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AbstractA continuum network model of the retina is

presented, consisting of an active implementation of the retinal

ganglion cell tissue layer and passive implementation of deeper

cell layers. The retinal ganglion cell layer receives excitatory

presynaptic inputs from the bipolar layer and inhibitory

presynaptic inputs from the amacrine layer. Simulations were

performed to investigate the behavior of retinal tissue activation

with epiretinal and suprachoroidal electrode stimulation. The

results indicated the presence of both early and late onset action

potentials consistent with experimental findings.

I. INTRODUCTIONetinitis pigmentosa and age-related macular

degeneration are two of the most prevalent retinal

diseases and leading causes of blindness in developedcountries [1]. Both of these diseases result in degeneration of

the retina, predominantly the outer retina where the

photoreceptors are located, leading to eventual loss of vision.

The inner retina however is largely left intact, even in

patients who have been clinically blind for many years [2, 3],

raising the possibility that these inner retinal neurons can be

electrically stimulated by nearby electrodes to elicit light

perception [4, 5].

The development of an intraocular vision prosthesis is

currently being pursued by several research groups around

the world [6, 7, 8]. A particular focus has been on eliciting

meaningful visual percepts through extracellular stimulation.Electrode placement strategies have been explored on the

epiretinal surface, sub retinal space and suprachoroidal

space.

Previous modeling studies on the effects of electrical

stimulation have been limited in their scope [9, 10]. These

isolated studies have only taken into account the behavior of

the retinal ganglion cells (RGCs) in response to electrical

stimulation and have largely ignored the presence of the rest

of the retinal network and passive propagation through

retinal layers. We believe these network effects play a

significant role in shaping the spiking activity of the RGC

layer and therefore the spatial and temporal responses to

excitation at the cortical level. It has been shown that

excitation of the cells in the inner nuclear layer, including the

bipolar and amacrine cells, produce excitatory and inhibitory

inputs respectively to the ganglion cells [11]. The presence

of these so-called late onsetor secondary spikes have been

S. Yin, S. Dokos, N. H. Lovell and G. J. Suaning are with the Graduate

School of Biomedical Engineering, University of New South Wales,

Sydney, NSW 2052, Australia (email: n.lovell@ unsw.edu.au).

observed in a variety of experimental studies [12, 13, 14].

Other groups have attempted to incorporate these

presynaptic inputs by modeling the retina as a discrete

network [15, 16]. These models however ignore the active

membrane properties of the RGCs.

We have developed a continuum model of the retinal

network which includes both passive retinal properties and

active ganglion cell behavior. Synaptic inputs from bipolar

and amacrine cells are also incorporated in shaping the

spiking activity at the ganglion level. A generalized retinal

network model of the ON system is presented where

parameters have been compiled from experimental data from

various studies. Results are shown for both epiretinal and

suprachoroidal electrode placement.

II. METHODSA. Model Formulation

To investigate patterns of retinal tissue activation due to

electrical stimulation, we have developed a 3D finite-element

model comprised of vitreous fluid and the neural retina (Fig.

1). The retinal section consists of an active domain of RGCs,

and two passive domains including that of the inner nuclear

layer (INL), (bipolar, horizontal, wide-field and narrow-field

amacrine cells) and sub retinal space (modeled with cone

photoreceptors). Additional conductive tissue layers in the

model include the inner plexiform layer (IPL), outer

plexiform layer (OPL), outer nuclear layer (ONL), retinal

pigment epithelium (RPE) and choroid.

A single pair of circular disc electrodes is used to apply

electrical stimulation in this study; one active and one return.

In all simulations the return electrode is connected to ground

(zero volts). The electrodes have a radius of 0.2 mm and are

placed in the vitreous fluid, 200 m above the upper surface

of the retina for epiretinal stimulation and placed 426 m

below the retinal pigment epithelium for suprachoroidal

stimulation (based on choroid thickness from in vivo

measurements of the human retina [17]).

The extracellular voltage distribution Ve within the vitreous

region was governed by Poisson's equation

( ) IVeb = (1)

where b is the conductivity of the bulk vitreous medium

andIis the volume current density source (A/m3) injected

into the vitreous at a given location. The value of b was

taken to be 1.25 S/m [18].

Within the active retinal ganglion cell region, an

adaptation of the bidomain equations was applied (Fig. 2 left

panel).

Shijie Yin, Nigel H. Lovell, Senior Member, IEEE, Gregg J. Suaning,Member, IEEE, Socrates Dokos,Member, IEEE

A Continuum Model of the Retinal Network and its Response to

Electrical Stimulation

R

32nd Annual International Conference of the IEEE EMBSBuenos Aires, Argentina, August 31 - September 4, 2010

978-1-4244-4124-2/10/$25.00 2010 2077Crown

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The intracellular potential Vi, of each cell is resistively

tied to a resting potential Vr, representing the intracellular

potential in the more distal portions of the neuron (axon and

dendrites). As a consequence, the intracellular potential isnot able to float freely with the extracellular potential during

extracellular stimulation. This model allows for local

excitation and activation of individual ganglion cells without

spread of activation to neighboring cells, important for

eliciting focal excitation of phosphenes.

The extracellular voltage is determined from

mee IV =2 (2)

where the extracellular retinal conductivity e of the

remaining layers are derived from [18, 19], and Im is the

RGC membrane current density per unit volume, given by

( )irrsnion

m

mm VVgiJt

VCI =

++

= (3)

and Vm is the transmembrane potential given by

eim

VVV = (4)

Cmis the membrane capacitance and is 1 F/cm2

for all cell

types, consistent with previous epiretinal stimulation models

[20] and also cellular models [10, 21].

denotes the surface to volume ratio of the ganglion cell

layer. We adopted a ganglion cell density of 2000 cells/mm2

[22] and determined the value as 9.25x10-4

m-1

by

assuming a spherical ganglion cell with a soma diameter of

18 m. This also assumes that extracellular currents

stimulate only the soma of the ganglion cell [15] as threshold

for activation is lowest near the soma or axon hillock [9].

Jion is determined based on the ionic formulation of

Fohlmeister and Miller [10]. The synaptic current, isn denotes

input from deeper layers: excitatory input feeds in from thebipolar cells and inhibitory input arrives from wide-field

amacrine cells.

( )snmsnsnsn EVgPi = (5)where gsn is the conductance of the synapse, Esn is the

reversal potential of the synaptically gated channel and Psn

represents the delayed response from presynaptic potentials

on the conductance of the synaptic channel. Psn is determined

by the synaptic transfer function with a center operating

point of V50 and steepness parameter 50. Synaptic transfer

parameter values were derived from [15]

( )sn

snsn tPpdt

dP= (6)

wherepis,

( )5050

5050

exp1

exp

VV

VVp

pre

pre

+

=

(7)

Vpre is the average presynaptic potential integrated over the

area of the dendritic receptive field. We assumed a dendritic

receptive field size of 100 m for the ON ganglion cell, this

is similar to previous modeling studies of ON-alpha ganglion

cell receptive fields [23].

We modeled the remainder of the retinal cells with a passive

implementation, where the membrane current Im wasexpressed as,

( )irr

m

rmmmm VVg

R

VV

dt

dVCI =

+= (8)

whereRmis the specific membrane resistance. For parameter

consistency, we have adopted values from [15] for all

relevant cell types.

Fig. 1. Schematic diagram of the retinal model with two circular disc

electrodes located epiretinally (solid line) and suprachoroidally

(dashed line). Dimensions of the rectangular domain are 4 x 4 x

0.805 mm. Thickness of retinal layers are: vitreous (200 m), RGC

layer (22 m), IPL (23 m), INL (27 m), OPL (16 m), ONL (31

m), sub retinal space (40 m), RPE (20 m) and choroid (426 m)

[17, 18]. Other key dimensions include: electrode radius 0.2 mm;

distance between electrode centers 1 mm. Electrodes are placed

centrally perpendicular to Y and symmetrically located about the

mid-plane perpendicular to X.

+

Ve

Cm Jion isn

gr

Vr +

gr

Vr

RmCm

Ve

Vi Vi

Fig. 2. RC circuit of the active RGC membrane potential (left), RC

circuit of the passive membrane potential implementation (right). Cm

represents the membrane capacitance, Jion is the ionic current per unit

area through gated channels in the cells soma, isn represents the

presynaptic current inputs from the retinal network and g r is the

resistive tie connecting the intracellular potential V i to a resting

potential Vr, Rm is the specific membrane resistance.

x

z

y

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B. Numerical ImplementationSimulations were conducted using COMSOL Multiphysics

Version 3.5a (COMSOL AB, Sweden) on a Quad Core

AMD Opteron Windows 64 server with 127 GB of RAM.

Simulation time varied from 2 to 4 hours depending on

server capacity and solver settings.

III.

RESULTS

Simulation results are shown in Fig. 3 for epiretinal and

suprachoroidal electrode placements. In both simulations a

monophasic current pulse of 0.0159 mC/cm2

charge density

was applied at t = 1 ms with a pulse width of 0.1 ms. RGC

activation patterns are also presented 0.1 ms after stimulus

onset.

The output shown in Fig. 3 for both stimulus strategies

was recorded 215 m below the vitreous surface at the center

of the stimulating electrode. The epiretinal simulation

elicited an early onset action potential (AP) as a result of

extracellular stimulus as well as a late onset AP. The

suprachoroidal simulation however displayed a subthreshold

response due to the extracellular stimulus, but it induced two

late onset APs. Initial inspection based on input currents

from the bipolar and amacrine cell layers suggest that these

late onset APs are of presynaptic origin. Removal of these

currents eliminated the late onset spiking activity, this was

true for both studies conducted (results not shown). The

latency of the early and late onset AP (measured from

stimulus onset to peak of the AP) for the epiretinal case was

0.8 ms and 6.2 ms respectively. For the two suprachoroidal

APs, these were 2.7 ms and 6.5 ms.

IV. DISCUSSIONThe epiretinal case was observed to have a lower current

threshold for AP generation compared to suprachoroidal,which displayed a subthreshold response. This is consistent

with previous experimental studies. Current threshold

densities for epiretinal stimulation have been reported to be

0.093 mC/cm2

in rabbits [13] and 0.073 mC/cm2

in rat

RGCs [14]. For suprachoroidal stimulation a more disparate

range of values were observed from 0.042 mC/cm2

to 0.375

mC/cm2

[7, 8, 24]. Variations between reported values are

largely due to differences in the experimental protocol and

threshold definitions. Our current density was observed to be

lower than that reported in the above experimental studies.

These threshold differences can be accounted for in part by

our use of bipolar monophasic stimulation, as it has been

suggested in prior studies that monophasic pulses have a

lower threshold than biphasic [8, 25], and also the choice of

parameter values we have adopted from various

experimental studies.

The occurrence of early onset or stimulus-locked APs as

well as late onset APs has been observed in several

experiments. Depending on the particular study, variations

Fig. 3. Simulation results 215 m below the vitreous surface in the RGC sub domain, stimulus applied at 1 ms (arrowhead) of 0.1 ms pulse

width with a simulation time of 10 ms. A constant 0.2 mA monophasic epiretinal stimulus, left: transmembrane potential (mV), right:

transmembrane potential (mV) at 0.1 ms after stimulus application, showing activation pattern of the RGC layer. B constant 0.2 mA

monophasic suprachoroidal stimulus, left: transmembrane potential (mV), right: transmembrane potential (mV) at 0.1 ms after stimulus

application, showing activation pattern of the RGC layer.

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exist in the classification of latency, in some instances as low

as 0.7 ms [13] for epiretinal stimulation. This was also seen

in [14] where the majority of short latency responses

occurred within 1 ms. In the same study, secondary spikes

were observed to occur with a latency of 5 ms. Interestingly

this was also the case with sub retinal stimulation [12]. The

latencies observed in these studies for both early and late

onset spikes are consistent with our model behavior under

similar pulse widths. For suprachoroidal studies, latency was

measured to the first peak of the electrically evoked response

(EEP) ranging from 9 ms to 25 ms [7, 8]. Since we did not

simulate EEP output, direct latency comparisons could not

be made.

The activation pattern of the epiretinal simulation shows a

much more focal response than that of suprachoroidal. We

believe this is a consequence of current flowing through the

highly resistive retinal pigment epithelium layer, resulting in

a spread of charge throughout the deeper retinal layers. This

behavior was also observed in suprachoroidal bipolar

stimulation of the cat retina [8]. As we have not modeled thecomplete retinal architecture for the ON system, there is an

absence of inhibitory inputs present in the model. This is

seen in the suprachoroidal study as the direct stimulation of

these deeper layers have resulted in more pronounced

presynaptic excitatory currents facilitating multiple late onset

APs as shown in Fig. 3.

V. CONCLUSIONThis study was undertaken to establish a basis for a retinal

model that can incorporate both active and passive properties

of the retina using published experimental data. We intend toexpand the model's retinal architecture in future studies, as

well as incorporate more complex electrode arrangements to

help in the design of vision prosthetic devices.

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