026
0.0031
0.00054
0.000011
0.000010
12k
58k
Error in the electrostatic model as a function of mesh element size. RMS error in current density is
normalized to theoretical geometric current density, J
0
=(4κaΔE / πa
2
). RMS error in potential normalized to
applied potential, ΔE.

DISCUSSION
The charging profile of a disk immersed in solution subject to a potential step changes
rapidly with time. Since charge drives both corrosion reactions and neural excitation,
understanding both the initial and subsequent charge profile has implications for the
design of stimulating electrodes. The presented model addresses only displacement
currents through the double layer (capacitive charging). Specific applications can define
Faradaic conduction currents to represent electrochemical red-ox reactions of the
chemical species involved and their diffusion rates.

43
Nonuniformity (14) in the current density, σ
J
(t) / J
geom
(t), is initially infinite in theory at
t=0 and falls rapidly as the perimeter of the electrode charges even slightly. Considering
the finite element model, or an electrode with an imperfect edge, the nonuniformity is
high but finite. After 0.1τ, the nonuniformity is 32.0% of J
geom
(t) (Fig. 19). A minimum
value is reached at the transition point from peripheral enhancement to central
enhancement at t=0.47τ. Then, for time greater than τ the mild central current density
enhancement maintains a stable current distribution having nonuniformity 15.3% of
J
geom
(t).

Changes in current density profile are accompanied by settling in the local time constants.
Radial positions less than 0.57a experience monotonic shortening in their local time
constants. All positions 0.57a < r < a, instead, experience a brief and rapid shortening
followed by prolonged elongation of time constant approaching 1.10τ (Figs. 21, 22).
After t=τ the local time constants are quite similar over the disk. Effective local time
constants range from 1.274τ to 0.801τ over 0 ≤ r ≤ 0.999a, which is narrow compared to
the initial range (Oldham, 2004), 2τ to zero.

Within the first τ /6 (Fig. 20), most charge is directed to the electrode periphery, where
the local time constants are short. In other words, the high frequency Fourier components
of a pulse drive current to areas with small local time constants. Retarding the rising edge
of the stimulus pulse to ramp up to full magnitude in time >τ /6 may reduce peripheral
corrosion.
44

Accumulated charge density is of paramount importance for applications concerned with
minimizing electrode corrosion, such as implantable neural stimulators (Robblee and
Rose, 1990). Taking the ratio Q
dens
(r, t) / γ, similar to Figure 20, gives the local potential
across the double layer. Corrosive processes can occur when the local double-layer
potential exceeds the activation overpotential of the relevant electrochemical processes.
Considering the double-layer model alone, Figure 20 indicates that pulse lengths of at
least 3τ will result in a fairly uniform charge density and thus a double-layer potential
without peripheral enhancement.

For example, let us assume that ΔE equals -1.0 V for a cathodic-first pulse within the
range of a conservative water window for a platinum disk in saline (Donaldson and
Donaldson, 1986; Rose and Robblee, 1990), and a required threshold charge for neural
stimulation in retina Q
th
= 3.1π a
2
*(1 pC/µm
2
) from the multiple-study best fit line in
(Sekirnjak et al., 2006). Since (16) gives Q = 0.94CΔE at t=3τ, we need γ=330 µF/cm
2

(geometric area) to meet the threshold charge Q
th
, regardless of electrode size. This
specific capacitance is easily attained for platinum electrodes (≥20 µF/cm
2
real area,
(Pajkossy and Kolb, 2001)) roughened 17 fold by electroplating (Marrese, 1987). Now
we must meet the condition of τ less than 1/3 the stimulation pulse width in order to
uniformly charge the entire electrode surface. Most of the studies from which we draw
our threshold charge used pulse widths of 100 µs to 1 ms, so let us take 300 µs and
assume τ ≤ 100 µs for the uniformity condition. Using (8), (9), and τ = R
s
C, we can
45
rewrite τ = γπa / 4κ. For an electrode placed in the vitreous humor of the eye, assuming
κ=0.65 S/m (Jurgens et al., 1996), we can solve for the maximum allowable disk radius, a
≤ 25 micrometers. Larger electrodes would have τ > 100 µs, and thus not reach
uniformity. It is advantageous to use the shortest pulses possible because they have lower
charge thresholds to stimulation (Bostock, 1983; Jensen et al., 2005; Mcneal, 1976).
Therefore, a roughened platinum electrode driven at -1.0 V for 300 µs can surpass
excitation threshold with a uniform charge density for electrodes of radius a ≤ 25 µm, in
this simplified example.

Error in the finite element model is characterized by several metrics in Table 2. Measures
of RMSE in potential or error in total current are both largely insensitive to a crude mesh
at the disk surface. The most sensitive to error in the region of interest (the interface) is
RMSE in J
z
at t=0. However, the error magnitude approaches infinity as r approaches a.
To obtain a finite value for this particular metric, we observe the region 0 ≤ r ≤ 0.999a.
Spatially-dependent RMSE measurements (current density, potential) must be weighted
by area or volume as appropriate to eliminate sampling point bias that would preclude
comparison to other studies.

Measurements of error under electrostatic conditions are worst-case values since the edge
enhancement that produces most of the error is absent following a tiny fraction of τ. Thus
there is a relationship between spatial resolution and temporal resolution given by (22)
and Fig. 21. Time steps should be chosen to be much less than the shortest local time
46
constant τ(r) over the region where high precision is desired. Additionally the time
resolution should correlate to the spatial resolution so computation is not wasted; set the
mesh element size m at the disk edge such that the local time constant at the last element
from the edge τ(a – 0.5m) is approximately equal to the time step following t=0. This
study resolved current density with normalized RMSE J
z
of 0.003 up to the radial
position 0.999a, by using time steps approximately τ(r) /30 at this position and matched
mesh elements of minimum size a/30,000.

This work provides a quantitative tool for assessing the likelihood of corrosion due to
peripheral current enhancement. These methods can be adapted in general to any
electrode geometry, material, and electrolyte. Addition of Faradaic currents and carrier
diffusion to the double-layer model will facilitate creation of specialized electrodes that
reduce undesired corrosion or optimize desired reactions for fast transient processes that
are hindered by double-layer charging.

47
Chapter 3. Experiment Design and Methods

Electrical stimulation thresholds for RGCs have been thoroughly investigated in animal
models and somewhat in humans. What is still poorly understood is the spatial shape of
the response and how it might be controlled. By taking an optical approach to measuring
thresholds, I acquired detailed spatial information. The results presented here are
intended to shed light on the factors that limit resolution of artificial vision, and to point
toward a means for control of perception.

While the most control over experimental parameters is had in vitro, it may be useful to
perform in vivo imaging of the response to electrical stimulation. Fundus imaging in the
near infrared (Okawa et al., 2007) can detect changes in reflectivity on timescale of
seconds in the retina caused by the stimulus, although the mechanism and relation to
spiking activity are not clear.

Figure 23. Differential fundus image showing the response to a 1-mm diameter subretinal electrode. From
Okawa, 2007.

48
3.1 Probing the interface from electrodes to tissue

Three key parameters were explored to understand how the retina perceives electrical
stimulation. Electrode size would ideally be very small (the size of a single cell), but
practical constraints of high in vivo perceptual thresholds and the safe charge injection
limits required larger electrodes in clinical trials. The relationship of electrode size to
both threshold and percept size are explored. The separation of the array from the
epiretinal surface is currently an unavoidable problem in patients. The influence of a
saline gel layer on threshold and percept size is explored. Pulse width can affect what cell
type is targeted for stimulation based on differences in chronaxie. The preferred cellular
target of stimulation and the percept size are determined for a range of pulse widths.

In addition to systematically testing the effects of electrode diameter, separation, and
pulse width, means for controlling the path of electric field lines are explored in an
attempt to selectively stimulate RGCs in close proximity to the electrode.

ANIMAL MODEL

Isolated larval tiger salamander retina is used as a model for degenerate retina because
this species lends itself to staining with calcium indicators. There are a number of
differences from human retina, but the commonalities of retinal architecture do make this
a good model. The axons of RGCs are not myelinated in humans or in salamander.
49
Rabbits do have myelination in the retina and not even in a uniform distribution. This
could complicate interpretation of results in rabbit, as the myelination would dramatically
alter threshold for axons relative to somata. The salamander retina is not degenerated, but
does slowly degenerate with age (Townes-Anderson et al., 1998). However,
photoreceptors are bleached by the blue fluorescence excitation, which dramatically
reduces their sensitivity to light. Since the illumination is constant and bright, the
photoreceptors stop releasing glutamate onto their bipolar cell dendrites. In this respect
the model is not unlike a degenerated retina. The main difference is that the retinal
architecture is not disorganized as in advanced degeneration (Marc et al., 2003). In mice
the stimulation threshold rises by about 25% after degeneration (Suzuki et al., 2004).

ELECTRODE SIZE

Stimulation thresholds have been measured under a variety of conditions and in various
animal models, but these studies are rarely systematic or carefully controlled. For a
thorough review of the literature on thresholds, see (Sekirnjak et al., 2006).

50

Figure 24. Threshold charge versus electrode size from animal models and humans. From Sekirnjak, 2006.
Blue dots are thresholds for this study.

Although thresholds are often measured, the size and shape of the response is largely
unexplored. In cat retina (Eckhorn et al., 2006), planar microelectrode 100 µm square
evoked percepts (cortical) 240 µm wide, and conical tip electrodes 80 µm by 30 µm
evoked 140-µm percepts. In an isolated rabbit retina (Jensen et al., 2005), response
regions (extents defined by 50% increase in threshold) were 100 µm and 600 µm for
electrodes 125 µm and 500 µm in diameter, respectively. My results also show a response
roughly matched to the electrode size for 200-µm electrodes, but for smaller electrodes,
resolution may not scale with electrode size.

51
PULSE WIDTH

Short pulses (500 µs) evoke transient inward current in RGCs while longer > 5 ms pulses
evoke sustained inward currents from bipolar cells (Margalit and Thoreson, 2006). The
inner retinal neurons have a longer chronaxie and are therefore targeted by long pulse
widths. Furthermore short pulses (< 150 µs) evoked a single spike with short latency
(Fried et al., 2006), but longer pulses evoked a burst of long latency spikes. To
investigate how pulse width affects the spatial properties of the response I stimulated at
60 µs, 400 µs, and 1000 µs in the cathodic phase. My data confirmed that short pulse
widths target RGCs directly while longer pulses preferentially stimulate the inner retina.
Additionally, short pulses evoked a smaller response area over the electrode.

STIMULATION OF AXON BUNDLES

In rabbit retina, the thresholds for axons and somata were not significantly different
(Jensen et al., 2005) with regard to electrode position and electrode diameter. However,
100-µs pulses significantly preferred somata to axons, compared to 1-ms pulses.
Therefore, selective stimulation of RGC somata over axons may be possible and demands
a more detailed investigation. A limitation to the rabbit study is that the axons are
partially myelinated, while in humans they are not. Additionally the current spread is
much different for the wire electrode, than a planar multielectrode array.

52
The orientation of bipolar electrodes can affect axon threshold (Grumet et al., 2000;
Ranck, 1975). Selectivity may be gained by controlling the orientation of multipolar
stimulation in the retina. My study measures axon bundle thresholds in addition to
somatic thresholds to study the contribution of axon bundles to perception. Although
thresholds can be more than doubled for axons transverse to the electrodes, other axons
will pass over the cathodic electrode and be stimulated with ease.

Figure 25. Orthogonal orientation of bipolar electrodes raises threshold by 65%. From Grummet, 2000.

There is mounting evidence that the site of action potential initiation in RGCs is at either
the initial segment of the axon or the axon hillock, in models (McIntyre and Grill, 1999)
and intracellular recordings (Carras et al., 1992), and correlates with a high density of
voltage-gated sodium channels (Wollner and Catterall, 1986) (Fried 2008, ARVO
unpublished data). In primates, 10-µm electrodes are most effective at 13 µm from the
soma (Sekirnjak et al., 2008). One model (Schiefer and Grill, 2006) predicts the axon
hillock or bend in the axon (from the soma into the nerve fiber layer) as the site of action
potential initiation. My data provide clear support for the initial segment hypothesis, but
not for the axon hillock or bend. Stimulation of the initial segments still drives somata
53
local to the electrode and does not threaten to distort percepts, as does stimulation of axon
bundles.

SEPARATION DISTANCE

Although the MEA is curvature-matched for in vivo implants, it tends lift off from the
retina because it is fixed against the retina with a single tack. Other complications of
cable tension and poorly matched curvature have contributed to a gap between the array
and the retina in patients in the Argus I and II trials. The separation distance can be
anywhere from zero to 1000 µm, and is not uniform over the array (de Balthasar et al.,
2008). In the future, bioadhesives may improve the contact of the MEA to the retina. To
understand how a gap affects electrode-electrode interactions and the response to
stimulation, I developed a novel technique to spin coat saline agarose gel onto the MEA
before placing the retina, borrowing from the concept of spin coating used in
photolithography processes. With separation, the responding region grows slightly and is
in accord with the finite element model of the epiretinal interface.

Stimulation from a distance was accomplished by spin deposition of liquid agarose gel
directly onto the MEA. Agarose is a polymer of the sugar D-galactose (derived from
seaweed) and is neutral to cells. Gel thickness was specified by the spin speed and the
number of layers applied (~8 µm each), with a maximum surface deviation of less than
+/- 10% over 5 mm. Gel solution was prepared by boiling 1% agarose in superfusion
54
medium without calcium or glucose. Liquid agarose was cooled to 45 ºC, then 500 µL
were pipetted into the recording chamber (at 0 PRM) and quickly ramped to 500
revolutions per minute (RPM). This step was critical to form the adhesion layer of gel.
Spin speed was raised to 1800 RPM. Subsequent layers of gel were applied by pipetting
50 µL at 1800 RPM. Gel was set at 4 ºC for 30 minutes (humidified), then trimmed to
remove the meniscus and rapidly warmed to room temperature. The retina was applied to
the gel-coated array before the gel could dehydrate. This gel is analogous to the vitreous
gel of the eye, which is composed of 1% hyaluronic acid in physiological saline.

Figure 26. Chemical structure of agarose.

3.2 Probing activity in excitable cells

When stimulating neurons in the retina it is necessary to record from a population of
these neurons to detect evoked spikes. Recording electrical activity from neurons has
traditionally been accomplished with electrodes to monitor intracellular or extracellular
potential. However, patch clamping and extracellular electrodes are both limited to
recording from a small number of cells, or limited in electrode size. In recent years
55
noninvasive fluorescent probes have been developed to monitor transmembrane potential
and intracellular calcium. Calcium imaging is an indirect means of monitoring spiking
activity of neurons, but has some advantages in simplicity of imaging. In addition to the
vast number of cells that can be observed through imaging techniques, the prime
motivator for optical probing of neuronal activity is that it is noninvasive. The physical
presence of a stimulating electrode precludes electrical recording from cells in its vicinity
or on its surface, in large part due to stimulus artifact. Calcium imaging permits
measurements from cells in any location relative to the stimulating electrode, which is
critical for these studies on the spatial characteristics of the ganglion cell response.

ELECTRICAL RECORDING

Patch electrodes, needle electrodes, and MEAs can be used to record spiking activity with
high temporal resolution in individual cells. Only MEAs (Morin et al., 2005) permit the
observation of a large population of neurons in a tissue. Large-scale electrical recordings
from a 512-electrode array (Dabrowski et al., 2004; Litke et al., 2004; Mathieson et al.,
2004) have been able to map receptive field mosaics in the primate retina (Field and
Chichilnisky, 2007). High-density arrays permit recording from most retinal ganglion
cells (RGCs). Extracellular metal electrodes often pick up signals from a few neurons in
the vicinity of the electrode. Individual neurons in a cluster over a recording electrode
can be identified by spike shape, through template matching (Segev et al., 2004), or by
principle components analysis and autocorrelation (Lewicki, 1998; Litke et al., 2004).
56

Using MEAs it has been established that RGCs can follow precise temporal patters of
stimulus pulses (Fried et al., 2006) and the latency of these spikes is about 200 µs
(Sekirnjak et al., 2006). Although the position of cells can be estimated from the spike
amplitude on a group of neighboring electrodes (Sekirnjak et al., 2008), the spatial
information is not as precise as with imaging. The primary limitation to MEA recordings
is that the electrodes must be small (10 µm) and sparse (60 µm center to center to allow
space for traces).

VOLTAGE SENSITIVE PROBES

Fluorescent voltage sensitive probes for transmembrane potential are lipophilic dyes that
integrate with one or both leaflets of the plasma membrane. FM4-64 is loaded
intracellularly to integrate with the internal lipid layer (Dombeck et al., 2005). Its
fluorescence signal is extremely small, but it exhibits a strong second harmonic
generation (SHG) signal of 7.5% per 100 mV. In second harmonic imaging, two infrared
photons are absorbed and emitted in the same direction of propagation as one photon at
twice the energy. The best two-photon fluorescent indicator is ANNINE-6 (Hubener et
al., 2003), with a fluorescence intensity change of 40% per 100 mV (Kuhn et al., 2004).
The ease of bath loading ANNINE-6 makes this the preferred indicator when a large
number of cells are imaged. In future work this dye will be tested in RGCs, but
57
challenges are expected because the signal is so rapid (1 ms) that single spikes may not
be detected.

INTRINSIC SIGNAL IMAGING

Using brightfield illumination in the near infrared, transient signals were detected in
individual cells from a frog retina, stimulated by a visible light spot (Yao and George,
2006). This imaging modality uses no fluorescent probe. The physiological basis of the
intrinsic signals is poorly understood, but it may be related to osmotic flux changing the
refractive index in individual cells or in the tissue structure during spiking activity.
Because this is such an indirect measure of neural activity it is not known precisely how
the signals relate to spiking activity patterns in neurons. Furthermore, the cell types
contributing to the signal are not readily identified.

CALCIUM IMAGING

It is well established that somatic calcium bursts are correlated with a rapid series of
action potentials (Lohmann et al., 2002; Wong, 1998), and even single spikes (Smetters
et al., 1999). We have verified in our preparation that spikes in indicator fluorescence are
correlated with a rapid burst of action potentials, by simultaneous optical and
extracellular recordings. Fluorescence signals were sensitive to both cadmium and TTX,
consistent with voltage-gated calcium influx mediated by sodium action potentials.
58
3.3 Calcium imaging in neurons

Many fluorescence indicators are available for measuring intracellular calcium
concentration. There is a large diversity of indicators derived from the calcium chelators
BAPTA and EDTA (Tsien, 1989). The following is a summary of the various methods
available to label cells with such indicators. Ultimately, retrograde loading of dextran-
conjugated calcium indicator was used in the salamander retina because it is selective for
RGCs and results in adequate staining intensity.

Genetically encoded calcium indicators using troponin (Mank et al., 2008) have shown
recent improvements in sensitivity and are becoming much more practical for measuring
small changes in cytoplasmic calcium (dissociation constant 800 nM). These proteins are
composed of a fusion of two fluorescent proteins linked by a calcium binding protein.
Upon binding calcium, the linker changes conformation to reduce the distance between
fluorescent proteins to enhance Forster resonance energy transfer (FRET) from the short
wavelength to the long wavelength protein. Thus the fluorescence emission balance is red
shifted in proportion to the calcium concentration. Expression of these indicators requires
that the DNA encoding them be transfected into the cells by electroporation, viral
delivery, or expressed in a transgenic animal. It may be difficult to selectively express the
indicator in RGCs, so a retrograde tracer may be applied to identify the RGCs for
imaging.

59
There are two hurdles to staining with fluorescent calcium indicator dyes: loading the
indicator into the cell and retaining the indicator inside the cell. Calcium indicators do not
cross cell membranes because they are strongly hydrophilic, with about 5 carboxylic acid
groups. In many preparations it is possible to use the acetoxymethyl ester (AM-ester)
form of the indicator, which caps each of the carboxylic acid groups with a more
lipophilic methyl group. Once inside the cell, endogenous esterases cleave the ester bond
to produce the active indicator. However, the dye is transported out via a class of organic
anion transporters (OATs) (Khamdang et al., 2004; Kusuhara and Sugiyama, 2004;
Mikkaichi et al., 2004). Since these indicators are so highly charged, the effect is
profound, especially in neural tissues such as the retina. OATP-E is expressed in RGCs of
the rat (Ito et al., 2003). Probenecid, a blocker of OATs (Di Virgilio et al., 1988a), was
only partially effective in retaining indicator in RGCs. Increasing the size of the indicator
by dextran conjugation makes it resistant to transport. However, the dextran conjugate
cannot cross membranes by bath loading like AM-esters. The following techniques are
capable of delivering dextran conjugated calcium indicators into neurons.

SCRAPE LOADING

Scrape loading transiently disrupts membrane integrity by mechanical means. Adherent
cells are scraped from their substrate by a rubber spatula or wooden probe and incubated
in suspension with the dye to be loaded (McNeil et al., 1984). About half of the cells
survive the procedure. This technique is not appropriate for tissue, but for confluent
60
adherent cells. Scrape loading was used to load cells with Lucifer Yellow and rhodamine-
dextran 10,000 MW to study gap junctional communication (el-Fouly et al., 1987).

MICROINJECTION

Microcellular injection of dye solutions into the cell can be accomplished with drawn
glass micro pipets. This technique is used to trace neuronal morphology. Due to the
labor-intensive nature of microinjection, references in (Wu et al., 2004), very few cells
can be labeled. The pipet can significantly dilute the intracellular contents, especially
proteins, thus affecting neural function and cell health on the order of 5 minutes.

IONTOPHORESIS

Iontophoresis is similar to microinjection but instead of expelling the contents by
application of pressure, a current of 1-2 nA (Wong ROL 1998) is applied to
electrophoretically move charged molecules into the cell through a sharper pipet tip. This
technique is also limited in application to a small number of cells. Practical aspects of
microcellular injection and iontophoresis can be found in Microelectrode Techniques
(Ogden, 1989).

61
ELECTROPORATION

Electroporation globally permeabilizes cells in suspension or tissue by application of
electric field pulses of kilovolts per meter for several milliseconds. In vivo
electroporation by application of five 50-ms pulses from tweezer electrodes was used to
transfect retinal cells after subretinal injection of DNA to mouse pups (Matsuda and
Cepko, 2004). In vitro electroporation of the retina was also accomplished by using an
electroporation cuvette, 100 V/cm, 50 ms, five square pulses. The duration of the
permeabilized state varies widely. The resealing time constant (Shirakashi et al., 2004) is
3 to 4 minutes for a typical application of 3 kV/cm, 20-microsecond pulses to cell
suspensions.

BIOLISTIC LABELING

A review of biolistic protocols in the literature, as well as my optimizations are found in:
/ Proposals /Biolistic procedure 20060809.doc

Biolistic delivery uses micron-sized particles as carriers for the material to be delivered
into the cytoplasm of a cell. The particles are propelled into tissue from a helium gun and
penetrate the cell membrane. Biolistic delivery of fluorescent probes is applicable to any
population of cells or tissue up to 85 µm at 200 PSI (Wu et al., 2004) and even 450 µm
thick (O'Brien et al., 2001). The staining is not selective for any particular cell type, so
62
although biolistic delivery is applicable to the retina, it was ultimately left aside in favor
of retrograde loading.

Biolistic delivery has been used for dextran-conjugated calcium probes in mouse cortical
slices (Kettunen et al., 2002), carbocyanide neural tracers (Gan et al., 2000) and DNA to
hippocampal neurons (Lo et al., 1994). This technique has the advantage of labeling
many neurons rapidly and simultaneously. The density of cells labeled is best controlled
by the filter membrane porosity and can be somewhat controlled by the particle
preparation procedure. Labeling is nonspecific but penetration depth is controllable.
Labeled cortical neurons showed normal spontaneous activity, glutamate-evoked activity,
and dendritic remodeling (Gan et al., 2000), indicating that cells remain healthy after
bombardment.

The following protocol developed for high density labeling using dextran-conjugated
indicators is similar to Gan’s method, but adapted for water-soluble dextrans. My
protocol is an advance relative to the Wong method for calcium indicators, because a
sonication step has been included to keep particles disaggregated. Dextran-TR was not
soluble to any degree in any of twelve common organic solvents tested. I have chosen
ethanol as the suspension medium for coated particles because it is safer and is a solvent
for polyvinylpyrolidone (PVP). Tefzel tubing is not precoated with PVP in order to
enhance repeatability.

63
1. Pre dry tefzel tubing (75-cm) 10 min under N2 0.4 L/min, ultra high purity (UHP)
grade gas

2. Dissolve 3 mg dextran-dye in 30 µL distilled water

3. Pipet 15 µL onto a heap of 25 mg tungsten 1.3-µm particles on glass slide
spread rapidly over 2/3 the slide area, aid drying with N2 2 L/min pointed at the
slide then air dry in dark until light gray color is uniform over the slide
repeat for 2 slides (50 mg total tungsten)

4. Prepare the PVP solution by serial dilution, add 15 µL PVP stock (20 mg/mL)
into 3 mL 100% EtOH, take 300 µL into 2.7 mL EtOH, final 10 µg/mL

5. Scrape off dye-logged edges on glass slide and discard

6. Scrape off coated particles onto wax weighing paper, pour into glass tube
suspend in 3 mL PVP solution in 10-mL glass culture tube

7. pipet up & down 10X, sonicate 5 min, repeat, verify homogeneous gray cloud,
pipet again

8. while sonicating again, draw suspension into tefzel

9. Place tubing into the Bio-Rad tubing prep station with syringe still attached
Let particles settle for 3-5 min

10. withdraw at 2.8 mL/min, using syringe pump (position 4, rate 85%)

11. immediately disconnect linker, rotate with simultaneous N2 flow at 0.4 L/min,
5 min

12. cut into 13-mm segments, store at 4 ºC in dark, desiccated

Notes (step #):
(1) Cut the tube with the V-tooth of wire strippers as this rounds the end for easy
insertion into the O-ring seal of the prep station. Before inserting the tubing for drying,
rub the thumb along the outer surface of the curved tube to straighten it slightly. Be
careful to not kink or stretch the tube.
64
(2) Place dye into the bottom of a PCR tube and gently tap it on the table to settle the dye
to the bottom. Pipet 30 µL water on top of the dye and dissolve first by stirring, then slow
pipetting up and down.
(5,6) Use a new razor blade to scrape dried particles for each batch.
(7) When suspending the coated particles in PVP solution the pipetting and sonication
steps are performed with the culture tube placed angled into a rack in the ultrasonic bath
to hold the tube at a 45-degree angle. While pipetting it is sometimes helpful to introduce
air bubbles into the suspension because they continuously stir the suspension under
ultrasonic vibration.
(8) When drawing the suspension into the tefzel tube, the distal end is placed into the
bottom of the glass tube and the proximal end is linked to a 10-mL syringe with a short
(10-cm) linker tube. The syringe plunger is always withdrawn (pulled), never push fluid
toward the distal end at any time.
(9) When placing the tube into the prep station, the tube will have a natural curve to it.
Keep the tube in the horizontal plane, holding it on each end and gently feed the tube into
the prep station without jarring the fluid position.

Place a 13-mm immobilization filter (Millipore # AABG01300) into the center of a 35-
mm culture dish. Place a large drop of Ames medium on it. Using an inverted Pasteur
pipet (rubber bulb on over the thin tip, use the wide end as the pipet) pick up a piece of
retina from the incubation dish, allow retina to settle down to the meniscus and transfer to
the immobilization membrane by touching it. Always transfer the retina to a pre-wetted
65
surface or to another dish of medium. Never bring retina in contact with a dry surface at
any time, even for fixed tissue. Suction excess medium from retina with fine tip of a
second pipet. Immediately place into gun chamber, cover with filter (Millipore #
TSTP04700) assembly and shoot. Transfer immobilization membrane to a well in a 24-
well plate. Immediately cover the retina with about 1.5 mL of Ames medium. During this
washing stage other dyes may be added for counter staining as needed. Replace with
fresh medium at least every 5 min or bubble to keep pH balance.

The baffled barrel is used to achieve high labeling density and permit lower gas pressure
versus a tapered barrel like that of the Bio-Rad gene gun. A nylon mesh filter membrane
of 70-µm pore size can be substituted for the 3-µm TSTP04700 to get even higher
labeling density or deeper penetration depth.

Figure 27. The barrel of the biolistic gun has baffle holes to improve collimation of the stream of particles.
The tefzel tubing segment is loaded into the bore of the luer connector on the right side.

66

Figure 28. The biolistic gun is built into a closed chamber for safety. The gun must only be fired in a fume
hood to prevent inhalation of the dust from the exhaust port.

3.4 Retrograde loading of calcium indicators into retinal ganglion cells

The detailed protocol for retrograde loading is located in:
/ Proposals / Retrograde loading protocol.doc

In order to optimize the design of implantable retinal prostheses, we needed a method to
measure the activity of retinal ganglion cells (RGCs) in wholemount retina interfaced
with prototype microelectrode arrays (MEAs). Of particular interest were the spatial
response properties from cells directly over the stimulating electrode. Given the number
67
of cells over the microelectrode (dozens) and the physical presence of the stimulating
microelectrode, traditional multi-electrode recording methods could not make these
measurements. Calcium imaging is a powerful tool for measuring the simultaneous
activity of a population of neurons, especially where precise spatial localization is desired
relative to a stimulation site. However, calcium imaging in mature neurons is often
prevented by the difficulty of delivering the dye to the cytosol of these cells.

Little staining is seen in the mature retina (Wong and Oakley, 1996). Membrane-
permeant acetoxymethyl-ester (AM-ester) calcium probes can readily be loaded in some
neurons of young animals, for example, cortical neurons in rats younger than P7 (Regehr
and Tank, 1991). Neonatal ferrets P10 and younger take up AM-esters into retinal
neurons (Wong and Oakley, 1996). Unfortunately, the retina is not fully developed in
young animals (before eye opening; (Young, 1985)). Seeking an alternative mode of
delivery, we pursued retrograde dye loading, similar to a technique previously described
(Zhan and Troy, 1997) for neurobiotin labeling of RGCs.

Our method incorporates three improvements on Zhan’s technique: specialized glue
improves assembly; the eyecup is held stable in a chamber that isolates the dye from the
saline medium; the eyecup is continuously superfused with very high turnover to
maintain viability, just as in a recording chamber. With these improvements and the use
of a salamander retina model, we have successfully imaged calcium activity in the
majority of retinal ganglion cells in a wholemount preparation.
68

Other investigators have used a more localized form of retrograde loading in the retina. A
small portion of RGCs can be retrogradely stained by cutting a slit on the surface of the
retina (ferret age P10-P30) with a super sharp blade and applying 1-3 µL of Fura-2 AM 1
µg/µL in DMSO (Wong and Oakley, 1996). Piercing the retina with a dye-laden syringe
needle introduced dextran-conjugated calcium indicator into RGC axons (Baldridge,
1996). These previous methods for applying calcium indicators to RGC axons have only
labeled a small population of cells affected by the local disruption of axons. Bath loading
of AM-esters is difficult in the mature retina, and not selective to RGCs regardless of the
loading conditions.

Thus, until now, no approach has stained a significant fraction of the RGCs with a
calcium indicator in a mature retina. Here, we report a new in vitro retrograde loading
approach that rapidly and selectively labels the majority of RGCs. When applied to the
wholemount retina of larval tiger salamanders, which have fully developed retinas, we
have been able to directly monitor electrical activity and correlate it with calcium activity
in individual RGCs. This new method of studying electrical activation of retinal cells
enables simultaneous measurement of multiple cells directly over the stimulating
electrode, a measurement not possible by any other means. Electrodes made from the
transparent conductor indium-tin-oxide permit visualization of these cells. With different
imaging equipment this loading technique could permit novel retina physiology
experiments to study vision.
69

MATERIALS AND METHODS

A. Overview

The optic nerve stump of the eyecup preparation is exposed to a solution of dye. A small
segment of tubing to contain the dye is first glued to the back of the eye encompassing
the optic nerve stump of the enucleated eye. The eyecup is held in a fixture keeping the
retina submerged in oxygenated saline medium at near-physiologic conditions while the
optic nerve and tubing with dye are kept above the fill level of saline.

B. Incubation assembly

The retrograde assembly (Fig. 29) is made from readily available materials. Tubing
segments are cut from thin-wall polyethylene or polyimide. A collar, which is applied
around the posterior portion of the eyecup, is made from polystyrene weighing boats by
drilling a small hole in the boat and cutting out a disk about this hole. An incubation
chamber can be made from nylon screen from a cell culture insert, an electroporation
cuvette, and culture dishes. A tubing segment and a collar are glued with alkoxyethyl
cyanoacrylate (Loctite 403, distributed by McMaster Carr) during preparation of the
eyecup. The choice of this particular adhesive is important to avoid the vapor-deposition
70
of cyanoacrylate (Wargacki et al., 2007), associated with common forms of this
superglue.

Figure 29. The eye cup is held in a compact superfusion chamber during retrograde dye loading to the
RGCs. (A) Dye dissolved in water is held on the optic nerve stump with a small segment of tubing. The
eyecup is held inverted on a chair platform having a nylon screen. (B) The chair platform is shown next to
the tubing segment and plastic collar that are glued onto the eyecup to form the retrograde assembly. A
Teflon syringe needle is used to dispense the fluorescent dye.

C. Retinal preparation

Larval tiger salamander (Ambystoma tigrinum) eyes were hemisected with a razor blade,
in a custom-made holding block, immediately after enucleation. Connective tissue was
removed around the optic nerve stump, while submerged in calcium-free medium. The
optic nerve was trimmed to 0.5 mm in length. The eyecup was then taken from the saline-
71
filled dissection dish and placed retina-side-down on the lid of a culture dish. Excess
saline was blotted away while holding the eyecup with fine forceps. Immediately, one
face of the tubing segment was swabbed across a thin smear of glue, and placed onto the
eyecup encompassing the optic nerve stump. Fluorescent dye (20 mM, 1.5 µL) was
quickly pipetted into the tube to fill above the nerve ending. A thin layer of glue was
applied to the perimeter of the hole in the collar, which was gently placed around the
tubing segment onto the eyecup, and let dry 15 seconds. Gripping the collar, the assembly
was transferred to the pre-wetted incubation platform and superfused at 5 mL/min in a
volume of less than 3 mL, for a period of at least 2 hours. All procedures were carried out
at 23 - 24 ˚C. Mammalian retina preparations were similar, except that the tubing and
collar were glued to the whole enucleated eye before hemisecting with dissection
scissors.

Animal protocols were approved by the Institutional Animal Care and Use Committee at
the University of Southern California. Larval Tiger salamanders (Charles D. Sullivan
Co., Inc., Nashville, TN) were maintained at 8 ˚C until use, and euthanized by rapid
decapitation and bilateral pithing of the spinal cord. Early post-natal Long Evans rats
were rapidly decapitated. Adult Long Evans rats (Harlan, Indianapolis, IN) were deeply
anesthetized with ketamine (80 mg/kg) and xylazine (8 mg/kg) by intramuscular
injection, and rapidly decapitated.

72
D. Imaging

Calcium imaging was performed on an inverted epifluorescence microscope using a
Nikon PlanApo 0.75 NA 20X objective, and an Andor Ixon electron multiplied CCD
camera. Fluorescence filters were from Semrock, set # FITC-3540B. Transparent
microelectrode arrays (MEAs) were fabricated by the authors at the University of
Southern California Keck Center for Photonics. Arrays were composed of patterned
indium-tin-oxide (ITO) on #1 cover glass substrates. An insulation layer of silicon-nitride
was patterned over the ITO to open the electrode surfaces, and contact pads on the
perimeter of the substrate.

E. Electrophysiology

Electrical stimulation thresholds of RGCs were measured via calcium imaging by
delivering a sequence of progressively increasing charge-balanced biphasic pulses to a
single electrode. Each stimulus event was a rapid burst of 40 biphasic pulses within 120
ms. The repetitive image acquisition period was 100 ms. The burst of pulses was intended
to evoke a burst of spikes to bring calcium influx to a detectable level. We estimate that
the concentration of indicator in the soma was roughly 5 µM, resulting in a very low
calcium binding ratio (see discussion). To maximize signal strength we chose a high
affinity calcium indicator that is bright and resists photobleaching, namely Oregon
73
Green-488-BAPTA-1 dextran. Alternatively, a ratiometric indicator such as fura-2 could
be used to more accurately measure changes in calcium, rather than calcium influx.

Average pixel intensity of each cell was extracted with Metamorph (regions of interest
for each cell were slightly smaller than the soma diameter), and processed in Matlab to
detect transient rises in the fluorescence, temporally correlated with a stimulus burst.
Each stimulus burst was delivered 25 times on 2-s intervals. A dose response curve for
each cell was fitted with a sigmoid to calculate threshold, where a stimulus has a 50%
chance of evoking a calcium response within the 25 replicates of fixed amplitude.

In dual (optical / extracellular) recording experiments, a 10-µm electrode was stimulated
by a train of 40 cathodic voltage pulses, 100-µs pulse width. Spikes were recorded on
distant electrodes with an MEA1060-BC (Multichannel Systems, GmbH) amplifier.
Stimulus artifact from a spike-free pulse was subtracted from other waveforms containing
a spike according to (Sekirnjak et al., 2006). Spikes were detected by setting a detection
threshold at 3 times the RMS noise level. Singular value decomposition was applied to
the set of spikes in Matlab, and two clusters were identified by separation of the
waveforms by scores along the first two principal components as described (Lewicki,
1998).

74
F. Materials

Fluorescent dyes, Alexafluor-594 hydrazide salt (Alexa-594), Oregon Green 488-
BAPTA-1 (OGB-1) hexapotassium salt, and Oregon Green 488-BAPTA-1 dextran 10
kDa, were purchased from Invitrogen (Carlsbad, CA). All other reagents were from
Sigma-Aldrich (Saint Louis, MO). Superfusate for salamander contained (in mM): 110
NaCl, 2 KCl, 1.6 MgCl
2
30 NaHCO
3
, 1.5 CaCl
2
, 0.01 EDTA, 10 glucose, equilibrated
with 5% CO
2
95% O
2
, adjusted to pH 7.40, and 270 – 275 mOsm. Dissection medium
was identical except with additional MgCl
2
substituted for CaCl
2
. Calcium was omitted
during preparation of the eyecup to avoid calcium-dependent resealing of the optic nerve
(McNeil, 2002; Yawo and Kuno, 1985). Superfusate for rat was Ames medium, buffered
with 1.9 g/L NaHCO
3
, equilibrated with 5% CO
2
95% O
2
, pH 7.40. Probenecid (2.5 mM)
was sometimes added to the superfusate when using calcium indicators, and final pH
adjusted to 7.40. Probenecid did not noticeably enhance staining for the salamander.

RESULTS

Two hours of retrograde loading in the eyecup stained axons and many ganglion cell
somata. At this point, the retina was isolated and mounted on the MEA recording
chamber for complete filling of RGC somata from the reservoir of dye in the axons. This
secondary incubation outside the eyecup also helped to reduce background fluorescence,
possibly from dye that leaked from the optic disk. A total of 4 to 6 hours was necessary to
75
achieve adequate staining of somata at 2 mm from the optic disk. The RGC density (Fig.
30) stained with the calcium indicator was 1460 ± 270 cells/mm
2
(mean ± SD), which is
consistent with thorough counts of 1400 cells/mm
2
obtained by retrograde tracing, optic
nerve sectioning, and recordings (Segev et al., 2004). Dendritic arbors of the RGCs were
also stained, and calcium transients were prominent in the proximal dendrites of the most
brightly stained RGCs. With two-photon imaging it may be possible to investigate
synaptic connections in these labeled cells (Reid et al., 2001; Yuste and Denk, 1995).

Figure 30. Salamander retina labeled with Oregon Green-BAPTA-1-dextran 10kDa, RGC density as a
function of position from the optic nerve. Fluorescing axon bundles obscure some somata with increasing
proximity to the optic disk.

Double labeling (Fig. 31) with an equimolar mixture (15 mM final) of the fluorophore
Alexa-594 hydrazide salt (759 g/mol) and the indicator OGB-1 dextran (10,000 g/mol)
revealed greater brightness and 2.4 times greater contrast with Alexa-594. Cells labeled
with OGB-1 dextran, whether bright or dim, were all co-labeled with Alexa-594. Cell
density with Alexa-594 was 1450 cell/mm
2
in Figure 31. Therefore, only RGCs were
stained with either dye, while some RGCs were weakly stained with OGB-1 dextran due
to its slower diffusion. The standard deviation in background-subtracted intensity for
76
somata (n=386) was 0.70 and 0.53 normalized to the mean for OBG-1 dextran and Alexa-
594, respectively. Staining was significantly more variable (p < 0.001, F-test) for OGB-1
dextran.

Figure 31. Salamander retina retrogradely stained with a mixture of Alexa-594 (top) and Oregon Green-
BAPTA-1-dextran 10 kDa (middle). In the merged image (bottom), staining is brighter with unconjugated
Alexa 594 (red cells); some red cells (arrow head) did not have visible staining with the calcium indicator,
but all Oregon Green-labeled cells were co-stained with Alexa 594 (yellow cells, arrow). Scale bar 200
mm.

Calcium transients, recorded from the stained RGCs in the wholemount, were correlated
with spiking activity in the same cells (Fig. 32). We stimulated RGC somata by nearby
electrodes and by distant electrodes via antidromic propagation of the spike. Extracellular
potentials were simultaneously recorded by 10-µm electrodes, along with the calcium
77
signals. Unique spike waveforms were separated by principal components analysis.
Stimulating with 40 pulses at near-threshold amplitude evoked spikes from two neurons
(Fig. 32), while only one of the four neurons (Fig. 32, top trace) near the recoding
electrode exhibited a calcium response. Single spikes did not elevate the calcium
fluorescence signal above the noise, but eliciting a rapid burst of 20-40 spikes resulted in
a strong fluorescence increase. Calcium signals rose to full magnitude within 2
acquisition frames (200 ms) of the stimulation onset, which lasted 120 ms. Fluorescence
decayed with a time constant of 0.75 s ± 0.01 SEM (somata; n=84) and 0.57 s ± 0.05
SEM (axon bundles; n=9).

Figure 32. Calcium bursting was correlated with a rapid series of evoked spikes (arrow). Near the
stimulation threshold, only one RGC shows a calcium response (top fluorescence trace), while the electrode
(black dot) detects spikes from two neurons in the cluster of cells. Spike traces were separated by principal
components analysis into two clusters of 13 and 26 spikes, and then averaged. Calcium traces are raw data.

Fluorescence signals were entirely abolished (118 somata, 12 axon bundles) within
minutes of applying 1-mM CdCl
2
to the superfusate (Fig. 33). Applying 1-µM
78
tetrodotoxin (TTX) in a separate experiment abolished responses to electrical stimulation
in over 80% of RGCs over a 200-µm electrode (n=84). The remaining cells roughly
doubled in threshold (x1.9 ± 0.1, mean ± SEM; n=16), and were located only on the
electrode surface. One out of nine axon bundles responded in the presence of TTX, with a
2.2-fold increase in threshold. Remnant calcium responses were likely due to
depolarization suprathreshold for voltage-gated calcium channels, as the increase in
threshold was consistent with the relative activation potentials for voltage-gated sodium
and calcium currents in RGCs (Lipton and Tauck, 1987).

Figure 33. Left: Cadmium abolished all calcium responses from axon bundles and somata. Middle: TTX
abolished responses from most RGCs, and all axon bundles except for one (bottom trace). Right: Persistent
calcium responses with TTX doubled in threshold and decreased slightly in magnitude. Traces were
averaged over 25 stimulus events. Arrows mark stimulus times.

79
STIMULATION THRESHOLD MAPPING

Threshold for every RGC near the stimulation site was calculated from the response of
each cell to a range of pulse amplitudes. Average threshold on the electrode was 4.52 ±
0.15 µA (mean ± SEM; n=98) for a 400-µs cathodic-first biphasic pulse, corresponding
to a charge of 1.8 nC and charge density of 5.8 µC/cm
2
on the 200-µm electrode. This
threshold is about 6-fold lower than that required to stimulate cells 187 µm from the
electrode in a previous study (Ahuja et al., 2008). Our average threshold charge is
comparable to that in a study of 125-µm electrodes in rabbit retina (Jensen et al., 2005),
which found thresholds of 0.22 nC for short latency and 2.2 nC for long latency
activation of RGCs with 0.5-ms pulses. Mapping the thresholds over the stimulation site
(Figs. 34, 35) revealed heterogeneity in RGC threshold over the surface of the electrode
and a trend toward increased threshold for cells farther from the electrode. Axon bundles
could be easily stimulated in addition to somata. Axon bundle stimulation was marked by
a strong fluorescence increase from the bundle and a streak of soma responses peripheral
to the stimulating electrode (Fig. 35).

80

Figure 34. Threshold map for somata (dots) and axon bundles (lines) over a transparent electrode (blue
outline), stimulated by 400-ms, cathodic-first biphasic pulses.

81

Figure 35. Threshold map showing a streak of antidromic stimulation from a 200-mm electrode (blue
outline), 400-ms pulse width. Color indicates threshold current. Small black dots are 10-mm electrodes.
Scale bar 50 mm.

CHOICE OF ANIMAL MODEL

The quality of staining with calcium indicators was affected by the choice of animal
model and the age of the animal (Fig. 36). We have achieved satisfactory results in
salamanders (Figs. 36A, 37) and in rats less than a week of age. The salamander retina is
fully developed in the larval stage, and thus we chose this as a model for retinal
stimulation. After eye opening in the rat, neither the potassium salt nor the dextran-
conjugate of OGB-1 stained the retina beyond the optic disk. Adding 2.5-mM probenecid
to the perfusate slightly improved staining in the rat. We also attempted to improve dye
82
retention by mixing probenecid with OGB-1-dextran 10 kDa before applying it to the
optic nerve stump, which yielded only marginal improvement. There appears to be an
export mechanism in adult rat RGCs unabated by probenecid and dextran conjugation at
10 kDa.

Figure 36. A: Salamander RGCs stained with Oregon Green BAPTA-1-dextran 10 kDa, on a
microelectrode array. The ITO electrode (200-µm) is centered in the field of view, with two 10-µm plated
electrodes in the upper left. B, C & D: Rat retina stained with Oregon Green BAPTA-1-dextran 10 kDa, at
age P6, eye opening, and P45 respectively. The inability of the mature mammalian retina to retain the
indicator is illustrated by the paucity of stained somata in C versus B. Probenecid (2.5 mM) was added to
the superfusate in B, C & D. Potassium probenecid was added to the retrograde dye solution in C (10 mM)
and in D (60 mM). Scale bars 100 µm.

83
DISCUSSION

Calcium imaging in the mature retina is not trivial, due to the difficulty in using AM-ester
conjugates. Other investigators have observed that Müller cells, pericytes, and endothelial
cells preferentially stain with calcium indicators (Wong, 1998), and thus the difficulty in
labeling RGCs in older animals with AM-ester calcium indicators has been attributed to
reduced uptake in older neurons. To bypass membrane permeability in RGCs, we
considered retrograde dye loading. Unfortunately, we have found that when the
unconjugated potassium salt form of OGB-1 is retrogradely loaded via the optic nerve
stump, it is excluded from RGC somata. In contrast, less highly charged tracer dyes were
not.

We then hypothesized that the main reason for the poor staining is that the dye is pumped
out of the cells, due to its being a highly negatively charged organic anion. Indeed,
addition of probenecid (Di Virgilio et al., 1988b; Khamdang et al., 2004), an organic
anion transport blocker, did improve retention of the calcium indicator in axons and
somata. Unfortunately, probenecid was only partially effective, as enough dye was
externalized to the make background fluorescence very high compared to the intracellular
fluorescence.

These observations led us to investigate the use of dextran-conjugated dyes, which should
not be pumped out of the cytoplasm. The dextran conjugate of OGB-1 successfully
84
stained RGCs in the salamander retina and young rat retina, but not in the mature rat
retina.

Figure 37. Wholemount stitched image of a salamander retina stained with Oregon Green-BAPTA-1-
dextran 10 kDa. Scale bar 200 mm.

Dextran conjugates are readily taken up by cells at an injection site and make excellent
neural pathway tracers (Reiner et al., 2000), conveyed by diffusion (Fritzsch, 1993). In
85
retrograde tracer studies, the axon uptake site was typically remote form the retina
(Dacey et al., 2003; Drager and Olsen, 1981; Sarthy et al., 1983; Yan et al., 1999)
necessitating a survival period of several days to stain cell bodies. Retrograde loading in
vitro stains more cells on a shorter time scale than injection to cortical projections of
RGCs.

We estimated the concentration of dye reaching the soma (neglecting dye removal
mechanisms, sequestration, or binding to immobile sites in the axon) by solving the
diffusion equation in one-dimension,
!
"#
"t
= D
"
2
#
"x
2
. (24)
The axon length was 2 mm, terminated by a constant concentration of 20 mM on the cut
end. The opposite end of the axon was terminated by the soma with a radius of 6 µm.
Concentration of the dye was considered uniform through the soma volume, since its
diameter is far less than the length of the axon. The concentration inside the soma φ
soma
is
the time integral of diffusive flux J into the soma, scaled by the soma volume V and axon
area A, and thus the boundary condition can be expressed as,
!
J =
"#
soma
"t
V
A
. (25)
The diffusion constant for OBG-1 dextran was assumed to be 15 µm
2
/s (Seksek et al.,
1997). The finite element model was solved using COMSOL Multiphysics ver 3.2
(COMSOL, Burlington, MA). After 4 hrs of retrograde loading, the somatic
86
concentration reached 3.6 µM and 13 µM for axon diameters of 0.5 µm and 1.0 µm,
respectively.

Assuming a resting calcium level ([Ca
2
]
i
) of 75 nM and indicator concentration ([B
T
]) of
5 µM, the binding ratio for OGB-1 (k
d
= 0.17 µM) is κ
B
=14, given by (Neher, 1995)
κ
B
=k
d
[B
T
] / (k
d
+ [Ca
2
]
i
)
2
. (26)
The time course of the fluorescence signal is probably not being altered by OGB-1,
assuming the endogenous calcium binding ratio is much larger than 14. In mouse RGCs
the endogenous calcium binding ratio is 87 to 122, with a time constant of 1.7 s (Mann et
al., 2005), and a calcium extrusion rate of 52 s
-1
. Our time constant was 0.75 s, leading us
to believe that in salamander the endogenous binding ratio is lower and/or the extrusion
rate is higher than in mouse.

Using this dye loading method, visual processing in the retina could be studied with high
spatiotemporal resolution by two-photon microscopy. Parallel imaging of many cells
would be a natural advancement of prior multiphoton studies (Denk and Detwiler, 1999)
involving a single labeled cell. The infrared excitation source would not interact with
photoreceptors, thus permitting optical stimulation. Such an experiment could be
implemented on an inverted two-photon microscope, with images presented to the
photoreceptors via the condenser or a water immersion objective above the retina.

87
Work remains to be done for mature mammalian retinas. New inhibitors of organic anion
transporters may be needed, or transgenic animals that do not express the pertinent
transporters into maturity may be required. In addition to calcium imaging, the retrograde
technique may find application in counting RGCs in glaucoma models. For cell counting,
a nuclear stain may be more appropriate than tracer dyes because the axon bundles can
easily obscure cells near to the optic disk.

The retrograde loading method presented here is a rapid means to complete labeling of
RGCs with calcium indicators. We have demonstrated that our retrograde loading process
preserves electrophysiological activity, and moreover that neuronal activity can be
observed in virtually all RGCs in a mature retina, with unambiguous identification of cell
locations. We are using threshold maps, as shown in this article, to study how electrical
stimulation interacts with the retina to produce a response in the ganglion cells.

88
Chapter 4. Apparatus Design

Carrying out experiments with electrical and optical interface to the retina required some
new tools. First, problems with imaging and stimulation were solved. Retrograde loading
stains the RGCs weakly. Therefore, MEAs needed to be fabricated on a coverglass
substrate to permit collection of a larger cone of fluorescence emission with high
numerical aperture optics. Next, an interface board was needed with low stray
capacitance to avoid shunting of the stimulus away from the MEA. High precision
current sources were needed because the MCS stimulator was not accurate at low
microamp levels.

To investigate separation distance from the retina to the MEA as a parameter affecting
threshold and response size, it was necessary to deposit thin films of agarose gel onto the
MEA. A gel spin coater and protocol were developed.

4.1 Electrophysiology rig overview

The rig primarily consists of a microscope, image acquisition, electrical stimulator, and
perfusion system. The retina is held in a recording chamber on the microscope stage. The
base of the recording chamber is the MEA with electrodes connected to the current
sources. A single computer controls stimulation and image acquisition parameters.

89
Images are acquired in Andor Solis using frame transfer mode with the high readout
speed settings. Images are streamed directly to hard disk, not to memory because the file
size is 3 GBytes. The camera is run in external trigger mode, receiving its trigger from a
sync output from the STG2008 stimulus generator (from MCS).

The MCS STG2008 stimulus generator drives all other apparatus and serves as the
central timekeeper for synchrony. Once programmed by the computer, the STG2008
outputs stimulus commands from its analog voltage outputs. These are converted to a
proportional current pulse by the current source board. One TTL sync channel drives the
camera exposure trigger with 1-ms pulses on 100-ms intervals. Another sync channel
triggers the oscilloscope to display electrode voltage waveforms. Two other sync
channels are available for driving shutters, the LED illumination source, or other devices.

Figure 38. The recording chamber is mounted over the objective lens of the microscope. The retina with
stained RGCs is placed RGC-side down on the MEA. Stimuli are delivered to electrodes with a return
electrode encircling the bath of the chamber.

90

Figure 39. The microscope has upright (top) and inverted (bottom) objective lenses. Images are acquired
from the inverted microscope. Patch clamp or optical stimulation can be done with the aid of the upright
microscope.

4.2 Microscope

TIFF image sequences were acquired by an Andor Ixon 885K-VP camera on an
epifluorescence, inverted microscope (objective: Nikon Plan Apo 20X 0.75 NA), at a rate
of 10 frame/s with 83% exposure duty. Fluorescence filters were purchased from
Semrock for Oregon-Green-488-BAPTA-1 dextran (filter set # FITC-3450B) and Alexa-
594 (filter set TXRED-4040B).

91

Figure 40. Spectra for Oregon-Green-488 (gray) and the FITC-3450B filter set. Blue, excitation, green
dichroic mirror, red, emission filter. From www.semrock.com

Figure 41. Spectra for Alexa-594 (gray) and the TXRED-4040B filter set. Blue, excitation, green dichroic
mirror, red, emission filter. From www.semrock.com

92
The fluorescence excitation source was a super bright white LED
(www.LEDLightingSupply.com part #XRE7090WT-U1-00C01).

Figure 42. Transient light flash detector.

4.3 Current sources

Electrical stimulation in all cases was delivered to single or multiple electrodes by a 16-
channel current source controlled by analog voltage pulses from a Multichannel Systems
STG2008 stimulator. The current source has +/-25-µA range with 50-nA resolution.
Pulses are asymmetric charge-balanced, cathodic-phase first, having an undelayed anodic
phase twice the duration of the cathodic. Two channels were connected in parallel when
more than 25-µA were required.

93

Figure 43. Circuit schematic for the current source base on the Texas Instruments INA326. Sixteen
individual channels of this circuit are on the current source board.

Figure 44. Circuit schematic for the on-board current sense and voltage sense.

94

Figure 45. Circuit board layout for the 16-channel current source.
/ Optical Electrophysiology / MEAs / current source /

4.4 Potentiostat

High quality electrodeposition is achieved when the electrode polarization is controlled.
This requires that the electrode voltage be referenced to the potential in the electrolyte,
not the potential of the counter electrode (a platinum wire). The reference electrode is a
Ag/AgCl electrode in 3M KCl. Such a reference electrode is nonpolarisable, meaning that
no potential exists across the metal to electrolyte interface. A potentiostat was built to
take a command voltage and mirror this to the MEA electrodes relative to the electrolyte.
The MEA electrodes were held at ground potential while the counter electrode was
cycled to achieve the desired potential in the electrolyte.

95

Figure 46. Schematic of the potentiostat for electroplating electrodes with voltage ramps referenced to a
Ag/AgCl electrode.

4.5 Gel Spinner

Agarose gels were spin coated onto the MEA using a variable speed spinner. A stepper
motor was used here, as I got a promo for a free motor, but a DC motor would be easier
to control (not be prone to stalling) in future models.

96

Figure 47. The gel spinner in operation with an MEA on the rotation platform. When applying agarose, the
plastic splashguard is lowered.

97

Figure 48. Circuit schematic for the gel spin coater. The stepper motor is guided by the selected speed and
by its current rotational position to avoid stalling.
/ Optical Electrophysiology / MEAs / spinner

98
4.6 Retrograde loading tools

Retrograde dye loading to staining RGCs is performed as described in chapter 3.4. The
detailed protocol for retrograde loading is located in:
/ Proposals / Retrograde loading protocol.doc

Parts that are important to the protocol are the tubing segment that holds dye on the optic
nerve stump, and the Teflon needle used to dispense dye into the tubing.

Small Parts #TWPT-050-12-10 polyimide tubing. ID 0.0508”, wall thickness 0.00375”
Small Parts #NE-024-10 Teflon 24 gauge needle

4.7 Fabrication of microelectrode arrays

Multielectrode arrays (MEAs) were fabricated by the authors in the W. M. Keck Center
for Photonics at the University of Southern California. Electrodes and traces were
patterned from indium-tin-oxide film (10 ohms/square) on glass substrates, similar to
others used for in vitro studies (Gholmieh et al., 2006; Gross et al., 1985). A 1- to 2-µm
thick layer of silicon nitride was deposited by plasma-enhanced chemical vapor
deposition, and then patterned by reactive ion etching in CF
4
plasma to open holes over
the electrode surfaces and perimeter contact pads. These MEAs have the same perimeter
contact pad layout as Multichannel Systems, GmbH (MCS) arrays, for compatibility.
99
Some arrays were fabricated on glass substrates, 1.5-mm thick. Most arrays were
fabricated on 22 x 26 x 0.13-mm thick ITO coverglass (SPI Supplies www.2spi.com, part
#06477), and then bonded with silver epoxy (CircuitWorks CW2400, distributed by SPI
Supplies, part #5000) to the traces of a circuit board mimicking the MCS arrays. All 10-
µm electrodes and some larger electrodes were electroplated with Pt/Ir by cyclic
voltammetery from -0.7 to +0.8 V versus Ag/AgCl reference electrode swept at a rate of
50 mV/s. Electrode arrays are entirely transparent except for plated electrode surfaces,
permitting an unobstructed view of ganglion cells.

Mask layout files are located in:
/ Optical Electrophysiology / MEAs / quad hex spiral 20071017 /

Design was made in the CAD layout tool Kic then converted to a postscript file
The chrome mask was printed by Photosciences (www.photo-sciences.com)
/ Optical Electrophysiology / MEAs / Mask Layout Tools CD /

100

Figure 49. Mask design for the three cover glass MEAs. Green layer is positive for the ITO film. Pink
layer is negative to the silicon nitride insulation (pink areas are void of insulation).

101

Figure 50. Scale layout of the Hex MEA with annotation for MCS electrode numbers.
102

Figure 51. Scale layout of the Quad MEA with annotation of the MCS electrode numbers. Note the
hexagonal group of 13 electrodes is 20 µm, not 10 µm in diameter.

103

Figure 52. Scale layout of the Spiral MEA with annotation of MCS electrode numbers.
104

Figure 53. Circuit board that carries the MEA. A square window is cut out from the center of the board and
the MEA pads are silver bonded to the central traces on the bottom of the board (green layer). This board is
a drop in replacement for MCS MEAs and fits the MCS-1060-BC preamp board. Pogo pins contact the
perimeter pads on the top layer (red) of this board. Express PCB layout file located in:
/ Optical Electrophysiology / MEAs / cover glass MEA 20070812.pcb

4.8 Recording chamber

The retina is held in a recording chamber on the MEA. It is gently kept flat by a
membrane on a titanium ring that covers the retina. The ring is gently nudged or picked
up to place the optic nerve about 2 mm away from the electrodes. The recording chamber
105
(attached to the MEA with Nusil Silicone Technology #MED2-4220) confines saline
perfusate to a small volume over the retina. Inlet and outlet slots accept glass capillary
tubes for the saline flow. Saline is fed into the chamber by gravity flow and removed by
suction. The suction capillary is beveled at roughly 45 degrees such that it sucks up both
air and saline at a continuous rate (avoids slurping). The perfusion lines are C-Flex tubing
with low oxygen permeability (Cole-Parmer #06422-02 C-Flex tubing ID 0.062”, OD
0.125’).

Figure 54. The MEA and recording chamber are held on the microscope stage by the interface board.
Stimulus pulses are delivered to electrodes via the DIP switches or the test sockets.

The membrane ring for holding the retina is made by machining titanium tubing to a thin
ring (Small Parts #TT-035/08-06 titanium tube, OD 0.5”, wall 0.035”), then gluing with
Loctite #403, a porous hydrophilic PTFE membrane (Millipore #JVWP01300, Billerica,
MA) to the ring.

106

4.9 Interface board

Design files for the interface borad are located in:
/ Optical Electrophysiology / MEAs / Interface board /

Figure 55. The interface board with prototype current source mounted on the left.
107
Chapter 5. Data processing

Stimulation thresholds of retinal ganglion cells are measured optically by collecting a
sequence of images during the delivery of a set of current pulses. The calcium indicator
used in these experiments brightens upon binding intracellular calcium and serves as a
reporter for spiking activity in individual cells. A set of progressively increasing current
pulses is delivered to determine the amplitude of stimulus that evokes a response.
Responses are detected as a rapid increase in fluorescence from a cell and must be
temporally correlated with the stimulus to be counted. Ultimately the image sequence is
reduced to a threshold map defining the coordinates of each cell relative to the
stimulating electrode and the optic disk. Data are then pooled from multiple experiments
under similar conditions to increase the spatial resolution of the threshold map.

Of particular interest is the size and shape of the evoked response because this is a
predictor for what a patient may see. From threshold maps I have quantified the
displacement position of the response relative to the electrode and the paraboloid fit to
the shape. This data is compared to the finite element model predictions of percept size in
chapter 6.

This chapter is meant as a guide to the data processing steps taken. The detailed protocol
for executing the processing pipeline can be found in the notes contained in the Matlab
script files and in the following Word document:
108
data processing code / calcium / raw data to threshold pipeline / Calcium Imaging Data
Processing Protocol.doc

Matlab scripts that convert raw data to measured thresholds are located in:
data processing code / calcium / raw data to threshold pipeline /

Copies of processed data and the Matlab script for post processing are located in:
data / processed salamander calcium / structured data / single electrode /
This post processing code is responsible for transforming coordinate systems to overlap
data from multiple experiments and then to quantify spatial properties of the response.

DATA ACQUISITION

Images are continuously acquired at 10 frames/s with an 83% exposure duty cycle. The
stimulation protocol (Fig. 56) begins with 5 s of delay before the first stimulus of
amplitude 1. The stimulus is repeated on 2-s intervals for a total of 25 stimuli at
amplitude 1 in a 50-s window. The next stimulus at amplitude 2 begins after a 10-s delay.
A total of 10 stimulus amplitudes are delivered, with the maximum amplitude usually set
by electrode corrosion limits. The 5-s delay immediately preceding each new stimulus
amplitude is a control region to measure the signal noise level. The fluorescence signal
without stimulation is used to set the response detection thresholds relative to the noise,
as described below (section 5.2). There are 25 replicates in each amplitude to reduce
109
detection noise. The stimulus is a burst of usually 40 pulses in 120 ms, which appears
nearly instantaneous relative to the slow acquisition rate. The purpose of the burst mode
stimulation is to trigger a sufficient influx of calcium for response detection.

Figure 56. Stimulation protocol and threshold measurement process. A trains of progressively increasing
amplitude biphasic pulses are delivered to the stimulating electrode. Each stimulus event is a rapid burst of
20 or 40 pulses. At threshold, half of the stimulus events evoke a detectable response (top traees).

5.1 Image data reduction

Fluorescence intensity and coordinates of each cell and axon bundle were extracted with
Metamorph, and then post processed in Matlab to calculate threshold and spatial
relationships. A region of interest slightly smaller than the soma diameter was manually
placed over each soma. A rectangular region was manually drawn over a peripheral
segment of each axon bundle with care to exclude fluorescence from somata. Metamorph
110
automatically assigns identity numbers to these regions. Using the graph intensities
application in Metamorph, the average intensity of each region was saved to a text file for
importation into Matlab.

Figure 57. Regions placed over cell features on the retina fluorescence micrograph for axons (left) and
somata (right). Red lines define the extents of the region with ID number marked in blue.

5.2 Response detection and threshold

Calcium response was detected as a sudden increase in fluorescence, temporally
correlated with the stimulus event. Raw data of average fluorescence intensity as a
function of time were convolved with a difference filter, [2 1 -1 -2] to reveal the sharp
rises in fluorescence characteristic of a calcium response. The difference-filtered
waveform for each cell was then thresholded at the RMS noise level for that individual
cell. Any point that crossed this detection threshold was counted as a putative response to
stimulation.
111

Figure 58. Raw fluorescence traces (black, top 3) from one RGC soma. As stimulation current is increased
(downward) more responses are seen to the sequence of 25 stimulation events. The time derivative of
fluorescence (blue, bottom 3) is formed by convolution with the difference filter. Red lines indicate the
detection limits, which are set to the RMS noise level.

5.3 Rejection of false responses

Detected responses were binned according to latency (Fig 59). The response percentage
to a given stimulus amplitude was found by taking crossings temporally correlated with
the stimuli, less the estimated number of uncorrelated crossings, and normalizing to the
112
number to stimulation events. Responses were counted with latency of 100 ms and 200
ms from the onset of stimulus (the first two image frames during a stimulus event).
Responses detected with latency from 0.3 s to 1.9 s were summed and divided by this
time span to estimate the false detection rate. This density was then subtracted from the
first two bins to obtain evoked responses only.

Figure 59. Latency histograms for the same RGC soma as above. False detections are randomly distributed
at low stimulation amplitudes. As current is increased (toward the right), responses accumulate in the first
two latency bins.
data./processed salamander calcium/data20081118/ 1000-µs e56 soma roi60

5.4 Measuring stimulation threshold

The dose-response curve over ten stimulation amplitudes was fitted by a sigmoid (27),
individually for each cell in the image. Threshold was defined as the stimulation
amplitude at 50% response. In cases where the response rate saturated at a value less than
one, the curve was rescaled to maximum amplitude of 1 before fitting, only if the
saturation response rate was greater than 50% and the response rate did not change by
more that 10% as stimulus amplitude increased.

113
(27)

5.5 Plotting threshold maps

In addition to the coordinates of cells, it is also important to identify the optic disk and
the electrode locations. The spatial properties of the responding region are not a simple
spot, as a consequence of the retinal anatomy. Threshold is lower on the peripheral side
of the electrode (away from the optic disk). Also, responding cells often form a streak
following the path of axon bundles that pass over the electrode.

At this point the threshold for each soma and axon bundle is either known or marked as
undefined for non-responding regions. A simple map (Fig 60) of the cells in the field of
view for each stimulation configuration is saved as a JPEG image. This can be used for
reference to patterns observed within a single experiment. At the same time all
comparable trials from an experiment are compiled into a single data structure describing
the stimulation parameters, the threshold values, and the coordinates of features.

The optic disk position is determined in one of two ways. The location can be calculated
from the convergence point of axon bundles in an image. This is accurate for a field of
view near to the optic disk where the angle between bundles is large. For peripheral fields
!
y=
1
1+e
"k(x" x
0
)
114
of view where bundles are highly parallel it is more accurate to identify the position
manually by collecting a panorama of images of the retinal wholemount. In this case an
override file is used to replace the calculated position with the manually identified optic
disk position.

Every image is acquired without regard for the orientation of the axons, but when
processing the data they must be controlled. Each map is therefore shifted and rotated
such that the stimulating electrode lies at the center and the optic disk is positioned to the
left. The original angle, θ, of the optic disk is measured between the horizontal and the
line extending from the electrode to the optic disk. Coordinates of every feature are
modified by the rotation matrix (28) as follows:
!
R
"
=
cos" #sin"
sin" cos"
$
%
&
'
(
)
(28)

aligned_coords = R
θ
* (raw_coords – electrode_coords) (29)
115

Figure 60. Threshold map for experiment 20081118, stimulating electrode 56 in frame 1, using 1000-µs
pulse width. Bilinear color map indicates stimulation threshold and numbers next to each cell specify the
exact value in microamps. The 200-µm electrode is marked by the blue circle.

116
Thresholds can vary from one experiment to another under the same conditions by nearly
two-fold. This appears to be inherent to variability in the animals used. Salamanders are
harvested in the wild and are not inbred as is typical of rodent strains used for research.
The size and/or age of the salamander affects the degree of natural degeneration
(Townes-Anderson et al., 1998) that occurs in the retinas of these animals. Also, seasonal
changes appear to affect their health. The photoreceptors are most sensitive to these
influences, but perhaps the ganglion cells are too. These variations can cause patterns to
appear in composite threshold maps that are merely artifacts of different sampling in
space of cells near the electrode. To cancel out variation between animals, thresholds are
normalized in each dataset to the average threshold within 20-µm outside of the
stimulation electrode perimeter. Composite maps are generated by overlapping and
averaging the normalized thresholds. The map is finally scaled by the cell-count-
weighted average of the normalization factors to return to a magnitude in microamps.
The normalized threshold for al cells, Tn(x,y), for an experiment i, and average threshold
near the electrode perimeter, Tavg,
!
Tn
i
(x,y) =
T
i
(x,y)
Tavg
i
. (30)
The averaged normalization value (microamps) across experiments is,
!
Tscale =
n
cells,i
Tavg
i
i=1
N
"
n
cells,i
i=1
N
"
. (31)
The effective threshold for cells in a position (x,y) is
117
!
Tavg(x,y) =Tscale
1
N
Tn
i
(x,y)
i=1
N
"
(32)

Figure 61. Threshold map compiled from several experiments. Stimulating electrode outlined in black.
Parabolic profile fit to low threshold region outlined in blue.
118
Chapter 6. A Conversation with the Retina

The experiment log file is located in:
/ Data / Electrophysiology log.doc

6.1 Correlation of calcium signals with electrical activity of the cell

Electrical recordings from two experiments established that calcium signals were
correlated with a burst of spikes from RGCs. Single spikes could not be detected by
imaging because a very small portion of the calcium influx becomes bound by the
calcium indicator dye. Therefore, a burst of 40 pulses was applied for each stimulus event
in threshold measurement experiments.

Figure 62. Dual recording from a ganglion cell over a 10-µm electrode. Stimulation was applied to the
neighboring 200-µm electrode (black electrode marked by lightning bolt).

119

Figure 63. Dual recording from a group of RGCs. At least 26 spikes were needed to detect a calcium
signal.

6.2 Repeatability of the threshold measurement

Trial to trial repeatability of the threshold measurement was measured by imaging two
identical stimulation runs with 40 minutes of imaging between them. Any difference
accounts for variance in individual cells, the influence of photobleaching on response
detection, and any possible accommodation of the retinal circuitry to stimulation.

Table 3. Measurement Repeatability
n Correlation
coefficient
Mean % change SD %
somata 146 0.692 -1.8 11.3
axon bundles 10 0.797 -3.9 7.55

120

Figure 64. Threshold change for 146 somata (black dots) and 10 axons (blue dots). Fit line slope is 0.966
with the intercept constrained to zero, having a coefficient of determination 0.33. Pulse width 1000 µs,
electrode 200 µm, gel spacer 43 µm. /data20081029/repeat stimulation

The correlation coefficient indicates that a linear relationship exists between the
thresholds in the two trials, but it is not strong. On average, the thresholds from
individual cells change by only a couple percent. The standard deviation in repeatability
is roughly 11% and provides estimation for the noise in the measured threshold of each
cell. The noise could increase from this value when binning data from multiple
experiments or when binning thresholds from cells with respect to some parameter such
as displacement from the electrode. Another assumption that could increase noise when
pooling data is that all RGCs have the same threshold without consideration of their
subclassification. Some cells are larger than others and some may have different
distributions of voltage-gated sodium channels.

121
6.3 Single electrode stimulation of somata and axons

Threshold was measured from the calcium fluorescence signal of RGC somata and axon
bundles. Electrode sizes were 10-µm, 30- µm, 60- µm, and 200- µm. The thickness of
spacer gel was 30- µm and 50- µm. Pulse width was set at 60- µm, 400- µm, and 1000-
µm. Within this parameter space, short pulses directly stimulated RGCs and has the most
focal response areas.

Axon bundle thresholds were measured from axon fluorescence signals and sometimes
from the threshold of distant somata far to the peripheral side of the electrode. Diffuse
calcium signals were observed from the inner plexiform layer (RGC dendritic arbors) and
there is the possibility of signal leakage into regions defined for some axon bundles.
Peripheral streaks of responding somata may provide a better measure of threshold for
axon bundles.

THRESHOLD MAPS

Response region measurements are predictors for the phosphene size, or spatial resolution
of the prosthesis. Fitting a paraboloid to the threshold data marked the response extents to
be the oval where threshold rises 50% above the minimum threshold. Curve fitting was
performed in transformed threshold space to improve the robustness of the fit.
Transforming to an exponential decay was necessary to reduce the influence from the
highly variable threshold in distant cells. Threshold maps were transformed from T(x,y)
122
to the form f(x,y) = exp(-T(x,y)), then rotated by an angle θ, and finally fitted by a
Gaussian-like function,
!
g(x,y) = g
max
e
"kT
min
(x"x
0
)
2
#
x
2
+
(y"y
0
)
2
#
y
2
$
%
&
&
'
(
)
)
(33)

where T
min
is the minimum threshold near the electrode, g
max
= e
-Tmin
, and the factor kT
min

is used to set the extents of σ
x
and σ
y
, which represent the position at which the threshold
becomes k times larger than the minimum threshold. This fitting is equivalent to a
paraboloid in the coordinate system of T(x,y), with the fit weighted in sensitivity for the
trough of the surface. The value of k was set to 0.5, so that the curve fitting search returns
values for σ
x
and σ
y
that mark the boundary at which threshold rises by 50% .

123

Figure 65. Threshold maps for single electrodes in direct contact with the retina. Electrode size ascends
ineach row. Pulse width in each column is 60 µs (left), 400 µs (middle), and 1000 µs (right). Curve fits for
the percept boundary were not meaningful for the smallest electrodes, which had scattered thresholds.

124
On large 200-µm electrodes, the responding region of RGCs is offset farther to the
periphery with short pulse widths, but more centered on the electrode for long 1000-µs
pulses. The offset of the responding regions is consistent with the hypothesis that the
axon initial segment is the site of action potential initiation. Interestingly, the site of
action potential initiation appears to shift from the initial segment to either the inner
retina or the RGC soma when pulse width is increased. Kynurenic acid treatment raised
the threshold by 93% (section 6.4) leading to the conclusion that the inner retina mediates
the RGC response to long pulses.

Axon bundles had nearly the same threshold as RGC somata when measuring calcium
signals from the axon bundle. Axon stimulation threshold was also measured by
observing the distant somata from which they originate. Axon threshold was about 60%
higher than somata when using the distant peripheral soma response as an indicator of
axon bundle stimulation. The latter method may be more reliable because it is not prone
to signal contamination from RGC dendrites near the electrode.

ANODIC FIRST PULSES

Pulses with a leading cathodic phase more easily stimulate neurons, because this leads to
depolarization of the membrane on the side of the cell facing the electrode. Current
density is weaker on the opposite side assuming the electrode is close to the cell. Anodic
leading phase pulses were compared to cathodic leading phase pulses. Anodic thresholds
125
for somata rose by 21% (n=121, SD=18 p<0.001), and for axons, 21% (n=12, SD=9,
p<0.001). For either leading phase (Fig 66), the stimulated region was approximately 230
µm in diameter with a peripheral offset of 30 µm for cathodic and 22 µm for anodic
pulses (400-µs).

Figure 66. Threshold increased globally by 21% for anodic first biphasic pulses (right) versus cathodic first
biphasic pulses (left). data20081020/anodic

AXONAL STIMULATION

A 200-µm electrode was stimulated 750 µm central to the field of view (400 µm x 400
µm) to produce antidromic spikes in the RGCs. To verify that the calcium responses were
due to antidromic spike propagation instead of distant inner retina stimulation, kynurenic
acid (1 mM) was applied in the superfusate to block glutamatergic transmission.
Thresholds rose significantly versus a repeat stimulation control (p<0.001), but the
increase in threshold was only 24.5%. Threshold for cells located near the stimulation site
Cathodic Anodic
126
rose by 93% (see section 6.4) under the same conditions (1000 µs pulses). Responses
from the strip of cells located up to 950 µm from the electrode had the same threshold
through the peripheral region, yet threshold rises sharply within tens of micrometers to
the superior or inferior sides of the electrode. This streak pattern, in addition to a
relatively small change in the presence of kynurenic acid indicate that the threshold
measured for these peripheral somata are representative of axon bundle thresholds.

Table 4. Threshold change for antidromic stimulation after kynurenic acid:
n correlation
coefficient
Mean % change SD
somata 174 0.567 24.5 21.2
axon bundles 11 0.983 15.6 5.6

Figure 67. Threshold change for somata (black dots) and axons (blue dots) after applying kynurenic acid.
Fit line slope is 1.22 with the intercept constrained to zero, having a coefficient of determination 0.34.
Pulse width 1000 µs, no gel spacer. Inset, distribution of somatic threshold change.
/data20081118/kynurenic acid control

127
6.4 Short pulses preferentially stimulate RGCs instead of the inner retina

With a 200-µm ITO electrode, different pulse widths were evaluated for preference of
cellular targets. Threshold at each pulse width was measured before and after application
of kynurenic acid (a broad spectrum blocker of glutamatergic transmission). A spacer gel
of 30 µm was used in this experiment. Long pulse widths of 1000 µs increased threshold
(p<0.001) by nearly two fold when synaptic transmission from the inner retina was
blocked, indicating that long pulses stimulate the inner retina at lower amplitudes than the
ganglion cells. There was only a 2.9% increase in threshold (p<0.001) for short pulse
widths of 60 µs, consistent with direct stimulation of the ganglion cells. Intermediate
pulse widths showed an intermediate change in threshold.

Table 5. Change in threshold after application of kynurenic acid:
1000 µs n correlation
coefficient
Mean % change SD p
somata 150 0.827 93.2 26.1 <0.001
axon bundles 20 0.891 88.5 21.8 <0.001

400 µs
somata 175 0.887 40.7 19.3 <0.001
axon bundles 21 0.916 36.4 16.4 <0.001

60 µs
somata 38 0.639 2.92 3.93 <0.001
axon bundles 7 0.099 4.02 2.19 0.009

128

Figure 68. Threshold change for somata (black dots) and axons (blue dots) after applying kynurenic acid.
Fit line slope is 1.92, 1.41, and 1.029 for pulse widths 1000 µs, 400 µs, and 60 µs, respectively. Gel spacer
is 30 µm.
/data20081016/kynurenic acid control

129
The target of stimulation for 1000-µs pulse width appears to be within the inner retina.
The responding region is centered on the electrode for 1000-µs pulses, instead of offset to
the periphery as with shorter pulses. Upon application of kynurenic acid, the responding
region then shifts to the periphery by 20 µm (Fig 69).

Figure 69. Left: response to 1000-µs pulses. Right: The response shifts to the periphery in the presence of
kynurenic acid.
/data20081016/kynurenic acid control

6.5 Separation from the array raises threshold

Separation of the retina from the MEA was expected to both raise threshold and increase
the response area, which were both true. Unfortunately adding the spacer did not appear
to raise axon bundle thresholds relative to somatic thresholds. These experiments should
be repeated with measurements from peripheral somata to verify axon bundle thresholds.

130
Agarose gel (1% agarose in saline) was spin coated onto the MEA before mounting the
retina. This gel is electrically equivalent to the saline perfusate and the vitreous humor of
the eye.

30 µm Gel

Figure 70. Threshold maps for stimulation through a 30-µm spacer gel.

131
50 µm Gel

Electrode size:

Figure 71. Threshold maps for stimulation through a 50-µm spacer gel.

132
6.6 Bipolar stimulation is advantageous only for small electrodes

To avoid stimulation of axon bundles, bipolar stimulation was directed transverse to the
axons. As an internal control, the cathodic electrode of the pair was also stimulated in
monopolar mode. Both bipolar and monopolar stimulation evoked a streak of somatic
responses characteristic of axonal stimulation for 30-µm and 60-µm electrodes. The 200-
µm electrodes also stimulated axons according to measurements from the bundle
fluorescence. Only 10-µm electrodes avoided axonal stimulation in bipolar mode, even
though the streak response was observed in monopolar mode. Although bipolar
stimulation has no benefit for the electrode dimensions of near term retinal implants, it
provides selectivity to stimulation of somata for 10-µm electrodes.
133
Phased Bipolar Bipolar Monopolar

Figure 72. Bipolar stimulation with electrodes of increasing size (downward in column) and for different
pulse types, phased bipolar (left column), ordinary bipolar (middle column), and monopolar stimulation
(right column).
processed salamander calcium/data20081020
processed salamander calcium/structured data/bipolar

134
For electrodes larger than 10 µm, bipolar stimulation between neighboring electrodes
increases the size of the responding region of RGCs versus monopolar control, but does
not change the minimum threshold. Axon bundle thresholds do not appear to be affected
by using bipolar stimulation of large electrodes. However, 10-µm electrodes can be
stimulated in bipolar mode to concentrate the responding cells near the two electrodes.
This could possibly reduce the percept size in patients. Thresholds rose by 120% (n=35,
SD=98, p<0.001) with bipolar stimulation on these small electrodes, and the peripheral
streak of low threshold cells vanished.

In an attempt to avoid stimulating axon bundles passing over the
cathodic electrode, a phased biphasic pulse was delivered to the pair of
electrodes (Fig 72, left column). Each biphasic pulse had a leading
anodic phase, and an overlapping phase of opposite polarity for bipolar
stimulation. Each electrode was charge balanced. The threshold rose for
phased biphasic pulses versus ordinary biphasic pulses. The following
table compares somata and axon bundles on an individual basis and
presents the average change. Qualitatively, thresholds rose on the
source electrode when it was changed to have a leading anodic phase,
while thresholds lowered slightly on the return electrode, possibly due
to changing from an asymmetric to a symmetric biphasic pulse.
Ultimately, no benefit was observed with this stimulation scheme.

phased
bipolar
135
Phased bipolar stimulation (triphasic bipolar) was compared to ordinary bipolar
stimulation using four electrode sizes. The mean threshold of cells over entire field of
view was used in the following table.

Table 6. Soma thresholds increased with phased bipolar stimulation
processed salamander calcium/data20081020/phasebp

Applying a saline spacer of 40 µm to the array raised the threshold for bipolar stimulation
by approximately 10 fold for electrodes 200 µm in diameter. Axon bundles were
stimulated just as easily as somata with the spacer.

Figure 73. Bipolar stimulation of 200-µm electrode pairs with 400-µs pulses. Left: no spacer 20081020.
Right: 40-µm spacer 20081029 and 20081111

200 60 30 10 Diameter
µm

Type
Thresh
Δ (%)
p Thresh
Δ (%)
p Thresh
Δ (%)
p Thresh
Δ (%)
p
Soma 20 <.001 29 <.001 10 0.0015 -6 0.3
Axon 23 <.001 22 0.03 11 0.14 -19 0.2
40-µm
spacer
136
Results from bipolar stimulation with and without spacer gels indicate that bipolar
stimulation only provides some benefit toward focal stimulation with 10-µm electrodes,
and that the array must be in direct contact with the retina to keep thresholds low.

6.7 Line pattern stimulation

The ability of the retina to respond to line pattern stimulation was evaluated with 10-µm
electrodes on a 100-µm grid, using 400 µs pulses. Groups of 4 electrodes in a row,
column, or diagonal, were stimulated in parallel. The response pattern was marked by
streaks along the path of axon bundles. In most cases, the response was not limited to the
vicinity of the active electrodes. More data are needed with small electrodes at shorter
pulse width to determine if coherent pattern stimulation is possible.

137

Figure 74. Line pattern stimulation from 10-µm electrodes (blue circles). Each row shows the pattern of
cells responding at the pulse amplitude written in the left column.

138
6.8 Stimulation under pressure

A small aluminum weight (89 mg, area 7.07 mm
2
, height 4.57 mm, density 2.7 g/cm
3
)
was applied on top of the membrane that holds the retina down on the MEA. To reduce
reflection of the excitation light, the weight was chemically etched briefly in pure HCl to
produce a roughened gray surface. After applying the weight, the retina noticeably
compressed; the ganglion cells spread out and continued to slowly creep thereafter by a
few micrometers. At all pulse widths, thresholds rose significantly for somata by a small
amount, but the change for axon bundles was not significant. Kynurenic acid was added
to the perfusate before the compression test. Subtracting the increase due to kynurenic
acid (section 6.4), only 1000-µs pulses had a lower threshold with compression.

139

Figure 75. Threshold before compression (black trace) and with compression (pink trace). Compression of
the retina raises threshold slightly for RGCs by an amount approximately equal to the standard deviation of
the threshold. Significance marker, # p <0.1, * p < 0.05. Somata were pooled over the electrode surface up
to 120 µm from the electrode center to determine statistical significance of the change in mean threshold
(table below). data20081118/weighted

60 µs 400 µs 1000 µs
140
Table 7. Compression thresholds (µA)

soma axon

Pulse width
(µs)
Compression

- + p - + p

1000

1.99 2.35 <0.001 2.65 2.31 0.13

400

3.07 4.12 <0.001 4.28 4.28 1

60

14.0 16.8 <0.001 - - -

6.9 Estimating the effective spatial resolution of prosthetic vision

Average displacement for 60-µm electrodes is (44, -11) µm, and for 200-µm electrodes
the displacement is (40, -6) µm. Regardless of electrode size and pulse width, the
responsive somata are located approximately 40 µm peripheral to the electrode. The size
of the responding region is smaller for short pulses. Separating the retina from the array
has little effect on the size of the responding area. More data with spacers are needed to
confidently state response area.

Even with small electrodes, the response area was not less than 100 µm in diameter.
Using smaller electrodes may not provide any gain in resolution if the response cannot be
focused to an area smaller than 100 µm. The greater limit to resolution is the stimulation
141
of axon bundles, which could span a several millimeters on the retina. Bipolar stimulation
with 10-µm electrodes may be able to avoid stimulation of axon bundles. The optimal
design for an implantable array is a conformal grid of bipolar electrode pairs, in which
each pair is transverse to the local orientation of axons on the retina.

Table 8. Effective diameter for the area of responding cells (A = pi * σ
x
* σ
y
), given by
2*sqrt(A/pi).

Spacer
µm
Pulse µs

Electrode µm
60 400 1000
10
30 112
72x43

60 Bad fit streak 96
92x100
0
200 130
55x76
146
145x105
328
193x139
10
60 94
50x44
114
63x52
186
106x82
30
200 Bad fit 274
140x134
310
165x146
60 136
82x57
50
200 Bad fit 446
206x241
234
88x155

142
Table 9. Center positions of responding regions (x,y) relative to the electrode center.

Spacer
µm
Pulse µs

Electrode µm
60 400 1000
10 Streak
30 (7, -4)
60 Bad fit streak (39, -60)
0
200 (38, -22) (59, 1) (-8, -1)
10
60 (50, 3) (69, -2) (34, 2)
30
200 (44, 9) (61, 17) (42, 10)
60 (92, -8) 50
200 Bad fit (36, -7) (32. -22)

143
Table 10. Low threshold value (µA)

Spacer
µm
Pulse µs

Electrode µm
60 400 1000
10 0.7
30 0.7
60 10 1.4 1.2
0
200 12 3.1 2.2
10
60 4.6 2.6 2.3
30
200 12 5.1 3.4
60 2.7 50
200 48 12 9

Finite element modeling of the epiretinal interface accurately predicted reponse area for
thin gel spacers, but not for spacers 25% of the electrode diameter (Fig 76). Interpretation
of the model assumed that threshold ws inversely proportional to absolute current
density. Consideration of the direction of current density may improve the model
predictions, since the initial segment is the site of action potential initiation. The
elongated structure of the initial segment introduces asymmetry into the system and
provides for greater sensitivity to stimuation for current directed along the length of the
initial segment. Future modeling studies will consider the current density vectors when
fitting the model to experimental data.
144

Figure 76. Stimulation of a 200-µm electrode with spacer gel thickness of 0-, 30-, and 50-µm. The
response area (yellow highlight) is in agreement with finite element modeling except at 50-µm.
Measured
Percept
(µm)

120

160

230
Model
Percept
(µm)

120

140

145
Spacer
(µm)

0

30

50
145
Chapter 7. Conclusions and Future Work

A high throughput recording of RGCs in a mature retina has been made possible by my
advances in retrograde loading. Fluorescent calcium indicator was loading into
essentially all RGCs of a salamander retina, which allowed precise spatial measurements
of the response to stimulation. Pulse width and the directionality of field lines were two
parameters identified in this study that could provide control of the stimulation target in
the retina.

TARGET OF STIMULATION

Modeling studies predict that the site of action potential initiation is the axon hillock
(McIntyre and Grill, 1999) or the initial segment of the axon (Carras et al., 1992). Three-
dimensional models that include a bend in the axon as it joins the nerve fiber layer
(Schiefer and Grill, 2006) predict that the axon bend is the site of action potential
initiation. Moreover, this model predicts a differential pulse-width dependency for local
stimulation of somata and axon bundles. Recent electrophysiological measurements by
Shelley Fried in rabbit retina support the initial segment hypothesis and correlate it with a
high density of sodium channels identified by immunostaining. Additionally, the local
orientation of current density vectors at this initial segment will influence threshold. Field
lines that run roughly parallel to an axon are far more effective in stimulating than field
lines crossing perpendicular to the axon (Ranck, 1975). Membrane potential perturbation
146
is proportional to the radius of the axon for transverse fields (Horch and Dhillon, 2004)
(vol. 2, pg 23).

Two pieces of evidence in my study support the hypothesis that the initial segment is the
site of action potential initiation in RGCs. First, at 60-µs and 400-µs pulse widths, the
center of the response is offset by about 40-µm to the retinal periphery from the center of
the electrode. Thus the initial segments of stimulated RGCs lay over the center of the
electrode. Second, long pulses are known to preferentially stimulate bipolar cells, and I
found that the response area was centered on the electrode. When applying kynurenic
acid to block synaptic transmission from bipolar cells, the RGC response shifted 20 µm
to the periphery.

My data indicate that axon bundles can be stimulated near the threshold for RGC somata.
Previously, axonal stimulation was unaddressed in two of the best studies on
microelectrode stimulation (Sekirnjak et al., 2006, 2008). The authors did not state if they
observed the phenomenon, let alone measure the axon bundle threshold.

Short pulses (60-µs), in addition to selecting RGCs over bipolar cells, were also selective
for RGC initial segments versus axon bundles. The axon threshold for distant peripheral
somata was more than double the threshold for RGCs over the electrode. Long pulses
stimulated axons at roughly 60% above the local RGC threshold. Therefore, short pulse
width may be advantageous for keeping the percept localized to the electrode.
147

Bipolar stimulation may provide another powerful means to avoid stimulation of axon
bundles, but only for small electrodes. Threshold for peripheral somata rose to more
180% of the local RGC threshold in transverse bipolar stimulation (Fig 72). The cathodic
electrode in monopolar mode stimulated axons at the same threshold as local RGCs.

MODELING

My modeling work dispels a misconception that cells are preferentially stimulated around
the perimeter of the electrode. Electrostatic models (solving Poisson’s equation) of the
current density on the surface of an electrode in conductive medium have long shown
than current injected into an electrode is not spread evenly over its surface, but sharply
enhanced on the peripheral edges (Newman, 1966). Simple intuition might take this to
mean cells have low threshold on the perimeter of an electrode. Here we observe that
threshold is fairly uniform over the surface of the electrode, with respect to eccentricity.
The models typically consider an electrode in contact with homogeneous, isotropic
media. However, the retina is 15 to 50 fold less conductive (Karwoski et al., 1985) than
physiological saline, for plexiform and perikarya layers, respectively. Any thin layer of
saline between the electrode and the retina, even as little as 1 µm will have a profound
effect on reshaping the paths of current to spread out before entering the retina with a
more uniform distribution. Additionally, dynamic simulations showed that any current
148
density imbalance on the surface of the electrode is very short-lived compared to the
pulse widths used for electrical stimulation.

The electrostatic model of the retinal interface also accounts for the insensitivity of
response area to separation from the retina. With a spacer gel up to 25% of the electrode
diameter, the response area increases by only 40% in diameter. The model and
experimental data agree on the spatial extents of response to stimulation.

IMAGING TOOLS

One difficulty in the present study was the low dye concentration in RGCs. Expressing a
genetically encoded calcium indicator in RGCs could dramatically improve sensitivity to
detection of spikes. Alternatively, voltage sensitive probes such as ANNINE-6 could be
used. Either approach will benefit from two-photon imaging to confine fluorescence
excitation to the ganglion cell layer. Since half of the somata in the ganglion cell layer
belong to amacrine cells (Perry, 1981), imaging studies should be designed to identify
RGCs. If voltage sensitive dyes or genetically encoded calcium indicators are used, the
RGCs should be co-stained with a tracer such as Alexafluor-594.

149
ROADMAP FOR HIGH-RESOLUTION STIMULATION

In principle it is possible to stimulate individual ganglion cells with a dense array of very
small electrodes. The charge density is well within safe limits for ordinary platinum
electrodes. Why then does stimulation in a clinical setting lag so far behind what the in
vitro studies claim is feasible? Primarily it is from a gap between the electrodes and the
epiretinal surface. We have shown experimentally that thresholds rise about 5-fold when
the separation distance is only 50 µm for 200-µm electrodes. Modeling predicts a 11-fold
increase in threshold for 10-µm electrodes when the gap is raised from 1 µm to 10 µm.

Threshold to evoke spikes in RGCs in vitro differs by up to three orders of magnitude
from threshold for cognitive perception. Thresholds are dramatically lower in vitro. One
contributing factor is that the degenerate retina simply has a high threshold, but this does
not bridge the gap observed. Stimulation of RGCs in both the on- and the off-pathway
simultaneously may raise perceptual thresholds. Another factor, which is under our
immediate control, is pulse timing. The retina encodes visual information by spike rate
(Gollisch and Meister, 2008). Our current clinical efforts to use stimulus pulse amplitude
to encode brightness may not be using the best approach. A single stimulus pulse per
image frame is unlikely to elicit the same response in visual cortex as a precisely formed
spike train mimicking natural visual information. Visual processing models (Pillow et al.,
2005) can predict at least 75% of the variance in RGC spiking activity evoked by simple
150
visual stimuli. Psychophysical testing with patients will hopefully tell us if pulse rate
coding can improve the quality of percepts and lower the threshold.

Two factors appear to limit the spatial resolution of the retina prosthesis. First, the
response area from electrodes 10-µm to 60-µm (Tbl 8) (Fig 65) is roughly 100 µm wide,
equal to 0.4° human visual field and Snellen acuity of 20/480. Using electrodes smaller
than 60-µm may not result in smaller percepts. Second, axon bundle stimulation could
make pattern stimulation of the retina impossible. Short pulse width and bipolar
stimulation are both potential solutions to the need for focal stimulation of RGCs near the
electrode. I propose two optimal MEA layouts for the prosthesis based on the above
results. The first design is a conformal array of 10-µm bipolar electrode pairs on a 100-
µm grid. Electrodes are oriented transverse to the local path of axon bundles. This option
may be less practical because the array must be in close contact with the retina to
stimulate from such small electrodes, and the placement of the array relative to the retinal
anatomy must be quite precise. In the second design, electrodes 60-µm in diameter on a
100-µm grid (center to center) are stimulated in monopolar configuration with 60-µs
pulses.

151

Figure 77. Top: conformal MEA of bipolar electrode pairs on a 100-µm grid. Red lines represent axon
bundles. Bottom: MEA of 60-µm electrodes on 100-µm grid, stimulated in monopolar configuration.

152
References

Ahuja AK, Behrend MR, Kuroda M, Humayun MS, Weiland JD. An in vitro model of a
retinal prosthesis. Ieee Transactions on Biomedical Engineering, 2008; 55: 1744-53.
Baldridge WH. Optical recordings of the effects of cholinergic ligands on neurons in the
ganglion cell layer of mammalian retina. Journal of Neuroscience, 1996; 16: 5060-72.
Behrend MR, Ahuja AK, Weiland JD. Dynamic current density of the disk electrode
double-layer. Ieee Transactions on Biomedical Engineering, 2008; 55: 1056-62.
Bennicelli J, Wright JF, Komaromy A, Jacobs JB, Hauck B, Zelenaia O, Mingozzi F, Hui
D, Chung D, Rex TS, Wei Z, Qu G, Zhou S, Zeiss C, Arruda VR, Acland GM, Dell'Osso
LF, High KA, Maguire AM, Bennett J. Reversal of blindness in animal models of leber
congenital amaurosis using optimized AAV2-mediated gene transfer. Mol Ther, 2008;
16: 458-65.
Bi A, Cui J, Ma YP, Olshevskaya E, Pu M, Dizhoor AM, Pan ZH. Ectopic expression of
a microbial-type rhodopsin restores visual responses in mice with photoreceptor
degeneration. Neuron, 2006; 50: 23-33.
Bostock H. The Strength Duration Relationship for Excitation of Myelinated Nerve -
Computed Dependence on Membrane Parameters. Journal of Physiology-London, 1983;
341: 59-74.
Boyden ES, Zhang F, Bamberg E, Nagel G, Deisseroth K. Millisecond-timescale,
genetically targeted optical control of neural activity. Nat Neurosci, 2005; 8: 1263-8.
Bradley DC, Troyk PR, Berg JA, Bak M, Cogan S, Erickson R, Kufta C, Mascaro M,
McCreery D, Schmidt EM, Towle VL, Xu H. Visuotopic mapping through a
multichannel stimulating implant in primate V1. Journal of neurophysiology, 2005; 93:
1659-70.
Carras PL, Coleman PA, Miller RF. Site of action potential initiation in amphibian retinal
ganglion cells. J Neurophysiol, 1992; 67: 292-304.
Chen SC, Hallum LE, Lovell NH, Suaning GJ. Visual acuity measurement of prosthetic
vision: a virtual-reality simulation study. Journal of neural engineering, 2005; 2: S135-45.
Dabrowski W, Grybos P, Litke AM. A low noise multichannel integrated circuit for
recording neuronal signals using microelectrode arrays. Biosens Bioelectron, 2004; 19:
749-61.
Dacey DM, Peterson BB, Robinson FR, Gamlin PD. Fireworks in the primate retina: in
vitro photodynamics reveals diverse LGN-projecting ganglion cell types. Neuron, 2003;
37: 15-27.
153
Daiger SP, Bowne SJ, Sullivan LS. Perspective on genes and mutations causing retinitis
pigmentosa. Archives of ophthalmology, 2007; 125: 151-8.
de Balthasar C, Patel S, Roy A, Freda R, Greenwald S, Horsager A, Mahadevappa M,
Yanai D, McMahon MJ, Humayun MS, Greenberg RJ, Weiland JD, Fine I. Factors
affecting perceptual thresholds in epiretinal prostheses. Investigative ophthalmology &
visual science, 2008; 49: 2303-14.
Denk W, Detwiler PB. Optical recording of light-evoked calcium signals in the
functionally intact retina. Proceedings of the National Academy of Sciences of the United
States of America, 1999; 96: 7035-40.
Di Virgilio F, Fasolato C, Steinberg TH. Inhibitors of membrane transport system for
organic anions block fura-2 excretion from PC12 and N2A cells. Biochem J, 1988a; 256:
959-63.
Di Virgilio F, Steinberg TH, Swanson JA, Silverstein SC. Fura-2 secretion and
sequestration in macrophages. A blocker of organic anion transport reveals that these
processes occur via a membrane transport system for organic anions. J Immunol, 1988b;
140: 915-20.
Dombeck DA, Sacconi L, Blanchard-Desce M, Webb WW. Optical recording of fast
neuronal membrane potential transients in acute mammalian brain slices by second-
harmonic generation microscopy. Journal of Neurophysiology, 2005; 94: 3628-36.
Donaldson ND, Donaldson PEK. Performance of Platinum Stimulating Electrodes
Mapped on the Limit-Voltage Plane .2. Corrosion Invitro. Medical & Biological
Engineering & Computing, 1986; 24: 431-8.
Drager UC, Olsen JF. Ganglion cell distribution in the retina of the mouse. Investigative
Ophthalmology & Visual Science, 1981; 20: 285-93.
Eckhorn R, Wilms M, Schanze T, Eger M, Hesse L, Eysel UT, Kisvarday ZF, Zrenner E,
Gekeler F, Schwahn H, Shinoda K, Sachs H, Walter P. Visual resolution with retinal
implants estimated from recordings in cat visual cortex. Vision Res, 2006; 46: 2675-90.
el-Fouly MH, Trosko JE, Chang CC. Scrape-loading and dye transfer. A rapid and simple
technique to study gap junctional intercellular communication. Experimental Cell
Research, 1987; 168: 422-30.
Elizabeth Rakoczy P, Yu MJ, Nusinowitz S, Chang B, Heckenlively JR. Mouse models
of age-related macular degeneration. Exp Eye Res, 2006; 82: 741-52.
Erles K, Sebokova P, Schlehofer JR. Update on the prevalence of serum antibodies (IgG
and IgM) to adeno-associated virus (AAV). J Med Virol, 1999; 59: 406-11.
154
Field GD, Chichilnisky EJ. Information processing in the primate retina: circuitry and
coding. Annu Rev Neurosci, 2007; 30: 1-30.
Fine I, Wade AR, Brewer AA, May MG, Goodman DF, Boynton GM, Wandell BA,
MacLeod DI. Long-term deprivation affects visual perception and cortex. Nature
neuroscience, 2003; 6: 915-6.
Foester O. Beitrage zur Pathophysiologie der Sehbahn und der Spehsphare. Journal of
Psychological Neurology, 1929; 39: 435-63.
Fried SI, Hsueh HA, Werblin FS. A method for generating precise temporal patterns of
retinal spiking using prosthetic stimulation. J Neurophysiol, 2006; 95: 970-8.
Friedman DS, O'Colmain BJ, Munoz B, Tomany SC, McCarty C, de Jong PT, Nemesure
B, Mitchell P, Kempen J. Prevalence of age-related macular degeneration in the United
States. Archives of ophthalmology, 2004; 122: 564-72.
Fritzsch B. Fast axonal diffusion of 3000 molecular weight dextran amines. Journal of
Neuroscience Methods, 1993; 50: 95-103.
Gan WB, Grutzendler J, Wong WT, Wong ROL, Lichtman JW. Multicolor "DiOlistic"
labeling of the nervous system using lipophilic dye combinations. Neuron, 2000; 27: 219-
25.
Gekeler F, Szurman P, Grisanti S, Weiler U, Claus R, Greiner TO, Volker M, Kohler K,
Zrenner E, Bartz-Schmidt KU. Compound subretinal prostheses with extra-ocular parts
designed for human trials: successful long-term implantation in pigs. Graefe's archive for
clinical and experimental ophthalmology = Albrecht von Graefes Archiv fur klinische
und experimentelle Ophthalmologie, 2007; 245: 230-41.
Gholmieh G, Soussou W, Han M, Ahuja A, Hsiao MC, Song D, Tanguay AR, Jr., Berger
TW. Custom-designed high-density conformal planar multielectrode arrays for brain slice
electrophysiology. Journal of Neuroscience Methods, 2006; 152: 116-29.
Gollisch T, Meister M. Rapid neural coding in the retina with relative spike latencies.
Science (New York, N.Y, 2008; 319: 1108-11.
Gross GW, Wen WY, Lin JW. Transparent indium-tin oxide electrode patterns for
extracellular, multisite recording in neuronal cultures. Journal of Neuroscience Methods,
1985; 15: 243-52.
Grumet AE, Wyatt JL, Jr., Rizzo JF, 3rd. Multi-electrode stimulation and recording in the
isolated retina. J Neurosci Methods, 2000; 101: 31-42.
155
Hayes JS, Yin VT, Piyathaisere D, Weiland JD, Humayun MS, Dagnelie G. Visually
guided performance of simple tasks using simulated prosthetic vision. Artificial organs,
2003; 27: 1016-28.
Hildinger M, Auricchio A, Gao G, Wang L, Chirmule N, Wilson JM. Hybrid vectors
based on adeno-associated virus serotypes 2 and 5 for muscle-directed gene transfer. J
Virol, 2001; 75: 6199-203.
Horch KW, Dhillon GS. Neuroprosthetics theory and practice. World Scientific: River
Edge, N.J., 2004.
Hubener G, Lambacher A, Fromherz P. Anellated hemicyanine dyes with large
symmetrical solvatochromism of absorption and fluorescence. Journal of Physical
Chemistry B, 2003; 107: 7896-902.
Humayun MS, de Juan E, Jr., Weiland JD, Dagnelie G, Katona S, Greenberg R, Suzuki S.
Pattern electrical stimulation of the human retina. Vision research, 1999; 39: 2569-76.
Hung A, Zhou D, Greenberg R, Judy JW. Dynamic electrochemical simulation of
micromachined electrodes for neural-stimulation systems. IEEE EMBS Conference on
Neural Engineering, 2003: 200-3.
Hung A, Zhou D, Greenberg R, Judy JW. Dynamic simulation and testing of the
electrode-electrolyte interface of 3-D stimulating microelectrodes. IEEE EMBS
Conference on Neural Engineering, 2005: 179-82.
Ito A, Yamaguchi K, Tomita H, Suzuki T, Onogawa T, Sato T, Mizutamari H, Mikkaichi
T, Nishio T, Suzuki T, Unno M, Sasano H, Abe T, Tamai M. Distribution of rat organic
anion transporting polypeptide-E (oatp-E) in the rat eye. Investigative Ophthalmology &
Visual Science, 2003; 44: 4877-84.
Jensen RJ, Ziv OR, Rizzo JF, 3rd. Thresholds for activation of rabbit retinal ganglion
cells with relatively large, extracellular microelectrodes. Invest Ophthalmol Vis Sci,
2005; 46: 1486-96.
Jurgens I, Rosell J, Riu PJ. Electrical impedance tomography of the eye: In vitro
measurements of the cornea and the lens. Physiological Measurement, 1996; 17: A187-
A95.
Karwoski CJ, Frambach DA, Proenza LM. Laminar profile of resistivity in frog retina. J
Neurophysiol, 1985; 54: 1607-19.
Kettunen P, Demas J, Lohmann C, Kasthuri N, Gong YD, Wong ROL, Gan WB.
Imaging calcium dynamics in the nervous system by means of ballistic delivery of
indicators. Journal of Neuroscience Methods, 2002; 119: 37-43.
156
Khamdang S, Takeda M, Shimoda M, Noshiro R, Narikawa S, Huang XL, Enomoto A,
Piyachaturawat P, Endou H. Interactions of human- and rat-organic anion transporters
with pravastatin and cimetidine. J Pharmacol Sci, 2004; 94: 197-202.
Kim Y, Benfahy J, Tupper BJ. Optimal Electrode Designs for Electrosurgery,
Defibrillation, and External Cardiac Pacing. Ieee Transactions on Biomedical
Engineering, 1986; 33: 845-53.
Klein R, Klein BE, Jensen SC, Meuer SM. The five-year incidence and progression of
age-related maculopathy: the Beaver Dam Eye Study. Ophthalmology, 1997; 104: 7-21.
Ksienski DA. A Minimum Profile Uniform Current-Density Electrode. Ieee Transactions
on Biomedical Engineering, 1992; 39: 682-92.
Kuhn B, Fromherz P, Denk W. High sensitivity of stark-shift voltage-sensing dyes by
one- or two-photon excitation near the red spectral edge. Biophysical Journal, 2004; 87:
631-9.
Kusuhara H, Sugiyama Y. Efflux transport systems for organic anions and cations at the
blood-CSF barrier. Advanced Drug Delivery Reviews, 2004; 56: 1741-63.
Lewicki MS. A review of methods for spike sorting: the detection and classification of
neural action potentials. Network (Bristol, England), 1998; 9: R53-78.
Lipton SA, Tauck DL. Voltage-dependent conductances of solitary ganglion cells
dissociated from the rat retina. Journal of Physiology, 1987; 385: 361-91.
Litke AM, Bezayiff N, Chichilnisky EJ, Cunningham W, Dabrowski W, Grillo AA,
Grivich M, Grybos P, Hottowy P, Kachiguine S, Kalmar RS, Mathieson K, Petrusca D,
Rahman A, Sher A. What does the eye tell the brain?: Development of a system for the
large-scale recording of retinal output activity. Ieee Transactions on Nuclear Science,
2004; 51: 1434-40.
Lo DC, McAllister AK, Katz LC. Neuronal transfection in brain slices using particle-
mediated gene transfer. Neuron, 1994; 13: 1263-8.
Lohmann C, Myhr KL, Wong RO. Transmitter-evoked local calcium release stabilizes
developing dendrites. Nature, 2002; 418: 177-81.
Mahadevappa M, Weiland JD, Yanai D, Fine I, Greenberg RJ, Humayun MS. Perceptual
thresholds and electrode impedance in three retinal prosthesis subjects. IEEE Trans
Neural Syst Rehabil Eng, 2005; 13: 201-6.

157
Mank M, Santos AF, Direnberger S, Mrsic-Flogel TD, Hofer SB, Stein V, Hendel T,
Reiff DF, Levelt C, Borst A, Bonhoeffer T, Hubener M, Griesbeck O. A genetically
encoded calcium indicator for chronic in vivo two-photon imaging. Nature Methods,
2008; 5: 805-11.
Mann M, Haq W, Zabel T, Guenther E, Zrenner E, Ladewig T. Age-dependent changes
in the regulation mechanisms for intracellular calcium ions in ganglion cells of the mouse
retina. The European journal of neuroscience, 2005; 22: 2735-43.
Marc RE, Jones BW, Watt CB, Strettoi E. Neural remodeling in retinal degeneration.
Progress in Retinal and Eye Research, 2003; 22: 607-55.
Margalit E, Maia M, Weiland JD, Greenberg RJ, Fujii GY, Torres G, Piyathaisere DV,
O'Hearn TM, Liu W, Lazzi G, Dagnelie G, Scribner DA, de Juan E, Jr., Humayun MS.
Retinal prosthesis for the blind. Survey of ophthalmology, 2002; 47: 335-56.
Margalit E, Thoreson WB. Inner retinal mechanisms engaged by retinal electrical
stimulation. Investigative Ophthalmology & Visual Science, 2006; 47: 2606-12.
Marrese CA. Preparation of Strongly Adherent Platinum Black Coatings. Analytical
Chemistry, 1987; 59: 217-8.
Masland RH. Neuronal diversity in the retina. Current opinion in neurobiology, 2001; 11:
431-6.
Mathieson K, Kachiguine S, Adams C, Cunningham W, Gunning D, O'Shea V, Smith
KM, Chichilnisky EJ, Litke AM, Sher A, Rahman M. Large-area microelectrode arrays
for recording of neural signals. Ieee Transactions on Nuclear Science, 2004; 51: 2027-31.
Matsuda T, Cepko CL. Electroporation and RNA interference in the rodent retina in vivo
and in vitro. Proceedings of the National Academy of Sciences of the United States of
America, 2004; 101: 16-22.
McIntyre CC, Grill WM. Excitation of central nervous system neurons by nonuniform
electric fields. Biophys J, 1999; 76: 878-88.
Mcneal DR. Analysis of a Model for Excitation of Myelinated Nerve. Ieee Transactions
on Biomedical Engineering, 1976; 23: 329-37.
McNeil PL. Repairing a torn cell surface: make way, lysosomes to the rescue. Journal of
cell science, 2002; 115: 873-9.
McNeil PL, Murphy RF, Lanni F, Taylor DL. A method for incorporating
macromolecules into adherent cells. Journal of Cell Biology, 1984; 98: 1556-64.
158
Mikkaichi T, Suzuki T, Tanemoto M, Ito S, Abe T. The organic anion transporter
(OATP) family. Drug Metabolism & Pharmacokinetics, 2004; 19: 171-9.
Morimoto T, Miyoshi T, Fujikado T, Tano Y, Fukuda Y. Electrical stimulation enhances
the survival of axotomized retinal ganglion cells in vivo. Neuroreport, 2002; 13: 227-30.
Morin FO, Takamura Y, Tamiya E. Investigating neuronal activity with planar
microelectrode arrays: Achievements and new perspectives. Journal of Bioscience and
Bioengineering, 2005; 100: 131-43.
Moskalenko M, Chen L, van Roey M, Donahue BA, Snyder RO, McArthur JG, Patel SD.
Epitope mapping of human anti-adeno-associated virus type 2 neutralizing antibodies:
implications for gene therapy and virus structure. J Virol, 2000; 74: 1761-6.
Myland JC, Oldham KB. How does the double layer at a disk electrode charge? Journal
of Electroanalytical Chemistry, 2005; 575: 81-93.
Nagel G, Szellas T, Huhn W, Kateriya S, Adeishvili N, Berthold P, Ollig D, Hegemann
P, Bamberg E. Channelrhodopsin-2, a directly light-gated cation-selective membrane
channel. Proc Natl Acad Sci U S A, 2003; 100: 13940-5.
Nanduri D, Humayun MS, Greenberg RJ, McMahon MJ, Weiland JD. Retinal prosthesis
phosphene shape analysis. Conf Proc IEEE Eng Med Biol Soc, 2008; 2008: 1785-8.
Neher E. The use of fura-2 for estimating Ca buffers and Ca fluxes. Neuropharmacology,
1995; 34: 1423-42.
Newman J. Resistance for Flow of Current to a Disk. Journal of the Electrochemical
Society, 1966; 113: 501-&.
O'Brien JA, Holt M, Whiteside G, Lummis SCR, Hastings MH. Modifications to the
hand-held Gene Gun: improvements for in vitro Biolistic transfection of organotypic
neuronal tissue. Journal of Neuroscience Methods, 2001; 112: 57-64.
Ogden D. Microelectrode Techniques - a Workshop. Trends in Neurosciences, 1989; 12:
147-.
Okawa Y, Fujikado T, Miyoshi T, Sawai H, Kusaka S, Mihashi T, Hirohara Y, Tano Y.
Optical imaging to evaluate retinal activation by electrical currents using suprachoroidal-
transretinal stimulation. Investigative Ophthalmology & Visual Science, 2007; 48: 4777-
84.
Oldham KB. The RC time "constant" at a disk electrode. Electrochemistry
Communications, 2004; 6: 210-4.
159
Ostrovsky Y, Andalman A, Sinha P. Vision following extended congenital blindness.
Psychol Sci, 2006; 17: 1009-14.
Overmyer KM, Pearce JA, Dewitt DP. Measurements of Temperature Distributions at
Electro-Surgical Dispersive Electrode Sites. Journal of Biomechanical Engineering-
Transactions of the Asme, 1979; 101: 66-72.
Oyster CW. The human eye : structure and function. Sinauer Associates: Sunderland,
Mass., 1999.
Pajkossy T, Kolb DM. Double layer capacitance of Pt(111) single crystal electrodes.
Electrochimica Acta, 2001; 46: 3063-71.
Perry VH. Evidence for an amacrine cell system in the ganglion cell layer of the rat
retina. Neuroscience, 1981; 6: 931-44.
Pillow JW, Paninski L, Uzzell VJ, Simoncelli EP, Chichilnisky EJ. Prediction and
decoding of retinal ganglion cell responses with a probabilistic spiking model. J
Neurosci, 2005; 25: 11003-13.
Potts AM, Inoue J. The electrically evoked response (EER) of the visual system. II.
Effect of adaptation and retinitis pigmentosa. Investigative ophthalmology, 1969; 8: 605-
12.
Ranck JB, Jr. Which elements are excited in electrical stimulation of mammalian central
nervous system: a review. Brain Research, 1975; 98: 417-40.
Regehr WG, Tank DW. Selective fura-2 loading of presynaptic terminals and nerve cell
processes by local perfusion in mammalian brain slice. Journal of Neuroscience Methods,
1991; 37: 111-9.
Reid CA, Fabian-Fine R, Fine A. Postsynaptic calcium transients evoked by activation of
individual hippocampal mossy fiber synapses. Journal of Neuroscience, 2001; 21: 2206-
14.
Reiner A, Veenman CL, Medina L, Jiao Y, Del Mar N, Honig MG. Pathway tracing
using biotinylated dextran amines. Journal of Neuroscience Methods, 2000; 103: 23-37.
Rizzo JF, 3rd, Wyatt J, Loewenstein J, Kelly S, Shire D. Perceptual efficacy of electrical
stimulation of human retina with a microelectrode array during short-term surgical trials.
Investigative ophthalmology & visual science, 2003; 44: 5362-9.
Robblee LS, Rose TL. Electrochemical guidelines for selection of protocols and electrode
materials for neural stimulation. Neural Prostheses Fundamental Studies, W. F. Agnew
and D. B. McCreery, Eds., 1990: 25-66.
160
Rose TL, Robblee LS. Electrical-Stimulation with Pt Electrodes .8. Electrochemically
Safe Charge Injection Limits with 0.2 Ms Pulses. Ieee Transactions on Biomedical
Engineering, 1990; 37: 1118-20.
Rosenfeld PJ, Heier JS, Hantsbarger G, Shams N. Tolerability and efficacy of multiple
escalating doses of ranibizumab (Lucentis) for neovascular age-related macular
degeneration. Ophthalmology, 2006; 113: 632 e1.
Rubinstein JT, Spelman FA, Soma M, Suesserman MF. Current-Density Profiles of
Surface Mounted and Recessed Electrodes for Neural Prostheses. Ieee Transactions on
Biomedical Engineering, 1987; 34: 864-75.
Santos A, Humayun MS, de Juan E, Jr., Greenburg RJ, Marsh MJ, Klock IB, Milam AH.
Preservation of the inner retina in retinitis pigmentosa. A morphometric analysis.
Archives of ophthalmology, 1997; 115: 511-5.
Sarthy PV, Curtis BM, Catterall WA. Retrograde labeling, enrichment, and
characterization of retinal ganglion cells from the neonatal rat. Journal of Neuroscience,
1983; 3: 2532-44.
Schiefer MA, Grill WM. Sites of neuronal excitation by epiretinal electrical stimulation.
IEEE Transactions on Neural Systems & Rehabilitation Engineering, 2006; 14: 5-13.
Segev R, Goodhouse J, Puchalla J, Berry MJ, 2nd. Recording spikes from a large fraction
of the ganglion cells in a retinal patch. Nat Neurosci, 2004; 7: 1154-61.
Sekirnjak C, Hottowy P, Sher A, Dabrowski W, Litke AM, Chichilnisky EJ. Electrical
stimulation of mammalian retinal ganglion cells with multielectrode arrays. J
Neurophysiol, 2006; 95: 3311-27.
Sekirnjak C, Hottowy P, Sher A, Dabrowski W, Litke AM, Chichilnisky EJ. High-
resolution electrical stimulation of primate retina for epiretinal implant design. Journal of
Neuroscience, 2008; 28: 4446-56.
Seksek O, Biwersi J, Verkman AS. Translational diffusion of macromolecule-sized
solutes in cytoplasm and nucleus. The Journal of cell biology, 1997; 138: 131-42.
Shirakashi R, Sukhorukov VL, Tanasawa I, Zimmermann U. Measurement of the
permeability and resealing time constant of the electroporated mammalian cell
membranes. International Journal of Heat and Mass Transfer, 2004; 47: 4517-24.
Smetters D, Majewska A, Yuste R. Detecting action potentials in neuronal populations
with calcium imaging. Methods, 1999; 18: 215-21.
161
Stone JL, Barlow WE, Humayun MS, de Juan E, Jr., Milam AH. Morphometric analysis
of macular photoreceptors and ganglion cells in retinas with retinitis pigmentosa.
Archives of ophthalmology, 1992; 110: 1634-9.
Suzuki S, Humayun MS, Weiland JD, Chen SJ, Margalit E, Piyathaisere DV, de Juan E.
Comparison of electrical stimulation thresholds in normal and retinal degenerated mouse
retina. Japanese Journal of Ophthalmology, 2004; 48: 345-9.
Townes-Anderson E, Colantonio A, St Jules RS. Age-related changes in the tiger
salamander retina. Experimental Eye Research, 1998; 66: 653-67.
Tsien RY. Fluorescent probes of cell signaling. Annual Review of Neuroscience, 1989;
12: 227-53.
Wargacki SP, Lewis LA, Dadmun MD. Understanding the chemistry of the development
of latent fingerprints by superglue fuming. Journal of Forensic Sciences, 2007; 52: 1057-
62.
Wiley JD, Webster JG. Analysis and Control of the Current Distribution under Circular
Dispersive Electrodes. Ieee Transactions on Biomedical Engineering, 1982; 29: 381-5.
Wollner DA, Catterall WA. Localization of Sodium-Channels in Axon Hillocks and
Initial Segments of Retinal Ganglion-Cells. Proceedings of the National Academy of
Sciences of the United States of America, 1986; 83: 8424-8.
Wong RO. Calcium imaging and multielectrode recordings of global patterns of activity
in the developing nervous system. Histochemical Journal, 1998; 30: 217-29.
Wong RO, Oakley DM. Changing patterns of spontaneous bursting activity of on and off
retinal ganglion cells during development. Neuron, 1996; 16: 1087-95.
Wu CC, Reilly JF, Young WG, Morrison JH, Bloom FE. High-throughput morphometric
analysis of individual neurons. Cerebral Cortex, 2004; 14: 543-54.
Yan Q, Wang J, Matheson CR, Urich JL. Glial cell line-derived neurotrophic factor
(GDNF) promotes the survival of axotomized retinal ganglion cells in adult rats:
comparison to and combination with brain-derived neurotrophic factor (BDNF). Journal
of Neurobiology, 1999; 38: 382-90.
Yanai D, Weiland JD, Mahadevappa M, Greenberg RJ, Fine I, Humayun MS. Visual
performance using a retinal prosthesis in three subjects with retinitis pigmentosa.
American Journal of Ophthalmology, 2007; 143: 820-7.
Yao XC, George JS. Dynamic neuroimaging of retinal light responses using fast intrinsic
optical signals. Neuroimage, 2006; 33: 898-906.
162
Yawo H, Kuno M. Calcium dependence of membrane sealing at the cut end of the
cockroach giant axon. J Neurosci, 1985; 5: 1626-32.
Young RW. Cell differentiation in the retina of the mouse. Anatomical Record, 1985;
212: 199-205.
Yuste R, Denk W. Dendritic spines as basic functional units of neuronal integration.
Nature, 1995; 375: 682-4.
Zhan XJ, Troy JB. An efficient method that reveals both the dendrites and the soma
mosaics of retinal ganglion cells. Journal of Neuroscience Methods, 1997; 72: 109-16.

Abstract (if available)

Abstract The aim of this study is to provide guidelines for the design of a retinal prosthesis with specific emphasis on spatial resolution. Optical recordings from retinal ganglion cells (RGCs) using novel methods provide the first clear picture of how the retina sees electrical stimuli. Analysis of the spatial properties of the response show that the site of action potential initiation is not in the soma, but in the initial segment of the axon, ~ 40 um from the soma. Furthermore, 60-us pulses directly stimulate RGCs, while longer pulses target inner retinal neurons. Short pulse widths have a more focal response area than long pulses. The smallest response area was about 100 um, even for electrodes as small as 30 um.

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Asset Metadata

Creator Behrend, Matthew R. (author)

Core Title Viewing the picture we paint

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 04/22/2009

Defense Date 03/16/2009

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag artificial vision,calcium imaging,electrical stimulation,neural stimulation,OAI-PMH Harvest,retina,retinal implant,retinal prosthesis

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Weiland, James D. (committee chair), Chow, Robert HP. (committee member), Gundersen, Martin A. (committee member), Nayak, Krishna S. (committee member)

Creator Email behrend@usc.edu,behrend04@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m2103

Unique identifier UC1469379

Identifier etd-Behrend-2755 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-230942 (legacy record id),usctheses-m2103 (legacy record id)

Legacy Identifier etd-Behrend-2755.pdf

Dmrecord 230942

Document Type Dissertation

Rights Behrend, Matthew R.

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu