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University of Southern California Dissertations and Theses
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Electrical stimulation approaches to restoring sight and slowing down the progression of retinal blindness
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Electrical stimulation approaches to restoring sight and slowing down the progression of retinal blindness
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Content
Electrical Stimulation Approaches to Restoring
Sight and Slowing Down the Progression of
Retinal Blindness
by
Javad Paknahad
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
May 2022
Copyright 2022 Javad Paknahad
Dedicated to my parents...
ii
Contents
Dedication ii
List of Figures vii
List of Tables xvii
Abstract xviii
1 Introduction 1
1.1 The Retina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Retinal Neurons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Retinal Degeneration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Current Treatment Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 Retinal Prostheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.6 Non-invasive Electrical Stimulation Strategy . . . . . . . . . . . . . . . . . . . . . . . 11
1.7 Dissertation Outline and Significance . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 Stimulation Waveforms for Improving the Spatial Resolution of Epiretinal Pros-
theses 17
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.1 Admittance Method (AM): Electronics and Retina Tissue . . . . . . . . . . . 22
2.2.2 NEURON Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.3 Extracellular Stimulation: Admittance Method Linked With NEURON . . . . 29
2.2.4 Stimulation Threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.5 Electrical Stimulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3.1 Single Cell Study of RGCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3.2 Larger Population of RGCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.4.1 Selective Stimulation of RGCs SOCB . . . . . . . . . . . . . . . . . . . . . . . 38
2.4.2 Impact of AIS Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.4.3 Clinical Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.4.4 Limitations of Neural Network Modeling . . . . . . . . . . . . . . . . . . . . . 41
2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
iii
3 Color Selectivity: “Frequency-amplitude” Modulation Stimulation Strategy for
Selective Activation of RGCs 43
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2.1 Extracellular Stimulation: Frequency Response of RGCs . . . . . . . . . . . . 47
3.2.2 Current Modulation at High Frequency . . . . . . . . . . . . . . . . . . . . . 48
3.2.3 Time Course Response at High Frequency . . . . . . . . . . . . . . . . . . . . 50
3.2.4 Sensitivity and Statistical Analysis of RGCs Morphology . . . . . . . . . . . . 51
3.2.5 Verification of Computational Results with In-vitro Experiments . . . . . . . 54
3.2.6 Clinical testing in a patient with retinal implant . . . . . . . . . . . . . . . . 56
3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4 Enhanced Chance for Selective Activation of Functionally Different Retinal Gan-
glion Cells 66
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.3.1 Frequency Response: Pulse Width Modulations . . . . . . . . . . . . . . . . . 73
4.3.2 Frequency Response: Interphase Gap Modulations . . . . . . . . . . . . . . . 74
4.3.3 Current Modulations: Effects of Pulse Width on RGCs Response . . . . . . . 75
4.3.4 Current Modulations: Effects of Interphase Gap on RGCs Response . . . . . 78
4.3.5 Impacts of Biophysics on RGCs Response . . . . . . . . . . . . . . . . . . . . 79
4.3.6 Role of Ca Channels in RGCs Excitability at High Frequency . . . . . . . . . 81
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.4.1 Impacts of PW and IPG on Frequency Response of RGCs . . . . . . . . . . . 82
4.4.2 Selective Activation of D1 cells with Short Pulse Width . . . . . . . . . . . . 84
4.4.3 Mechanisms Underlying RGCs Response at High Stimulation Frequency . . . 86
4.4.4 Sensitivity of RGCs to the Presence of IPG . . . . . . . . . . . . . . . . . . . 87
4.4.5 Implications for Clinical Applications . . . . . . . . . . . . . . . . . . . . . . . 89
5 On the Design of Stimulus Waveforms for Selective Stimulation of RGCs 91
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.2 Modeling Approach and Stimulus Parameters . . . . . . . . . . . . . . . . . . . . . . 93
5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.3.1 Frequency Response of RGCs . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.3.2 Charge-dependent Response of RGCs at High Frequency . . . . . . . . . . . . 97
5.3.3 Time Course Response of RGCs at High Frequency . . . . . . . . . . . . . . . 102
5.3.4 Mechanisms Underlying RGCs Selectivity at High Frequency . . . . . . . . . 103
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.4.1 Verification of computational results with experimental data . . . . . . . . . . 108
5.4.2 Selective activation of RGCs through frequency-amplitude modulations . . . . 108
5.4.3 Stimulation threshold and axonal activation of RGCs . . . . . . . . . . . . . . 110
5.4.4 Temporal response of RGCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.4.5 Factors affecting excitability of RGCs at high Frequency . . . . . . . . . . . . 113
5.4.6 Color selectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
iv
5.4.7 Model limitations and future steps . . . . . . . . . . . . . . . . . . . . . . . . 116
6 Modeling ON Bipolar Cells for Electrical Stimulation 118
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.2.1 NEURON Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.2.2 AM-NEURON Computational Platform . . . . . . . . . . . . . . . . . . . . . 123
6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.3.1 Verification of the model with Experiments . . . . . . . . . . . . . . . . . . . 124
6.3.2 Sensitivity of BCs Response to Na channel . . . . . . . . . . . . . . . . . . . . 126
6.3.3 Blockage of L-type Ca channel . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.4 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7 Mechanisms Underlying Sensitivity of Bipolar Cells to Long Stimulation Pulses129
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
7.2.1 Constructing the Retina Tissue and Electrodes . . . . . . . . . . . . . . . . . 133
7.2.2 NEURON: Bipolar Cells Modeling . . . . . . . . . . . . . . . . . . . . . . . . 134
7.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.3.1 Intracellular Stimulation: NEURON Simulation . . . . . . . . . . . . . . . . . 135
7.3.2 Extracellular Stimulation: AM/NEURON Modeling . . . . . . . . . . . . . . 136
7.3.3 Role of hyperpolarization activated current (HCN) . . . . . . . . . . . . . . . 140
7.3.4 The Influence of Waveform Asymmetry . . . . . . . . . . . . . . . . . . . . . 141
7.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
7.4.1 Computational Modeling of DB4-BCs . . . . . . . . . . . . . . . . . . . . . . 143
7.4.2 Sensitivity of BCs Response to Electrical Stimulation . . . . . . . . . . . . . . 144
7.4.3 Asymmetric Electrical Stimulation of Retinal Neurons . . . . . . . . . . . . . 145
7.4.4 Clinical Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
7.4.5 Limitations and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
8 Non-invasive Electrical Stimulation Strategy to Slow Down the Progression of
Retinal Blindness 149
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
8.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
8.2.1 Computational Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
8.2.2 In-vivo experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
8.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
8.3.1 Computational Modeling: Segmented Rat Model . . . . . . . . . . . . . . . . 156
8.3.2 In-vivo experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
8.3.2.1 OCT and FAF Imaging . . . . . . . . . . . . . . . . . . . . . . . . . 161
8.3.2.2 Histology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
8.3.3 Computational Modeling: Segmented Human Head Model . . . . . . . . . . . 164
8.3.3.1 Coarse Resolution Human Head Model . . . . . . . . . . . . . . . . 165
8.3.3.2 High Resolution Human Head Model . . . . . . . . . . . . . . . . . . 167
v
8.3.3.3 The DTL Stimulating Electrode . . . . . . . . . . . . . . . . . . . . 167
8.3.3.4 The Ring Stimulating Electrode . . . . . . . . . . . . . . . . . . . . 168
8.3.3.5 The Proposed Return Electrode Configuration . . . . . . . . . . . . 171
8.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
9 Summary and Future Steps 176
References 180
vi
List of Figures
1.1 Structure of the eye and retinal neurons. Left figure from www.sunledind.com; Right
figure from (Ferrara et al., 2021) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 The circuitry for the blue-yellow color opponent pathway (Thoreson and Dacey, 2019). 4
1.3 The timeline of retinal degeneration.The images of human retina before and after the
degeneration are shown in the left panel (Loizos et al., 2018). . . . . . . . . . . . . . 5
1.4 Different types of retinal prosthetic systems. The placement of the stimulating elec-
trode arryat varies among retinal implants to target retinal neurons of interests (Tong
et al., 2020). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 The Argus II retinal implant. The camera is attached to sunglasses capturing the
image. The video processing unit (VPU) processes the information and send it to
the external transmitter coil which is placed close to the temporal side. The power
and data are transferred wirelessly from the external to implant coil and the elec-
tronics case send the spatiotemporal electric signals to the electrode array. The
multi-electrode array is placed epiretinally on the surface of RGCs layer (Figures
courtesy of Second Sight Medical Products, Inc.). . . . . . . . . . . . . . . . . . . . . 9
1.6 Three possible retinal ganglion cells responses to epiretinal electrical stimulation. A)
Directly activating RGCs cell bodies; B) Activation of RGCs axon bundles, leading
to elongated phosphenes perceived by subjects; C) Network mediated response of
RGCs by targeting the outer retinal neurons such as BCs (Tong et al., 2020). . . . . 10
1.7 Transcorneal electrical stimulation (TES). Top: The DTL-Plus electrode is placed on
the lower side and above the open eyelid. Bottom: The ERG-Jet electrode is placed
on the sclera (Cela, 2010). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1 Multiscale model of electrical stimulation of the retina tissue. (a) A 3D voxelized
model, consisting of bulk retina tissue with a single stimulating electrode. (b) The
distributed voltage inside the retina tissue using Admittance Method (AM). This
voltage is applied as an extracellular voltage in the NEURON model. (c) Electrical
stimulation waveform applying symmetric charged-balanced biphasic with alterations
in cathodic and anodic pulse durations. . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 A2-type and D1-type RGCs morphology as implemented and coded in our multiscale
Admittance Method/NEURON computational platform. (a): The dendrites of the
A2-RGC are ramified in the inner part of inner plexiform layer (IPL), while the
dendrites of the D1-RGC are placed in both inner and outer part of the IPL. The
morphology was extracted as a SWC file from the NeuroMorpho dataset (Ascoli,
2006; Ascoli et al., 2007; Yin-Peng and Chiao, 2014). (b): Different axonal segments
representation of both cells. AH: axon hillock; SOCB: sodium channel band; NS:
narrow segment; DA: distal axon; L: length of each band; D: diameter of each band. 24
vii
2.3 Comparisonbetweenexperimental(top)andcomputational(bottom)membranevolt-
ages in the cell body (soma) in response to intracellular stimulation. The hyperpo-
larizing step current stimulation was applied between 100 ms and 500 ms. (a): A2
cell; (b): D1 cell. Experimental data obtained from Qin et al. (Qin et al., 2017). . . 25
2.4 A large population of RGCs. A single cell was tiled to populate the entire ganglion
cell and IPL (3 mm× 3 mm). The center to center distance between the nearby cells
is set to 50µm and the stimulating electrode is placed at the center of the model. The
axon is oriented in x-direction, this would allow us to better determine the impact of
axonal pathway on distorted phosphenes. A2 and D1 cells were simulated separately
to better investigate the axonal activation threshold difference between the two cells. 30
2.5 Stimulation threshold of A2 and D1 RGCs as alterations in position of stimulating
electrode. Dash lines: point source, solid lines: disk electrode (200 µm diameter).
We used a symmetric charge-balanced cathodic-first waveform with a pulse duration
of 0.5 ms. Results show that while the stimulus threshold of the AIS varies between
the RGCs, the difference in the activation threshold of DA is almost negligible. . . . 33
2.6 2D stimulus threshold map for A2 and D1 RGCs. Each dot represents the center of
the corresponding cell body. The stimulating electrode is positioned at the center
of the model. Left: A2 RGCs; right: D1 RGCs. Symmetric biphasic cathodic-first
waveforms with pulse widths of (a) and (b) 0.5 ms; (c) and (d) 0.1 ms, are applied
to the electrode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.7 Activation threshold difference between the SOCB and DA of A2 and D1 cells as a
function of change in pulse duration. Symmetric cathodic-first biphasic pulses are
applied. Dash lines: the SOCB stimulus threshold, solid lines: the DA stimulus
threshold (axonal activation). The gray and black lines show the passing axons
diameters of 1.2 µm and 0.8 µm, respectively. Shorter pulse width of 0.1 ms resulted
in the highest excitation threshold difference between the SOCB and DA over a range
of variations in passing axon diameters. . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.8 Anodic-first (AF). vs cathodic-first (CF) symmetric biphasic pulses: the SOCB and
DA stimulus threshold difference for A2 and D1 cells. Results indicate that the
sensitivity of the SOCB threshold is low not only to pulse duration changes, but also
to modulations in polarity. Whereas, the DA threshold significantly changes with
alterations in both pulse widths and stimulus polarity. Therefore, the excitation
threshold difference between the SOCB and DA is greater using a short anodic-first
biphasic waveform, offering a higher chance for more focalized response of RGCs. . . 37
2.9 Charge threshold as alterations in pulse durations for both A2 and D1 RGCs using
cathodic-first biphasic pulses. The solid and dash lines represent the charge threshold
of the DA and the SOCB, respectively. Data show that although current threshold
increases as we shorten pulse widths, charge threshold remains low using short pulse
durations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
viii
3.1 A2 and D1 realistic morphologies as implemented and coded in our multiscale Admit-
tance Method/NEURON computational platform (Cela, 2010; Loizos et al., 2016a,
2018, 2016b). Left: A2-monostratified RGC ramified in the inner part of inner plexi-
formlayerandhasalargersomaanddendriticfielddiameters. Right: D1-bistratified,
their dendrites are placed in both inner and outer part of the inner plexiform layer
and this cell has relatively smaller soma and dendritic field diameters. GCL: ganglion
cell layer; IPL: inner plexiform layer; AH: axon hillock; SOCB: sodium channel band;
NS: narrow segment; DA: distal axon; L: length of each band; D: diameter. The
morphology of RGCs was extracted from the NeuroMorpho dataset (Ascoli, 2006;
Ascoli et al., 2007; Chen and Chiao, 2014). . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2 Responsiveness of RGCs at high stimulation frequency. A, Computational results
showing the difference in response between A2 and D1 retinal ganglion cells at high
frequency. B, Firing rate as a function of pulse amplitude for both A2 and D1 cells
at 200 Hz stimulus frequency. Data show the effects of stimulus amplitude on the
responsiveness of both cell types. Slower rate of changes in firing rates of A2-RGC
with increasing amplitude is shown which indicates less excitability of this RGC
subtype at high frequency. The greatest difference in rate of firing between A2 and
D1 cells is observed at the point where D1 cell begins firing at its maximum rate of
200 Hz. The difference in the computationally determined frequency response can
potentially help identifying the mechanism to selectively target RGCs. . . . . . . . . 48
3.3 Time course of RGCs response. Membrane potential as a function of time at stim-
ulation frequency of 200 Hz and 100 µA current amplitude: A, D1-bistratified. B,
A2-monostratified. D1 cells can better sustain repetitive spikes at high frequency of
stimulation compared to A2 cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.4 The impacts of the AH and SOCB length on D1-RGCs sensitivity to high frequency
electrical stimulation relative to the soma diameter. Firing rate is plotted as a func-
tion of modulations in current amplitude at 200 Hz. Analysis of firing rate with single
variation of morphological parameters: soma diameter, SOCB length, and AH and
SOCB lengths. Results show that while reduction in the length of the SOCB and
AH decreases the responsiveness of D1 cells to high stimulus frequency, the influence
of increase in the soma diameter (from 12 µm to 17 µm) on the reduced sensitivity
of the cell to high stimulus frequency is more pronounced. . . . . . . . . . . . . . . . 51
3.5 Response (firing rate) of A2 and D1 RGCs to electrical stimulation at 200 Hz with
modulations in morphometric parameters. The soma diameter (SD), axon diame-
ter (AD), and SOCB length (SOCBL) alterations of the two cells within one stan-
dard deviation of the mean have been investigated. The weighted average firing rate
(WAFR) of the cells indicates the higher excitability of D1 cells at high frequency
with relatively smaller SD, AD, and SOCBL. A2 RGCs: SD = 23 ± 4;AD = 1± 0.2;SOCBL= 30± 10. D1RGCs:SD = 14± 3;AD = 0.9± 0.1;SOCBL=25± 5. 53
ix
3.6 The model verification with in-vitro experimental results. A, Suprathreshold current
required to reach at least 90 % efficacy as alterations in stimulus frequency for both
small and large A2-cells using asymmetric cathodic-first stimulus waveform (nor-
malized to 1 Hz). The solid and shaded bars demonstrate the normalized stimulus
threshold of large and small cells, respectively. The Figure clearly shows the greatest
stimulus threshold difference between small and large cells at high frequency. B, Im-
pacts of soma and dendritic field sizes on efficacy for a given pulse amplitude (435 µA
cathodic phase amplitude). Small cells are able to maintain their response at higher
efficacy compared to large cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.7 Color perception in a blind RP patient fitted with the Argus II retinal prosthesis. A,
Fundus image showing the location of the electrode array on the retina; B, Mapping
of the electrodes selected for testing in the visual field; C, Color sensations elicited by
differentelectrodesunderfrequencymodulation; D,Bluescoresofthecolorsensations
calculated by the following scaling system: 0 – no blue or purple perception; 1 – blue
or purple sensation reported, but the color is highly unsaturated (saturation ⩽ 0.2);
2 – more significant blue or purple sensation reported (0.2 < saturation ⩽ 0.5); 3 –
strong blue or purple sensation reported (saturation > 0.5). The gray shaded area
represents the standard error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.8 The influence of electrode-cell distance on response and selective activation of RGCs
at 200 Hz. A, Firing rates of the A2 and D1 RGCs as function of current amplitude
for four difference electrode-soma distances (20 µm, 50 µm, 100 µm, and 200 µm).
B, Current amplitude difference between the two cells required to obtain firing rates
(FRs)of20Hz,100Hz,and200Hzwithincreaseintheelectrode-somadistance. Data
show that the differential firing rate and current amplitude of RGCs increased with
increasing electrode-cell distance, suggesting the enhanced chance for preferential
activation of D1 cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.1 An overview of the analysis performed in this paper. Using a symmetric charge-
balanced biphasic pulse, we first explored the impacts of modulations in pulse du-
ration and interphase gap on the frequency response of RGCs. We compared the
firing rate difference between A2 and D1 cells at high frequency over a range of pulse
widths and interphase gaps. Then, the firing rates of RGCs over a range of current
amplitude were compared and we characterized the effect of both PW and IPG on
the response of RGCs at high stimulus frequency of 200 Hz. . . . . . . . . . . . . . . 70
4.2 A) The minimum current amplitude required to achieve 100 % spike probability at
120 Hz (120 Hz firing rates) for a given pulse duration, B) the difference in frequency
response between the A2 and D1 RGCs at 200 Hz. Results demonstrate that the
firing rates of cells can be better differentiated using shorter pulse widths. . . . . . . 73
4.3 A) The minimum current amplitude required to achieve 100 % spike probability at
120 Hz (120 Hz firing rates) for a range of IPGs and PW of 0.5 ms; B) The difference
in firing rate between A2 and D1 RGCs at 200 Hz for a range of interphase gaps.
Resultsshowthateventhoughtheadditionofinterphasegapdecreasethestimulation
threshold of RGCs, it does not increase the differential response of cells. . . . . . . . 74
x
4.4 Firing rate as a function of pulse amplitude for both A2 and D1 cells at 200 Hz
stimulation frequency: A) short pulse duration of 0.1 ms; B) long pulse duration
of 1 ms. Data represent the impacts of pulse width on the response of A2 and D1
RGCs. Results demonstrate that the differential responsiveness of RGCs is higher
usingshorterpulsedurations. Thissuggeststhegreateststimulusthresholddifference
and a better chance of selective activation of D1 cells using short pulse width with a
proper selection of current amplitude at high frequency. . . . . . . . . . . . . . . . . 75
4.5 Firing rates of A2 and D1 cells as a function of pulse amplitude at 200 Hz stimulus
frequency for both the presence (dash lines) and absence of IPG (solid lines). (A)
PW = 0.1 ms; (B) PW = 0.5 ms; (C) PW = 1 ms. Results show that the differential
response of RGCs is reduced with the inclusion of an interphase gap of 1 ms, lowering
chance of RGCs select excitation with the inclusion of IPGs. . . . . . . . . . . . . . . 77
4.6 The impact of soma diameter on RGCs sensitivity to the addition of interphase gap
at 200 Hz stimulus frequency. Response curves of small and large D1 cells with
and without the presence of IPGs are shown by dash and solid lines, respectively.
Data show that soma size changes do not significantly influence RGCs responsiveness
to alterations in IPG. Similar differential response of small and large cells can be
achieved with and without the presence of IPG. . . . . . . . . . . . . . . . . . . . . . 79
4.7 The influence of maximum ionic membrane conductance difference between the two
cellsontheelicitedactionpotential. Resultsindicatethesignificantimpactofcalcium
(Ca) channel density on RGCs spike width, and the influence of hyperpolarization-
activated (h) channel on RGCs refractory period. . . . . . . . . . . . . . . . . . . . . 80
4.8 The role of Ca channel in excitability of RGCs at high frequency for a pulse duration
of 0.1 ms. Data show that reducing the density of Ca channel of the A2 cell to the Ca
conductance value of the D1 cell enhances the excitability of the cell and decreases
the saturation window in the absence of IPG. However, in the presence of IPG the
influence of the Ca channel on the cell response is less pronounced. . . . . . . . . . . 81
4.9 Membrane voltage recorded from the cell body in response to electrical stimulus
pulses of 0.1 ms in duration during the saturation window of (A) A2 cell; (B) D1 cell
as shown in Fig. 4a. The small spikes were observed in the A2 cell response with
lower responsiveness at a high frequency relative to the D1 cell. . . . . . . . . . . . . 85
4.10 Comparison of the membrane voltages resulting from symmetric cathodic-first bipha-
sic waveforms with and without the presence of interphase gap. The current ampli-
tude is set to 100 µA. Data show that the A2 cell can maintain one spike per each
stimulus pulse with the inclusion of IPG, while this is not the case when the IPG is
not present. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.1 An overview of the analysis performed in this study. The frequency response of the
two RGCs subtypes (A2 and D1) was analyzed up to 200 Hz stimulation frequency
for a range of asymmetric charge-balanced biphasic pulses. The rate of changes in
the firing rate of the cells with an increase in charge amplitude was investigated. The
difference in the level of monotonic spiking activities across stimulus pulses at high
frequency offers an intriguing opportunity for selective activation of A2 cells or D1
cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
xi
5.2 The response of RGCs a function of alteration in stimulation frequency for the four
types of asymmetric pulses. The A2 and D1 cells show a different level of excitability
forgivenasymmetricwaveformsathighfrequency. WhileD2cellsaremoreresponsive
compared to A2 cells using the CF-APWM and AF-APWM stimulations, the CF-
CPWM waveforms lead to higher firing rates of A2 cells relative to D1 cells. . . . . . 96
5.3 Chargeamplitude-dependentresponseofRGCsusingasymmetriccathodic-firstpulses
withcathodicandanodicpulsewidthmodulations(CF-CPWM & CF-APWM).The
response of D1 cells to the cathodic-first pulse width of 2 ms and following anodic
pulse of 0.5 ms has been significantly decreased, offering a chance for preferential
activation of A2 cells over D1 cells. Data indicate that D1 cells are able to better
maintain the spikes while increasing the charge amplitude relative to A2 cells using
the CF-APWM stimulation, suggesting the possibility for selective stimulation of D1
cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.4 Response of RGCs as a function of varying charge amplitude using asymmetric
anodic-first pulses with cathodic and anodic pulse width modulations (AF-CPWM
and AF-APWM). The difference in the elicited spikes of the two cells is negligible
using the AF-CPWM stimulation, offering less chance for selectively targeting RGCs.
The D1 cell is more responsive at high rates of firing compared to the A2 cell with
the AF-APWM stimulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.5 Differential firing rate (DFR) of A2 and D1 cells. The difference in the firing rate
between the D1 cell and the A2 cell at 200 Hz stimulation frequency as alterations
in charge amplitude (10 nC to 70 nC). The DFR is positive when the D1 cell is more
responsive at high frequency stimuli, and when the DFR is negative the A2 cell can
better maintain spikes compared to the D1 cell. . . . . . . . . . . . . . . . . . . . . . 99
5.6 . Charge stimulation thresholds of A2 and D1 RGCs. The charge threshold is deter-
mined as the minimum charge amplitude required to achieve 50 % spike probability.
The sensitivity of RGCs response to electrical stimulation is different across various
stimulus pulses. While the D1 cells threshold is the lowest with the CF-APWM stim-
ulation, the long anodic-first asymmetric pulses lead to the lowest threshold of A2
cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.7 The temporal response of the D1 RGC at 50 nC charge amplitude and 200 Hz stim-
ulation frequency. The stimulation duration is applied and set to 250 ms after 100
ms delay. The response of the D1 cell was compared between the asymmetric long
cathodic-first (C = 2 ms) and short anodic-second (A = 0.5) pulse and the symmet-
rical cathodic-first stimulus pulse of 0.5 ms pulse width (C = 0.5 ms & A = 0.5
ms). The elicited numbers of spikes were diminished using the asymmetric stimulus
pulse. The bottom figures show the superposition of the two stimulus pulses and
the associated membrane potentials of the D1 cell for the first 50 ms duration of
stimulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.8 The time course response of the A2 RGC at 50 nC charge amplitude comparing the
asymmetrical long cathodic-first (C = 2 ms) and short anodic-second (A = 0.5) pulse
and the symmetrical cathodic-first stimulus pulse of 0.5 ms pulse width (C = 0.5 ms
& A = 0.5 ms). Data indicate the similar sensitivity of the A2 cell to both stimulus
pulses at 200 Hz stimulation frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . 102
xii
5.9 The temporal response profiles of the A2 and D1 cells using the two stimulus wave-
forms represented in the figure. Plots indicate the difference in the elicited spike
width of the two cells. The stimulus waveforms lead to modulations in the onset of
action potentials as well as changes in spiking rates of the two cells. . . . . . . . . . . 103
5.10 The sensitivity of the RGCs response to alterations in the density of potassium chan-
nelsasafunctionofchargeamplitudeusingtheasymmetriclongcathodic-firstcharge-
balanced stimulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.11 Sensitivity of RGCs selectivity to modulations in biophysical features. (A) The fir-
ing rate is plotted vs. charge amplitude for the two stimulus pulses for the original
biophysics of the cells. (B) The ionic channel expressions and densities of the two
cells are exchanged. The relationship between the spiking rate and the charge ampli-
tude modulations. Data show that the biophysical differences may not be significant
enough to change the relative responsiveness of the A2 and D1 cells. . . . . . . . . . 105
5.12 Influence of soma size on RGCs selectivity. (A) The sensitivity of small and large
cells to alterations in charge amplitude for ionic channel properties presented in the
present study and in Paknahad et al (Paknahad et al., 2020). (B) small and large
cells response as a function of charge amplitude. Our computational results again
demonstrated the significant contribution of soma diameter to selective stimulation
of RGCs using the two stimulus pulses. The intrinsic biophysical features have minor
impact on altering the potential for RGCs selectivity. . . . . . . . . . . . . . . . . . . 106
5.13 The influence of biophysical properties exchange between A2 and D1 cells on the
firing patterns of RGCs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.14 Influence of color perception on object recognition at low spatial resolution. The
four objects are represented in this picture: white plate, banana, blueberry, and
strawberry. Reduction in the number of pixels significantly diminishes the ability to
distinguishtheobjectsintheabsenceofcolorvision. Thepresenceofcolorperception
represents an immense improvement to objects recognition and to the current state
of the art in retinal prosthetic systems. . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.1 Multi-scale model consisting of (a) bulk tissue model with microelectrode, various
retinal layers (GC: ganglion cell; IPL: inner plexiform layer; INL: inner nuclear layer;
OPL: outer plexiform layer; ONL: outer nuclear layer; PR: photoreceptor) and (b)
morphologically detailed retinal bipolar cell model. The stimulating electrode of 200
µm diameter is placed 50 µm from the synaptic terminals of BCs. The bulk retinal
tissue model is utilized to compute the voltages at every node of the model due to
the stimulating microelectrode. These extracellular voltages are then applied to the
bipolar cell model to simulate its spatio-temporal response to electrical stimulation. . 121
6.2 The response of the ON-type BCs to epiretinal electrical stimulation of various pulse
amplitudes using symmetric biphasic cathodic-first charge-balanced stimulus pulses
of 8 ms and 25 ms durations. Top figures: experimental recording signals (Walston
etal.,2018). Bottomfigures: modelingresultsusingAM-NEURONplatform. Results
indicate that the model can closely predict the experimentally recorded response
characteristics of ON-BCs to epiretinal electrical stimulation. . . . . . . . . . . . . . 124
6.3 The transmembrane potential elicited by the extracellular stimulation of a symmetric
cathodic-first biphasic pulse of 25 ms in the presence and absence of the Na channel.
(b) The ionic currents in different regions of the cell at 93 µA stimulus amplitude.
The membrane conductance value of the Na channel in the axon is set to 300 mS/cm2.125
xiii
6.4 The role of L-type calcium channel at the terminal of BCs in the depolarizing voltage
transients at the onset of the cathodic stimulation pulse. The stimulus pulse duration
is set to 8 ms. Data show that the active response properties of the cell is eliminated
in the absence of the L-type channel, even at higher current amplitude of 120 µA. . . 126
7.1 The verification of the developed model of spiking bipolar cells in response to in-
tracellular stimulation. (a) The morphology of the DB4 BC; (b) Experimental data
showing the response of the cell to a sinusoidal current of 10 pA in amplitude at
the frequency of 20 Hz (Puthussery et al., 2013); (c) The response of our multi-
compartment model of the DB4 cell to the sinusoidal input current. The model can
closely replicate the experimentally recorded signal and the characteristics of sodium
and calcium spikes have been further shown in the figure. . . . . . . . . . . . . . . . 133
7.2 The response of spiking BCs to electrical stimulation of various pulse durations using
AM-NEURON modeling framework. (a) the simulated membrane potentials as a
function of time for pulse widths (PWs) ranging from 0.1 ms to 25 ms. (b) Response
latency as a function of variations in pulse durations. Results indicate the sensitivity
of BCs response to changes in pulse durations. . . . . . . . . . . . . . . . . . . . . . . 135
7.3 Modulations in the response of BCs a function of changes in current amplitude. (a)
The response latency of BCs as a function of modulations in current amplitude. (b)
The time course of the membrane voltage for a range of current amplitudes. Data
show the significant impact of current amplitude on the response latency and the
membrane potential peak. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
7.4 Stimulation strength-duration curve of BCs for cathodic monophasic, cathodic-first
and anodic-first biphasic pulses. Our data show that stimulation amplitudes are
higher for anodic-first biphasic with shorter stimulus pulse durations. However, the
presence of the anodic phase prior to the cathode significantly reduces the threshold
of BCs for longer pulse durations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7.5 The membrane potential of spiking BCs in response to electrical stimulation of both
cathodic monophasic (top) and symmetric anodic-first biphasic (bottom) using a
pulse width of PW = 8 ms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
7.6 The role of the HCN channels in response of BCs to electrical stimulation. (a) Stimu-
lation BCs threshold difference between simulations with and without the expression
of HCN channels. (b) The impact of HCN density on the response of BCs. . . . . . . 141
7.7 The impact of the asymmetric biphasic pulses on the stimulus threshold of DB4-
BCs. The cathodic pulse duration is set to 0.5 ms and the anodic pulse duration is
modulated from 0.5 ms to 8 ms. The asymmetric anodic-first stimulation has been
shown to reduce the BCs threshold compared to the anodic-first symmetric, and the
cathodic-first symmetric and asymmetric biphasic waveforms. . . . . . . . . . . . . . 142
8.1 Multiscale Admittance Method/NEURON computational platform capable of con-
structing a large-scale rat voxel model, fine details of the eye, retinal layers, and
cellular-level modeling of retinal network including retinal ganglion cells and bipolar
cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
xiv
8.2 The two placements of the stimulating ring and ground electrodes and their configu-
rations (TES 1 & TES 2). The slide of resulting voltages from AM is shown. The
extracellular voltages were extracted from the central retina (the box in the figure)
and applied to each compartment in multi-compartment models of RGCs and BCs as
shown. A 3D interpolation function has been utilized to count for micro-scale details
of retinal cells and particularly small dendrites of bipolar cells. . . . . . . . . . . . . 155
8.3 The ratio of RGCs and BCs stimulation thresholds of TES1 to TES2 setups for a
range of stimulus pulse durations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
8.4 (A) The placements of the stimulating ring on the sclera and the ground needle
electrode on the temporal region (TES 3). The slice of resulting voltages as well
as the extracellular electric potential generated in the retina are shown. (B) The
strength-duration curves plotted for a range of pulse durations from 0.1 ms to 25 ms
for both monophasic and biphaisc stimulus pulses; Computational results show that
long biphasic pulse durations can augment the chance for the excitations of retinal
bipolar cells and further reduce the differential stimulation threshold of RGCs and
BCs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
8.5 In-vivo electrical stimulation setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
8.6 Fundus Autofluorescence image of one animal treated in the 100 uA group. Image
A shows the non-treated eye where hypopigmentations are observed (inside dotted
circle). ImageBshowsthetreatedeyewhereearlystagesofdegenerationareobserved
as sparse hyperpigmented spots (blue arrow). (Figure from Alejandra Gonzalez-Calle)161
8.7 Summary of the retinal thicknesses from the three stimulation groups stratified as
non-treated vs. treated eyes. The grey bars represent the mean per group (n = 8)
and the error bars denote the standard error of the mean. (Figure from Alejandra
Gonzalez-Calle) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
8.8 Cross section of histological slides comparing the treated vs the non-treated eye of an
animal stimulated from the 100uA group. Image A shows loss and disorganization of
the ONL layer while treated eye shows preservation of the ONL layer compared with
the non-treated eye. GCL: Ganglion Cell Layer. INL: Inner Nuclear Layer. ONL:
Outer Nuclear Layer. (Figure from Alejandra Gonzalez-Calle) . . . . . . . . . . . . . 163
8.9 Coarse human head models: Three different placements and configurations of the
ground electrode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
8.10 The slices of the current density magnitude distribution for the three ground config-
urations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
8.11 Theslicesoftheelectricfieldmagnitudedistributionforthethreegroundconfigurations.166
8.12 The placement of the stimulating DTL electrode: A) on the sclera; B) on the eyelid. 167
8.13 The slices of the current density magnitude distribution. A) DTL stimulating elec-
trode on the sclera; B) DTL stimulating electrode on the eyelid. . . . . . . . . . . . . 168
8.14 The slices of the electric potential distribution. A) DTL stimulating electrode on the
sclera; B) DTL stimulating electrode on the eyelid. . . . . . . . . . . . . . . . . . . . 169
8.15 Comparison of two stimulating electrode configurations. A) DTL electrode; B) Ring
electrode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
8.16 The slices of the current density magnitude distribution for the two stimulating elec-
trode configurations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
8.17 Theslicesoftheelectricfieldmagnitudedistributionforthetwostimulatingelectrode
configurations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
xv
8.18 The configuration of the proposed ground electrode for delivering more effective and
safe TES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
8.19 The slices of the current density magnitude distribution. A) The proposed ground
system of Figure 8.18; B) The disk ground electrode on the temple. . . . . . . . . . . 172
8.20 The slices of the electric field magnitude distribution. A) The proposed ground
system of Figure 8.18; B) The disk ground electrode on the temple. . . . . . . . . . . 172
8.21 The slices of the voltage distribution. A) The proposed ground system of Figure
8.18; B) The disk ground electrode on the temple. The reduced peak voltage of the
proposed system compared to the common small ground electrode on the temporal
region is shown in the figure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
xvi
List of Tables
2.1 Rate constants of ionic currents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2 Maximum conductance values for A2 and D1 cells [S/cm2]. . . . . . . . . . . . . . . 29
2.3 Maximum conductance values of the axon for A2 and D1 cells [S/cm2]. . . . . . . . . 29
3.1 Maximum conductance values of the axon for A2 and D1 cells [S/cm2]. . . . . . . . . 52
4.1 Maximum conductance values for A2 and D1 cells [S/cm2]. . . . . . . . . . . . . . . 71
4.2 Maximum conductance values of the axon for A2 and D1 cells [S/cm2]. . . . . . . . . 71
7.1 Maximum ionic conductance values [mS/cm2]. . . . . . . . . . . . . . . . . . . . . . . 134
8.1 The procedures performed in all animals during the 7-week experiment, according to
the designed stimulation strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
8.2 The electrical stimulation parameters and the number of animals that were included
for each set of stimulation parameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
8.3 Summary of the photoreceptor counts acquired from all stimulated and sham groups.
(Figure from Alejandra Gonzalez-Calle) . . . . . . . . . . . . . . . . . . . . . . . . . 163
xvii
Abstract
Retinal diseases, such as retinitis pigmentosa (RP), age-related macular degeneration (AMD),
and glaucoma (POAG), are characterized by unrelenting neuronal death. Although treatments to
ameliorate these conditions exist, there is no cure. Therefore, attempts have been made to restore
partial sight to the blind or slow down the progression of retinal blindness. For instance, epiretinal
prosthetic devices have been developed to electrically stimulate the surviving retinal neurons and
restore some forms of visual function. While these devices have had a significant impact on the lives
of totally blind patients, several challenges - such as limited spatial resolution and the inability of
subjects to perceive color and contrast - have yet to be addressed.
In this dissertation, we applied a three-dimensional Admittance Method (AM)-NEURON multi-
scale computational modeling platform to gain an understanding of the mechanisms underlying the
response of retinal neurons to electrical stimulation, and their functional implications. The AM-
NEURON computational platform is capable of modeling complex, large-scale, heterogeneous bio-
logical tissues as well as micro-scale modeling of biophysically and morphologically realistic models
of neurons; its multiphysics nature enables us to design electrical stimulation strategies for enhanc-
ing the efficacy of current epiretinal prosthetics systems, with the ultimate goal of developing the
next generation of retinal prostheses.
While current retinal prosthetic systems are intended for blind patients that are at late stages
of retinal degeneration, approaches to delaying the onset of blindness and progressive retinal degen-
eration at the early stage of degeneration would make a significant impact in the lives of patients
suffering from these conditions. We introduce in this dissertation a strategy that relies on controlled
electromagnetic (EM) retinal stimulation to induce neuroprotective changes in the retina. Toward
xviii
this goal, our computational modeling platform was utilized to design a non-invasive electrical stim-
ulator to maximize the induced electric fields in the retina, thus likely increasing the potential
for neuroprotective effects and potentially opening avenues to slow down the progression of retinal
blindness.
xix
Chapter 1
Introduction
1.1 The Retina
The retina is a multilayer tissue consists of functionally different neurons and located at the
back of the eye (Figure 1.1). The process starts with light rays coming into the eye through the
cornea and the lens, which refract the light and mostly focus it onto the small area of the retina
with high densities of retinal neurons called fovea. There are several retinal layers and neurons that
contribute to the transmission of visual signals to the brain. From the outermost to the innermost
layers of the retina, there are the retinal pigmented epithelium (RPE), photoreceptor layer, outer
nuclear layer (ONL), outer plexiform layer (OPL), inner nuclear layer (INL), inner plexiform layer
(IPL), retinal ganglion cell (RGC) layer, and nerve fiber layer. The RPE is a melanin-dense layer
that absorbs light and maintains the health of the photoreceptor. The photoreceptor detects the
photons of light and through the phototransduction process converts the light into electrical signals
and passes onto the inner most layers of the retina, the optic nerve and ultimately to the visual
cortex in the brain.
1
1.2 Retinal Neurons
Cone and rods are the two types of photoreceptors. Rods detect motion and function in low light
levels (scotopic) while cones detect color, responsible for central vision, and function in medium
to bright light (photopic). Rods are located throughout the retina and mostly populated in the
retina periphery, but cones are mostly present in a small area called the macula. In the middle
of the macula there is a region with highly dense light-sensitive cells, called the fovea, where only
cone photoreceptors reside that play roles in color vision and visual acuity. There are multiple
types of cones with variations in their spectral sensitivity. Several factors contribute to the spectral
sensitivitysuchasthewavelengththatlight-sensitiveopsinshavethepeakrateofphotonsabsorption
along with the properties of opsin protein spectral absorption. There are three main classes of
primate cone opsins with the peak sensitivity at short (S)-419 nm, medium (M)-535 nm, and long
(L)-565 nm wavelengths respectively. The perception of color starts with the absorption of light
by these three light-sensitive opsins. While the density of M and L cones are relatively high in the
fovea of the primate retina, the density of rods and S cones are significantly reduced (Thoreson and
Dacey, 2019).
There are several downstream neurons that receive inputs from rods and cones photoreceptors.
Bipolar cells (BCs) and horizontal cells (HCs) are postsynaptic to photoreceptors. The inhibitory
HC neurons are ramified in the ONL and provide lateral negative feedback to cones and make in-
hibitoryfeedforwardsynapticconnectionswithBCsbyreleasinggamma-aminobutyricacid(GABA)
neurotransmitter(Wu,1986). HCsmostlyhavelargereceptivefieldsandmakestronggapjunctional
couplings with the neighboring HCs. The negative feedback from HCs to cones contribute to the
center-surround receptive field arrangement. Center-surround receptive fields enhance the efficacy
of visual signally and mediate spatial contrast encoding in the retina (Turner et al., 2018).
2
Figure 1.1: Structure of the eye and retinal neurons. Left figure from www.sunledind.com; Right
figure from (Ferrara et al., 2021)
Bipolar cells consist of rod and cone BCs. Rod BCs make a presynaptic connection with rod
photoreceptors and mediate low light levels. There are 9 different subtypes of cone BCs in the
human retina (Kolb et al., 1992). They are classified based on the level of ramification of bipolar
cells terminals in the inner plexiform layer. BCs can be divided into ON and OFF types depending
upon the depolarized or hyperpolarized signals received from photoreceptors. OFF BCs preserve
the sign of signals received from cones, whereas ON BCs reverse the sign of cones. In the light,
photoceptors are hyperpolarized and therefore ON-type BCs receive excitatory inputs from cones
via metabotropic glutamate (mGluR6) receptor. In contrast, OFF-type BCs receive sign-conserving
signals through ionotropic AMPA receptors leading to depolarization of OFF cells (DeVries, 2000).
In the primate retina, there are two common pathways: parvocellular and magnocellular pathways.
Only bipolar cells within the magnocellular pathway express active voltage gated ionic currents and
play roles in motion and flicker detection as high temporal resolution is required. While most of the
BCs subtypes transmit signal via graded potentials, BCs in the magnocellular pathway have the
capability to generate spikes (Puthussery et al., 2013; Rattay et al., 2017). This results in greater
neurotransmitter releases at the terminal of cells and faster signals transmission to the downstream
retinal ganglion cells (RGCs).
3
Figure1.2: Thecircuitryfortheblue-yellowcoloropponentpathway(ThoresonandDacey,2019).
.
Another retinal neuron which is laterally resided in the INL is amacrine cell (AC). The cell
bodies of cells lie in the proximity of the inner most part of the INL (Vaney, 1990). Like horizontal
cells, Amacrine cells are mostly inhibitory interneurons that laterally interact with bipolar cells and
ganglion cells using GABA and glycine inhibitory neurotransmitters (Tachibana and Kaneko, 1987).
There are morphologically different ACs with varying size, shape, and stratification patterns. For
instance, AII ACs typically have narrow-field with multilayers of stratification and play roles in
scotopic signals collection from rod BCs and distributing them to ON and OFF cones via inhibitory
synapses and gap junctions (Marc et al., 2014).
Retinal ganglion cells are the inner most retinal neurons and mostly receive inhibitory and
excitatory inputs from bipolar cells and carry visual signals to the brain. There are almost 15-17
different ganglion cells in the retina and almost 12-15 of them are well-defined and classified by
their morphological and biophysical characteristics. These ganglion cells are classified based on the
size of cell body, dendritic field, and the level of dendritification in the IPL (Huxlin and Goodchild,
1997; Sun et al., 2002). The graded potentials generated at the level of BCs are transmitted to
4
Healthy
Degenerated
Figure 1.3: The timeline of retinal degeneration.The images of human retina before and after the
degeneration are shown in the left panel (Loizos et al., 2018).
RGCs leading the trains of action potentials. RGCs can be divided into ON, OFF, and ON-OFF
RGCs. While ON RGCs increases the rate of spikes with light increment, the spiking frequency
augments with light decrement in OFF RGCs (Maturana et al., 2014). RGCs express different
morphological and biophysical properties and carry particular types of visual information such as
color and contrast (Maturana et al., 2014). For instance, small bistratified RGCs has been shown
to play roles in blue-yellow color opponent pathway in the retinal circuitry (Dacey and Lee, 1994;
Dacey and Packer, 2003; Lee et al., 2010; Silveira et al., 1999). Short wavelength sensitive (S)
cone photoreceptors make selective connection with S-cone ON blue cone bipolar cells, which is
presynaptic to our dendritic branches of small bistratified RGCs. L and M cones are presynaptic to
OFF cone bipolar cells, then signals are transmitted to outer dendrites of small bistratified ganglion
cells as illustrated in Figure 1.2 (Thoreson and Dacey, 2019).
5
1.3 Retinal Degeneration
Age-related macular degeneration (AMD) is a common cause of vision loss among Americans
over age 50 and affects 30 million people worldwide and 2 million in the US (Friedman et al.,
2004). AMD mostly damage cone photoreceptors in the macula leading to initiation of vision
loss at the center of the visual field. Retinitis pigmentosa (RP) is the leading reason of inherited
blindness that affects nearly 1 in 4000 people. In RP, degeneration starts to occur at the level of
rod photoreceptors with high density in the retina periphery following with the degeneration of
innermost retinal layers. Therefore, RP patients first have trouble seeing at night and they loss
their peripheral vision following with the loss of central vision at late stages of retinal degeneration
(Hartong et al., 2006). The impact of AMD and RP diseases on the visual field of patients is
represented in Figure 1.3 (Yue et al., 2016). The timeline of degeneration can be broken down into
4 phases as seen in Figure 1.3. Throughout the first two phases, photoreceptors are stressed, and
cellular death occurs. At the later stage, remodeling in the retinal circuitry and cellular migration
initiate, eventually leading to the substantially degenerated and disorganized retina in late stages
of degeneration as illustrated in the figure (Jones et al., 2011).
1.4 Current Treatment Approaches
There is currently no known cure for either RP or AMD. Several therapeutic approaches to
slowing down or restoring some forms of visual function have been proposed. Gene therapy is
under development for RP and several animal models for specific gene mutations have been studied
(Beltran et al., 2012). However, there are many mutations of gene that lead to RP, which can limit
the number of RP patients that can benefit from this therapy (Yue et al., 2016). Another novel
6
Figure 1.4: Different types of retinal prosthetic systems. The placement of the stimulating
electrode arryat varies among retinal implants to target retinal neurons of interests (Tong et al.,
2020).
treatmentwithactiveongoingresearchanddevelopmentisstemcelltransplantation. Thistechnique
aims at replacing the damaged RPE or photoreceptors by healthy and normal cells at late stages of
degeneration (Sadaoka et al., 2018). This approach has led to promising results demonstrating the
possibility of restoring some forms of visual functions in animal models (Huang and Thesleff, 2013).
Despite the success, challenges such as the proper neuronal network connectivity of transplanted
cells with remaining healthy neurons of the retina for achieving more meaningful form of visual
signals require further investigation.
Theemergingoptogeneticshavebeendevelopedtogeneticallyinducelightstimulationsensitivity
to cells that do not intrinsically evoke response to light stimuli (BARRETT et al., 2014; Montazeri
et al., 2019; Tochitsky et al., 2014). Most recently, a novel developed light-sensing protein called
the MCO1 opsin has been proposed to restore partial sight in mice models by inducing the opsin
to retinal bipolar cells (Batabyal et al., 2021). There are other stimulation techniques such as
ultrasonic retinal modulation and photochemical currently being under development (Lo et al.,
7
2020; Polosukhina et al., 2012). A wide range of stimulation strategies have been proposed in the
literature to electrically stimulate the surviving retinal neurons. Different types of retinal prostheses
have been developed aiming at helping both RP and AMD patients with significant visual loss and
function (Humayun et al., 1999; Palanker et al., 2020; Stingl et al., 2015; Zrenner et al., 2011).
Visual cortical prosthetic systems bypass the entire retinal network and optic nerve and directly
stimulate the visual cortex in the brain, offering the potential for restoring vision to blind patients
who are not eligible for other treatment options (Kosta et al., 2018; Lewis et al., 2014). In-depth
review of various therapeutic techniques can be found in Yue et al. for interested readers (Yue et al.,
2016). In addition to direct and invasive electrical stimulation of the retina and visual cortex, less
invasive ocular electrical stimulation strategies such as transcorneal electrical stimulator (TES) have
been also proposed to preserve retinal neurons and slow down the progression of retinal blindness
(Schatz et al., 2017). Retinal prosthetic systems and applications of TES which are the focus of
this of this work will be discussed in more details.
1.5 Retinal Prostheses
Several retinal prosthetic systems have been developed to electrically stimulate healthy retinal
neurons for enhancing the outcome of visual function in blind patients. There are three main bio-
electronic implants based on the placement of multi-electrode array: Epiretinal, subretinal, and
suprachoroidal as shown in Figure 1.4. The initial target of epiretinal implants is retinal ganglion
cells which are known to have a moderate survival rate during the degeneration process. The stim-
ulating electrodes are placed on the surface of retinal ganglion cell layer in these devices. The
electrodes of subretinal implants are imbedded between BCs and RPE hoping to replace the func-
tion of photoreceptors and generate more natural physiological visual signals for vision restoration.
8
Figure 1.5: The Argus II retinal implant. The camera is attached to sunglasses capturing the
image. The video processing unit (VPU) processes the information and send it to the external
transmitter coil which is placed close to the temporal side. The power and data are transferred
wirelessly from the external to implant coil and the electronics case send the spatiotemporal electric
signalstotheelectrodearray. Themulti-electrodearrayisplacedepiretinallyonthesurfaceofRGCs
layer (Figures courtesy of Second Sight Medical Products, Inc.).
Suprachoroidal prostheses consist of an electrode array which is located between the choroid and
sclera as shown in the figure.
Several types of retinal prostheses have been currently commercialized including Argus I and II,
Second Sight Medical Product (SSMP) Inc. (Ahuja et al., 2008), Alpha IMS (Stingl et al., 2015),
Epiret3 (Menzel-Severing et al., 2012), Boston Retinal Implant (Rizzo, 2011), BVA Implant (Ayton
et al., 2014), PRIMA Vision Restoration System based on Stanford array (Palanker et al., 2020;
Wang et al., 2012), and STS System (Fujikado et al., 2012). Most attempts have been made towards
the research and development of epiretinal prostheses and the present study is largely centered on
epiretinal electrical stimulation of the retina.
Argus II retinal implant and electronic components are represented in Figure. 1.5. A camera
9
Figure 1.6: Three possible retinal ganglion cells responses to epiretinal electrical stimulation. A)
Directly activating RGCs cell bodies; B) Activation of RGCs axon bundles, leading to elongated
phosphenes perceived by subjects; C) Network mediated response of RGCs by targeting the outer
retinal neurons such as BCs (Tong et al., 2020).
that is mounted on a pair of glasses captures the image and send the information to the video pro-
cessing unit (VPU). The VPU unit is responsible for digitizing the input data and applying a series
of image processing filter. The image processing system converts an image captured by a camera
into a stimulus pattern. The data and power are transmitted wirelessly from the external coil to the
curved elliptical implant coil. The electronics case generates the stimulus pattern and send signals
to a multi-electrode array on the surface of RGC layer. The device has a 6× 10 electrode array and
the platinum disk electrode has a diameter of 200 µm. Stimulation strategies have been proposed
to enhance the efficacy of current epiretinal prostheses. Electrical stimulation of varying stimulus
waveform parameters results in different types of retinal neurons activation. Figure 1.6 illustrates
three possible activations of cells in response to epiretinal extracellular electrical stimulation. Ex-
citation of RGCs cell bodies or axon initial segment (AIS) is known as direct stimulation. High
stimulus amplitude can lead to activation of RGCs axon bundles, thereby activating a population of
RGCs along the axon fiber pathway. The RGCs axonal activation is one of the current challenges of
these devices leading to the elongated phosphenes that varies in size and shape across the subjects.
In fact, the reported orientation of phosphenes by the Argus II subjects was aligned with the tangent
10
line of RGCs nerve fiber bundles beneath the stimulating electrode (Beyeler et al., 2019). To avoid
axonal stimulation and therefore enhance the spatial resolution of current devices, indirect RGCs
stimulation strategies are suggested to initially activate the outer retinal neurons such as BCs and
indirectly evoke spikes in RGCs (Freeman et al., 2010; Weitz et al., 2015).
The size of the stimulating electrode is relatively large and therefore covering tens or hundreds of
retinal neurons. Simultaneous activation of retinal neurons as well as different subtypes of particular
neurons are significant issues, reducing the likelihood for meaningful elicited signals transformation
and therefore affecting the outcome of current devices. The ability of selectively stimulate retinal
neurons can significantly improve the efficacy of current devices. For instance, selective activation of
functionally distinct RGCs that information such as color would be hugely important. Interestingly,
electrical stimulation of Argus II subjects revealed that increasing the stimulation frequency and
modulations in current amplitude can result in blue/purple color perception (Yue et al., 2021).
Therefore, further understanding the mechanisms underlying the color encoding in the electrically
stimulated degenerated retina would offer the intriguing potential to develop the next generation of
epiretinal prosthetic systems.
1.6 Non-invasive Electrical Stimulation Strategy
Patientsattheearlystagesofdiagnoseswithretinalblindnessdiseasescannotbenefitfromvisual
prostheticdevicesastheystillhavemeaningfulvisualsight. Inthisregard,therapeuticapproachesto
slowing down or halting the progression of prevalent retinal blindness are significantly important. In
1960s, it was first demonstrated that electrical stimulation of cornea results in phosphene sensation
and response in visual cortex (Potts et al., 1968). Many attempts have been made since then to
investigatethepotentialimpactofnon-invasivestimulationtechniquessuchastranscornealelectrical
11
stimulation (TES) on the likelihood for preservation of photoreceptors and retinal ganglion cells.
Figure 1.7 provides examples of TES stimulator utilizing different types of stimulating electrodes
(Xie et al., 2011). TES has proven effective in preserving the thickness of outer nucleus layer and
enhancing the electroretinography function (ERG) after 6 weeks of stimulation (Morimoto et al.,
2007). Further, it has been shown that TES preserves visual function after optic nerve crush injury,
and the number of damaged RGCs is significantly diminished after the application of TES (Miyake
et al., 2007; Morimoto et al., 2005). A number of factors have been identified as how electrical
stimulation can benefit neurons preservation such as modulations in neurotropic factors after a
session of TES (Fu et al., 2015), however the underlying mechanisms have not been well understood
yet. Several electrical stimulation parameters and positions of the stimulation and return electrodes
have been utilized to better understand the influence of TES stimulator on retinal neurons survival
(Sehic et al., 2016). However, it has been no systematic study investigating the most effective
stimulation strategy to maximize the induce electric fields and selectively stimulate retinal neurons.
1.7 Dissertation Outline and Significance
The overall goal of this thesis is to deploy computational methods for advancing our understand-
ing of retinal neurons response to electrical stimulation. The computational modeling approach al-
lows us to design electrical stimulation strategies for enhancing the efficacy of induced electric fields
and therefore elicited neuronal activations due to electrical stimulation. Throughout this thesis, a
3D multi-scale combined Admittance Method (AM)-NEURON computational modeling platform
has been utilized to investigate in depth the response of retinal neurons to electrical stimulation.
The modeling framework enables us to capture challenges associated with current neuroprosthetic
devices including epiretinal prostheses and design stimulation techniques to address and ultimately
12
Figure 1.7: Transcorneal electrical stimulation (TES). Top: The DTL-Plus electrode is placed on
the lower side and above the open eyelid. Bottom: The ERG-Jet electrode is placed on the sclera
(Cela, 2010).
overcome these issues. Utilizing this platform, we can further delve into mechanisms underlying
the activation of cells and identify the contributions of biophysical and morphological properties to
spatiotemporal neuronal activities of cells in response to electrical stimulation.
This method first involves constructing the large-scale heterogenous biological tissues as well as
modeling micro-scale complex features of neurons at the cellular level including biophysical proper-
ties, neuronalnetworkconnectivity, andrealisticmorphologicalrepresentationofcells. Bioelectronic
components are then constructed and the response of neurons to electrical stimulation of varying
stimulus parameters is investigated. The results from the computational modeling are verified with
experimental data from the literature and experiments performed in this work. This predictive com-
putational tool is further utilized to develop novel stimulation strategies such as designing stimulus
waveforms for enhancing the effectiveness of current retinal prosthetic systems and TES stimula-
tors. This methodology can be expanded to be deployed for a wide range of neural stimulation
13
applications.
In chapter 2, we first developed morphologically and biophysically realistic models of two classi-
fied RGCs, A2-monostratified and D1-bistratified, using NEURON computational simulator (Hines
and Carnevale, 1997), and verified the response with the experimentally recorded signals of cells
in response to intracellular electrical stimulation (Qin et al., 2017). Then, the axonal of activation
of retinal ganglion cells in response to epiretinal electrical stimulation was predicted by construct-
ing the synthetic network of a large population of the two developed RGCs using AM-NEURON
platform. We designed stimulus parameters for enhancing the chance for more focal response of
RGCs and therefore improving the spatial resolution of current epiretinal implants. The underly-
ing biophysical factors leading to more round shape of spatial RGCs activation with the proposed
waveform have been further identified.
Although efforts to develop more dense electrode arrays for providing higher vision resolution to
patients implanted with artificial retinas are currently underway, a significant loss of spatial visual
information with respect to normal vision is inevitable. In light of this, color vision would represent
an additional significant element to compensate for the limited visual acuity achieved with current
devices. RecenttestsperformedbyourgroupwithArgusIIimplantssubjectsrevealedthatelectrical
stimulation can indeed result in color percept; most strikingly, these experiments reveal that color
perception is dependent upon stimulation parameters such as frequency of stimulation, pulse width.
In chapter 3, applying the computational method, we designed a “frequency-amplitude” stimulation
technique to selectively target D1 small bistratified RGCs with the role in blue-yellow color vision
(Dacey and Lee, 1994; Dacey and Packer, 2003). Our findings appear to be well correlated with the
clinical and in-vivo experimental data. We further utilized this predictive platform and stimulation
strategy to analyze the influence of pulse width and interphase gap modulations on the likelihood
14
for enhancing RGCs selectivity in chapter 4.
In chapter 5, we explore the role of asymmetric stimulation pulses on selective activation of
RGCs. While stimulation methods for selective excitation of one particular RGC subtype have
been proposed, it has been quite challenging to preferentially stimulate functionally different RGCs
subtypes. We, for the first time, designed stimulus waveforms for selective activation of A2 cells
over D2 cell, or D1 cells over A2 cells. This modeling framework and the ability to target RGCs
selectively provide intriguing opportunities for: i) improving the outcome of current prosthetic
systems; ii) further augmenting our fundamental knowledge of color perception; iii) enabling the
opportunity to “code colors” in future generation of retinal prosthetic systems.
We extended this modeling platform to augment our understanding of the network-mediated
response of RGCs through bipolar cells activation in response to epiretinal electrical stimulation.
To this goal, in chapter 6 we develop a biophysically more realistic compartmental model of ON
cone BCs for electrical stimulation applications. The response of the cell to epiretinal electrical
stimulation is compared with the recent patch clamp recording of ON-type BCs. The developed
model allowed to capture the main ionic channel membrane contributor to the generated graded
membrane potential in response to electrical stimulation. In chapter 7, we focus on a subtype of
BCs with the capability to generate action potential and design stimulus waveforms for reducing
the stimulation threshold of BCs. We further go over mechanisms underlying the reduced threshold
of BCs using long stimulation pulses as reported from experimentally data in the literature.
We recently have shown in our group that controlled electrical stimulation can induce epigenetic
changes in the retina to slow down the progression of retinal blindness. Therefore, we developed
a multi-scale models and modeling platform to predict electric field parameters and waveform effi-
cacious for this purpose and to design a TES stimulator to induce epigenetic changes and preserve
15
retinal neurons more effectively. In chapter 8, the AM-NEURON modeling methodology is further
extended for the application of TES. We, for the first time, assessed the response of retinal neurons
to transcorneal electrical stimulation. We designed a non-invasive electrical stimulator to maximize
the induced electric fields in the retina and enhance the potential for neuroprotective effects and
epigenetic changes. We found that long charge-balanced biphasic stimulus pulse durations enable us
to better target cells such as BCs that are affected first at early stages of retinal degeneration. Our
findings indicate the potential for a more effective therapeutic approach to slowing or halting the
progression of retinal diseases. The summary of this dissertation and potential future steps towards
the development of new therapeutic approaches using electrical stimulation are discussed in chapter
9.
16
Chapter 2
Stimulation Waveforms for Improving
the Spatial Resolution of Epiretinal
Prostheses
© 2020 TNSRE. Paknahad J, Loizos K, Humayun M, Lazzi G. Targeted Stimulation of Retinal
Ganglion Cells in Epiretinal Prostheses: A Multiscale Computational Study. IEEE Transactions
on Neural Systems & Rehabilitation Engineering (2020).
Abstract
Retinal prostheses aim at restoring partial sight to patients that are blind due to retinal degenera-
tive diseases by electrically stimulating the surviving healthy retinal neurons. Ideally, the electrical
stimulation of the retina is intended to induce localized, focused, percepts only; however, some
epiretinal implant subjects have reported seeing elongated phosphenes in a single electrode stimu-
lation due to the axonal activation of retinal ganglion cells (RGCs). This issue can be addressedby
properlydevisingstimulationwaveformssothatthepossibilityofinducingaxonalactivationofRGCs
is minimized. While strategies to devise electrical stimulation waveforms to achieve a focal RGCs
response have been reported in literature, the underlying mechanisms are not well understood. This
17
article intends to address this gap; we developed morphologically and biophysically realistic com-
putational models of two classified RGCs: D1-bistratified and A2-monostratified. Computational
results suggest that the sodium channel band (SOCB) is less sensitive to modulations in stimulation
parameters than the distal axon (DA), and DA stimulus threshold is less sensitive to physiologi-
cal differences among RGCs. Therefore, over a range of RGCs distal axon diameters, short-pulse
symmetric biphasic waveforms can enhance the stimulation threshold difference between the SOCB
and the DA. Appropriately designed waveforms can avoid axonal activation of RGCs, implying a
consequential reduction of undesired strikes in the visual field.
2.1 Introduction
Retinitis pigmentosa and age-related macular degeneration are retinal degenerative diseases,
which start with the degeneration of photoreceptors. In early stages of degeneration, while pho-
toreceptors are largely damaged, inter retinal neurons and ganglion cells remain mostly intact. To
restore partial vision for patients suffering from blindness by degenerative diseases, retinal pros-
thetic devices have been developed. These devices electrically stimulate surviving neurons in the
degenerated retina to evoke visual percepts. The efficacy of this approach has been proven by sev-
eral research groups and led to the development of various retinal prosthetic systems (Humayun
et al., 1999; Lin et al., 2018a; Palanker et al., 2020; Stingl et al., 2015; Zrenner et al., 2011). While
clinical trials have shown the effectiveness of these devices, further understanding of neuronal re-
sponse to electrical stimulation is vital to improve the performance of such devices for patients to
better recognize patterns, such as objects and letters (Zrenner et al., 2011). In epiretinal prosthetic
devices, retinal ganglion cells (RGCs) are the main target of electrical stimulation. There are many
challenges with this stimulation strategy. For example, a wide activation range of retinal neurons
18
due to the close proximity of two neighboring electrodes in a high-density multi-electrode array
has been shown to limit the spatial resolution of these devices (Wilke et al., 2011). To focus the
stimulation site, hexapolar electrode configurations (Abramian et al., 2011; Habib et al., 2013), and
virtual electrode designs (Loizos et al., 2016a) have been utilized. Recently, a ‘shaping’ algorithm
has been proposed to predict the pattern of retinal activity from simultaneous stimulation of the
multielectrode and optimize the electrical stimulation pattern of the multielectrode array to match
with a target activation pattern (Spencer et al., 2019).
Evidence suggests that axonal activation of RGCs is also one of the main critical challenges
with current epiretinal implants. Clinical studies on Argus II patients have revealed that a single
electrode stimulation resulted in activation of RGCs axonal pathways and therefore the elongated
phosphenes perceived by subjects (Beyeler et al., 2019; Nanduri et al., 2012). Several attempts have
been made towards developing stimulation waveforms utilizing direct and indirect stimulation of
RGCs to improve the efficacy of current devices (Freeman et al., 2010; Hadjinicolaou et al., 2015;
Im and Fried, 2015; Im et al., 2018; Jensen et al., 2009; Palanker et al., 2004; Tong et al., 2020; Weitz
et al., 2015).Sinusoidal electrical stimulation at 25 Hz resulted in selective activation of bipolar cells
(BCs) (Freeman et al., 2010); in fact, it has been further shown that electrical stimulation with
a longer pulse duration (25 ms) can reduce the spatial pattern of activated RGCs and avoid the
activation of passing axonal fibers (Weitz et al., 2015). However, clinical and animal studies have
also reported the percept fading due to repetitive indirect stimulation of RGCs which has led to
desensitization (Ahuja et al., 2008; Freeman and Fried, 2011; Stronks and Dagnelie, 2014); therefore,
direct electrical stimulation of RGCs with short pulse durations has been utilized to obtain focal
activation of RGCs (Chang et al., 2019; Fried et al., 2006; Jensen et al., 2005; Raghuram et al.,
2019; Sekirnjak et al., 2008) and overcome desensitization and phosphene fading challenges.
19
Experiments have been performed to identify optimal stimulation waveforms to avoid axonal
activation and selectively targeting RGC somas (Chang et al., 2019; Jensen et al., 2005; Schiefer
and Grill, 2006). Biphasic charge-balanced stimulus waveforms with a relatively short pulse width
(120 µs) are shown to result in more focal responses from RGCs and only activation of RGC somas
using a calcium imaging technique (Chang et al., 2019). However, there are a wide range of different
RGCs subtypes sending unique visual information to the brain (Huxlin and Goodchild, 1997; Sun
et al., 2002; Walsh et al., 2000). Previous calcium imaging approaches indiscriminately visualize
responses of a large number of RGCs to epiretinal electrical stimulation and provide no information
regarding the differential stimulus threshold of the axon initial segment (AIS) and passing axons
(Chang et al., 2019). Therefore, it would be essential to capture the response of various RGCs
subtypes to electrical stimulation and further characterize factors affecting the axonal activation of
morphologically and biophysically different types with different sensitivity to electrical stimulation.
While these studies are promising towards improving the effectiveness of epiretinal implants,
limited progress has been made towards the development of a computational platform to predict
the response of a large population of different RGCs subjected to external stimulation. Predictive
computational tools would help gain additional insights into underlying mechanisms and physiolog-
ical changes due to direct electrical stimulation of RGCs. Using our group’s Admittance Method
(AM)/NEURON computational platform (Bingham et al., 2020; Cela, 2010; Cela et al., 2011; Kosta
et al., 2020; Loizos et al., 2018, 2016b), we focused on exploring the sensitivity of passing axons
and the SOCB of RGCs to both cathodic and anodic-first symmetric biphasic stimulus pulses with
various durations.
Biophysical properties of different RGC subtypes estimated from experimental data in vitro
have been used to implement a single-compartment model (Qin et al., 2017). For this paper,
20
morphologically and biophysically realistic models of two subtypes of RGCs, A2-monostratified and
D1-bistratified, havebeendevelopedandtheiraccuracyhasbeentestedbycomparingcomputational
results with neural recordings from experiments reported in (Hadjinicolaou et al., 2016; Qin et al.,
2017). The modeled RGCs have realistic representation of axons, including the initial segment
which plays a significant role in the response of RGCs to epiretinal electrical stimulation. This
multiscale platform, in conjunction with the developed RGC models, allow us to determine the
field distribution inside the retina tissue and predict the response of a large population of realistic
RGCs to electrical stimulation. We centered our focus on neuronal responses of A2 and D1 RGCs
to epiretinal stimulation of different pulse widths considering first a single cell, and later a large
population of cells.
Our results show that the AIS, and particularly the SOCB, is less sensitive to modulations
in pulse durations compared to the DA. We further demonstrate that morphological (soma and
dendriticfieldsize)andbiophysicaldifferencesbetweenthetwoRGCsdonotsignificantlycontribute
to the stimulus threshold of RGCs distal axon. This indicates that the DA properties are largely
responsible for the sensitivity of passing axons to electrical stimulation. Considering the passing
axon diameter variations between the cells, our computational findings suggest that modulations in
pulse durations can influence the differential stimulus threshold between the SOCB and DA. This
can potentially improve the chance for select activation of the SOCBs and avoid axonal excitation
of RGCs. More focalized response of RGCs to direct electrical stimulation can enhance the spatial
resolution of current epiretinal prosthetic systems.
21
Microelectrode
Retina layers
Retinal ganglion cells
3000 µm
3000 µm
160 µm
(a)
(b)
PW
IPG A
1/F
Cathodic
Anodic
IPG=0
F=1Hz
PW:0.1to10ms
PW
IPG A
1/F
Cathodic
Anodic
(c)
Figure 2.1: Multiscale model of electrical stimulation of the retina tissue. (a) A 3D voxelized
model, consisting of bulk retina tissue with a single stimulating electrode. (b) The distributed
voltage inside the retina tissue using Admittance Method (AM). This voltage is applied as an ex-
tracellular voltage in the NEURON model. (c) Electrical stimulation waveform applying symmetric
charged-balanced biphasic with alterations in cathodic and anodic pulse durations.
2.2 Methods
2.2.1 Admittance Method (AM): Electronics and Retina Tissue
To calculate the extracellular voltage generated due to electrical stimulation, we constructed a
model of bulk retina tissue and an electrode. Material properties are assigned for each voxel in the
model. Current is injected to the electrode and the resulting voltage is computed at each node in
the voxel using the AM model. Then, to obtain the extracellular voltage input to each neuronal
compartment, a linear interpolation function is used to calculate the voltage at each compartment in
multicompartments model of RGCs. The anatomy of healthy mammalian retina has been modified
22
to represent the degenerated retina tissue, shrinking the thickness of the outer part of the retina
including the outer plexiform and outer nuclear layers. The retina tissue laminar properties are
identical to those provided in Loizos et al. (Loizos et al., 2018). An electrode with diameter of
200 µm is placed on the center of the bulk retina tissue with 18 million computational cells. A 3D
computational model of retinal electrical stimulation and the resulting voltage are shown in Figures
2.1A, and B. The biphasic charge-balanced electrical stimulation waveform and parameters utilized
in this study are provided in Figure 2.1C. Further details about the AM modeling platform can be
found in the previous works published by our group (Cela, 2010; Loizos et al., 2018; Stang et al.,
2019).
2.2.2 NEURON Model
The A2 and D1 RGCs morphology was extracted from the NeuroMorpho dataset (Ascoli, 2006;
Ascolietal.,2007), andimportedtoNEURONsoftware(HinesandCarnevale,1997). Morphological
parameters of the extracted cells can be found in (Yin-Peng and Chiao, 2014). Figure 2.2A shows
the morphology of the cell, including the levels of stratification in the inner plexiform layer (IPL) of
the retina. As can be seen, D1-bistratified cells consist of two levels of dendritification, in which one
layer of dendritic tree is ramified inside the inner part, and another is placed in the outer section
of the IPL. Whereas, the dendritic structure of the A2-monostratified cell types is only distributed
in the inner part of the IPL. The axon of the cells was patched to the cell body and includes four
different regions. The axon hillock (AH) is the closest portion that connects to the soma. The
nearest segment of the AH to the soma is extended 20 µm down and 20 µm to the left. The second
band next to the AH is the SOCB that has the highest density of sodium channel. The narrow
segment (NS) of the axon is connected to the distal end of the SOCB. The remaining portion of the
23
A2 type (Monostratified)
x
y z
z
y
x
D1 type (Bistratified)
GCL
IPL
Outer
Inner
(a)
L = 40 µm L = 500 µm L = 90 µm
D = 1 µm D = 0.4 µm
AH SOCB NS DA
D = 1 µm
L = 40 µm
D = 1 µm
(b)
Figure 2.2: A2-type and D1-type RGCs morphology as implemented and coded in our multiscale
Admittance Method/NEURON computational platform. (a): The dendrites of the A2-RGC are
ramified in the inner part of inner plexiform layer (IPL), while the dendrites of the D1-RGC are
placed in both inner and outer part of the IPL. The morphology was extracted as a SWC file
from the NeuroMorpho dataset (Ascoli, 2006; Ascoli et al., 2007; Yin-Peng and Chiao, 2014). (b):
Different axonal segments representation of both cells. AH: axon hillock; SOCB: sodium channel
band; NS: narrow segment; DA: distal axon; L: length of each band; D: diameter of each band.
axon adjacent to the distal end of the NS is called distal axon (DA). The morphological parameters
of axonal sections are adapted from Jeng et al. (Jeng et al., 2011) as shown in Figure 2.2B.
This morphologically realistic cell is finely compartmentalized and its response to electrical stim-
ulation is solved using a multi-compartmental Hodgkin–Huxley model. Each compartment includes
several ionic channels modeled as a voltage-dependent conductance in parallel with the membrane
capacitance. In addition to the five ionic channel models from Fohlmeister and Miller (Fohlmeister
and Miller, 1997a,c) and Fohlmeister et al. (Fohlmeister et al., 2010) for the ganglion cells, two
24
-100
-60
-20
20
60
0 500 1000
Vm (V)
Time (ms)
-100
-50
0
50
0 500 1000
Vm (V)
Time (ms)
Time (ms)
Vm (V)
-200 pA
Vm (V)
Time (ms)
-200 pA
D1 A2
(a) (b)
Figure 2.3: Comparison between experimental (top) and computational (bottom) membrane
voltages in the cell body (soma) in response to intracellular stimulation. The hyperpolarizing
step current stimulation was applied between 100 ms and 500 ms. (a): A2 cell; (b): D1 cell.
Experimental data obtained from Qin et al. (Qin et al., 2017).
more ionic currents have been considered to more accurately represent the intrinsic electrophysio-
logical properties of different RGCs. This includes the difference between ON and OFF cell types
(Kameneva et al., 2011) and the phenomenon of rebound excitation, which plays a fundamental role
in encoding the visual percept (Guo et al., 2013; Maturana et al., 2014). The hyperpolarizationacti-
vated and LVA calcium ionic channels were modelled similar to the previous works in the literature
(Wang et al., 1991; Welie et al., 2006). The seven non-linear ionic currents plus the leakage channel
of ganglion cells are modeled based on Kirchoff’s law:
C
m
dE
dt
= ¯g
Na
m
3
h(E− E
Na
)+¯g
Ca
c
3
(E− E
Ca
)
+¯g
k
n
4
(E− E
k
)+¯g
A
a
3
h
A
(E− E
k
)
+g
k,Ca
(E− E
k
)+¯g
h
l(E− E
h
)
+¯g
T
m
3
T
h
T
(E− E
T
)+¯g
L
(E− E
L
)+I
stim
(2.1)
25
Where E is the membrane potential, C
m
is the membrane capacitance and ¯g is the maximum
conductance of ionic channels including sodium, calcium, delayed rectifier potassium, A type and
Ca-activated potassium, and leak. The membrane capacitance and intracellular resistivity are set to
1 µF/cm2 and 110 ohm.cm, respectively. The leaky current is assumed to be distributed uniformly
throughout the cells. The reversal potential and conductance values of the leak ion channel are
-60 mV and 0.05 mS/cm2. The reversal potentials of these channels are E
Na
= 35 mV, E
k
= 70
mV, E
h
=0 mV, E
T
=120 mV, and E
L
=60 mV. The time-dependent reversal potential equation
of calcium channel, E
Ca
, and the ligand gated, g
k
, Ca, formula are similar to those provided by
Fohlmeister et al. (Fohlmeister and Miller, 1997a). The reversal potential of the calcium channel is
computed as the Nernst potential depending upon the intracellular and extracellular concentrations
of calcium ions.
E
Ca
=10
3
× R× T
2× F
× Ln
[Ca]
e
[Ca]
i
(2.2)
d[Ca]
i
dt
=− i
Ca
2× F× d
− [Ca]
i
− [Ca]
res
τ (2.3)
The intracellular calcium concentration[Ca]
i
changes as a function of time, time course response
depends on the influx of calcium ions, Faradays’ constant is F = 9.64× 10
4
C mol-1, the deter-
mined depth of intracellular calcium concentration d = 3 µm, time constant τ = 10 ms, and the
residual calcium level [Ca]
res
= 0.1 µM. NEURON computational software (NEURON 7.4v) was
used for neuron modeling and analyzing the response of cells to both intracellular and extracellular
stimulations.
The gating variables m, h, c, n, a, h
A
, l, m
T
were described using first-order kinetic equation:
26
dx
dt
=− (α x
+β x
)x + α x
(2.4)
Where α and β are rate constants for voltage-dependent ion channels, and x is the gating
variable. However, the gating variable for the hyperpolarization-activated current (hT) does not
follow the above formula. The rate of transition for IT current is the second-order dynamic as
following:
dh
T
dt
=α h
T
(1− h
T
− d)− β h
T
h
T
(2.5)
dd
dt
=β d
(1− h
T
− d)− α d
d (2.6)
The expression of rate constants for different ionic channels is listed in Table 2.1.
Recently, single-compartment models of ganglion cells were used to find the constraints for the
maximum ionic conductance values, in which the model output can replicate the electrophysiological
properties of different RGC types (Qin et al., 2017). First, the results of this article were repro-
duced; second, the models of RGCs were further developed to a multicompartmental model of both
morphologically and biophysically realistic RGCs by tuning the density of ion channels accordingly
in the soma, dendrites, and axon. The axon conductances only consist of sodium, potassium, and
leakage channels. The biophysical properties of the axon were adapted from the work of (Jeng et al.,
2011). The experimentally recorded signals of the A2 and D1 cells were used for the model tuning
(Qin et al., 2017). The range of variation in the density of ion channels of the dendrites and axon is
based on the constraints demonstrated by Fohlmeister et al. (Fohlmeister et al., 2010). The tuned
27
Table 2.1: Rate constants of ionic currents.
1
TABLE I
RATE CONSTANTS OF IONIC CURRENTS
Na
Channel
Ca
Channel
K
Channel
A
Channel
h
Channel
T
Channel
TABLE II
MAXIMUM IONIC CONDUCTANCE VALUES FOR A2 AND D1 CELLS [S/CM
2
].
RGC types
A2 D1
Soma Dendrite Soma Dendrite
gNa 0.3 0.1 0.2
0.08
gK 0.12 0.05 0.211 0.08
gK,A 3*gK
3*gK
3*gK 3*gK
gK,Ca 0.004*gK 0.004*gK 0.004*gK 0.004*gK
gCa 0.137 0.05 0.013 0.01
gh 0 0 0.0001 3e-5
gT 0.004 0 0.0024 0.001
biophysical properties of the cell for the soma, dendrites, and axonal segments are represented in
Table 2.2 and Table 2.3.
This leads to the most realistic model representing the experimental data for A2 and D1 cells
as shown in Figure 2.3. Intracellular hyperpolarizing step currents of 200 pA with 400 ms duration
were injected into the cell, and the response was recorded from the cell body. As illustrated,
the RGC model can closely reproduce the experimental data. This includes the rebound excitation
phenomenon, whichisdescribedasactionpotentialsinitiationafterterminationofahyperpolarizing
current.
28
Table 2.2: Maximum conductance values for A2 and D1 cells [S/cm2].
1
TABLE I
RATE CONSTANTS OF IONIC CURRENTS
Na
Channel
Ca
Channel
K
Channel
A
Channel
h
Channel
T
Channel
TABLE II
MAXIMUM IONIC CONDUCTANCE VALUES FOR A2 AND D1 CELLS [S/CM
2
].
RGC types
A2 D1
Soma Dendrite Soma Dendrite
gNa 0.3 0.1 0.2
0.08
gK 0.12 0.05 0.211 0.08
gK,A 3*gK
3*gK
3*gK 3*gK
gK,Ca 0.004*gK 0.004*gK 0.004*gK 0.004*gK
gCa 0.137 0.05 0.013 0.01
gh 0 0 0.0001 3e-5
gT 0.004 0 0.0024 0.001
Table 2.3: Maximum conductance values of the axon for A2 and D1 cells [S/cm2].
1
TABLE I
RATE CONSTANTS OF IONIC CURRENTS
Na
Channel
Ca
Channel
K
Channel
A
Channel
h
Channel
T
Channel
TABLE II
MAXIMUM IONIC CONDUCTANCE VALUES FOR A2 AND D1 CELLS [S/CM
2
].
RGC types
A2 D1
Soma Dendrite Soma Dendrite
gNa 0.3 0.1 0.2
0.08
gK 0.12 0.05 0.211 0.08
gK,A 3*gK
3*gK
3*gK 3*gK
gK,Ca 0.004*gK 0.004*gK 0.004*gK 0.004*gK
gCa 0.137 0.05 0.013 0.01
gh 0 0 0.0001 3e-5
gT 0.004 0 0.0024 0.001
TABLE III
MAXIMUM IONIC CONDUCTANCE VALUES OF THE AXON FOR A2 AND D1 CELLS
[S/CM
2
].
AH SOCB NS DA
gNa 0.2 2.4 0.4 0.2
gK 0.1 0.8 0.2 0.1
gK,A 3*gK
3*gK
3*gK
3*gK
2.2.3 Extracellular Stimulation: Admittance Method Linked With NEURON
Resulting extracellular voltages induced in the tissue from the AM model were applied to multi-
compartmentmodelsofneuronsusingNEURONsoftware, andthenneuronalresponsesofindividual
RGCs were recorded. The AM and NEURON are sharing the same coordinates. Thus, a script was
written to superimpose the voltage calculated in the tissue volume onto the NEURON model and
apply it as an extracellular voltage to each compartment using the “extracellular” mechanism built
into NEURON. The output of this modeling framework has been extensively verified with several
experimental data in the retina and hippocampus and other numerical techniques over the past
decade by our group (Bingham et al., 2020; Cela, 2010; Cela et al., 2011; Kosta et al., 2020; Loizos
et al., 2018, 2016b).
29
3
2
1
0 1 2 3
Microelectrode
Axons
X (mm)
Y (mm)
Figure 2.4: A large population of RGCs. A single cell was tiled to populate the entire ganglion
cell and IPL (3 mm× 3 mm). The center to center distance between the nearby cells is set to
50 µm and the stimulating electrode is placed at the center of the model. The axon is oriented
in x-direction, this would allow us to better determine the impact of axonal pathway on distorted
phosphenes. A2 and D1 cells were simulated separately to better investigate the axonal activation
threshold difference between the two cells.
2.2.4 Stimulation Threshold
In this work, we centered our focus on two cases: i) single cell analysis of RGCs, ii) a large
population of RGCs, considering their response to epiretinal electrical stimulation.
1)A Single Sell Study: The stimulation threshold of the two cells was measured as alterations
in the position of the electrode along a straight line with a 20 µm spacing from, and in parallel
to, the axon. This study first helped validate our multiscale computational modeling results with
physiological experiments and previously published modeling with the NEURON simulation (Jeng
et al., 2011). Further, we were able to compare the stimulus threshold sensitivity of the two RGCs
passing axons (distal axon) to electrical stimulation. It is vital to explore whether cells with high
AIS sensitivity to electrical stimulation indeed experience a greater sensitivity of passing axons to
electrical stimulation.
30
2) A large population of RGCs: We constructed a large population of RGCs and measured the
stimulation threshold of each cell. The developed RGCs were tiled to populate the inner layers of
retina (inner plexiform and ganglion cell layers) using the AM as described in the previous section.
The population of RGCs includes 30× 40 individual RGCs populated over a 3 mm × 3 mm area
of the inner retina. The center to center distance between cells is set to 50 µm. This resulted in
1200 cells and each is simulated independently. A synthetic network of RGCs including the position
of the stimulating electrode and the axonal direction is shown in Figure 2.4. For a given input
current, we estimated the spatial pattern of elicited RGCs using the 2D stimulus threshold map.
This would help us determine the AIS and DA activation areas depending on the relative position of
the cells and their DAs with respect to the stimulating electrode. A range of stimulation waveforms
was applied to find stimulus pulse widths that allow for a more focal response of RGCs for a given
current magnitude. We were also interested to find the difference in the axonal activation area of
the two cells.Therefore, we simulated and analyzed the cells separately in a similar fashion.
To find the stimulation threshold, a script was written giving an initial guess and changing the
input current accordingly. If there is no action potential, the input current is incremented by a
factor up to the point that the action potential is observed, and vice versa. To obtain the minimum
current with a higher precision (± 0.1), this process is further repeated by reducing this factor by
half until an action potential (or no action potential) is observed. This estimated stimulus threshold
is then set as an initial guess for the next electrode position (for a single cell study) or the next cell
(for a large population of RGCs study).
31
2.2.5 Electrical Stimulation
1) Single Cell Study: Here, we focused on a charge-balanced biphasic stimulus waveform due
to the tissue safety concern of using monophasic pulses. We applied a cathodic-first symmetric
stimulus pulse with a constant pulse width of 0.5 ms to a point source and a disk electrode with a
diameter of 200 µm and analyzed the response of both A2 and D1 RGCs to electrical stimulation
as the stimulating location changed along and in parallel to the axonal pathway.
2) Large Population of RGCs: Distorted phosphenes observed by users of the epiretinal implant
(Argus II by Second Sight: 0.45 ms pulse duration, no interphase gap) (Beyeler et al., 2019) is
theorized to be due to the axonal activation of RGCs. A computational model of the topographic
structure of optic nerve fibers showed that the orientation of the perceived phosphenes by the Argus
II subjects are well aligned with the tangent line of the axonal pathway of RGCs (Beyeler et al.,
2019). Using our computational platform, we applied a similar biphasic symmetric charge-balanced
waveform with a pulse duration of 0.5 ms. We plotted the 2D stimulus threshold map of the two
RGCs to predict the elongated percepts related to the axonal activation of RGCs to epiretinal
electrical stimulation.
3) Stimulus Waveform to Eliminate the Axonal Activation of RGCs: Most recent experiments
on the responses of a population of RGCs to electrical stimulation have shown the possibility of
avoiding the axonal activation of RGCs (Chang et al., 2019). It is shown that a symmetric biphasic
waveform with a short pulse duration has the ability to selectively target the RGC somas and
achieve a more focal shape of percept. Here, we developed the realistic models of two different
subtypes of RGCs with the use of our multi-scale computational platform. We applied charge-
balanced, biphasic waveforms: symmetric cathodic-first, symmetric anodic-first, with a range of
32
0
10
20
30
40
0 50 100 150 200 250 300 350 400 450 500 550 600 650 700
Threshold (µA)
Electrode position along the axon (µm)
D1: point source A2: point source
D1: disk electrode A2: disk electrode
D1 Cell
A2 Cell
AH SOCB NS DA
20 µm
Figure 2.5: Stimulation threshold of A2 and D1 RGCs as alterations in position of stimulating
electrode. Dash lines: point source, solid lines: disk electrode (200 µm diameter). We used a sym-
metric charge-balanced cathodic-first waveform with a pulse duration of 0.5 ms. Results show that
while the stimulus threshold of the AIS varies between the RGCs, the difference in the activation
threshold of DA is almost negligible.
pulse durations from 0.1 ms to 10 ms (Figure 2.1c). This would help us deepen our understanding
of underlying mechanisms affecting the selective activation of RGCs somas.
2.3 Results
2.3.1 Single Cell Study of RGCs
Stimulation thresholds of the two RGCs as the position of the stimulating source (point source
and disk electrode with diameter of 200 µm) changes along the axon is shown in Figure 2.5. In
agreement with physiological experiments and NEURON modeling of an individual RGC (Fried
et al., 2009; Jeng et al., 2011), the minimum stimulus threshold of both cells was observed when the
electrode is placed above the SOCB for the point source simulations. However, the disk electrode
has a higher stimulus threshold and the site of the lowest threshold is shifted to the right and further
33
0
20
40
60
80
90
Threshold (µA)
0 1 2 3
1
2
3
X (mm)
Y (mm)
PW = 0.5 ms
0
20
40
60
80
90
Threshold (µA)
0
1 2 3
1
2
3
X (mm)
Y (mm)
PW = 0.1 ms
0
20
40
60
80
90
Threshold (µA)
0 1 2 3
X (mm)
Y (mm)
0
20
40
60
80
90
Threshold (µA)
0 1 2 3
1
2
3
X (mm)
Y (mm)
PW = 0.5 ms
PW = 0.1 ms
A2 RGCs D1 RGCs
1
2
3
(a)
(b)
(c)
(d)
Figure 2.6: 2D stimulus threshold map for A2 and D1 RGCs. Each dot represents the center of
the corresponding cell body. The stimulating electrode is positioned at the center of the model.
Left: A2 RGCs; right: D1 RGCs. Symmetric biphasic cathodic-first waveforms with pulse widths
of (a) and (b) 0.5 ms; (c) and (d) 0.1 ms, are applied to the electrode.
from the soma at the narrow segment as shown in Figure 2.5. This is mainly due to the higher
electric field gradient (the activation function) (Rattay, 1999) at the disk electrode periphery. We
assumed identical axonal properties for both RGCs to identify the impacts of morphological and
biophysical differences between the cells on the stimulus threshold of passing axons separately from
the potential difference in the length and ionic channel density of the RGCs axon initial segment.
This assumption arises from the fact that the previous study has shown that the SOCB band
length, location, and the sodium channel density do not influence the DA threshold (Jeng et al.,
2011). Figure 2.5 further indicates that the stimulus threshold of DA was not significantly altered
by the physiological differences between the two RGCs, suggesting that passing axons threshold can
be exclusively determined by properties of the DA.
34
2.3.2 Larger Population of RGCs
The spatial activation patterns of the two RGCs due to a symmetric biphasic cathodic-first
electrical stimulation with pulse widths of 0.1 ms and 0.5 ms are shown in Figure 2.6. Each dot
in the figure represents the location of a RGC cell body and the color bar indicates the stimulus
threshold of the corresponding cells. As shown in Figure 2.6A and B, the relative longer pulse width
of 0.5 ms resulted in the distal axons activation of RGCs (axonal activation). While the spatial
activation threshold and area of those A2 and D1 RGCs whose cell bodies are either overlaid by
the stimulating disk electrode or are close to the electrode have shown dissimilarity, the axonal
excitation area and threshold difference between the two cells are negligible. The elongated area of
activation computed using this multiscale modeling platform supports the fact that the orientation
of the distorted phosphenes is aligned with the RGCs axonal pathway (Beyeler et al., 2019). Figure
2.6C and 2.6D represent the spatial threshold patterns of RGCs for a shorter pulse width of 0.1
ms. As shown, a more focal response of RGCs can be achieved using a shorter pulse duration.
The stimulation threshold of the D1 cell was previously shown to be lower (see Figure 2.5) and
therefore the activation region of this cell is larger compared to the A2 cell. To better understand
the mechanisms leading to a more focal response of RGCs using short pulse durations, the lowest
stimulation threshold originated in the SOCB was compared with the excitation threshold of the DA
for pulse durations ranging from 0.1 ms to 10 ms for both A2 and D1 RGCs, as depicted in Figure
2.7. Results demonstrate that as we shorten the pulse duration, the greatest difference between the
SOCB and axonal thresholds can be achieved. This indicates the possibility of selective activation
of the AIS with the highest safety margin of avoiding RGCs axonal activation using short pulse
durations.
Computational modeling reveals less sensitivity of the SOCB to modulations in stimulus pulse
35
0
50
100
150
200
250
0.1 1 10
Current amplitude (µA)
Pulse width (ms) at log scale
D1 - DA
D1 - SOCB
A2 - DA
A2 - SOCB
DA D: 1.2 µm
DA D: 0.8 µm
0.2 0.5 1.5 4
Figure 2.7: Activation threshold difference between the SOCB and DA of A2 and D1 cells as a
function of change in pulse duration. Symmetric cathodic-first biphasic pulses are applied. Dash
lines: the SOCB stimulus threshold, solid lines: the DA stimulus threshold (axonal activation).
The gray and black lines show the passing axons diameters of 1.2 µm and 0.8 µm, respectively.
Shorter pulse width of 0.1 ms resulted in the highest excitation threshold difference between the
SOCB and DA over a range of variations in passing axon diameters.
durations relative to the DA. While there is a difference in the stimulation threshold of the two cells
over a range of pulse widths at the SOCB, this difference cannot be seen at the DA (Figure 2.7).
This demonstrates a strong contribution of DA difference among RGCs to activation threshold of
passing axons. Therefore, we modulated the DA diameter of the two cells over their maximum range
of changes (0.8 µm and 1.2 µm) (Huxlin and Goodchild, 1997; Walsh et al., 2000) and monitored
its impact on the DA threshold. The gray and black curves in Figure 2.7 represent the stimulation
threshold of the DA with 1.2µm and 0.8µm diameters, respectively. As shown, there is still a wide
window for the preferential excitation of the SOCB over the DA using a short pulse duration.
The resulting stimulus threshold from the symmetric biphasic cathodic-first waveform is com-
pared with an anodic-first waveform in Figure 2.8. As expected, similar to the symmetric cathodic-
first pulses, the greater difference between the SOCB and DA threshold of RGCs has been observed
with a shorter pulse duration. However, stimulation threshold of anodic-first stimulation waveforms
36
0
50
100
150
200
250
300
PW = 0.1 ms PW = 0.5 ms
Current amplitude (µA)
A2_AF_DA D1_AF_DA
A2_AF_SOCB D1_AF_SOCB
A2_CF_DA D1_CF_DA
A2_CF_SOCB D1_CF_SOCB
Cathodic-first vs. Anodic-first
Cathodic-first Anodic-first Cathodic-first Anodic-first
Figure 2.8: Anodic-first (AF). vs cathodic-first (CF) symmetric biphasic pulses: the SOCB and
DA stimulus threshold difference for A2 and D1 cells. Results indicate that the sensitivity of
the SOCB threshold is low not only to pulse duration changes, but also to modulations in polarity.
Whereas, the DA threshold significantly changes with alterations in both pulse widths and stimulus
polarity. Therefore, the excitation threshold difference between the SOCB and DA is greater using a
short anodic-first biphasic waveform, offering a higher chance for more focalized response of RGCs.
is higher compared to cathodic-first waveforms (Hadjinicolaou et al., 2015; Rattay, 1999; Rattay
et al., 2012). As a result, we observed the greater differential stimulus threshold between the SOCB
and DA using an anodic-first pulse compared to a cathodic-first pulse, indicating a higher chance
for selective activation of the AIS. This is due to the lower sensitivity of the SOCB to changes in
polarity of stimulus waveforms relative to the DA as represented in Figure 2.8. Our computational
findings are in good agreement with recent experiments on the spatial response of RGCs to electrical
stimulation showing that focal activation can be obtained using a symmetric biphasic stimulation
with a shorter pulse width (Schiefer and Grill, 2006). This modeling framework further enabled us
to identify factors leading to a more focalized response of RGCs by investigating realistic models of
two different classified RGCs: D1-bistratified and A2-monostratified.
37
2.4 Discussion
We applied a multiscale AM/NEURON computational platform to better understand the spa-
tial activation pattern of a large population of RGCs to different electrical stimulation parameters.
We have considered studies of a single cell and a large population of cells, analyzing the stimula-
tion threshold and the activated area of a synthetic network of RGCs through different symmetric
biphasic waveforms with various pulse durations.
2.4.1 Selective Stimulation of RGCs SOCB
Our computational modeling framework correctly predicts phosphene shape and elongated ax-
onal activation of RGCs reported in both clinical research studies and electrophysiological experi-
ments (Chang et al., 2019; Weitz et al., 2015). Results show that RGCs somas with the periphery
of stimulating electrode (the greatest electric field gradient) placed above the SOCB can be selec-
tively targeted using short pulse durations. This results in more focal shape of activated region and
therefore the spatial resolution improvement of epiretinal implants.
Prior physiological experiments and multi-compartment modeling of a single RGC found that
the SOCB has the lowest stimulation threshold with the highest density of voltage-gated sodium
channels (Fried et al., 2009; Jeng et al., 2011). Here, we modeled two different subtypes of RGCs,
A2 and D1 cells, with the aim of exploring the impact of morphological and biophysical differences
between the two cells on activation threshold of passing axons as well as validating the modeling
framework. It was thought that different sensitivity of AIS among RGCs to electrical stimulation
could lead to activation threshold difference of RGCs passing axons and therefore a major challenge
for avoiding RGCs axonal activation (Freeman et al., 2011b). However, our both single cell and a
large population of RGCs studies demonstrated that while the stimulus threshold of the two cells
38
are different at the SOCB, this differential threshold is negligible at the DA assuming identical
axonal properties for the cells (Figures. 2.5 and 2.6).
2.4.2 Impact of AIS Properties
The AIS properties can vary among different types of RGCs and as a result can modulate the
AIS stimulation threshold of cells (Fried et al., 2009; Jeng et al., 2011; Raghuram et al., 2019;
Werginz et al., 2020). We assumed identical AIS properties for the cells because the stimulation
threshold difference between the cells at the AIS was not the focus of this study. Moreover, a prior
work showed that the density, length, and location of the SOCB did not alter the threshold of DA
(Jeng et al., 2011). The computational findings of this study explored that passing axons threshold
is most likely determined by the properties of distal axon. Over a range of DA diameter alterations
between the two cells, the differential threshold of the SOCB and DA remains high enough for select
excitation of the SOCB with short stimulus pulses (Figure 2.7). We observed that the SOCB is less
sensitive to both pulse duration and polarity changes relative to the distal axon (Figures. 2.7 and
2.8), offering a chance to avoid activating RGCs axon bundles with pulse duration modulations.
The previous calcium imaging approach may not be sensitive enough to detect the threshold of AIS
regions such as the SOCB (Chang et al., 2019).
2.4.3 Clinical Implications
In this work, we used the same system and electrode size implemented in current epiretinal
implants to predict the elongated phosphene reported by Argus II patients (Beyeler et al., 2019).
While very short pulse durations can avoid axonal activation, the required threshold for neural
activation and power consumption are high. Figure 2.9 compares charge threshold of the SOCB
39
0
20
40
60
80
100
120
0.1 1 10
Charge threshold (nC)
Pulse width (ms) at log scale
D1 - DA
D1 - SOCB
A2 - DA
A2 - SOCB
0.2 0.5 1.5 4
Figure 2.9: Charge threshold as alterations in pulse durations for both A2 and D1 RGCs using
cathodic-first biphasic pulses. The solid and dash lines represent the charge threshold of the DA
and the SOCB, respectively. Data show that although current threshold increases as we shorten
pulse widths, charge threshold remains low using short pulse durations.
and DA as a function of pulse duration for the A2 and D1 cells. As shown, charge threshold
remains almost constant using pulse widths less than 0.5 ms. However, charge threshold increases
using longer pulse durations. This indicates the possibility of safe delivery of electrical stimulation
using very short pulse durations, although high power consumption leads to generation of more
heat.
There are other approaches aiming at improving the spatial resolution of retinal implants by
localizing the electric field near the stimulation electrodes and manipulating the spread of current.
Studies have investigated the use of small electrodes (Behrend et al., 2011; Sekirnjak et al., 2006) as
well as local return electrodes of different configurations to control the spread of RGCs activations
(Fan et al., 2019; Tong et al., 2019). However, these studies may not necessarily guarantee to avoid
axon bundle activation. For example, the use of 10 µm stimulating electrode diameter has been
shown to result in RGCs axonal activations (Behrend et al., 2011). Therefore, future work will
40
incorporate stimulation strategies to avoid activation of axon bundles and at the same time limit
the current distribution near each stimulating electrode to achieve focalized response from RGCs in
high-density electrode arrays.
2.4.4 Limitations of Neural Network Modeling
While our AM-NEURON computational platform correctly predicts the activation of axon bun-
dles, the spread of RGCs activation near the stimulating electrode may not be precisely modeled.
For instance, it has been reported the presence of electrical couplings between neighboring RGCs
(Bloomfield and Völgyi, 2009; Völgyi et al., 2009) and in fact research has shown that the appli-
cation of gap junction blocker can limit the RGCs activated region (Haq et al., 2018). Further,
the network-mediated response can also influence the spatial activation of RGCs in response to
epiretinal stimulation (Hosseinzadeh et al., 2017). There are synaptic connections between ganglion
cells and intermediate neurons such as horizonal, amacrine, and bipolar cells, which may have con-
tributions on the extracellular response of cells. This was limited in this study to only consider
the neural activity of individual ganglion cells in direct response to electrical stimulation. This as-
sumption is due to the fact in the late-stage of degeneration, synapses likely lose their functionally
and connectivity (Humayun et al., 1994; Margalit et al., 2011). Moreover, it is well demonstrated
in the literature that while indirect stimulation of RGCs can be achieved using long pulse widths
(Boinagrov et al., 2014; Eickenscheidt et al., 2012; Freeman et al., 2010; Jalligampala et al., 2017;
Lee and Im, 2019; Weitz et al., 2015), direct activation of ganglion cells can be obtained using short
phase durations (Chang et al., 2019; Jensen et al., 2005; Schiefer and Grill, 2006). Since the main
stimulation waveform carried out in this study is a symmetric biphasic waveform with a short pulse
width, it is admissible to only assess directly activated RGCs. In the future, we will incorporate
41
other subtypes of RGCs as well as outer retinal neurons and their chemical and electrical synaptic
and gap junctional connectivity.
2.5 Conclusion
A multi-scale computational study using a combined AM/NEURON model was applied to better
understand RGCs response to electrical stimulation. We developed morphologically and biophysi-
cally realistic models of two classified RGCs, D1 and A2 cells. Our model shows that the difference
in stimulus threshold of AIS across RGCs does not necessarily lead to the difference in the stimula-
tion threshold of RGCs passing axons. We found the SOCB threshold to be less sensitive to pulse
duration modulations relative to the DA threshold. Further, the DA threshold increases more with
reversing the polarity of stimulation (anodic-first) compare to the SOCB threshold. Therefore, very
short pulse widths significantly augment stimulus threshold difference between the SOCB and DA,
offering less chance for activation of axon bundles. Correlation of our computational findings with
recent experiments allowed us to better capture RGCs axonal activation and closely replicate the
elongated phosphene drawn by patients. We further utilized this tool to design electrical stimulation
parameters and gain additional insights leading to more focal activation of RGCs. This computa-
tional platform can lead into a generalized modeling framework capable of evaluating responses of a
large population of RGCs to different electrical stimulation waveforms and designing new electrode
geometry to improve the spatial resolution of epiretinal prostheses in high density electrode arrays.
42
Chapter 3
Color Selectivity: “Frequency-amplitude”
Modulation Stimulation Strategy for
Selective Activation of RGCs
© 2020 EMBC. Paknahad J, Loizos K, Humayun M, Lazzi G. Paknahad J, Loizos K, Humayun
M, Lazzi G. Responsiveness of Retinal Ganglion Cells Through Frequency Modulation of Electrical
Stimulation: AComputationalModelingStudy. Annual International Conference of the IEEE Engi-
neering in Medicine and Biology Society.IEEE Engineering in Medicine and Biology Society.Annual
International Conference (2020).
© 2021 Scientific reports. Paknahad J, Loizos K, Yue L, Humayun MS, Lazzi G. Color and
cellular selectivity of retinal ganglion cell subtypes through frequency modulation of electrical stim-
ulation. Scientific reports (2021).
Abstract
Epiretinal prostheses aim at electrically stimulating the inner most surviving retinal cells - retinal
ganglion cells (RGCs) - to restore partial sight to the blind. Recent tests in patients with epiretinal
implants have revealed that electrical stimulation of the retina results in the percept of color of
43
the elicited phosphenes, which depends on the frequency of stimulation. This paper presents com-
putational results that are predictive of this finding and further support our understanding of the
mechanisms of color encoding in electrical stimulation of retina, which could prove pivotal for the
design of advanced retinal prosthetics that elicit both percept and color. This provides, for the first
time, a directly applicable “amplitude-frequency” stimulation strategy to “encode color” in future
retinal prosthetics through a predictive computational tool to selectively target small bistratified
cells, which have been shown to contribute to “blue-yellow” color opponency in the retinal circuitry.
The presented results are validated with experimental data reported in the literature and correlated
with findings in blind patients with a retinal prosthetic implant collected by our group.
3.1 Introduction
RETINAL and cortical visual prostheses have been developed to restore partial sight to the
patients who have been blinded for decades by neurodegenerative diseases, such as retinitis pigmen-
tosa (RP), age-related macular degeneration (AMD), and Primary Open-Angle Glaucoma (POAG).
Restoration in vision lost has been generally attempted by either stimulating the surviving neurons
in the degenerated retina to elicit visual percepts or bypassing the visual pathway and directly
stimulating the visual cortex. These approaches have proven effective and led to the development
of several visual prosthetic systems (Cruz et al., 2016; Humayun et al., 1999; Kosta et al., 2018;
Stingl et al., 2015; Weiland and Humayun, 2014; Weiland et al., 2016).
The target of electrical stimulation in epiretinal prostheses is the innermost layer of the retina -
the population of retinal ganglion cells (RGCs) - which remain mostly intact in the early stages of
degeneration. Researchhasbeenconductedtowardsimprovingtheefficacyandsafetyofsuchdevices
using computational and experimental methods. While these devices have shown to be effective at
44
restoring some limited form of sight, several challenges still need to be addressed. A critical issue
with current epiretinal prosthetic systems, for example, is the limited ability to focally activate a
population of RGCs. Reports from clinical studies have revealed that axonal activation of RGCs can
result in elongated phosphenes (Beyeler et al., 2019). Direct and indirect electrical stimulation of
RGCs have been attempted using long and short pulse durations to achieve more focalized response
from a population of RGCs (Freeman et al., 2010; Mueller and Grill, 2013; Schiefer and Grill, 2006;
Weitz et al., 2015). However, percept fading and desensitization with indirect stimulation, and high
required current amplitude with direct stimulation of RGCs remained a challenge (Freeman and
Fried, 2011).
Further understanding of how different subtypes of RGCs respond to electrical stimulation,
and the mechanisms underlying the preferential activation of each cell type, could significantly
improve the efficacy of retinal prostheses. A number of studies have focused on RGCs excitability
to high frequency electrical stimulation (up to 300 Hz) (Fried et al., 2006; Hadjinicolaou et al.,
2015; Jensen and Rizzo, 2007; Sekirnjak et al., 2006; Soto-Breceda et al., 2018). Further, there
have been attempts towards preferentially targeting ON and OFF RGCs at very high stimulation
frequency (⩾ 1 kHz) (Guo et al., 2019; Im et al., 2018; Twyford et al., 2014). Despite these successes,
to the best of our knowledge there has been no specific work on analyzing the responsiveness of
classified RGCs subtypes to high frequency of stimulation. Prior studies have been mostly limited
to the response to light stimuli of ON and OFF RGCs, or one morphological RGC type to electrical
stimulation. However, therearesubtypesofRGCswithineachgroup(ON,OFF,andON-OFF)that
are characterized by physiological and morphological differences (Huxlin and Goodchild, 1997; J.
et al., 2002; Sun et al., 2002; Walsh et al., 2000). These classified RGCs carry specific types of visual
information, such as color and contrast, features which may therefore be possible to leverage in a
prosthetic through selective stimulation. For example, previous studies have shown the contribution
45
of small bistratified ganglion cells to “blue-yellow” color opponency in the retinal circuitry (Dacey,
1996; Dacey et al., 2014; Dacey and Lee, 1994; Dacey and Packer, 2003; Lee et al., 2010).
Recent clinical studies of patients with retinal prostheses have shown that electrical stimulation
can result in some variation of color perception (Humayun et al., 2003; Lin et al., 2018b; Yue et al.,
2021). Specifically, these experiments revealed that color percept is dependent upon stimulation
parameters such as frequency of stimulation. These findings suggest the possibility of encoding
color in retinal prostheses. Significant loss of spatial visual information in degenerate retina with
respect to normal vision is inevitable; indisputably, the addition of color vision would represent a
tremendous improvement to the efficacy of current devices.
In this work, we developed biophysically and morphologically detailed models of D1-bistratified
andA2-monostratifiedRGCsandvalidatedtheirresponsewithexperimentallyrecordedsignals(Qin
et al., 2017). We utilized our combined Admittance method (AM)/NEURON multiscale computa-
tional method to determine whether different RGCs exhibit different responses as a function of the
stimulation frequency (up to 200 Hz). We found that D1-bistratified cells are better able to follow
high stimulus frequency compared to A2-monostratified cells. Our computational platform helps
gain further insights into the underlying mechanisms affecting the differential excitability of RGCs
at high frequency. This differential response of RGCs with the proper current amplitude modula-
tion can help identify the mechanisms linked to preferential activation of RGCs, and different color
percepts observed in clinical studies.
46
x
y z
z
y
x
GCL
IPL
Outer
Inner
AH: L = 40 µm, D = 1 µm
SOCB: L = 40 µm, D = 1 µm
NS: L = 90 µm, D = 0.8 µm
DA: L = 250 µm, D = 1 µm
A2-RGC (Monostratified) D1-RGC (Bistratified)
Soma D: 20 µm
Dendritic field D: 320 µm
Soma D: 12 µm
Dendritic field D: 144 µm
Figure 3.1: A2 and D1 realistic morphologies as implemented and coded in our multiscale Admit-
tance Method/NEURON computational platform (Cela, 2010; Loizos et al., 2016a, 2018, 2016b).
Left: A2-monostratified RGC ramified in the inner part of inner plexiform layer and has a larger
soma and dendritic field diameters. Right: D1-bistratified, their dendrites are placed in both inner
and outer part of the inner plexiform layer and this cell has relatively smaller soma and dendritic
field diameters. GCL: ganglion cell layer; IPL: inner plexiform layer; AH: axon hillock; SOCB:
sodium channel band; NS: narrow segment; DA: distal axon; L: length of each band; D: diameter.
The morphology of RGCs was extracted from the NeuroMorpho dataset (Ascoli, 2006; Ascoli et al.,
2007; Chen and Chiao, 2014).
3.2 Results
3.2.1 Extracellular Stimulation: Frequency Response of RGCs
The morphology of the two developed RGCs, D1-bistratified versus A2-monostratified, and the
levels of stratification in the inner plexiform layer of the retina are depicted in Figure 3.1. The
stimulating electrode of diameter 200 m is placed on the top-center of the bulk retina tissue and is
positioned 50µm from the cell bodies of computational models of the RGCs. We applied symmetric
charge-balanced electrical stimulation waveforms to characterize RGCs responsiveness as a function
ofstimulus frequency. Wecompared the responses of D1-bistratified versusA2-monostratifiedRGCs
to alterations in stimulation frequency. Figure 3.2A shows the firing rates of both A2 and D1 cells
47
0
40
80
120
160
200
240
20 40 60 80 100 120 140
Firing rate (Hz)
Current amplitude (µA)
D1-bistratified
A2-monostratified
maximum firing
rate difference
22 µA
A
B Stimulation frequency: 200 Hz
0
40
80
120
160
200
240
0 50 100 150 200
Firing rate (Hz)
Stimulus frequency (Hz)
D1-Bistratified
A2-Monostratified
Current amplitude: 100 µA
Figure 3.2: Responsiveness of RGCs at high stimulation frequency. A, Computational results
showing the difference in response between A2 and D1 retinal ganglion cells at high frequency.
B, Firing rate as a function of pulse amplitude for both A2 and D1 cells at 200 Hz stimulus
frequency. Data show the effects of stimulus amplitude on the responsiveness of both cell types.
Slower rate of changes in firing rates of A2-RGC with increasing amplitude is shown which indicates
less excitability of this RGC subtype at high frequency. The greatest difference in rate of firing
between A2 and D1 cells is observed at the point where D1 cell begins firing at its maximum rate
of 200 Hz. The difference in the computationally determined frequency response can potentially
help identifying the mechanism to selectively target RGCs.
as a function of stimulation frequency at 100 µA current amplitude. As shown in the Figure, the
firing rate of the D1 cell is greater compared to the A2 cell at high frequency, and the spiking
rate observed in the A2-monostratified cell cannot follow the stimulus pulses with a similar rate.
However, each stimulus pulse results in spiking of the D1-RGC. The importance of this finding lies
in the potential to exploit the differential RGCs response in retinal prosthetic systems by varying
stimulation frequency to controllably induce different percepts such as color.
3.2.2 Current Modulation at High Frequency
Figure 3.2B represents the rate of spikes as a function of current amplitude ranging from 20-
140 µA at 200 Hz. As shown, firing rate increases with increasing stimulus strength up to 100 %
response probability (200 Hz firing rate) for each cell. However, slower rate of increase in firing rate
is observed for A2 cells compared to D1 cells. The differential excitation rates of the RGCs increases
with increasing the pulse amplitude. D1-RGC reaches its maximum firing rate at 86 µA, as noted
48
-75
-50
-25
0
25
50
0 100 200 300 400 500
Membrane voltage (mV)
Time (ms)
-150
-100
-50
0
50
100
150
100 110 120 130 140 150
Membrane voltage (mV)
Time (ms)
Stimulus current (µA)
A2-monostratified
-100
-70
-40
-10
20
50
80
0 100 200 300 400 500
Membrane voltage (mV)
Time (ms)
A B D1-bistratified
-150
-100
-50
0
50
100
150
100 110 120 130 140 150
Membrane voltage (mV)
Time (ms)
Stimulus current (µA)
Figure 3.3: Time course of RGCs response. Membrane potential as a function of time at stimula-
tion frequency of 200 Hz and 100 µA current amplitude: A, D1-bistratified. B, A2-monostratified.
D1 cells can better sustain repetitive spikes at high frequency of stimulation compared to A2 cells.
in Figure 3.2B. This further indicates that the D1 cell is more responsive at high stimulus frequency
over a range of current amplitudes. Figure 3.2B also shows that with a proper choice of current
amplitude, D1 cells can be selectively activated at 200 Hz. The typical stimulus frequency used in
epiretinal prosthetic systems is 20 Hz, and RGCs are capable of firing at the same rate. One of the
hypotheses is that we can control the cells’ firing rate to remain at 20 Hz by tuning the current
amplitude at 200 Hz stimulus frequency, and therefore increase the likelihood for selective activation
of D1 cells. For example, the intersections of the horizontal dashed line and the response curves
in Figure 3.2B represents the current amplitude difference between the cells ( ≈ 22 µA) required to
achieve 20 Hz firing rate. While the current amplitude to reach 20 Hz spiking rate for the A2-cell is
58 µA, this current is almost 22 µA smaller for the D1-cell, offering a current window for selective
activation of this cell.
Many studies have investigated RGC responses to a single stimulus pulse (Jeng et al., 2011;
Mueller and Grill, 2013; Werginz et al., 2020). However, the stimulation threshold differences
49
among RGCs are small at low frequencies, which makes the potential for preferential activation of
RGCs challenging (Raghuram et al., 2019). For instance, the difference in the stimulus thresholds
of the A2 and D1 RGCs in response to a single stimulation pulse is only 1.6 µA (The A2 cell
threshold: 27.3 µA; the D1 cell threshold: 25.7 µA), reducing the current window for targeting
the D1 cell. Therefore, this control of excitability of cells over a range of stimulation frequencies
is effective for selective activation of RGCs and is attainable with proper selection of stimulus
frequency and current amplitude. Under the assumption that small bistratified retinal ganglion
cells play a significant role in the percept of the blue color, our findings correlate well with early
experimental results in patients with epiretinal implants (Yue et al., 2021), perceiving blue as the
dominant color in their visual percept at high frequency of stimulation as discussed in the section
discussing our results in a patient.
3.2.3 Time Course Response at High Frequency
To better understand the physiological differences between these two RGCs, the time course
of the response was compared at 200 Hz using a symmetrical biphasic pulse train with a stimu-
lation duration of 250 ms, as indicated in Figure 3.3. The results demonstrate that the spiking
rate observed in the A2-monostratified cell cannot follow the stimuli pulses at a similar rate. In
contrast, each stimulus pulse results in depolarization events in the D1-bistratified cell. There are
electrophysiological properties that are different between these two RGC subtypes. It can be clearly
seen that the spike width of the D1-RGC is shorter than that of the A2-RGC. In addition, there is
a spike latency in the A2 cell response to some of the stimulus pulses, offering an additional reason
for lower responsiveness of this cell at high stimulus frequency. This agrees with experiments on
RGCs, showing that retinal ganglion cells with longer spike latency cannot sustain repetitive firing
50
0
50
100
150
200
20 35 50 65 80 95 110
Firing rate (Hz)
Current amplitude (µA)
D1: Soma D=17 µm_AH L=40 µm_SOCB L=40 µm
D1: Soma D=12 µm_ AH L=40 µm_SOCB L=40 µm
D1: Soma D=12 µm_AH L=40 µm_SOCB L=20 µm
D1: Soma D=12 µm_AH L=20 µm_SOCB L=20 µm
Figure 3.4: The impacts of the AH and SOCB length on D1-RGCs sensitivity to high frequency
electrical stimulation relative to the soma diameter. Firing rate is plotted as a function of modula-
tions in current amplitude at 200 Hz. Analysis of firing rate with single variation of morphological
parameters: soma diameter, SOCB length, and AH and SOCB lengths. Results show that while
reduction in the length of the SOCB and AH decreases the responsiveness of D1 cells to high stimu-
lus frequency, the influence of increase in the soma diameter (from 12 µm to 17 µm) on the reduced
sensitivity of the cell to high stimulus frequency is more pronounced.
at high frequency (Sekirnjak et al., 2006). There are also morphological factors that can influence
their response to high rate of stimulus pulses.
3.2.4 Sensitivity and Statistical Analysis of RGCs Morphology
We further investigated the effects of morphological changes on response of RGCs to high stim-
ulation frequency. We performed a parametric analysis for a larger population of RGCs taking into
account morphological variations within a single RGC type. We separately altered the diameters of
the soma and axon within one standard deviation of the mean for both cells based upon the quan-
titative data available from the literature (Huxlin and Goodchild, 1997; Sun et al., 2002). Then,
the weighted average firing rates (WAFR) of each cell at two stimulation frequencies of 120 Hz and
51
Table 3.1: Maximum conductance values of the axon for A2 and D1 cells [S/cm2].
RGC types
Measure A2-monostratified
D1-bistratified
Morphologic
al data
Axon diameter (μm)
mean ± SD
Soma diameter (μm)
mean ± SD
Axon diameter (μm)
mean ± SD
Soma diameter (μm)
mean ± SD
1 ± 0.2 23 ± 4 0.9 ± 0.1
14 ± 3
SF (Hz)
120 200 120 200 120 200 120 200
WAFR (Hz)
116 121 114.9 113.7 120 185.2 119.5 152.5
* SF: Stimulus Frequency
* WAFR: Weighted Average Firing Rate
200 Hz were computed (Table 3.1). We focused our analysis on RGCs response at high frequency
because of our interests in excitability of cells at a high rate of stimulation.
While spiking activity in both cells follows the monotonous stimulus pulse at 120 Hz, the overall
WAFR of D1-bistratified cells is greater than A2-monostratified cells at 200 Hz considering changes
in both soma and axon diameters. Both soma and axon diameters influence RGCs firing rates,
however the impact of soma diameter is more pronounced at high frequency. We also considered the
effects of the sodium channel band (SOCB) and axon hillock (AH) length modulations on sensitivity
of RGCs to high frequency electrical stimulation. Recent studies have shown that cells with smaller
soma size may have in average smaller SOCB and AH length (Raghuram et al., 2019; Werginz
et al., 2020). Therefore, we decreased the length of the SOCB and AH in D1 cells with 12 µm soma
diameter (from 40µm to 20µm) and compared the sensitivity of D1 cells to high stimulus frequency
with D1 cells having soma the size of 17 µm as shown in Figure 3.4. Although the reduced length
of the SOCB has lowered the stimulus threshold, we observed that the contribution of soma size
alterations to the sensitivity of RGCs to high stimulus frequency remains superior.
Given the positive correlations of the soma diameter, axon diameter, and axon initial segment
(AIS) lengths, we investigated the firing rates of these RGCs as a function of amplitude modulations
52
0
50
100
150
200
10 30 50 70 90 110 130
Firing rate (Hz)
Current amplitude (µA)
D1: SD = 11 µm_AD = 0.8 µm_SOCBL = 20 µm
D1: SD = 14 µm_AD = 0.9 µm_SOCBL = 25 µm
D1: SD = 17 µm_AD = 1 µm_SOCBL = 30 µm
D1-bistratified_WAFR
A2: SD = 19 µm_AD = 0.8 µm_SOCBL = 20 µm
A2: SD = 23 µm_AD = 1 µm_SOCBL = 30 µm
A2: SD = 27 µm_AD = 1.2 µm_SOCBL = 40 µm
A2-monostratified_WAFR
Figure 3.5: Response (firing rate) of A2 and D1 RGCs to electrical stimulation at 200 Hz with
modulations in morphometric parameters. The soma diameter (SD), axon diameter (AD), and
SOCB length (SOCBL) alterations of the two cells within one standard deviation of the mean
have been investigated. The weighted average firing rate (WAFR) of the cells indicates the higher
excitability of D1 cells at high frequency with relatively smaller SD, AD, and SOCBL. A2 RGCs:
SD = 23 ± 4;AD = 1± 0.2;SOCBL = 30 ± 10. D1RGCs : SD = 14± 3;AD = 0.9± 0.1;SOCBL=25± 5.
at 200 Hz. We incorporated modulations in soma diameter, axon diameter, and SOCB length
within one standard deviation of the mean for both cells (Figure 3.5). The WAFR of D1 cells
remained greater relative to A2 cells, suggesting the strong contribution of the soma diameter to
the responsiveness of RGCs at high frequency. We found a slower rate of change in the number of
spikes in A2 cells compared to D1 cells, indicating the difference in the kinetics and densities of
ionic channels across RGCs may also influence the rate of spikes at high stimulation frequency. The
A2 cell response further shows lower sensitivity to modulations in morphological parameters than
that of the D1 cell at high firing rates (Figure 3.5). In the next section, we validate our findings
with experiments on epiretinal electrical stimulation of A2-type RGCs (Hadjinicolaou et al., 2015),
showing that small cells can better maintain their response at high stimulus frequency compared to
large cells.
53
A B
0
0.5
1
1.5
2
2.5
1 2 5 10 20 50 100 200
Normalized Suprathreshold
Frequency (Hz)
Small cell Large cell
0
30
60
90
120
2 3 4 5 6
Efficacy (%)
Frequency (Hz)
Soma_17 µm_DF_320 µm
Soma_17 µm_DF_500 µm
Soma_26 µm_DF_500 µm
Soma_26 µm_DF_320 µm
200 100 50 20 10
Figure 3.6: The model verification with in-vitro experimental results. A, Suprathreshold current
required to reach at least 90 % efficacy as alterations in stimulus frequency for both small and large
A2-cells using asymmetric cathodic-first stimulus waveform (normalized to 1 Hz). The solid and
shaded bars demonstrate the normalized stimulus threshold of large and small cells, respectively.
The Figure clearly shows the greatest stimulus threshold difference between small and large cells at
high frequency. B, Impacts of soma and dendritic field sizes on efficacy for a given pulse amplitude
(435µAcathodicphaseamplitude). Smallcellsareabletomaintaintheirresponseathigherefficacy
compared to large cells.
3.2.5 Verification of Computational Results with In-vitro Experiments
To consolidate our observations on the impacts of morphological structure, we reproduced the
experimental results on the responsiveness of A2-RGC subtype to high epiretinal electrical stimu-
lation frequency using our morphologically and biophysically realistic A2 cell model (Hadjinicolaou
et al., 2015). We modified the A2-cell morphology to divide the cell size into small and large based
on both soma and dendritic field sizes. The small cell has soma and dendritic field diameters of 17
µm and 320µm, respectively and the large cell has soma and dendritic field diameters of 26 µm and
500 µm, respectively.
We applied the same stimulus waveform used for the frequency response of RGCs in Hadjinico-
laou et al. (Hadjinicolaou et al., 2015), the asymmetric biphasic pulse with a short cathodic phase of
60µs and 120µm interphase gap followed with a longer anodic phase of 480µm duration. Similarly,
the efficacy is defined as the minimum current amplitude to achieve more than 90 % spikes from the
stimulus pulses Figure 3.6A shows suprathreshold current normalized to threshold at 1 Hz for both
54
the small and large cells over a range of frequencies. The stimulus threshold remains unchanged
up to 10 Hz as expected since the membrane voltage settles back at resting potential prior to the
following stimulus pulse. Increasing stimulus frequency increases suprathreshold current required
to maintain the same efficacy, and the level of increase in current is higher for large A2-cells at
high frequency (Figure 3.6A). This indicates the highest threshold percentage difference between
low and high frequency for large cells, which directly affects the probability of generating spikes at
high frequency.
There are electrophysiological and morphological factors affecting the responsiveness of RGCs
at high stimulus frequency. In this section, similar to the performed experiment, we analyzed effects
of cell size on maintaining excitability of cells at high rate of stimulation. Figure 3.6B demonstrates
changes in efficacy as alterations in stimulus frequency. Efficacy reduces as frequency is increased,
and large cells have lower efficacy at high repetitive stimulus pulses compared to small cells. This
agrees with experiments on A2-RGCs, showing smaller cells can better sustain high stimulation
frequency (Hadjinicolaou et al., 2015). Using our computational platform, we were able to move
forward to consider the impact of dendritic field size separately from the soma size. We changed
the size of the dendritic field for the given soma diameters of the small and large RGCs (17 µm
and 26 µm), comparing solid and dash lines in Figure 3.6B. Alterations in the dendritic field size
has negligible effect on the efficacy of both small and large A2 RGCs, which explains the dominant
effect of soma size on the excitability of these cells.
55
Figure 3.7: Color perception in a blind RP patient fitted with the Argus II retinal prosthesis.
A, Fundus image showing the location of the electrode array on the retina; B, Mapping of the
electrodes selected for testing in the visual field; C, Color sensations elicited by different electrodes
under frequency modulation; D, Blue scores of the color sensations calculated by the following
scaling system: 0 – no blue or purple perception; 1 – blue or purple sensation reported, but the
color is highly unsaturated (saturation⩽ 0.2); 2 – more significant blue or purple sensation reported
(0.2 < saturation⩽ 0.5); 3 – strong blue or purple sensation reported (saturation > 0.5). The gray
shaded area represents the standard error.
3.2.6 Clinical testing in a patient with retinal implant
Earlier studies in blind RP subjects fitted with the Argus II and the IMI retinal prosthesis
demonstrated that color sensation could be elicited by electrical stimulation of the photoreceptor-
less retina and that the colors perceived may be shifted by the stimulation frequency. More recently,
Yue et al. found that when phosphene brightness was maintained, increased stimulation frequency
consistently shifted phosphene perception to blue tinted colors in 5/7 Argus II subjects tested (Yue
etal.,2021). ThesesubjectswerevisuallydeprivedbyRPsinceadolescenceorearly-to-middleadult-
hood, having been blind for decades without light or color perception. An example of the changes
in color perception in one subject is shown in Figure 3.7. The electrode array was implanted in the
parafoveal locations superior temporal to the optic disc (Figure 3.7A). Color perception was tested
in five individual electrodes (Electrodes 1-5) and one group of 4 neighboring electrodes (Electrode
Quad 6). Relative locations of these electrodes in the visual field are mapped in Panel B. Hue
and saturation of the colors reported were depicted in Panel C, in which two colors simultaneously
perceived in one phosphene were presented in concentric rings. When the stimulation frequency
56
increased from 6 to 120 Hz, the phosphene perceived changed from yellow/white dominated colors
to blue dominated colors. Other colors such as black and pink were sporadically reported only.
Quantification of the blue sensation yielded a blue score that consistently increased with the fre-
quency, suggesting the possibility of using frequency modulation to selectively activate different
color pathways in the inner retina, bypassing the cone photoreceptors.
3.3 Discussion
A multi-scale computational study using a combined AM-NEURON model was conducted to
further our understanding of the cellular, and potentially color, selectivity of RGC subtypes in the
electrically stimulated degenerated retina. We first developed realistic models of the two classified
ganglion cells known as D1-bistratified and A2-monostratified. Their responses to electrical stim-
ulation with alterations in stimulation frequency were further evaluated. Our findings show that:
i) the greatest differential firing rate between D1-RGCs and A2-RGCs can be achieved at high
stimulation frequency; ii) with the proper choice of current amplitude at high frequency, D1-RGCs
can be selectively activated; iii) there are electrophysiological and morphological factors influencing
RGCs response to high stimulus frequency; iv) RGCs with a relatively small soma size are more
responsive to high stimulus frequency.
Our results show that D1 cells can be selectively activated at a 20 Hz firing rate, similar to the
typical stimulus frequency employed in the epiretinal prosthetic systems, which is found to induce
stable phosphenes (Ahuja and Behrend, 2013; Ahuja et al., 2008, 2011) with a proper selection
of current amplitude at 200 Hz stimulus frequency. We found that the greatest difference in the
current amplitude required to reach 20 Hz firing rate in both cells ( ≈ 22µA) can be achieved using
a high frequency of 200 Hz. The differential current threshold between low and high stimulation
57
frequencies is further supported in Figure 3.6A, comparing the suprathreshold current required to
reach 90 % efficacy (spike probability) for small and large A2 cells using the optimized waveform in
(Hadjinicolaou et al., 2015). Using our computational platform, we found a small difference in the
required current for gaining 90 % efficacy between the cells at low stimulation frequency compared
to a significant difference in the current amplitude at high frequency, as shown in Figure 3.6A (12.5
µA at 10 Hz, compare to 109 µA at 200 Hz). Again, this manifests the greatest chance for selective
activation of small cells at high frequency.
Wegainedadditionalinsightsintotheunderlyingmechanismsleadingtoincreasedresponsiveness
of D1 cells and the potential for selective excitation of this cell type at high frequency. We found the
greatest impact on the capability of these cells to elicit spikes at high frequency to be related to the
soma diameter compared to the axon diameter (Table I). Our analysis shows that D1 RGCs with
in average smaller soma size are better able to follow high repetitive stimulus pulses. We further
considered the impact of possible differences in AIS properties between the two RGC subtypes on
their response to high frequency stimuli. Recently, a positive correlation has been reported between
the length of the AIS and the soma size across a population of S RGCs (Raghuram et al., 2019). In
addition, increase in the length of the SOCB has shown to reduce the stimulation threshold of RGCs
to electrical stimulation (Jeng et al., 2011). Our computational models allowed us to separately
investigate the role of modulations in the length of the AH and SOCB on the sensitivity of RGCs
to high stimulation frequency. Although reducing the length of SOCB in D1 cells with smaller
soma size decreased the responsiveness of this cell to high stimulus frequency, the contribution of
soma diameter changes is found to be more significant. Comparing the response of the two cells
with simultaneous modulations in the soma diameter, axon diameter, and SOCB length established
higher responsiveness of D1 cells compared to A2 cells at a high stimulus frequency (Figure 3.5).
58
This finding is consistent with the experiments on frequency response of A2-RGC type, showing
that small cells can better sustain high rate of spikes at high frequency.
Consistent with a recent study in α RGC (Raghuram et al., 2019), we found negligible influence
of the AH length and dendritic field size, and a relatively strong impact of soma size on soma RGCs
threshold. The significant contribution of the AIS length relative to other morphological factors to
the AIS threshold of RGCs with a point-source electrical stimulation was reported (Werginz et al.,
2020). In the previous chapter, an almost two-fold increase in the differential AIS threshold of these
morphologically- and biophysically-distinct RGCs using a disk electrode was found for fixed AIS
properties of the cells. This indicates the increased sensitivity of RGCs threshold to soma diameter
changes when using the large disk electrode currently used in Argus II prosthetic systems, rather
than a point source. In the present study, we further explored the enhanced current window required
for selective activation of RGCs in response to high stimulus frequency relative to single stimulus
pulseandlowstimulationfrequency. Thedifferencesinthebiophysicalproperties, spikewidth, spike
latency, and the duration of the refractory period across RGCs can contribute to the slow-moving
firing rate of the A2 cell with increases in the current amplitude, suggesting the reduced potential
for preferential excitation of this cell type at high frequency.
It is also worth noting that while there is a positive correlation between soma diameter and axon
diameter of monostratified cells, this correlation is shown to be not significant in bistratified RGCs
in the primate retina (Walsh et al., 2000). Therefore, not only smaller soma size, but also relatively
larger axon diameter of D1-type would lead to higher chance of spikes in this RGC type at high
stimulation frequency. Hence, a plausible explanation behind the domination of the blue percept
at high frequency in Argus II patients could be relatively large axon and small soma diameters of
small bistratified RGCs, assuming their contributions to “blue-yellow” color opponent pathway in
59
the retinal circuitry (Dacey, 1996; Dacey and Lee, 1994; Dacey and Packer, 2003; Thoreson and
Dacey, 2019).
Studies reported the gradual changes in the electrode impedance and therefore the perceptual
threshold of Argus I and II implants (Mahadevappa et al., 2005; Yue et al., 2020). Increase in
electrode to retina distance was shown to increase the perceptual threshold of Argus I subjects
(Mahadevappaetal.,2005). However,therecentclinicaldatafromonesubjectwithArgusIIimplant
reported no significant changes in the electrode-retina distance up to 40 months after implantation,
suggesting the contribution of other factors, such as changes in impedance due to electrochemical
reactions on the electrode surface, to the perceptual threshold changes of the subject (Yue et al.,
2020). More tests need to be done clinically to measure the electrode-retina distance/orientation
variations across the electrodes and Argus II subjects, and analyze the impact on the perceptual
threshold. Using our multi-scale computational modeling platform, we explored the influence of
modulations in the electrode-to-retina distance on the response of RGCs at high frequency. So far,
we have only considered the response of the two cells for a given 50 µm electrode-to-cell distance.
Figure 3.8A compares the firing rates of the A2 and D1 RGCs as alterations in the current amplitude
for 20 µm, 50 µm, 100 µm, and 200 µm electrode-soma distances at 200 Hz. Increased distance
between the electrode and cell bodies leads to increased current threshold (Mueller and Grill, 2013).
Further, we computed the difference in the required current amplitude to reach firing rates of 20
Hz, 100 Hz, and 200 Hz for both cells (Figure 3.8B). The differential response of the two cells
significantly increases with increase in the electrode-cell distance, suggesting the enhanced chance
for selective activation of the D1-bistratified cell.
Recent clinical data reported that 2 of the 7 Argus II subjects did not perceive blue color at
high stimulation frequency (Yue et al., 2021). Interestingly, the perceptual thresholds in the two
60
non-blue-sensing subjects were found to be lower in average compared to the other 5 subjects.
The lowest perceptual threshold was also perceived by the non-blue-sensing subject. Although
no significant difference in the electrode-retina interface among the subjects was observed, our
computational analysis suggests that even small variations in the electrode-retina distance across
the electrodes and among the Argus II subjects can provide a plausible explanation of the blue
perceptiondifferencebetweenthetwogroups. Thelowthresholdofthenon-blue-sensingsubjectmay
indicate the closer electrode-to-retina distance and therefore less likelihood of selectively activating
the small bistratified RGCs. Further investigation is required to better understand the correlation
between electrode-retina distance and blue sensation of the subjects.
Our computational findings, along with the experimental verifications, suggest that there are
electricalstimulationparameterswiththegreatestcontributiontochangesinRGCsstimulusthresh-
old and perceptual threshold. These parameters consist of stimulation frequency, electrode-retina
distance, electrode impedance, and pulse duration that can play significant roles in possible selective
activation of different RGCs, as well as avoiding activation of RGCs axon bundles. For example,
short stimulus pulse durations with relatively higher stimulation thresholds have proven effective
in achieving a more focal response in RGCs. While the impact of pulse width modulations on the
blue sensation of the Argus II subjects was found to be negligible (Yue et al., 2021), we will further
investigate the influence of pulse duration changes on selective activation of RGCs. Increasing both
stimulation frequency and current amplitude results in an increase in phosphene brightness with a
more pronounced impact of stimulation frequency (Nanduri et al., 2012).
Saturation in brightness and increase in phosphene size have been reported with increasing
current amplitude (Nanduri et al., 2012; Stronks and Dagnelie, 2014). Lowering the current ampli-
tude as the simulation frequency increases is required for controlling the perceptual brightness and
61
0
50
100
150
200
250
0 100 200 300 400 500 600 700
Firing rate (Hz)
Current amplitude (µA)
A2-monostratified
D1-bistratified
Electrode-soma distance
20 µm 50 µm 100 µm 200 µm
0
50
100
150
200
20
Differential current (µA)
Electrode-soma distance (µm)
FR: 200 Hz
FR: 100 Hz
FR: 20 Hz
50 100 200
A B
Figure 3.8: The influence of electrode-cell distance on response and selective activation of RGCs
at 200 Hz. A, Firing rates of the A2 and D1 RGCs as function of current amplitude for four
difference electrode-soma distances (20 µm, 50 µm, 100 µm, and 200 µm). B, Current amplitude
difference between the two cells required to obtain firing rates (FRs) of 20 Hz, 100 Hz, and 200 Hz
with increase in the electrode-soma distance. Data show that the differential firing rate and current
amplitudeofRGCsincreasedwithincreasingelectrode-celldistance,suggestingtheenhancedchance
for preferential activation of D1 cells.
perceiving the color of the phosphene, including the blue percept by Argus II subjects. Our compu-
tational results indicate that increasing either the stimulation frequency or current amplitude leads
to an increase in firing rate. For example, as shown in Figure 3.6B, for a given current amplitude of
435 µA, while the efficacy of small cells at 200 Hz is 30.5 % (0.305× 200 = 61 Hz firing rate), the
efficacy is 100 % at 20 Hz which means the firing rate of 20 Hz. Taken together, evidence suggests
a positive correlation between rate of RGCs spikes and phosphene brightness. Therefore, electrical
stimulation at high frequency with a proper current amplitude tuning for brightness control results
in a better chance for selective activation of RGCs and sensation of blue percept in the subjects.
The current amplitudes associated with the maximum firing rates of A2 and D1 RGCs do not
necessarily mean the saturation of perceptual brightness in the subjects. While the maximum
spiking frequency of RGCs has been reached with direct activation, network-mediated response
of RGCs may further alter the firing rates of RGCs. We did not consider the presynaptically
driven response of RGCs in the present study. Further, high frequency of stimulation may result in
phosphenes fading and cessation of indirect RGCs excitation (Ahuja et al., 2008; Fornos et al., 2012;
62
Horsager et al., 2010). The cross-talk across the electrodes using synchronous stimulus pulses has
been reported to increase the brightness of phosphenes as well (Horsager et al., 2010). Given direct
and indirect activations of RGCs using the 0.46 ms pulse width, the rate of RGCs spikes leading to
a moderate perceptual brightness of the subjects is not known.
Therefore, we compared the differential amplitude of RGCs leading to 20 Hz, 100 Hz, and 200
Hz firing rates of the cells at 200 Hz frequency stimuli as depicted in Figure 3.8B. Center-surround
receptive field structure (S ON versus L+M OFF, S: short L: long, M: middle wavelength), or
“blue-yellow” opponent visual pathway has already been identified. Short wavelength sensitive (S)
cone photoreceptors make selective connection with S-cone ON bipolar cells, and L and M cones
are presynaptic to OFF cone bipolar cells, then signals from these pathways are transmitted to
inner and outer dendrites of small bistratified ganglion cells. A recent study has suggested that,
although small bistratified RGCs play a role in blue-yellow perception in periphery, this percept is
mediated by other pathways in central retina (Neitz and Neitz, 2017). This hypothesis is based on
testing in patients with congenital stationary night blindness (CSNB), who lack the metabotropic
glutamate receptor (mGluR6), which is leading to loss of response sensitivity to ON pathway and
presumably eliminating the synaptic connection from S cone to S cone ON bipolar cells (Terasaki
et al., 1999). Terasaki et al. observed that blue/yellow color vision of these subjects was intact
in central retina, but impaired in peripheral retina, suggesting S-ON bipolar cells and therefore
small bistratified RGCs do not contribute to blue-yellow perception in central retina. However,
most recently Thoreson and Dacey have stated that while S-ON response is diminished in CSNB
patients, L+M OFF response remains preserved (see Figure 3.10A in (Thoreson and Dacey, 2019)),
(Crook et al., 2009), and OFF inputs can be sufficiently strong enough to carry information about
the light response and compensate for lack of inputs from ON pathway. They further raised this
63
theory to be doubtful by stating: “there are also no obvious deficits in the perception of ON versus
OFF luminance contrast in CSNB patients” (Thoreson and Dacey, 2019).
In the primate visual system, there are three pathways: parvocellular (P), magnocellular (M),
and koniocellular (K) (Casagrande, 1994; Kandel et al., 2013). Parasol ganglion cells with large
soma and dendritic field size project to the M pathway and are color insensitive (Silveira et al.,
1999). However, midget and bistratified ganglion cells with small cell bodies and dendritic fields
send neural signals to the P and K pathways and they are involved in color vision (Leventhal et al.,
1981; Monasterio and Gouras, 1975; Shapley and Perry, 1986). Even if small bistratified RGCs are
not involved in blue-yellow color opponency, the large soma size of color insensitive parasol cells and
small soma size of color selective midget cells possibly explain the importance of our computational
findings, particularly due to the fact that the subjects could occasionally see other colors such as
purple and gold at high frequency as well (Tochitsky et al., 2014).
Our results are limited to only two types of RGCs and the sensitivity of other RGCs to high
stimulation frequency requires further investigation. Since the band information is not clearly
identified for the two RGCs, in this work we assumed identical axonal biophysics for both cells and
focused on morphological factors such as soma, dendritic field, axon diameters, and the length of
the AIS. The impact of retinal degeneration on changes in the morphometric parameters of the cells
assumed to be negligible in the present study. We identified the soma diameter, SOCB length, and
biophysical differences between the cells as critical factors affecting responsiveness of RGCs at high
frequency. Future studies will incorporate morphologically and electrophysiologically other types of
RGCs with a wide range of cell body sizes as well as the effect of electrode position on response of
RGCs to high stimulation frequency. We will develop a synthetic retinal network, modeling a large
population of different RGCs and analyzing the sensitivity of cells response to various morphological
64
changes and modulations in electrode orientations with respect to the surface of the retina. We will
further design electrical stimulation waveforms with the aim of independent activation of various
RGCs at high stimulation frequency.
This study is motivated by our intent to identify mechanisms that will allow us to potentially
encode additional information such as color in a visual prosthetic system. Our multi-scale com-
putational framework helped us further our understanding of the color-coding sensitivity in the
electrically stimulated degenerated retina. Assuming significant contribution of small bistratified
retinal ganglion cells in blue-yellow color vision, we were able to selectively target these cells with in
average small soma size at high stimulus frequency with a careful modulation of current amplitude.
Our computational finding may be correlated with the clinical study in patients with epiretinal
prostheses showing that stimulation frequency played a role in the percept of colors, and partic-
ularly the blue percept at high frequency. The verification of the computational models with the
experimental data in rats and preliminary experimental results in patients with epiretinal implants,
allowed us to better elucidate the underlying mechanisms of differential percept and provide more
insights toward the development of visual prosthetic systems with increased information content for
the patient.
65
Chapter 4
Enhanced Chance for Selective
Activation of Functionally Different
Retinal Ganglion Cells
Paknahad J, Loizos K, Yue L, Humayun MS, Lazzi G. Selective Activation of Retinal Ganglion
Cell Subtypes Through Targeted Electrical Stimulation Parameters. IEEE Transactions on Neural
Systems & Rehabilitation Engineering (Under review, 2021).
Abstract
To restore vision to the blind, epiretinal implants have been developed to electrically stimulate the
healthyretinalganglioncells(RGCs)inthedegenerateretina. Giventhediversityofretinalganglion
cells as well as the difference in their visual function, selective activation of RGCs subtypes can
significantly improve the quality of the restored vision. Our recent results demonstrated that with
the proper modulation of the current amplitude, small D1-bistratified cells with the contribution to
blue/yellow color opponent pathway can be selectively activated at high frequency (200 Hz). The
computationalresultscorrelatedwiththeclinicalfindingsrevealingthebluesensationof5/7subjects
with epiretinal implants at high frequency. Here we further explored the impacts of alterations
66
in pulse duration and interphase gap on the response of RGCs at high frequency. We used the
developed RGCs, A2-monostratified and D1-bistratified, and examined their response to a range of
pulse durations (0.1 – 1.2 ms) and interphase gaps (0 - 1 ms). We found that the use of short pulse
durations with no interphase gap at high frequency increases the differential response of RGCs,
offering better opportunities for selective activation of D1 cells. The presence of the interphase
gap has shown to reduce the overall differential response of RGCs. We also explored how the low
density of calcium channels enhances the responsiveness of RGCs at high frequency. The ability to
selectively activate RGCs that carry particular types of visual signals can significantly improve the
performance of current epiretinal implants.
4.1 Introduction
RETINAL implants have been developed to restore partial sight to patients who have been
blinded by degenerative diseases such as retinitis pigmentosa (RP) and age-related macular de-
generation (AMD). These devices convert visual information into spatiotemporal electrical stimuli
patterns and aim at activating healthy retinal neurons (Cruz et al., 2016; Humayun et al., 1999;
Kosta et al., 2018; Stingl et al., 2015; Weiland and Humayun, 2014; Weiland et al., 2016). In the
early stages of degeneration, while photoreceptors are largely damaged, inter retinal neurons includ-
ing retinal ganglion cells (RGCs) remain mostly intact (Jones et al., 2011). Hence, retinal ganglion
cells are often the primary target of electrical stimulation in epiretinal prosthetic systems.
Many attempts have been made towards improving the efficacy of current devices using both
computational and experimental approaches. However, there are still many challenges that limit
the spatial resolution of vision acquired through these devices. One of the most critical issues with
epiretinal stimulation is the activation of RGCs axons of distant cell bodies (Behrend et al., 2011;
67
Beyeler et al., 2019; Nanduri et al., 2012). Clinical studies of patients with epiretinal implants
reported that a single stimulating electrode can result in perception of an elongated phosphene
which is aligned with the RGCs axonal pathway (Beyeler et al., 2019).
Direct and indirect stimulations of RGCs have been proposed to avoid axonal activation and
achieve a more focalized response from a population of RGCs. Studies have shown that bipolar
cells (BCs) can be preferentially activated using long pulse durations (25 ms) (Weitz et al., 2015)
or sinusoidal stimulation of low frequency (25 Hz) (Freeman et al., 2010). This indirect RGCs
stimulation can avoid activating axons underneath electrodes and improve the spatial resolution of
epiretinal implants. However, it has been reported that the response of RGCs to a train of stimulus
pulses has been desensitized (Freeman and Fried, 2011). Research has been performed to directly
stimulate RGCs using extremely short pulse durations in order to increase the stimulation threshold
difference between the distal axon and the axon initial segment, and therefore reduce the chance
for axonal excitation of RGCs (Jensen et al., 2005; Schiefer and Grill, 2006).
Several studies have focused on the selective activation of RGCs to improve the quality of
the restored vision. Jepson et al. demonstrated the possibility of activating a single cell type
without simultaneous activation of neighboring cells in the primate retina (Jepson et al., 2013).
High frequency electrical stimulation (1 kHz) with a proper current amplitude modulation has been
shown to preferentially activate ON and OFF RGCs (Cai et al., 2013; Guo et al., 2019; Twyford
et al., 2014). Further, the greater sensitivity of ON RGCs to electrical stimulation with long pulse
durations relative to OFF RGCs has been observed, offering the stimulation strategy to selectively
activate ON RGCs (Im et al., 2018; Lee and Im, 2019). While significant progress has been made
towards preferential activation of ON and OFF RGCs, no stimulation strategies have been proposed
to selectively activate morphologically different subtypes of RGCs and cells that carry specific types
68
of visual information such as color and contrast (Dacey and Lee, 1994; J. et al., 2002). For instance,
small bistratified RGCs have been shown to contribute to blue/yellow color vision (Dacey and Lee,
1994; Lee et al., 2010). Also, clinical studies of subjects with epiretinal implants have demonstrated
that blue color is perceived at high stimulus frequency (Tochitsky et al., 2014). The ability to
characterize the response of RGCs to electrical stimulation and selectively target cells based on their
morphological and physiological properties would represent a significant impact on the performance
of current retinal prosthetic systems.
In chapter 2, we developed morphologically and biophysically realistic models of the two classi-
fied RGCs, A2-monostratified and D1-bistratified. We validated these models by comparing them
with the single-compartment models and experimentally recorded signals of the two cells using in-
tracellular stimulations (Qin et al., 2017). Using the typical stimulus parameters in Argus II devices,
a symmetric charge-balanced with no interphase gap (IPG) and pulse width (PW) of 0.5 ms, we
observed that D1 cells are more responsive to high frequency extracellular stimulation relative to
A2 cells. This differential response of RGCs offers potential for select activation of individual cells
at high frequency (200 Hz). Our previous computational findings indicated that, with a careful se-
lection of current amplitude, D1 small bistratified cells can be selectively targeted at high frequency
with implications for encoding colors in future retinal prosthetic systems. These results were verified
with experimental data from the literature and correlated with the clinical data from the Argus II
subjects.
In this chapter, using our combined Admittance method (AM)/NEURON multiscale computa-
tional platform, we further characterized the impacts of pulse duration and interphase gap on the
differential response of RGCs at 200 Hz. To better understand the sensitivity of RGCs to different
stimulus parameters, we analyzed the firing rates of cells as a function of modulations in current
69
Symmetric cathodic-first biphasic pulses
Current modulation at high frequency F = 200 Hz
Frequency response of RGCs IPG = 0
PW = 0.5 ms
F = 6 Hz to 200 Hz
A2 vs. D1
Impact of pulse width
at 200 Hz
IPG = 0
PW = 0.1 ms to 1.2 ms
F = 120 Hz & 200 Hz
Impact of interphase gap
at 200 Hz
IPG = 0.1 to 1 ms
PW = 0.5 ms
F = 120 Hz & 200 Hz
A2 vs. D1
Figure 4.1: An overview of the analysis performed in this paper. Using a symmetric charge-
balanced biphasic pulse, we first explored the impacts of modulations in pulse duration and inter-
phase gap on the frequency response of RGCs. We compared the firing rate difference between A2
and D1 cells at high frequency over a range of pulse widths and interphase gaps. Then, the firing
rates of RGCs over a range of current amplitude were compared and we characterized the effect of
both PW and IPG on the response of RGCs at high stimulus frequency of 200 Hz.
amplitude. Our results show that the difference in response between the two RGCs is highly de-
pendent on modulations in both pulse durations and interphase gaps. Greater sensitivity of the A2
cell to the addition of interphase gap was observed compared to the D1 cell. We found that the
addition of IPG reduces the likelihood for selective activation of RGCs at high frequency. Further,
we investigated the role of calcium (Ca) channels on the responsiveness of RGCs at high frequency.
The enhanced selectivity of RGCs can be achieved with a proper selection of the current amplitude
at high frequency using short pulse durations with no IPG. This differential response of RGCs and
therefore the ability to selectively target specific types of cells at high frequency can potentially
help identify the mechanisms linked to different percepts and improve the effectiveness of current
epiretinal prosthetic systems.
70
Table 4.1: Maximum conductance values for A2 and D1 cells [S/cm2].
1
TABLE I
RATE CONSTANTS OF IONIC CURRENTS
Na
Channel
Ca
Channel
K
Channel
A
Channel
h
Channel
T
Channel
TABLE II
MAXIMUM IONIC CONDUCTANCE VALUES FOR A2 AND D1 CELLS [S/CM
2
].
RGC types
A2 D1
Soma Dendrite Soma Dendrite
gNa 0.3 0.1 0.2
0.08
gK 0.12 0.05 0.211 0.08
gK,A 3*gK
3*gK
3*gK 3*gK
gK,Ca 0.004*gK 0.004*gK 0.004*gK 0.004*gK
gCa 0.137 0.05 0.013 0.01
gh 0 0 0.0001 3e-5
gT 0.004 0 0.0024 0.001
Table 4.2: Maximum conductance values of the axon for A2 and D1 cells [S/cm2].
1
TABLE I
RATE CONSTANTS OF IONIC CURRENTS
Na
Channel
Ca
Channel
K
Channel
A
Channel
h
Channel
T
Channel
TABLE II
MAXIMUM IONIC CONDUCTANCE VALUES FOR A2 AND D1 CELLS [S/CM
2
].
RGC types
A2 D1
Soma Dendrite Soma Dendrite
g
Na
0.3 0.1 0.2
0.08
g
K
0.12 0.05 0.211 0.08
g
K,A
3*g
K
3*g
K
3*g
K
3*g
K
g
K,Ca
0.004*g
K
0.004*g
K
0.004*g
K
0.004*g
K
g
Ca
0.137 0.05 0.013 0.01
g
h
0 0 0.0001 3e-5
g
T
0.004 0 0.0024 0.001
TABLE III
MAXIMUM IONIC CONDUCTANCE VALUES OF THE AXON FOR A2 AND D1 CELLS
[S/CM
2
].
AH SOCB NS DA
g
Na
0.2 2.4 0.4 0.2
g
K
0.1 0.8 0.2 0.1
g
K,A
3*g
K
3*g
K
3*g
K
3*g
K
AH SOCB NS DA
g
Na
0.8 2.4 0.9 0.8
g
K
0.6 0.8 0.6 0.6
g
K,A
3*g
K
3*g
K
3*g
K
3*g
K
4.2 Methods
The details on the NEURON modeling of these RGCs and AM simulations are discussed in
chapter 2. The ionic channel conductance values of both A2 and D1 cells for the soma, dendrites,
and axon are listed in Tables 4.1 and 4.2. The impacts of morphological variations including the
sodium channel band (SOCB) length, soma diameter, and axon diameter as well as the position
of the electrode with respect to cells and along the axon on the differential response of the two
subtypes of RGCs have been comprehensively discussed in previous chapters. Given the greatest
excitability of the D1 cells to high stimulation frequency (Figure 4.1B), we only centered our focus
on the role of PW and IPG in the response of RGCs to electrical stimulation, particularly at high
frequency.
The primary goal of this study is to determine the effects of different electrical stimulation
parameters on the frequency response of RGCs. We used symmetric charge-balanced biphasic
71
waveforms in all performed simulations to avoid charge accumulation and damage to the tissue. We
previously used the typical stimulus waveform in Argus II devices (symmetric cathodic-first with
no interphase gap and 0.5 ms pulse duration). Here we evaluated the impacts of a range of pulse
durations from 0.1 ms to 1.2 ms, and interphase gaps ranging from 0 to 1 ms on RGCs frequency
response. To assess the possibility of enhancing selective activation of RGCs, the response of the
cells over a range of current amplitudes was compared at 200 Hz as shown in Figure 4.1.
The influence of pulse width and interphase gap on RGCs response to electrical stimulation
has proven in the literature (Hadjinicolaou et al., 2015; Weitz et al., 2014). Therefore, a fixed
current amplitude cannot be used for comparing the RGCs frequency response of varying pulse
durations and interphase gaps. It is important to eliminate the effects of stimulus threshold (charge
threshold) difference among different pulse widths and interphase gaps on RGCs firing rate. A
proper current amplitude needs to be set for a given electrical stimulation parameter before any
comparisons between the responsiveness of RGCs to high stimulation frequency. Therefore, we
defined the current amplitude as the minimum current required to achieve the spike probability
(the total number of spikes divided by the total number of delivered stimulus pulses) of 100 percent
at a lower frequency of 120 Hz in both A2 and D1 cells for a range of pulse durations and interphase
gaps. Then, the adjusted current associated with each pulse duration and interphase gap was used
to illustrate how the two RGCs can maintain their response at 200 Hz stimulus frequency. This
strategy could minimize the number of plots and analysis required to evaluate the impacts of several
pulse durations and interphase gaps on the response of RGCs over a range of frequencies.
We further compared the firing rate difference between the two cells as a function of pulse
amplitude for the two pulse durations of 0.1 ms and 1 ms without the IPG. Similarly, we analyzed
the differential response of RGCs for a pulse duration of 0.5 ms without and with the IPG of 1 ms
72
0
100
200
300
400
500
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2
Pulse amplitude
(μA)
Pulse duration (ms)
0
50
100
150
200
250
0.1 0.2 0.5 0.6 0.8 1.2
Spiking Frequency
(Hz)
Time (ms)
A2 D1
A
B
Figure 4.2: A) The minimum current amplitude required to achieve 100 % spike probability at
120 Hz (120 Hz firing rates) for a given pulse duration, B) the difference in frequency response
between the A2 and D1 RGCs at 200 Hz. Results demonstrate that the firing rates of cells can be
better differentiated using shorter pulse widths.
as a function of current amplitude. Figure 4.1C provides an overview of the analysis performed in
this paper. All the simulations were done using the AM-NEURON computational platform.
4.3 Results
4.3.1 Frequency Response: Pulse Width Modulations
We analyzed the influence of pulse width variations from 0.1 to 1.2 ms on the frequency response
and the level of excitability of the two RGCs at high frequency. Figure 4.2A shows the tuned current
amplitude for each pulse width to achieve 100 percent spike probability at 120 Hz in both cells.
As expected, the strength-duration curve is decaying exponentially, and the curve flattens out at
around 0.8 ms pulse duration. The current associated with each pulse duration was used to compare
the responsiveness of RGCs to 200 Hz stimulus frequency. Figure 4.2B shows the spiking frequency
73
70
75
80
85
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Pulse amplitude
(μA)
Interphase gap (ms)
0
25
50
75
100
125
150
175
0.1 0.2 0.4 0.6 0.8 1
Spiking Frequency
(Hz)
Interphase gap (ms)
A2 D1
A
B
Figure 4.3: A) The minimum current amplitude required to achieve 100 % spike probability at
120 Hz (120 Hz firing rates) for a range of IPGs and PW of 0.5 ms; B) The difference in firing rate
between A2 and D1 RGCs at 200 Hz for a range of interphase gaps. Results show that even though
the addition of interphase gap decrease the stimulation threshold of RGCs, it does not increase the
differential response of cells.
of D1 and A2 cells as a function of pulse duration. Responses of both cell types illustrate that
pulses with shorter durations result in greater differentiation in RGCs firing rate at high frequency,
although the required current is higher. This differential response became smaller and both RGCs
almost follow a similar rate of firing as the pulse duration is increased.
4.3.2 Frequency Response: Interphase Gap Modulations
So far, we assumed that there is no interphase gap in the stimulation waveform. Here we
examined the change in the differential response of RGCs in the presence of IPGs at high frequency
(200 Hz). We compared the responsiveness of A2 and D1 cells to modulations in IPGs. Figure
4.3A illustrates a decrease in the current amplitude with increasing the interphase gap up to around
0.8 ms. However, the effect of IPG on the current amplitude is negligible at values higher than
0.8 ms. A comparison of firing rate difference between the D1-bistratified and A2-monostratified
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B
Figure 4.4: Firing rate as a function of pulse amplitude for both A2 and D1 cells at 200 Hz
stimulation frequency: A) short pulse duration of 0.1 ms; B) long pulse duration of 1 ms. Data
represent the impacts of pulse width on the response of A2 and D1 RGCs. Results demonstrate
that the differential responsiveness of RGCs is higher using shorter pulse durations. This suggests
the greatest stimulus threshold difference and a better chance of selective activation of D1 cells
using short pulse width with a proper selection of current amplitude at high frequency.
RGCs with variations in the interphase gap ranging from 0.1 to 1 ms is represented in Figure 4.3B.
Interestingly, the difference between the excitability of these cells at high frequency was reduced
and converged to zero at IPGs greater than 0.2 ms. Our observation of the similarity of the two
RGCs responsiveness to longer IPGs suggests that the likelihood for preferential activation of cells
is reduced in the presence of IPG.
4.3.3 Current Modulations: Effects of Pulse Width on RGCs Response
To better understand the sensitivity of RGCs to high stimulation frequency of varying pulse
durations, we plotted the cells firing rate as a function of current amplitude at 200 Hz. The current
is incremented every 5 µA and the number of spikes per second are recorded for both cells. The A2
and D1 response curves for the impulse of 0.1 ms width and current amplitudes ranging from 150
75
to 600 µA are shown in Figure 4.4A. Overall, the greater difference in the rate of response between
the cells can be seen using short pulse durations. As we increase the pulse amplitude, D1 cells show
a higher probability of excitation at higher firing rate relative to A2 cells.
Our computational modeling further reveals that there is a wide saturation window at 100 Hz
firing rate (50 percent spike probability) for both cells. This window is almost three times larger
for the A2-monostratified cell relative to the D1-bistratified cell (Figure 4.4A). This also leads to
the great suprathreshold difference between the cells to achieve 200 Hz spiking rate (100 percent
spike probability), indicating that A2 cells are less responsive at higher firing rates. Figure 4.4b
compares the firing rate of both RGCs as alterations in pulse amplitude ranging from 20 to 80 µA
for the longer pulse duration of 1 ms. While a slower rate of response in A2 cells can be seen here
as well, the differential response of cells is significantly lower compared to short-duration pulses.
No saturation window was observed with long stimulus pulse durations. The stimulus threshold
difference between the cells to elicit one spike per each delivered pulse (200 Hz firing rate) became
smaller (10 µA) for 1 ms pulse width, suggesting the reduced chance for preferentially targeting
RGCs. Although the level of current amplitude is lower using long pulse durations, the charge
threshold appears to be greater compared to pulses with short durations (See Figure 4.4A and B).
For example, the minimum current to achieve 200 Hz firing rate in A2 cells for the short pulse width
is 550 µA, indicating 55 nC charge. However, the current and charge for the long pulse duration (1
ms) are 75µA and 75 nC, respectively. This offers a plausible explanation that the close sensitivity
of the two RGCs to long stimulus pulses can be due to the large charge threshold associated with
long pulse durations.
ThetypicalstimulationfrequencyappliedinepiretinalprostheticsystemsandparticularlyArgus
II is 20 Hz (Ahuja and Behrend, 2013; Ahuja et al., 2008). Therefore, with a proper modulation
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D1: IPG = 0 ms
A2: IPG = 0 ms
C
Figure 4.5: Firing rates of A2 and D1 cells as a function of pulse amplitude at 200 Hz stimulus
frequency for both the presence (dash lines) and absence of IPG (solid lines). (A) PW = 0.1 ms;
(B) PW = 0.5 ms; (C) PW = 1 ms. Results show that the differential response of RGCs is reduced
with the inclusion of an interphase gap of 1 ms, lowering chance of RGCs select excitation with the
inclusion of IPGs.
of current amplitude at 200 Hz stimulus frequency, the spiking rate of RGCs can be controlled to
remain at 20 Hz (similarly to the current range of RGCs’ firing rate). This technique leads to the
elevated differential response of RGCs and the enhanced possibility for preferential activation of
RGCs. Figure 4.4 indicates that the current amplitude difference between the two cells to reach 20
Hz firing rate is much larger using the short 0.1 ms pulse duration (100 µA) relative to the long 1
ms pulse duration (10 µA), offering a greater chance for selective activation of D1 cells using short
pulse durations.
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4.3.4 Current Modulations: Effects of Interphase Gap on RGCs Response
To better examine the effect of interphase gap on RGCs response, we plotted the firing rate of
both A2 and D1 cells as a function of current amplitude for three pulse widths of 0.1, 0.5, and 1 ms
with and without the presence of IPG (IPG = 1 ms) at 200 Hz as shown in Figure. 4.5. The addition
of IPG and pulse width alterations significantly modulate the response of RGCs with increasing
current amplitude. The short pulse width of 0.1 ms with IPG of 1 ms reduces the stimulation
threshold and enhances the excitability of RGCs at high frequency (Figure 4.5A). However, the
presence of IPG decreases the differential response of cells and the likelihood of selective activation
of RGCs for all pulse widths. The reduced threshold is less pronounced using the PW of 0.5 ms
(Figure 4.5B). Figure. 4.5C shows that the responsiveness of RGCs at high frequency is reduced
using long PW and IPG of 1 ms. This agrees with results from the literature, showing the blocking
effect of high stimulation frequency with long IPGs (Weitz et al., 2014). The anodic phase of the
stimulus waveforms with long PWs and IPGs hyperpolarizes the membrane, therefore increasing the
current amplitude required for eliciting an action potential for the following cathodic stimulation
phase. Comparing the solid and dashed lines in Figure 4.5 illustrates that the addition of IPGs
decreases the differential response of RGCs, reducing the likelihood for selective activation of RGCs
at high frequency.
A2 cells have a larger soma diameter compared to D1 cells (Sun et al., 2002). Therefore, we
tested whether the soma diameter difference between the two cells plays a role in the decreased
differential response of RGCs. We altered the soma diameter of the D1 cell to 20 µm and compared
the results with the original 12 µm soma size of this cell. Figure 4.6 compares the firing rates of
small and large D1 cells with modulations in current amplitude in the presence (IPG = 1 ms) and
absence of IPGs. Results show that cells with large soma sizes are less responsive to high stimulation
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D1: No IPG_Soma 12 um
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D1: No IPG_Soma 20 um
D1: IPG = 1 ms_ Soma 20 um
Figure 4.6: The impact of soma diameter on RGCs sensitivity to the addition of interphase
gap at 200 Hz stimulus frequency. Response curves of small and large D1 cells with and without
the presence of IPGs are shown by dash and solid lines, respectively. Data show that soma size
changesdonotsignificantlyinfluenceRGCsresponsivenesstoalterationsinIPG.Similardifferential
response of small and large cells can be achieved with and without the presence of IPG.
frequency as the response curve is shifted to the right, indicating the higher activation threshold
of large cells. The figure further indicates that soma size has a negligible effect on RGCs response
sensitivity to the addition of IPGs. Small and large cells experience a similar rate of changes in
their response to high stimulation frequency as current amplitude increases. A plausible underlying
mechanism affecting the greater sensitivity of A2-monostratified RGCs to modulations in interphase
gaps is discussed in the discussion.
4.3.5 Impacts of Biophysics on RGCs Response
We further delved into other potential underlying mechanisms contributing to the differential
sensitivity of RGCs to high stimulation frequency in the presence and absence of IPGs. Figure
4.7 demonstrates the effect of the biophysical properties of the two RGCs on the elicited action
potential. We first changed the maximum ionic conductance of each channel in the A2 cell to that
of the D1 cell based on the ionic properties provided in Table 4.1. This allowed us to examine the
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A2: Biophysics of D1
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Figure 4.7: The influence of maximum ionic membrane conductance difference between the two
cells on the elicited action potential. Results indicate the significant impact of calcium (Ca) channel
density on RGCs spike width, and the influence of hyperpolarization-activated (h) channel on RGCs
refractory period.
role of each channel in shaping the response of the two cells to electrical stimulation. We found that
reducing the density of Ca decreases the spike width (Figure 4.7). An increase in the potassium (K)
density modulates the resting membrane potential to a lower value. Sodium (Na) does not play a
major role in shaping the response of the cell and reducing the Na conductance slightly enhances
the response latency of the cell. The addition of the hyperpolarization-activated channel (h) to
the A2 cell, changing the ionic conductance value from 0 to 0.0001 S/cm2 (Table 4.1), reduces the
refractory period of the A2 cell approximately from 25 ms to 18 ms (red vs. blue round dot curves).
This agrees with the experimental data observing a longer refractory period with the lower value of
Ih current (Welie et al., 2006). Taken together, Ca and h channels play significant roles in the firing
pattern difference between the A2 and D1 cells. Intrinsic electrophysiological differences among
RGCs and between these two classified cells have been shown in the literature (Qin et al., 2017).
For instance, the depolarizing sag, the change in the membrane potential from the onset to the end
of an intracellular hyperpolarizing step current, has been shown to be greater for D1 cells compared
to A2 cells (Qin et al., 2017). Further, the low density of h channels has been shown to reduce the
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A2: IPG = 1ms
A2: IPG = 0 ms
Figure 4.8: The role of Ca channel in excitability of RGCs at high frequency for a pulse duration
of 0.1 ms. Data show that reducing the density of Ca channel of the A2 cell to the Ca conductance
value of the D1 cell enhances the excitability of the cell and decreases the saturation window in
the absence of IPG. However, in the presence of IPG the influence of the Ca channel on the cell
response is less pronounced.
depolarizing sag and enhance the refractory period of pyramidal neurons (Welie et al., 2006).
4.3.6 Role of Ca Channels in RGCs Excitability at High Frequency
GiventhesignificantcontributionofCachanneldensitytothedifferentialfiringpatternofRGCs,
we examined the role of this channel in the greater saturation window and lower responsiveness of
the A2 cell compared to the D1 cell at high frequency (Figure 4.4). We also investigated the reduced
differential response of RGCs due to the addition of IPG (Figure 4.5). Figure 4.8 compares the firing
rate of A2 cells as a function of current amplitude for the pulse duration of 0.1 ms at 200 Hz in
the presence and absence of IPG = 1 ms. We investigated alterations in the cell response as the
maximum Ca conductance of the A2 cell was reduced to the value of the D1 cell. Lowering the Ca
density channel augments the responsiveness of the cell and further reduces the saturation window
of the cell. Figure 4.8 further illustrates that only by modulating the Ca channel density the reduced
differential response of RGCs in the presence of IPG can be predicted. Therefore, our computational
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findings indicate the role of the difference in the Ca density of RGCs in the excitability of cells and
lowered differential response of RGCs with the addition of IPG.
4.4 Discussion
Using our combined AM-NEURON multi-scale computational platform, we developed morpho-
logically and biophysically realistic models of two classified RGCs, A2- monostratified and D1-
bistratified. This modeling framework has enabled us to have a more precise prediction of retinal
neuron activities due to electrical stimulation, and particularly in this work the response of RGCs to
epiretinal electrical stimulation of various stimulation parameters. We assessed the impact of pulse
duration and interphase gap in a symmetric cathodic-first biphasic waveform on the frequency re-
sponse of RGCs, and their responsiveness to high stimulus frequency. We have explored different
aspects of RGCs response sensitivity to varying stimulus pulse widths and interphase gaps. Our
computational findings reveal that modulations in pulse durations and involvement of interphase
gap can significantly influence the differential firing rates of RGCs and the possibility of selectively
activating RGCs at high stimulation frequency.
4.4.1 Impacts of PW and IPG on Frequency Response of RGCs
Several studies have focused on the responsiveness of RGCs to high stimulation frequency. How-
ever, conflicting results have been reported regarding the ability of RGCs to maintain their response
at high rates of electrical stimulation. While it has been shown that RGCs can manage to spike at
a high stimulation frequency of 250 Hz with direct stimulation (Fried et al., 2006; Sekirnjak et al.,
2006), Jensen et al. observed that RGCs cannot maintain their firing rates at stimulus frequencies
higher than 40 Hz (Jepson et al., 2013). Cai et al. further demonstrated that the responsiveness
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of RGCs to a range of stimulation frequencies from 100 to 700 Hz varies across cell types. Even
within one morphological subtype of RGCs (Cai et al., 2011), small cells have shown to be more
responsive to high frequency relative to large cells (Fornos et al., 2012). These findings suggest that
different types of RGCs may experience differences in their response at a high stimulation frequency
of varying electrical stimulation parameters.
In the present study, we investigated the effects of pulse duration and interphase gap on the
frequencyresponseofA2andD1RGCs. Tothisaim,weadjustedthecurrentamplitudeofeachpulse
width and interphase gap to achieve one spike per stimulus pulse (100 percent spike probability)
at 120 Hz. Using the tuned current amplitude, the firing rates of cells at 200 Hz for a range of
pulse widths and interphase gaps were computed. One may ask why we did not adjust the current
amplitude to obtain an identical level of charges for each delivered stimulus pulse. The reason
behind using this strategy is the fact that charge threshold varies across pulse durations and a
shorter pulse duration leads to a lower charge threshold. Therefore, the equal charge assumption
leads to higher rates of spikes at extremely shorter pulse widths relative to long pulse durations (Lee
et al., 2013) and makes it difficult to compare the differential response of RGCs over a range of pulse
durations at high stimulus frequency. We found this approach to be more effective in eliminating
the effects of stimulus threshold difference among various pulse durations and interphase gaps on
the responsiveness of RGCs.
Consistently with previous reports (Hadjinicolaou et al., 2015; Weitz et al., 2014), the adjusted
current amplitudes exponentially decay with an increase in both pulse duration and interphase gap.
The strength-duration and -interphase gap curves flatten out at approximately 0.8 ms and 0.6 ms,
respectively as shown in Figure 4.2A and 3B. Our results further show that shorter pulse durations
can increase the differential response of RGCs. While the addition of an interphase gap can reduce
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the stimulus threshold, the IPG appears to minimize the firing rate difference between the two cells
at high frequency.
4.4.2 Selective Activation of D1 cells with Short Pulse Width
ON and OFF RGCs have been known to be the key components of signaling in the normal retina
for relaying visual information to the brain. In natural signaling of the retina, ON and OFF RGCs
do not fire simultaneously due to their exclusive response to light increments and decrements (Im
and Fried, 2015). Therefore, several stimulation strategies have been reported to selectively activate
ON and OFF RGCs. High stimulation frequency (1 kHz) of varying current amplitudes has been
used to preferentially target ON and OFF RGCs (Cai et al., 2013; Guo et al., 2016, 2019). Indirect
stimulation has shown to result in a closer correlation between the electrically-elicited and light-
elicitedresponseofONRGCsrelativetoOFFRGCs,suggestingmorephysiologicallyrealisticsignals
by targeting ON RGCs (Im and Fried, 2016). Accordingly, there have been more recent attempts
towards selective activation of ON RGCs and increasing the ON/OFF RGCs response ratios by
modulating stimulation frequency, pulse duration, and stimulus charge (Lee and Im, 2019).
Despite these efforts, selective activation of a broader range of morphologically different RGCs
has remained a significant challenge. Retinal ganglion cells are not only limited to ON, OFF, and
ON-OFF types and there is a wide range of morphologically different subtypes of RGCs that convey
specific types of visual information to the brain. Jepson et al. found that spatial selectivity of RGCs
can be achieved using a small stimulating electrode (10 µm) in the primate retina (Jepson et al.,
2013). However, this single RGC activation without simultaneous activation of nearby cells depends
onthepositionofthestimulationelectrode. Largechargedensityassociatedwiththesmalldiameter
of the electrode can damage the retina tissue as well (Shannon, 1992). The ability to selectively
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Figure 4.9: Membrane voltage recorded from the cell body in response to electrical stimulus
pulses of 0.1 ms in duration during the saturation window of (A) A2 cell; (B) D1 cell as shown in
Fig. 4a. The small spikes were observed in the A2 cell response with lower responsiveness at a high
frequency relative to the D1 cell.
target individual RGCs subtypes with the current stimulation electrode which covers a large number
of RGCs would significantly improve the performance of epiretinal implants.
Therefore, we characterized how a change in pulse duration and interphase gap in a symmetric
cathodic-first biphasic waveform can influence the potential for more selective excitation of indi-
vidual RGCs at high frequency. Assuming RGCs firing rate of current epiretinal implants to be
approximately 20 Hz (typical stimulation frequency of Argus II (Ahuja and Behrend, 2013)), the
greatest current amplitude difference to reach 20 Hz firing rate in both cells can be achieved using
a short pulse duration of 0.1 ms at 200 Hz (Figure 4.4A). This leads to the greater likelihood of
preferential activation of D1-bistratified RGCs over A2-monostratified RGCs. On the contrary, the
firing rate difference between the two cells and therefore the likelihood for selective activation were
reduced using the long pulse duration (1 ms) as shown in Figure 4.4B.
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4.4.3 Mechanisms Underlying RGCs Response at High Stimulation Frequency
The underlying mechanisms affecting the significant difference in RGCs differential response to
pulse duration modulations can be related to the difference in the total delivered charge between
long and short duration pulses. We observed a certain spike latency in the time course response
of the A2 cell at 200 Hz (See Figure 4.10, the A2 response with no IPG), which this latency was
not significant in D1 cells (data not shown). This latency in spike has shown to be another factor
in addition to the soma diameter contributing to the less excitability of A2 cells and therefore
slower rate of firing rate changes with an increase in current amplitude. This is in line with the
experimental data showing RGCs with long spike latencies are less responsive to high stimulus
frequencies (Sekirnjak et al., 2006). As a result, a reduction in spike latency can improve the ability
of RGCs to maintain their response at high frequency. Interestingly, it has been shown that a high
level of delivered charge leads to lower averaged spike latency of RGCs (Lee et al., 2013). Together,
on average, greater stimulus charge thresholds associated with long pulses compared to short pulses
play an essential role in the reduced differential response of RGCs and consequently the lower chance
for selective activation of RGCs.
A long saturation window was observed in the A2 cell compared to the D1 cell using the short
pulse width of 0.1 ms and no IPG (Figure 4.4A). This saturation effect is in agreement with ex-
perimental data on RGCs responsiveness at high stimulus frequencies, indicating that some RGC
subtypes cannot follow high rate of stimulus pulses even with increasing current amplitude (Cai
et al., 2011). We found that the lower Ca density of the D1 cell relative to the A2 cell contributes to
this period of unchanged firing rates of the A2 cell with an increase in the current amplitude (Figure
4.8). Figure 4.9 compares the membrane voltage of the two cells within their current window of
86
saturation in response to a short stimulus pulse of 0.1 ms according to Figure 4.4A. While increas-
ing the current amplitude does not change the number of elicited spikes in the A2 cell, it generates
small spikes following every standard action potential (Figure 4.9A). The small waveforms are not
elicited in the D1 cell with the greater responsiveness at high frequency as shown in Figure 4.9B.
Our computational results correlate well with the electrophysiological experiments measuring the
response of different RGCs subtypes to high stimulation frequencies up to 700 Hz (Cai et al., 2011).
The small waveforms were recorded in all types of RGCs except the brick transient (BT) cell with
the highest ability to follow high rates of stimulus pulses (Cai et al., 2011).
Figure 4.9A further supports the role of injected charge in the response latency of the cell. An
increase in the current amplitude and therefore the injected charge reduces the spike latency of the
A2cell. WealsofoundthatthedifferenceinthedensityoftheCachannelcanimpactthedifferential
sensitivity of RGCs to high stimulation frequency (Figure 4.8). Further, the longer refractory period
of the A2 cell compared to the D1 cell due to the lower sag and absence of h channel (Table 4.1) may
influence the ability of the cell to follow high rates of stimulus pulses. We could not examine the
role of hyperpolarization-activated (h) ionic channel in RGCs responsiveness in isolation because of
modulations in the resting membrane potential and activation threshold of RGCs with changes in
the h maximum conductance value.
4.4.4 Sensitivity of RGCs to the Presence of IPG
Our computational modeling indicates that the presence of an interphase gap decreases the
averaged differential response of A2 and D1 cells. Even though the addition of IPG reduces the
stimulationthreshold, theoverallpotentialofselectactivationofRGCsisdeclined. Wealsoobserved
that the inclusion of IPG leads to greater changes in the response of A2 cells relative to D1 cells.
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Figure4.10: Comparisonofthemembranevoltagesresultingfromsymmetriccathodic-firstbipha-
sic waveforms with and without the presence of interphase gap. The current amplitude is set to 100
µA. Data show that the A2 cell can maintain one spike per each stimulus pulse with the inclusion
of IPG, while this is not the case when the IPG is not present.
Similarly to the role of stimulus charge on spike latency, we hypothesize that IPGs can also influence
the spike timing of RGCs per each stimulus pulse. It is well-known that the addition of IPG reduces
the activation threshold of not only RGCs (Weitz et al., 2014), but also auditory and motor nerves
(Gorman and Mortimer, 1983; Prado-Guitierrez et al., 2006). This arises from the fact that voltage-
gated sodium channels require more time for depolarization events before reversing the polarity of
stimulation, thereby affecting the stimulus threshold and possibly leading to the delay in eliciting
action potentials. Therefore, the addition of IPGs decreases the spike latency observed in A2 cells,
leading to a greater rate of changes in firing rate with an increase in current amplitude relative to
that of D1 cells (Figure 4.5).
Figure4.10comparesthemembranepotentialoftheA2cellforsymmetriccathodic-firstbiphasic
pulses with and without the inclusion of IPG at 200 Hz. The current amplitude is set to 100 µA
and pulse width is 0.5 ms. Results indicate that the IPG helps the A2 cell elicit spike per each
stimulus pulse, thereby enhancing the firing rate of this cell type. We further investigated the effect
88
of the soma size difference between the two cells on their response sensitivity to the addition of
IPG. Both small and large cells response showed similar sensitivity to the addition of IPG and
no obvious correlations with soma diameter changes were found (see Figure 4.6). It is also worth
noting that consistent with the experimental data from the literature (Hadjinicolaou et al., 2015),
we demonstrated that small cells are more responsive to high stimulus frequency relative to large
cells.
4.4.5 Implications for Clinical Applications
Various electrical stimulation strategies have been proposed to improve the effectiveness of cur-
rent epiretinal prosthetic systems. However, there are challenges associated with many systems: i)
they are not currently implementable clinically; ii) more likely can damage the tissue using asym-
metric waveforms, symmetric long pulse durations, and small electrode sizes. In this work, we used
the same stimulating electrode in current epiretinal implants and limited our study to the clinically
applicable range of electrical stimulation parameters. We proposed electrical stimulation strategies
that not only enhance focalized activation of RGCs, but also effectively increase the chance for
selective activation of RGCs subtypes.
The differential response of RGCs discussed in this work can be linked to different percepts such
as color and contrast. Recent clinical testing has revealed that Argus II subjects perceived some
variations in color perceptions particularly at high stimulation frequency. Our most recent compu-
tational results were well correlated with this clinical data and verified with the in-vitro experiments
on RGCs. The simulation results of this paper further show the potential of maximizing the differ-
ential response of RGCs using the currently developed epiretinal prosthetic system. Modeling two
subtypes of RGCs allowed us to examine both morphological and physiological factors affecting the
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response of RGCs to high frequency electrical stimulation. Future steps will incorporate a large
population of various RGCs subtypes as well as modeling primate retinal cells. We will investigate
the impact of stimulation frequency and stimulus waveforms on synthetic retinal network response
and axonal activation of RGCs. This positive correlation between the computationally-determined
difference in firing rate of RGCs and the experimental results with patients is augmenting our fun-
damental knowledge of color perception, as well as enabling the opportunity to encode colors in the
future generation of retinal prosthetics.
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Chapter 5
On the Design of Stimulus Waveforms
for Selective Stimulation of RGCs
Paknahad J, Humayun M, Lazzi G. On the Design of Stimulus Waveforms for Selective Stimu-
lation of RGCs. Frontiers in Neuroscience (Under review, 2021).
Abstract
Epiretinal prostheses have been developed to restored partial sight to the blind by bypassing the
damaged retinal neurons and electrically stimulating the surviving retinal ganglion cells (RGCs).
Stimulation strategies for selective activation of RGCs that carry particular types of visual infor-
mation to the brain can augment the outcome of these devices. Using our 3D Admittance Method
(AM)-NEURON computational platform, we previously showed that small bistratified RGCs with
a contribution to blue/yellow color vision can be selectively activated at high frequency when ap-
plying a symmetric cathodic-first biphasic stimulus pulse. The computational findings were verified
with in vitro experiments and correlated with clinical data from epiretinal implant subjects. Here,
we applied this modeling framework to expand our exploration and study the frequency response
(up to 200 Hz) of the previously developed RGCs models, A2-monostratified and D1-bistratified,
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to a range of asymmetric charge-balanced stimulus pulses. We further analyzed the response of
RGCs as a function of modulations in charge amplitude over a range of asymmetric and symmetric
biphasic pulses at 200 Hz. Our results indicate that D1 cells are more responsive to high stimu-
lus frequency using symmetric, asymmetric short cathodic-first, and asymmetric long anodic-first
biphasic pulses. However, the differential response of cells and therefore the chance for RGCs se-
lectivity were mostly diminished using asymmetric short anodic-first stimulus pulses. Interestingly,
asymmetric long cathodic-first stimulus pulses alter the excitability of RGCs such that A2 cells can
better follow high rates of firing at high frequency compared to D1 cells. Our findings suggest the
intriguing potential for designing a “amplitude-waveform-frequency” modulations stimulation strat-
egy to independently target RGCs. While the differential biophysical properties slightly changed the
response of the cells, we found the soma size to be a predominant factor leading to this reciprocal
differential response of RGCs at high frequency across stimulus pulses. The differential sensitivity
of stimulus strength-dependent response of RGCs at high frequency to various stimulus waveforms
offers a great opportunity for selective activation of individual RGCs. This enables the possibility
of encoding additional visual information such as color in future retinal prosthetics systems.
5.1 Introduction
In this work, we examine the impact of asymmetry in charge-balanced stimulus waveforms on
the chance for selective excitation of RGCs. We investigated the frequency response of RGCs
(up to 200 Hz) using a range of asymmetric stimulus pulses for a given charge amplitude. We
further compared the charge amplitude-dependent response of RGCs from asymmetric cathodic
and anodic-first stimulus pulses of varying pulse duration ratios with symmetric charge-balanced
biphasic pulses. We found that modulations in the level of asymmetry and the polarity of stimulus
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pulses can alter the sensitivity of RGCs to electrical stimulation at high frequency. The differential
impact of the waveform asymmetry on the sensitivity of RGCs to high frequency indicates the
enhanced chance for selective activation of functionally different RGCs. While many asymmetric
parameters led to better responsiveness of D1 cells to high stimulation frequency, interestingly A2
cells experienced a better rate of firing compared to D1 cells for specific stimulus parameters. This
reciprocal differential excitability of RGCs allowed us to design stimulus parameters not only for
preferential activation of a selected RGC but also for independent excitation of individual RGCs.
We also examined the mechanisms underlying the enhanced chance for differential excitability and
therefore selective activation of RGCs at high frequency stimuli. We were able to determine the
main morphometric contributor to the differential sensitivity of RGCs to various stimulus pulses at
high frequency.
5.2 Modeling Approach and Stimulus Parameters
The multi-scale computational modeling approach allows us to compute the electric potential
distribution inside the large-scale bulk tissue model, as well as the response of neurons to electrical
stimulation of various parameters. The following sections briefly describe our stimulation strat-
egy including the multi-compartmental models of neurons, construction of the retina tissue and
electronic components, and stimulation parameters. The computational modeling technique and
electrical stimulation set up have been extensively discussed in the previous chapters.
The typical stimulus waveform of Argus II prosthetic device is a symmetric cathodic-first charge-
balanced biphasic pulses with a duration of 0.45 ms and no interphase gap at 20 Hz (Ahuja et al.,
2008). Here, we further extended our previous work to incorporate the impact of asymmetric
charge-balanced stimulation waveforms on the responsiveness of RGCs over a range of stimulation
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Frequency response of RGCs A2 vs. D1
F = 6 Hz to 200 Hz
Cathodic-first Anodic-first
Cathodic pulse variation Anodic pulse variation Cathodic pulse variation
C = 1 ms A = 0.5 ms
C = 2 ms A = 0.5 ms
A = 0.5 ms
A = 0.5 ms
C = 3 ms
C = 4 ms
Asymmetric charge-balanced pulse
C = 0.5 ms A = 1 ms
C = 0.5 ms A = 2 ms
A = 3 ms
A = 4 ms
C = 0.5 ms
C = 0.5 ms
A = 0.5 ms C = 1 ms
A = 0.5 ms C = 2 ms
C = 3 ms
C = 4 ms
A = 0.5 ms
A = 0.5 ms
A = 1 ms C = 0.5 ms
A = 2 ms C = 0.5 ms
C = 0.5 ms
C = 0.5 ms
A = 3 ms
A = 4 ms
Anodic pulse variation
Charge modulation at high frequency A2 vs. D1
F = 200 Hz
CF-CPWM CF-APWM AF-APWM AF-CPWM
Figure 5.1: An overview of the analysis performed in this study. The frequency response of the
two RGCs subtypes (A2 and D1) was analyzed up to 200 Hz stimulation frequency for a range of
asymmetric charge-balanced biphasic pulses. The rate of changes in the firing rate of the cells with
an increase in charge amplitude was investigated. The difference in the level of monotonic spiking
activities across stimulus pulses at high frequency offers an intriguing opportunity for selective
activation of A2 cells or D1 cells.
frequencies. Figure 5.1 describes an overview of the analysis conducted in this paper. We applied
both asymmetric cathodic-first and anodic-first biphasic pulses for different anodic versus cathodic
pulse duration ratios (PDRs). The stimulation parameters can be divided into four categories: i)
cathodic-first with cathodic pulse width modulations (CF-CPWM); ii) cathodic-first with anodic
pulse width modulations (CF-APWM); iii) anodic-first with cathodic pulse width modulations (AF-
CPWM); iv) anodic-first with anodic pulse modulations (AF-APWM). The cathodic and anodic
pulse widths are shown by the letters “C” and “A” in the figures, respectively. The pulse width of
either cathodic or anodic phase was fixed to 0.5 ms and the width of the other opposite polarity
94
stimulus pulse was modulated (1 ms, 2 ms, 3 ms, and 4 ms) to acquire charge balance and different
PDRsasillustratedinFigure5.1. Thestimulusstrengthisdefinedintermsofchargeamplitude(nC)
instead of current amplitude (uA) due to the varying stimulus current in each phase of asymmetric
waveforms. We did not incorporate the impact of total stimulus pulse width modulations on the
frequency response of RGCs in the present study as the charge threshold varies across pulse widths
(discussed in chapter 2).
Therefore, we only centered our focus on the level of asymmetry in each waveform and its
influence on the responsiveness of RGCs over a range of frequencies. The firing rate of RGCs was
computed for stimulation frequencies ranging from 6 Hz to 200 Hz for a given charge amplitude of Q
=50nC.Weinvestigatedtheresponseofcellsasafunctionofchargeamplitudemodulationsranging
from 10 nC to 70 nC at 200 Hz unless otherwise noted. The charge stimulation thresholds of RGCs
at high frequency in response to asymmetric stimulus parameters were computed and compared
with symmetric cathodic and anodic-first biphasic pulses as well. The threshold is defined as the
minimum charge that leads to 50 % spikes in total stimulus pulses. The stimulus waveforms in this
study are not only charge-balanced but also the delivered charge across stimulus pulses is equal,
which reduces the risk of tissue damage.
5.3 Results
The frequency response, temporal response, and charge-amplitude-dependent response of A2
and D1 RGCs to both symmetric and asymmetric stimulation pulses were investigated. We further
identified the mechanisms underlying the differential RGCs excitability at high frequency across a
range of stimulus waveforms. The differential firing rate of RGCs and charge amplitude-dependent
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Asymmetric charge-balanced pulse
Cathodic-first Anodic-first
Anodic pulse variation Cathodic pulse variation Anodic pulse variation Cathodic pulse variation
0
40
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120
160
200
240
0 50 100 150 200
Spiking Frequency (Hz)
Stimulus Frequency (Hz)
C = 2 ms, A = 0.5 ms
D1-bistratified
A2-monostratified
0
40
80
120
160
200
240
0 50 100 150 200
Spiking Frequency (Hz)
Stimulus Frequency (Hz)
C = 4 ms, A = 0.5 ms
D1-bistratified
A2-monostratified
0
40
80
120
160
200
240
0 50 100 150 200
Spiking Frequency (Hz)
Stimulus Frequency (Hz)
C = 0.5 ms, A = 2 ms
D1-bistratified
A2-monostratified
0
40
80
120
160
200
240
0 50 100 150 200
Spiking Frequency (Hz)
Stimulus Frequency (Hz)
C = 0.5 ms, A = 4 ms
D1-bistratified
A2-monostratified
0
40
80
120
160
200
240
0 50 100 150 200
Spiking Frequency (Hz)
Stimulus Frequency (Hz)
A = 0.5 ms , C = 2 ms
D1-bistratified
A2-monostratified
0
40
80
120
160
200
240
0 50 100 150 200
Spiking Frequency (Hz)
Stimulus Frequency (Hz)
A = 0.5 ms , C = 4 ms
D1-bistratified
A2-monostratified
0
40
80
120
160
200
240
0 50 100 150 200
Spiking Frequency (Hz)
Stimulus Frequency (Hz)
A = 2 ms , C = 0.5 ms
D1-bistratified
A2-monostratified
0
40
80
120
160
200
240
0 50 100 150 200
Spiking Frequency (Hz)
Stimulus Frequency (Hz)
A = 4 ms , C = 0.2 ms
D1-bistratified
A2-monostratified
Injected charge = 50 nC
CF-CPWM
CF-APWM AF-APWM AF-CPWM
Figure 5.2: The response of RGCs a function of alteration in stimulation frequency for the four
types of asymmetric pulses. The A2 and D1 cells show a different level of excitability for given
asymmetric waveforms at high frequency. While D2 cells are more responsive compared to A2 cells
using the CF-APWM and AF-APWM stimulations, the CF-CPWM waveforms lead to higher firing
rates of A2 cells relative to D1 cells.
response analysis at high frequency provide opportunities for designing waveforms that ultimately
lead to an enhanced chance for selective activation of RGCs.
5.3.1 Frequency Response of RGCs
Figure 5.2 shows the firing rates of the A2 and D1 cells using the four classes of asymmetric
waveforms for a short pulse width of 0.5 ms and the opposite polarity longer pulse durations of 2 ms
and 4 ms up to 200 Hz frequency stimuli. The results indicate the differential sensitivity of RGCs
frequency response to the varying asymmetry of electrical stimulation waveforms. The CF-APWM
and AF-APWM stimulus pulses lead to the greater responsiveness of D1 cells compared to A2 cells
at high frequency. Both cells can maintain their monotonic firing response using the AF-CPWM
stimulation, indicating the relatively lower charge threshold of this stimulus pulse and similar sensi-
tivity of both RGCs to the AF-CPWM stimulation. Interestingly, the A2 cell experiences a higher
96
Asymmetric charge-balanced pulse
Cathodic-first
Anodic pulse variation Cathodic pulse variation
0
50
100
150
200
250
20 30 40 50 60 70 80
Firing rate (Hz)
Charge (nC)
C =1 ms, A = 0.5 ms
C = 2 ms, A = 0.5 ms
C = 3 ms, A = 0.5 ms
C = 4 ms, A = 0.5 ms
0
50
100
150
200
250
20 30 40 50 60 70 80
Firing rate (Hz)
Charge (nC)
C = 1 ms, A = 0.5 ms
C = 2 ms, A = 0.5 ms
C = 3 ms, A = 0.5 ms
C = 4 ms, A = 0.5 ms
A2-monostratified
D1-bistratified
0
50
100
150
200
250
20 30 40 50 60 70 80
Firing rate (Hz)
Charge (nC)
C = 0.5 ms, A = 1 ms
C = 0.5 ms, A = 2 ms
C = 0.5 ms, A = 3 ms
C = 0.5 ms, A = 4 ms
A2-monostratified
0
50
100
150
200
250
20 30 40 50 60 70 80
Firing rate (Hz)
Charge (nC)
C = 0.5 ms, A = 1 ms
C = 0.5 ms, A = 2 ms
C = 0.5 ms, A = 3 ms
C = 0.5 ms, A = 4 ms
D1-bistratified
0
50
100
150
200
250
10 20 30 40 50 60 70
Firing rate (Hz)
Charge (nC)
C = 1 ms, A = 0.5 ms
C = 2 ms, A = 0.5 ms
C = 3 ms, A = 0.5 ms
C = 4 ms, A = 0.5 ms
0
50
100
150
200
250
10 20 30 40 50 60 70
Firing rate (Hz)
Charge (nC)
C = 1 ms, A = 0.5 ms
C = 2 ms, A = 0.5 ms
C = 3 ms, A = 0.5 ms
C = 4 ms, A = 0.5 ms
0
50
100
150
200
250
10 20 30 40 50 60 70
Firing rate (Hz)
Charge (nC)
C = 0.5 ms, A = 1 ms
C = 0.5 ms, A = 2 ms
C = 0.5 ms, A = 3 ms
C = 0.5 ms, A = 4 ms
A2-monostratified
D1-bistratified
0
50
100
150
200
250
10 20 30 40 50 60 70
Firing rate (Hz)
Charge (nC)
C = 0.5 ms, A = 1 ms
C = 0.5 ms, A = 2 ms
C = 0.5 ms, A = 3 ms
C = 0.5 ms, A = 4 ms
A2-monostratified
D1-bistratified
Figure5.3: Chargeamplitude-dependentresponseofRGCsusingasymmetriccathodic-firstpulses
with cathodic and anodic pulse width modulations (CF-CPWM & CF-APWM). The response
of D1 cells to the cathodic-first pulse width of 2 ms and following anodic pulse of 0.5 ms has
been significantly decreased, offering a chance for preferential activation of A2 cells over D1 cells.
Data indicate that D1 cells are able to better maintain the spikes while increasing the charge
amplitude relative to A2 cells using the CF-APWM stimulation, suggesting the possibility for
selective stimulation of D1 cells.
rate of firing relative to the D1 cell with increasing the stimulation frequency using the CF-CPWM
stimulation. Notably, the activation rate of the D1 cell is significantly suppressed using the long
cathodic-first pulse duration of 2 ms followed by a pulse width of 0.5 ms (C = 2 ms & A = 0.5
ms). The D1 response saturates to around 70 Hz rate of spikes for stimulation frequencies above
20 Hz. In the next sections, we will further investigate factors leading to this remarkable response
behavior of the D1 cell, offering the potential for selective activation of cells.
5.3.2 Charge-dependent Response of RGCs at High Frequency
Based upon the difference in the response of RGCs at high frequency for a given charge ampli-
tude, we further analyzed the rate of changes in RGCs spikes as modulations in charge amplitude
at 200 Hz (Figures 5.3 and 5.4). Figure 5.3 compares the response of the two cells for cathodic-first
97
Asymmetric charge-balanced pulse
Anodic-first
Cathodic pulse variation Anodic pulse variation
0
50
100
150
200
250
20 30 40 50 60 70 80
Firing rate (Hz)
Charge (nC)
A = 0.5 ms, C = 1 ms
A = 0.5 ms, C = 2 ms
A = 0.5 ms, C = 3 ms
A = 0.5 ms, C = 4 ms
0
50
100
150
200
250
20 30 40 50 60 70 80
Firing rate (Hz)
Charge (nC)
A = 0.5 ms, C = 1 ms
A = 0.5 ms, C = 2 ms
A = 0.5 ms, C = 3 ms
A = 0.5 ms, C = 4 ms
A2-monostratified
D1-bistratified
0
50
100
150
200
250
20 30 40 50 60 70 80
Firing rate (Hz)
Charge (nC)
A = 1 ms, C = 0.5 ms
A = 2 ms, C = 0.5 ms
A = 3 ms, C = 0.5 ms
A = 4 ms, C = 0.5 ms
0
50
100
150
200
250
20 30 40 50 60 70 80
Firing rate (Hz)
Charge (nC)
A = 1 ms, C = 0.5 ms
A = 2 ms, C = 0.5 ms
A = 3 ms, C = 0.5 ms
A = 4 ms, C = 0.5 ms
A2-monostratified
D1-bistratified
0
50
100
150
200
250
10 20 30 40 50 60 70
Firing rate (Hz)
Charge (nC)
A = 1 ms, C = 0.5 ms
A = 2 ms, C = 0.5 ms
A = 3 ms, C = 0.5 ms
A = 4 ms, C = 0.5 ms
0
50
100
150
200
250
10 20 30 40 50 60 70
Firing rate (Hz)
Charge (nC)
A = 1 ms, C = 0.5 ms
A = 2 ms, C = 0.5 ms
A = 3 ms, C = 0.5 ms
A = 4 ms, C = 0.5 ms
0
50
100
150
200
250
10 20 30 40 50 60 70
Firing rate (Hz)
Charge (nC)
A = 0.5 ms, C = 1 ms
A = 0.5 ms, C = 2 ms
A = 0.5 ms, C = 3 ms
A = 0.5 ms, C = 4 ms
0
50
100
150
200
250
10 20 30 40 50 60 70
Firing rate (Hz)
Charge (nC)
A = 0.5 ms, C = 1 ms
A = 0.5 ms, C = 2 ms
A = 0.5 ms, C = 3 ms
A = 0.5 ms, C = 4 ms
A2-monostratified
D1-bistratified
A2-monostratified
D1-bistratified
Figure5.4: ResponseofRGCsasafunctionofvaryingchargeamplitudeusingasymmetricanodic-
first pulses with cathodic and anodic pulse width modulations (AF-CPWM and AF-APWM). The
difference in the elicited spikes of the two cells is negligible using the AF-CPWM stimulation,
offering less chance for selectively targeting RGCs. The D1 cell is more responsive at high rates of
firing compared to the A2 cell with the AF-APWM stimulation.
asymmetric pulses of varying anodic and cathodic pulse durations as a function of charge ampli-
tude. The greater sensitivity of the cells to the CF-CPWM stimulation compared to the CF-APWM
stimulation can be recognized from the figure. The D1 cell response is modulated the most using
the CF-CPWM stimulation, with the lowest excitability of the D1 cell using the cathodic pulse of 2
ms wide followed by the anodic pulse width of 0.5 ms. With the CF-CPWM stimulation, the rate of
firing of A2 cells is relatively higher than that of D1 cells, indicating the great potential for selective
excitation of A2 cells. Further, the CF-APWM has the effect of increasing the responsiveness of the
D1 cell at high firing rates with negligible sensitivity to anodic pulse width modulations, suggesting
the enhanced likelihood for selective stimulation of D1 cells.
Figure 5.4 illustrates the activation rate of the two cells as alterations in charge amplitude using
the anodic-first waveforms of varying pulse duration ratios. Data suggest the similar sensitivity of
both A2 and D1 cells to the AF-CPWM stimulation, thereby indicating the decreased chance for
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0
50
100
150
10 20 30 40 50 60 70
Differential Firing Rate (Hz)
Charge amplitude (nC)
CF-CPWM
C = 0.5 ms, A = 0.5 ms
C = 1 ms, A = 0.5 ms
C = 2 ms, A = 0.5 ms
C = 3 ms, A = 0.5 ms
C = 4 ms, A = 0.5 ms
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0
50
100
150
10 20 30 40 50 60 70
Differential Firing Rate (Hz)
Charge amplitude (nC)
CF-APWM
C = 0.5 ms, A = 0.5 ms
C = 0.5 ms, A = 1 ms
C = 0.5 ms, A = 2 ms
C = 0.5 ms, A = 3 ms
C = 0.5 ms, A = 4 ms
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0
50
100
150
10 20 30 40 50 60 70
Differential Firing Rate (Hz)
Charge amplitude (nC)
AF-APWM
A = 0.5 ms, C = 0.5 ms
A = 1 ms, C = 0.5 ms
A = 2 ms, C = 0.5 ms
A = 3 ms, C = 0.5 ms
A = 4 ms, C = 0.5 ms
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50
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10 20 30 40 50 60 70
Differential Firing Rate (Hz)
Charge amplitude (nC)
AF-CPWM
A = 0.5 ms, C = 0.5 ms
A = 0.5 ms, C = 1 ms
A = 0.5 ms, C = 2 ms
A = 0.5 ms, C = 3 ms
A = 0.5 ms, C = 4 ms
Figure 5.5: Differential firing rate (DFR) of A2 and D1 cells. The difference in the firing rate
between the D1 cell and the A2 cell at 200 Hz stimulation frequency as alterations in charge
amplitude (10 nC to 70 nC). The DFR is positive when the D1 cell is more responsive at high
frequency stimuli, and when the DFR is negative the A2 cell can better maintain spikes compared
to the D1 cell.
selective activation of RGCs. The D1 cell relatively better follows high rates of elicited spikes com-
pared to the A2 cell using the AF-APWM stimulation. All stimulus pulses experience a saturation
window usually at a 100 Hz firing rate where the elicited spikes remain unchanged.
To better quantify the level of responsiveness of RGCs at the high frequency of varying stimulus
pulses we compared the differential firing rate (DFR) between D1 and A2 cells as a function of
charge amplitude as illustrated in Figure 5.5. The symmetric charge-balanced cathodic and anodic-
first biphasic stimulus pulses of 0.5 ms duration are also incorporated into the figure for comparison.
The DFR enables us to better examine the effect of stimulus waveforms (symmetry, asymmetry, and
polarity) on the differential response of RGCs at high frequency and therefore on RGCs selectivity.
As shown in Figure 5.5A, the D1 cell is more responsive compared to the A2 cell over a range of
charge amplitude using symmetric cathodic-first pulses (DFR > 0). Interestingly, increasing the
cathodic-first pulse duration augments the excitability of the A2 cell compared to the D1 cell (DFR
99
42
42
43
45
37
38
41
42
44
36
36
37
40
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49
34
33
34
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35
36
39
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37
36
37
38
0 10 20 30 40 50 60
C = 4 MS A = 0.5 MS
C = 3 MS A = 0.5 MS
C = 2 MS A = 0.5 MS
C = 1 MS A = 0.5 MS
C = 0.5 MS A = 4 MS
C = 0.5 MS A = 3 MS
C = 0.5 MS A = 2 MS
C = 0.5 MS A = 1 MS
C = 0.5 MS A = 0.5 MS
A = 4 MS C = 0.5 MS
A = 3 MS C = 0.5 MS
A = 2 MS C = 0.5 MS
A = 1 MS C = 0.5 MS
A = 0.5 MS C = 4 MS
A = 0.5 MS C = 3 MS
A = 0.5 MS C = 2 MS
A = 0.5 MS C = 1 MS
A = 0.5 MS C = 0.5 MS
Charge threshold (nC)
Stimulus waveforms
D1-bistratified
A2-monostratified
Selective activation of
D1 cells
Selective activation of
A2 cells
We can design electrical stimulation
waveform to independently
activate RGCs subtypes.
0.5 ms
2 ms 0.5 ms
The lowest charge
threshold of D1 cells
The lowest charge
threshold of A2 cells
Stimulus waveforms
Figure 5.6: . Charge stimulation thresholds of A2 and D1 RGCs. The charge threshold is
determined as the minimum charge amplitude required to achieve 50 % spike probability. The
sensitivity of RGCs response to electrical stimulation is different across various stimulus pulses.
While the D1 cells threshold is the lowest with the CF-APWM stimulation, the long anodic-first
asymmetric pulses lead to the lowest threshold of A2 cells.
< 0), offering the potential for preferential excitation of A2 cells over D1 cells (Figure 5.5A). Figures
5.5B and 5D indicate that selective activation of D1 cells may also be achieved using the CF-APWM
and AF-APWM stimulations with the greater responsiveness of these cells compared to A2 cells
(DFR > 0). The more randomly distributed the DFR polarity and on average lower DFRs of the
AF-CPWM stimulation over a range of charge amplitudes indicate the less likelihood for preferential
activation of RGCs (Figure 5.5C).
We further compared the required charge amplitude to obtain 100 Hz spike rate in both A2 and
D1 cells at 200 Hz stimulation frequency as shown in Figure 5.8. The lowest charge stimulation
threshold of D1 cells (33 nC) is achieved with the asymmetric short cathodic-first and long following
anodic pulses (C = 0.5 ms & A = 3 ms). However, the asymmetric long anodic-first pulse of 4
ms and immediate short cathodic pulse of 0.5 ms (A = 4 ms & C = 0.5 ms) leads to the least
charge threshold of the A2 cell (36 nC). Our computational findings suggest that the stimulation
threshold of RGCs may vary across subtypes of cells depending on stimulus waveforms and the level
100
D1-RGC
Asymmetric Biphasic Stimulation
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Vm (mV)
Time (ms)
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Time (ms)
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Istim_C_2ms_A_0.5ms
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Vm (mV)
Time (ms)
Symmetric Biphasic Stimulation
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Time (ms)
Vm_C_0.5ms_A_0.5ms
Istim_C_0.5ms_A_0.5ms
2 ms 0.5 ms
0.5 ms
Membrane Voltage (mV)
Stimulus Current (µA)
Membrane Voltage (mV)
Stimulus Current (µA)
Figure 5.7: The temporal response of the D1 RGC at 50 nC charge amplitude and 200 Hz
stimulation frequency. The stimulation duration is applied and set to 250 ms after 100 ms delay.
The response of the D1 cell was compared between the asymmetric long cathodic-first (C = 2 ms)
and short anodic-second (A = 0.5) pulse and the symmetrical cathodic-first stimulus pulse of 0.5 ms
pulse width (C = 0.5 ms & A = 0.5 ms). The elicited numbers of spikes were diminished using the
asymmetric stimulus pulse. The bottom figures show the superposition of the two stimulus pulses
and the associated membrane potentials of the D1 cell for the first 50 ms duration of stimulation.
of asymmetry. Figure 5.6 clearly shows stimulus pulses leading to a lower charge threshold of D1
cells compared to A2 cells and vise versa. The charge threshold difference between the D1 and A2
RGCs is maximized using the symmetric charge-balanced cathodic-first biphasic of 0.5 ms stimulus
duration, again demonstrating the enhanced chance for selective stimulation of D1 cells. On the
other hand, using the cathodic-first stimulation pulse duration of 2 ms followed immediately by an
anodic pulse width of 0.5 ms leads to the greatest charge threshold difference between the A2 and
D1 cells. Therefore, this asymmetric stimulus waveform augments the opportunity for preferential
activation of A2 cells over D1 cells.
101
A2-RGC
Asymmetric Biphasic Stimulation Symmetric Biphasic Stimulation
2 ms 0.5 ms
0.5 ms
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Vm_C_0.5ms_A_0.5ms
Istim_C_0.5ms_A_0.5ms
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Time (ms)
Vm_C_2ms_A_0.5ms
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Membrane Voltage (mV)
Stimulus Current (µA)
Membrane Voltage (mV)
Stimulus Current (µA)
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Voltage (mV)
Time (ms)
Figure 5.8: The time course response of the A2 RGC at 50 nC charge amplitude comparing
the asymmetrical long cathodic-first (C = 2 ms) and short anodic-second (A = 0.5) pulse and the
symmetrical cathodic-first stimulus pulse of 0.5 ms pulse width (C = 0.5 ms & A = 0.5 ms).
Data indicate the similar sensitivity of the A2 cell to both stimulus pulses at 200 Hz stimulation
frequency.
5.3.3 Time Course Response of RGCs at High Frequency
Given the explored stimulus waveforms for selective activation of one type over another subtype
of RGCs, we compared the temporal response of the two cells at 200 Hz. Figure 5.8 compares
the time course of the D1 cell response to a symmetric cathodic-first biphasic pulse (right panel)
and an asymmetrical cathodic-first (C = 2 ms) and anodic-second (A = 0.5 ms) stimulus pulse
(left panel) at a given charge amplitude of 50 nC. There is a significant difference in the elicited
numbers of spikes between the two stimulus pulses. The peak hyperpolarizing membrane potential
generatedfromtheasymmetriclongcathodic-firstpulseisrelativelyhighcomparedtothesymmetric
cathodic-first stimulus pulse. This difference may play a role in the suppressed firings of D1 cells
using the asymmetric pulse. While the depolarization occurs after the termination of the anodic
stimulation using the asymmetric pulse, the cathodic phase of the symmetrical biphasic pulse leads
to the elicited spikes as shown in the left and right panels of Figure 5.8. The temporal response of
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Membrane Voltage (mV)
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Figure 5.9: The temporal response profiles of the A2 and D1 cells using the two stimulus wave-
forms represented in the figure. Plots indicate the difference in the elicited spike width of the two
cells. The stimulus waveforms lead to modulations in the onset of action potentials as well as
changes in spiking rates of the two cells.
the A2 cell to the two stimulus waveforms is shown in Figure 5.9. The spiking rate of the cell is
slightly greater using the asymmetric pulse compared to the symmetric waveform. The difference
in the temporal response of RGCs to high-frequency trains of stimulus pulses further indicates the
enhanced activation selectivity between A2 and D1 cells.
5.3.4 Mechanisms Underlying RGCs Selectivity at High Frequency
Our computational findings indicate the contribution of the suppressed response of D1 cells
using the asymmetric long cathodic-first pulse to the increased chance for selective activation of A2
cells over D1 cells. To better capture the mechanisms underlying the notable differential response
of the two cells to both asymmetrical long cathodic-first and symmetrical biphasic pulses (C = 2 ms
& A = 0.5 ms, C = 0.5 ms & A = 0.5 ms), we directly compared the temporal response profiles
of the cells for the two waveforms as illustrated in Figure 5.9. Comparing the membrane potentials
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Charge (nC)
gk = 0.111 S/cm2
gk = 0.211 S/cm2
gk = 0.311 S/cm2
gk = 0.411 S/cm2
D1 RGCs
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gk = 0.12 S/cm2
gk = 0.24 S/cm2
gk = 0.36 S/cm2
gk = 0.48 S/cm2
A2 RGCs
Figure 5.10: The sensitivity of the RGCs response to alterations in the density of potassium
channels as a function of charge amplitude using the asymmetric long cathodic-first charge-balanced
stimulation.
of the two cells indicates a significant difference in the firing shape of the two cells, particularly the
width of the elicited spikes and peak membrane potential. The longer plateau phase and more rapid
repolarization response of the A2 cell compared to that of the D1 cell can be detected from Figure
5.9. The efflux of the potassium ion current and thereby the density of voltage-gated potassium
(K) ionic channel contributes to the differential elicited spike width of the two cells.
Therefore, we investigated the sensitivity of the RGCs robustness response to modulations in the
potassium channel density as a function of charge amplitude using the asymmetric long cathodic-
first charge-balanced stimulation (Figure 5.10A). Results show that increases in the K channel
density would shift the strength-dependent response of both cells to the right and therefore increase
the overall charge threshold of RGCs. However, the response of the D1 cell is not modulated
with changes in the maximum K conductance value at high firing rates using the asymmetric long
cathodic-first waveform compared to the A2 cell (Figure 5.10B). This indicates that the lower K
channel density of the A2 cell relative to the D1 cell may contribute to better responsiveness of the
A2 cell at high rates of spikes with the asymmetric long cathodic-first pulse. To examine the role
of biophysical differences between the two cells in RGCs selectivity, we exchanged the biophysical
properties of the two cells and analysed the number of elicited spikes as modulations in charge
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2 ms 0.5 ms
0.5 ms
Exchanging the biophysics of the two cells
Original biophysical properties
Figure 5.11: Sensitivity of RGCs selectivity to modulations in biophysical features. (A) The
firing rate is plotted vs. charge amplitude for the two stimulus pulses for the original biophysics
of the cells. (B) The ionic channel expressions and densities of the two cells are exchanged. The
relationship between the spiking rate and the charge amplitude modulations. Data show that the
biophysical differences may not be significant enough to change the relative responsiveness of the
A2 and D1 cells.
amplitude. Figure 5.11 compares the charge-dependent response of the cells to both symmetric
and asymmetric long cathodic-first pulses using the original and exchanged biophysics. While the
response of the A2 cell to the asymmetric cathodic-first pulse is relatively reduced at higher rates
of firing using the D1 biophysics, the A2 cell remains more excitable compared to the D1 cell
incorporating the A2 biophysics. The A2 cell response with the D1 biophysics appears to have a
higher rate of changes in the number of spikes at lower charge amplitude compared to the original
A2 cell response (comparing the red curves in Figure 5.11A and B). This suggests that the impact
of ionic channel properties on the differential response of cells is not strong enough to modulate the
potential for selective activation of cells. Therefore, morphological differences across RGCs may be
the prominent contributors to differential sensitivity of cells to symmetric and asymmetric stimulus
pulses. The morphometric parameters such as dendritic structure, cell body size, and the level of
stratification of cells in the inner plexiform layer (IPL) can potentially play roles in the differential
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Selective stimulation of small cells
Selective stimulation of large cells
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2 ms 0.5 ms
RGCs model: based on Fohlmeister et al., 2010
Figure 5.12: Influence of soma size on RGCs selectivity. (A) The sensitivity of small and large
cells to alterations in charge amplitude for ionic channel properties presented in the present study
and in Paknahad et al (Paknahad et al., 2020). (B) small and large cells response as a function
of charge amplitude. Our computational results again demonstrated the significant contribution
of soma diameter to selective stimulation of RGCs using the two stimulus pulses. The intrinsic
biophysical features have minor impact on altering the potential for RGCs selectivity.
response of RGCs. It is difficult to isolate the impact of each variable on RGCs responsiveness
at high frequency. Therefore, to separately examine the influence of the soma diameter difference
of the cells on RGCs selectivity we performed simulations in the absence of dendrites for given
axonal properties. Figure 5.12 compares the relationship between the charge amplitude and spiking
frequency for the two soma diameters, 12 um and 20 um, and the two proposed symmetric and
asymmetric stimulus waveforms at given biophysical properties, which is the D1 cell for this case
study. Intriguingly, while the smaller soma size cell (blue curves) is more responsive at 200 Hz
compared to the large 20 um soma diameter cell (red curves) using the symmetric cathodic-first
charge-balanced biphasic of 0.5 ms pulse width, the number of elicited spikes and therefore the
excitability of the large cell is higher relative to the small cell using the asymmetric long cathodic-
first charge-balanced stimulus pulse (C = 2 ms & A = 0.5 ms) as shown in Figure 5.12A. To
further verify the strong influence of soma size difference on RGCs selectivity, we modeled the
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RGC membrane dynamics based on the commonly utilized RGCs model as previously developed
by Fohlmeister et al. (Fohlmeister et al., 2010). A similar analysis was carried out using this RGC
model as illustrated in Figure 5.12B. Results demonstrate that the chance for selective stimulation
of large cells over small cells using the asymmetric long cathodic-first pulse, or small cells over large
cells using the symmetric cathodic-first pulse remains true regardless of modulating the membrane
channel properties. Therefore, our computational findings indicate the significant impact of soma
diameter on selective activation of one particular cell type over another subtype or vice versa at
high stimulation frequency.
5.4 Discussion
The goal of this study was to examine the influence of asymmetric charge-balanced biphasic
pulses on the responsiveness of RGCs over a range of frequencies and identify stimulus pulses lead-
ing to the augmented chance for selective activation of RGCs. Using the developed compartmental
models of the RGCs subtypes, D1-bistratified and A2-monostratified, our computational results
show that differential response of RGCs varies across a wide range of tested asymmetric waveforms
at 200 Hz stimulation frequency. The charge amplitude-dependent response of the cells at high
frequency was altered with the level of asymmetry and stimulus polarity. Comparing the charge
threshold and charge modulated response of RGCs across a wide range of asymmetric waveforms
with those generated from the symmetric charge-balanced biphasic pulses indicated that selective
activation of D1 cells over A2 cells, or A2 cells over D1 cells can be achieved using the specified
stimulus pulses. Our multi-scale AM-NEURON computational platform allowed us to further cap-
ture the underlying mechanisms leading to the differential excitability of RGCs and the modulated
chance for RGCs selectivity among various stimulus waveforms.
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5.4.1 Verification of computational results with experimental data
We previously developed the models of the two A2 and D1 RGCs using NEURON and coupled
with the multi-scale AM numerical approach. The models were verified by comparing the response
of the cells to intracellular electrical stimulation with the experimental data. The response of the
cells to extracellular epiretinal electrical stimulation was further compared to the in-vitro exper-
iments using the patch-clamp recording technique as extensively discussed in previous chapters.
The D1 cell with an average small soma size can better manage to elicit spikes at high stimulation
frequencies relative to the A2 cell with a relatively large soma diameter. It is worth noting that the
computational platform reproduced the experimentally recorded signals from A2-RGCs in response
to asymmetric charge-balanced stimulus pulses, showing small cells are more responsive relative to
large cells at high frequency (Hadjinicolaou et al., 2015). Therefore, our verified computational
modeling platform has proven effective and allowed us to further investigate the activation of cells
as well as the mechanisms leading to differential activation of RGCs in a highly controlled fashion
that would be difficult to execute experimentally.
5.4.2 Selective activation of RGCs through frequency-amplitude modulations
Stimulation threshold variations across RGCs in response to low stimulation frequencies or single
stimulus pulses are very small and therefore it is quite challenging and less likely to selectively
activate morphologically and biophysically different RGCs subtypes (Fried et al., 2009; Werginz
et al., 2020). Attempts have been made towards increasing the potential for preferential activation
of different RGCs by modulating the range of stimulation frequency and amplitude (Cai et al., 2011,
2013; Twyford et al., 2014). The differential capability of RGCs to follow trains of high-frequency
stimulus pulses may enable selective stimulation of RGCs subtypes. Studies reported differ findings
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regarding the ability of RGCs to generate action potentials in response to high frequency stimuli.
Ahuja et al. showed that RGCs enable to maintain their rates of firings up to 500 Hz (Ahuja and
Behrend, 2013; Ahuja et al., 2008). In other studies, RGCs are found to be able to elicit spikes in
each stimulus pulse for frequencies higher than 200 Hz with direct activation using short stimulus
pulses (Fried et al., 2006; Sekirnjak et al., 2006). However, Jenson et al. found that the response
of RGCs is desensitized with increasing the stimulation frequency of the retinal network and cells
cannot follow firing rates greater than 40 Hz using a symmetric charge-balanced biphasic pulse of 1
ms duration per phase (Jensen and Rizzo, 2007). Although, the impact of increasing the strength of
stimulation on modulating the spiking frequency of RGCs was not investigated. Cai et al. tested 5
different types of RGCs and their responsiveness to 100-700 Hz stimulation frequencies (Cai et al.,
2011). They showed that while OFF-brisk transient (OFF-BT) could elicit more than 600 spikes
per second, the other types were reluctant to fire at high rates. The sensitivity of RGCs response to
a range of sinusoidal stimulations (both intracellular and extracellular) at frequencies ranging from
2 to 2048 Hz and varying current amplitude was examined by Kotsakidis et al., and they found that
the current amplitude and frequency at which the firing rate is maximized are different among ON,
OFF, and ON-OFF RGCs (Kotsakidis et al., 2018). Together, the heterogeneity of morphological
and biophysical features among RGCs subtypes, stimulus waveform, amplitude, and frequency can
significantly contribute to the monotonic and non-monotonic response of RGCs to high stimulus
frequencies.
High stimulation frequency of 2 kHz with low and high current amplitudes was shown to be
effective in achieving selective activation of OFF-BT and ON-OFF directionally selective RGCs
(Cai et al., 2013). Twyfold et al. showed that the differential temporal response of ON and OFF
RGCs with careful amplitude modulations at 2 kHz enables activation of cells in a selective manner
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(Twyford et al., 2014). Selective activation of ON and OFF RGCs offers the chance to better repli-
cate the natural physiological patterns of the normal retina in response to light stimuli. However,
preferential activation of a broader range of RGCs carrying particular visual information is crucial
for enhancing the efficacy of current retinal prosthetic systems. Therefore, selective stimulation of
two morphologically and biophysically different RGCs subtypes using computational modeling tools
would enable us to characterize factors leading to the differential response of RGCs, offering oppor-
tunities for preferential activation of a wider range of RGCs. In the present study, we showed that
differential responsiveness of A2 and D1 RGCs varies across a range of asymmetric stimulus pulses
for a given charge amplitude (Figure 5.2). While the CF-APWM and AF-APWM stimulations
resulted in the greater excitability of the D1 cell relative to the A2 cell, the CF-CPWM stimulation
suppressed the firing activity of the D1 cell and therefore led to more responsiveness of the A2 cell
at the high frequency of 200 Hz.
5.4.3 Stimulation threshold and axonal activation of RGCs
The high-density electrode array is required for enhancing the spatial resolution of epiretinal
prostheses. However, there have been several limiting factors such as high charge density associated
withsmallelectrodesizeandactivationofRGCsaxonbundles. Therefore,itisessentialtoreducethe
stimulation threshold of RGCs for high-density electrode design, enhancing the efficacy of electrical
stimulation. A recent clinical study has shown that increasing the stimulation frequency (up to 200
Hz) reduces the perceptual threshold of subjects with Argus II retinal implants. Horsager et al.
also found that the phosphene threshold was decreased as the stimulation frequency was increased
(Horsager et al., 2009). In congruent with the experimental data, we previously demonstrated that
highstimulationfrequenciesaugmentthefiringrateofRGCsandthereforealowercurrentamplitude
is required at high frequency to accomplish the same firing rate at low stimulation frequencies.
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Together, high stimulation frequency may provide an opportunity to reduce charge threshold and
stimulating electrode diameter in retinal prostheses, neglecting the impact of stimulation frequency
on tissue damage. Gonzalez Calle et al. found that a high stimulus frequency of 200 Hz may damage
the retina tissue, but the current amplitude leading to the noticeable tissue damage was much higher
than the stimulus strength of current Argus II systems (Calle, 2018). Long term influence of high
stimulation frequency on the perceptual threshold and tissue damage requires further investigation
in the future.
In addition to stimulation frequency, stimulus waveform can contribute to activation thresholds
of RGCs. Hadjinicolau et al. systematically studied the impact of varying stimulus pulses on the
stimulation threshold of RGCs and found that asymmetric short cathodic-first followed by an inter-
phase gap and a long anodic pulse reduces the stimulation threshold of RGCs (Hadjinicolaou et al.,
2015). In another study using calcium imaging technique, the RGCs threshold was significantly
decreased using asymmetric long anodic-first charge-balanced biphasic pulses (Chang et al., 2019).
The anodic break mechanism was shown to play a role in the reduced stimulus threshold of asym-
metric long anodic-first pulses (Ghaffari et al., 2020). Remarkably, here we found that while the
lowest stimulus threshold A2 cells can be accomplished by the asymmetric long anodic-first pulse
(A = 4 ms & C = 0.5 ms), the D1 cells stimulation threshold is the least with the asymmetric
short cathodic-first pulse (C = 0.5 ms & A = 3 ms). This indicates that the anatomical and
biophysical features of RGCs may modulate the stimulus waveform leading to the lowest threshold
of cells. Our modeling results may explain the discrepancy in the experimental data regarding the
lowest stimulation threshold of RGCs across waveforms. It is worth noting that stimulation pulses
may alter the amount of neurotransmitter releases at pre-synaptic terminals of RGCs and therefore
contribute to the indirect activation threshold of cells.
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Behrend et al. found that focal activation of RGCs is not limited by the size of the stimulation
electrode and the activation of RGCs axon bundles was a limiting factor even for the electrode size
as small as 10 µm in diameter (Behrend et al., 2011). Therefore, electrical stimulation strategies
have been proposed to prevent axonal activation of RGCs in epiretinal prostheses. Cho et al.
showed experimentally that the asymmetric long cathodic-first charge-balanced biphasic pulse (C
= 2 ms & A = 0.5 ms) increases the stimulation threshold difference between the distal axon
and cell body, offering the enhanced likelihood for a more focal response of RGCs compared to
symmetric biphasic pulses (Cho et al., 2016; Cho, 2014). McIntyre and Grill proposed asymmetric
charge-balanced stimulus pulses to selectively activate passing fibers over cell bodies, or cells over
passing fibers in central nervous system (CNS) neurons (McIntyre and Grill, 2000). Further, clinical
data indicated that increasing stimulation frequency may not significantly alter the phosphene size
reported by the subjects, and the phosphene area was mostly sensitive to amplitude modulations
(Nanduri et al., 2012). Together, the proposed stimulation strategy in the present study is not only
functional for selective activation of RGCs, but also effective for achieving a more focal shape of
phosphenes, thereby increasing the spatial resolution of current retinal prosthetics. We previously
demonstrated that the distal axon activation threshold was not sensitive to morphological and
biophysical differences among RGCs and purely affected by the properties of RGCs distal axon.
Therefore, the axonal activation of RGCs may diminish the potential for preferential excitation
of RGCs. It remains to be investigated the optimum stimulus waveforms leading to a maximized
chance for selective activation of cells as well as avoiding the activation of RGCs axon bundles.
5.4.4 Temporal response of RGCs
The number of elicited spikes in response to light stimuli may vary across RGCs and the rate
of RGCs firing can be greater than 100 Hz (Cai et al., 2011; J. et al., 2002). Therefore, electrical
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stimulation of RGCs to accomplish identical rates of spikes cannot result in transferring physio-
logically realistic visual signals to the brain, and therefore limits the efficacy of retinal prosthetic
systems. Here, we showed that the sensitivity of RGCs firing rate varies across RGCs as well as
among a range of stimulus pulses at high stimulation frequency. This provides the potential for
modulating the temporal response of cells using different stimulus pulses, possibly improving the
quality of evoked visual information, and therefore the outcome of retinal implants. In the future,
a closed-loop feedback system can be proposed based upon the reported shape, size, and color of
the phosphene by subjects to optimize electrical stimulation parameters that lead to better efficacy
of retinal prostheses.
5.4.5 Factors affecting excitability of RGCs at high Frequency
Understanding the mechanisms underlying selective activation of RGCs at high frequency using
the proposed stimulus waveforms would allow us to expand our predictive computational results and
design stimulation strategies for preferential activation of other cell types in CNS. We previously
investigated the influence of morphological factors such as soma, axon, AIS, and dendritic field sizes
on the excitability of RGCs at 200 Hz. We found the impact of soma size to be more pronounced and
small cells were more responsive compared to large cells considering variations in all morphometric
parameters. Therefore, in this study, we only focused on the impact of soma diameter on selective
activation of A2 and D1 RGCs using the two selected stimulus pulses. Data show that small cells
are more excitable using the symmetric biphasic waveform and less responsive using the asymmetric
long cathodic-first biphasic pulses compared to large cells (Figure 5.12). The influence of membrane
properties and voltage-dependent ionic channel densities on RGCs selectivity was small relative to
soma size. Further, the temporal response of the two cells exchanging the biophysical properties
demonstrated that modulations in firing patterns such as elicited spike width and peak membrane
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Membrane Voltage (mV)
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Figure 5.13: The influence of biophysical properties exchange between A2 and D1 cells on the
firing patterns of RGCs.
potential do not significantly alter RGCs selectivity (Figure 5.13). The remarkable role of soma size
regardlessofbiophysicsathighfrequencyinRGCsselectivitysuggeststhattheproposedstimulation
parameters in the present work can be possibly extended beyond RGCs and be applied for a wide
range of neurons in CNS.
5.4.6 Color selectivity
OurrecenttestwithArgusIIpatientsrevealedthatelectricalstimulationofhighfrequency(upto
200Hz)canresultinsomevariationofcolorperception. Thesensationofthebluecolorwasincreased
with increasing the stimulation frequency. Notably, our computational findings correlated well with
this clinical study, showing that small bistratified RGCs with the contribution to blue/yellow color
vision (Dacey and Lee, 1994) can be selectively targeted at high frequency with proper current
amplitude modulation. The ability to activate color-sensitive RGCs in a selective manner would
hugely improve the efficacy of current prostheses and grant for further development of the next
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2560 x 1920 pixels 50 x 37 pixels 20 x 14 pixels
Figure5.14: Influence of color perception on object recognition at low spatial resolution. The four
objects are represented in this picture: white plate, banana, blueberry, and strawberry. Reduction
in the number of pixels significantly diminishes the ability to distinguish the objects in the absence
of color vision. The presence of color perception represents an immense improvement to objects
recognition and to the current state of the art in retinal prosthetic systems.
generation of retinal prosthetic systems. The proposed stimulation strategy in this study may
providetheintriguingopportunitytocontrolthecolorsensationandaugmenttheobjectsrecognition
capability of subjects with retinal implants. The immense importance that preferential stimulation
of color selective RGCs and therefore color cues would add can be easily understood by thinking of
three fruits such as blueberry, strawberry, and banana as illustrated in Figure 5.14. The three fruits
plus the white plate in the black and white picture are practically indistinguishable with a very
small number of pixels (10× 7 pixels). Therefore, the addition of color perception is significantly
helpful in distinguishing the objects and therefore compensating for the inability to spatially resolve
the objects even at the very low spatial resolution.
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5.4.7 Model limitations and future steps
The study of extracellular electrical stimulation of RGCs was done using our computational
framework under a controlled stimulation condition to better capture factors leading to RGCs se-
lectivity. While the stimulation electrode to cells distance and the position of the electrode with
respecttothecellswerefixed, theorientationofaxonsandelectrode-to-celldistancemayvaryacross
RGCs subtypes. A randomly distributed large population of RGCs subtypes in the close vicinity of
the stimulation electrode requires further investigation. McIntyre and Grill randomly distributed
populations of neurons including the fibers of passage and cells, and they proposed stimulus wave-
forms for selective activation of neurons (McIntyre and Grill, 2000, 2002). The population-based
technique did not significantly alter the chance for populated neurons selectivity across a range of
stimulus pulses. In the future, a large population of RGCs with close and far distance from the
stimulating electrode and considering the heterogeneity of RGCs distribution inside the ganglion
cell layer will be studied to better explore its influence on RGCs selectivity.
Although the layers of constructed bulk retina tissue are shrunk to represent the degenerated
retina, the morphological and biophysical features are extracted from the healthy retina. It is well
established that the late stage of retinal degeneration can result in the migration of neurons to other
layers (Marc et al., 2003) and therefore may affect the sensitivity of RGCs to electrical stimulation
of varying stimulus parameters. We previously found that the large disk electrode increases the
differential threshold of RGCs and therefore augments the role of soma size for given AIS properties
compared to the point source. The threshold difference between the A2 and D1 cells was almost
similar while moving the position of the electrode from the soma to the AIS region. In addition,
the increased electrode-retina distance was also shown to enhance the current amplitude range
for selective activation of small D1 cells. We did not investigate the impacts of pulse duration
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and interphase gap on RGCs excitability and selectivity in the present work. The center of our
attention was on the influence of the level of asymmetry of waveforms on frequency response and
the likelihood for selective activation of RGCs under identical delivery of stimulation charge.
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Chapter 6
Modeling ON Bipolar Cells for Electrical
Stimulation
Paknahad J, Kosta P, Iseri E, Farzad S, Bouteiller JM. C, Humayun M, Lazzi G. Modeling ON
Cone Bipolar Cells for Electrical Stimulation. 43rd Annual International Conference of the IEEE
Engineering in Medicine and Biology Society, Oct 30, 2021, Virtual, Mexico. (Accepted)
Abstract
Retinal prosthetic systems have been developed to help blind patients suffering from retinal degener-
ative diseases gain some useful form of vision. Various experimental and computational studies have
been performed to test electrical stimulation strategies that can improve the performance of these
devices. Detailed computational models of retinal neurons, such as retinal ganglion cells (RGCs)
and bipolar cells (BCs), allow us to explore the mechanisms underlying the response of cells to
electrical stimulation. While electrophysiological studies have shown the presence of voltage-gated
ionic channels in different regions of BCs, many of the existing cone BCs models are assumed to be
passive or only contain calcium channels at the synaptic terminals. We have utilized our Admittance
Method (AM)-NEURON computational platform to implement a more realistic model of ON-BCs.
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Our model closely replicates the recent patch-clamp experiments directly measuring the response
of ON-BCs to epiretinal electrical stimulation and thereby predicts the regional distributions of the
ionic channels. Our computational results further indicate that outward potassium current strongly
contributes to the depolarizing voltage transient of ON-BCs in response to electrical stimulation.
6.1 Introduction
Retinal implant-based prosthetic systems focus on the electrical stimulation of the surviving cells
of degenerated retina to restore sight to the blind. Several prosthetic systems have been developed;
however, the efficacy of these devices is still limited. One of the problems faced with epiretinal
implants is the axonal activation of retinal ganglion cells (RGCs) which contributes to the elongated
phosphene reported by the subjects, leading to the reduced spatial resolution of these devices
(Beyeler et al., 2019). In addition, activation threshold of RGCs has also been shown to be higher
in degenerated retina (Loizos et al., 2018), thereby requiring higher stimulation amplitudes which
may lead to tissue damage. Therefore, it is essential to maximize the efficiency of the stimulation
while reducing the stimulation threshold to avoid activation of RGCs axon bundles and potential
tissue damage.
Many attempts have been conducted to enhance the efficacy of current epiretinal implants by
directly and indirectly targeting RGCs (Freeman et al., 2010; Jensen et al., 2005; Schiefer and
Grill, 2006; Twyford and Fried, 2016; Weitz et al., 2015). Similarly, different electrical stimulation
strategies have been proposed to enhance the efficacy of these devices and reduce the excitation
threshold of RGCs (Chang et al., 2019; Hadjinicolaou et al., 2015). Several computational modeling
approaches have been investigated to further understand the underlying mechanisms that result in
varying sensitivity of retinal neurons to electrical stimulation. For example, the low stimulation
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threshold of the axon initial segment (AIS) of RGCs relative to the distal axon using short pulse
durations has been shown to be effective in achieving more focal response of RGCs (chapter 2).
In addition to comprehensive development of RGCs models, there have been electrophysiological
studies focusing on identifying the expression of voltage-gated ionic channels in BCs (Puthussery
et al., 2013; Werginz et al., 2015). A detailed model of spiking BCs in the magnocellular pathway
of the primate retina, diffuse bipolar cells (DB4), has been implemented by Rattay et al. (Rattay
etal.,2017,2018). AlthoughthepresenceofactivemembranepropertieshasbeenshowninbothON
and OFF BCs, the other available BC models were either assumed to be passive or only expressed
L-type and T-type calcium channels at the presynaptic terminals of the cells (Freeman et al., 2011a;
Kosta et al., 2021; Publio et al., 2009; Werginz et al., 2015; Werginz and Rattay, 2016). In a few
studies, the reported impact of potassium reversal potential on the calcium reversal potential of
BCs has been incorporated into the model of BCs (Werginz et al., 2015). The role of other regional
voltage-gated ionic channels in shaping the BCs response to external stimulation was assumed to be
negligible (Werginz and Rattay, 2016). However, no experiment was performed to investigate the
sensitivity of BCs response to variations in densities and distributions of ionic channels to support
this assumption.
Recently, a novel photoreceptor peeling technique has been developed to directly record the
ON-type mouse BCs response to epiretinal electrical stimulation (Walston et al., 2017). The depo-
larizing voltage transients have been measured at the cell bodies of the ON-BCs (Walston et al.,
2018). In this study, we have utilized the multi-scale Admittance Method (AM)-NEURON com-
putational platform, integrating the recent experimentally recorded signals of BCs, to predict the
expressions and distributions of ionic channels in each cellular region of the cell. The biophysically
detailed and realistic model of ON-BCs would allow us to better capture the mechanisms underlying
120
Terminal
(g
CaL
= 2 mS/cm
2
)
Axon
(g
k
fast
= 2 mS/cm
2
)
Presynaptic Terminals
(g
CaL
= 2 mS/cm
2
)
Dendrite
(g
CaT
= 1 mS/cm
2
, g
k
slow
= 2.4 mS/cm
2
)
Soma
(g
CaT
= 1 mS/cm
2
, g
k
slow
= 0.6 mS/cm
2
)
Dendritic Terminals
(g
CaT
= 1 mS/cm
2
, g
k
slow
= 2.4 mS/cm
2
)
Figure 6.1: Multi-scale model consisting of (a) bulk tissue model with microelectrode, various
retinal layers (GC: ganglion cell; IPL: inner plexiform layer; INL: inner nuclear layer; OPL: outer
plexiform layer; ONL: outer nuclear layer; PR: photoreceptor) and (b) morphologically detailed
retinal bipolar cell model. The stimulating electrode of 200 µm diameter is placed 50 µm from
the synaptic terminals of BCs. The bulk retinal tissue model is utilized to compute the voltages
at every node of the model due to the stimulating microelectrode. These extracellular voltages
are then applied to the bipolar cell model to simulate its spatio-temporal response to electrical
stimulation.
their response to electrical stimulation. The implemented model was able to closely reproduce the
response of ON-BCs measured experimentally to epiretinal electrical stimulation (Walston et al.,
2018). The model also suggests the contribution of the outward potassium current, along with
the L-type calcium channel, to the depolarizing transient response of BCs to epiretinal electrical
stimulation.
121
6.2 Methods
6.2.1 NEURON Simulation
Thechangeincellmembranepotentialinresponsetoanappliedexternalstimulationiscomputed
usingNEURONcomputationalsoftware(HinesandCarnevale,1997). Thecellismodeledinamulti-
compartmental approach, where the soma, axon, terminals, and dendrites are defined as separate
compartments (Figure 6.1). The morphology of the cell is extracted as an SWC file from the
previous work. Each cell branch has unique biophysical properties that are expressed as passive or
active ionic membrane channels. Therefore, the mechanism of current flow and potential generation
varies across the cell depending on the channel distributions at various cell regions. The membrane
conductance values, and distributions of ionic channels are represented in Figure 6.1. Most of the
voltage-dependent rate constants and ionic kinetics can be found in (Rattay et al., 2018). The L-
type Ca channel has been adjusted from the previous work and its kinetics are governed by (Werginz
and Rattay, 2016):
i
CaL
=g
caL
c
3
(E − E
caL
) (6.1)
dc
dt
=− (α c
+β c
)c + α c
(6.2)
α c
=
− 0.3(E+70)
e
− 0.1(E+70)
− 1
(6.3)
122
β c
= 10 e
− (E+38)/9
(6.4)
Where g
Ca
L
is the maximum membrane conductance of the L-type calcium and the activation
gating variable is c. The rate constants α and β represent opening and closing of the channels.
The reversal potential of the calcium channel (E
Ca
L
) is formulated based on the intracellular con-
centration of the calcium, according to Fohlmeister et al. (Fohlmeister and Miller, 1997b). The
extracellular calcium concentration is set to 1.8 mM. The depth of the calcium pump and the time
constant of the calcium current are 0.1 m and 1.5 ms, respectively. The membrane capacitance
and intracellular resistivity are set to 3 F/cm2 and 100 ohm.cm. The resting membrane voltage is
-55 mV, and the reversal potential of the potassium is adjusted to -90 mV to better replicate the
experimental recorded signals, including the peak and resting membrane potentials. Further details
of the remaining parameters and variables can be found in the recent publication (Rattay et al.,
2018).
6.2.2 AM-NEURON Computational Platform
The NEURON simulations are combined with the AM to obtain cell response to an external
electrical stimulation. This multi-scale simulation framework simulates a 3D bulk tissue model and
the neuronal model as shown in Figure 6.1. The stimulating electrode and various retina layers
with respective resistivity properties are implemented in the bulk tissue model. The AM discretizes
the bulk tissue model and computes the voltage induced due to electrical stimulation at every
node of computational cells. These computed voltage values are then interpolated at the center of
each compartment of the neuron model. Finally, neuronal response is simulated by applying the
interpolated voltages as the extracellular voltage at every compartment. Further details about the
123
-80
-70
-60
-50
-40
-30
-20
15 20 25 30 35 40
Voltage (mV)
Time (ms)
93 µA
94 µA
96 µA
100 µA
110 µA
Experiment Model
PW = 25 ms PW = 8 ms
Cathodic-first biphasic pulses
-80
-70
-60
-50
-40
-30
-20
15 35 55 75
Voltage (mV)
Time (ms)
90 µA
93 µA
94 µA
96 µA
110 µA
130 µA
-70
-60
-50
-40
-30
15 35 55 75
Voltage (mV)
Time (ms)
0.8 µA
1.2 µA
1.4 µA
1.6 µA
1.8 µA
2 µA
-80
-70
-60
-50
-40
-30
-20
15 20 25 30 35 40
Voltage (mV)
Time (ms)
90 µA
93 µA
94 µA
96 µA
100 µA
110 µA
-70
-65
-60
-55
-50
-45
-40
15 20 25 30 35 40
Voltage (mV)
Time (ms)
0.8 µA
1.2 µA
1.4 µA
1.6 µA
1.8 µA
2 µA
Figure 6.2: The response of the ON-type BCs to epiretinal electrical stimulation of various pulse
amplitudes using symmetric biphasic cathodic-first charge-balanced stimulus pulses of 8 ms and 25
ms durations. Top figures: experimental recording signals (Walston et al., 2018). Bottom figures:
modeling results using AM-NEURON platform. Results indicate that the model can closely predict
the experimentally recorded response characteristics of ON-BCs to epiretinal electrical stimulation.
modeling approach, including the properties of the retinal layers, can be found in chapter 2. Using
this method, we can predict how cells might respond to stimulation waveforms generated by an
implanted electrode in the 3-D space.
6.3 Results
6.3.1 Verification of the model with Experiments
The ionic channels distributions and densities in each region of the multi-compartment model
of the ON-BCs have been selected to closely predict the behavior of the cells to epiretinal electri-
cal stimulation. Figure 6.2 shows the membrane voltage recorded from the soma in response to
epiretinal electrical stimulation for both the implemented model and experimental measurements
provided by Walston et al. (Walston et al., 2018). The symmetric cathodic-first charge-balanced
124
-80
-70
-60
-50
-40
-30
-20
15 25 35 45 55 65 75
Voltage (mV)
Time (ms)
89.7 µA
93 µA
93 µA
-20
0
20
40
60
80
100
15 25 35 45 55 65 75
Current (pA)
Time (ms)
Terminal_CaL
Presynapses_CaL
Axon_Kfast
Soma_Kslow
Dend_Kslow
Soma_CaT
Axon_Na
With Na
Without Na
Figure 6.3: The transmembrane potential elicited by the extracellular stimulation of a symmetric
cathodic-first biphasic pulse of 25 ms in the presence and absence of the Na channel. (b) The ionic
currents in different regions of the cell at 93 µA stimulus amplitude. The membrane conductance
value of the Na channel in the axon is set to 300 mS/cm2.
biphasic pulses are applied and the response of the cell is compared for pulse widths (PW) of 8
ms and 25 ms. The BCs model closely predicts the response characteristics of the cell to electrical
stimulation of varying pulse widths and amplitudes. At the onset of the cathodic phase, the mem-
brane potential at the soma hyperpolarizes due to the longer distance of the stimulating electrode
from the cell body relative to the terminals (Rattay et al., 2017). The depolarized signals from the
terminal of the cell backpropagate towards the soma, thereby leading to the depolarization of the
cell following the hyperpolarization (Figure 6.2). The strong depolarizing voltage response occurs
after the termination of the cathodic stimulation (the onset of the anodic stimulation). An increase
in the current amplitude slightly increases the maximum negative potential at the onset of the
cathodic phase (Figure 6.2). A stronger current stimulus is shown to reduce the duration of the
negative potential. This may arise from the delayed opening of the voltage-gated ionic channels at
the threshold compared to high suprathreshold current amplitudes.
125
-80
-60
-40
-20
15 20 25 30 35 40
Voltage (mV)
Time (ms)
110 µA_Na=300_With_CaL
110 µA_Na=300_Without_CaL
120 µA_Na=300_Without_CaL
Figure 6.4: The role of L-type calcium channel at the terminal of BCs in the depolarizing voltage
transients at the onset of the cathodic stimulation pulse. The stimulus pulse duration is set to 8
ms. Data show that the active response properties of the cell is eliminated in the absence of the
L-type channel, even at higher current amplitude of 120 µA.
6.3.2 Sensitivity of BCs Response to Na channel
We investigated the contribution of each active ionic current to the response properties of the
ON-BCs. We further considered the sensitivity of the BCs response to the presence of sodium (Na)
current concentrated in the axon of spiking BCs. For a given current amplitude, the duration of
the hyperpolarized potential is reduced in the presence of the Na current as shown in Figure 6.3A.
Due to the opening of the Na channel, the delayed response of the peak membrane potential during
the cathodic phase has been decreased. The addition of the Na current decreases the stimulation
threshold of BCs (Figure 6.3A). The ionic currents of each section are represented in Figure 6.3B.
The strong outward potassium currents in the axon and soma of the cell are predicted from the
BCs model, which contribute to the peak depolarization of membrane after the termination of the
cathodicpulsestimulation. Thisisinagreementwiththeresultsofrecentvoltage-clampexperiments
ontheON-typemouseBCs, suggestingthepresenceofastrongoutwardrectifyingpotassiumcurrent
in this cell type (Walston et al., 2017).
126
6.3.3 Blockage of L-type Ca channel
We examined the role of the L-type Ca channel in the response of ON-BCs to electrical stim-
ulation. Interestingly, the removal of the L-type Ca channel eliminated the depolarizing voltage
transients of the cell at the onset of the cathodic phase as shown in Figure 6.4. Further increase
in the strength of the electrical stimulation to 120 µA for a given pulse duration of 8 ms did not
result in the opening of the voltage-gated ionic channels. This indicates the significant contribution
of the calcium channels concentrated at the synaptic terminals of BCs to the active response of
cells to electrical stimulation. The depolarizing voltage transients are originated in the terminals
of the cell and mediated by the L-type Ca channels (Figure 6.4). This correlates well with the
recent experimental data suggesting the addition of the cadmium chloride (Cdcl2), pharmacological
blocker of the calcium current, eliminates the depolarizing voltage transient response of ON-BCs to
epiretinal electrical stimulation.
6.4 Discussion and Conclusion
We have utilized our 3D combined AM-NEURON computational platform to estimate the dis-
tribution and density of voltage-gated ionic channels in ON-BCs. Research has been conducted
in developing biophysical properties of cells in response to intracellular stimulation and predicting
the expression and kinetics of each ion in isolation (Publio et al., 2009; Rattay et al., 2017, 2018;
Werginz and Rattay, 2016). However, extracellular stimulation may allow us to better determine
the distribution of ions and their roles in forming the response to electrical stimulation. Using this
modeling framework, we developed the ON-BCs model incorporating more realistic channel alloca-
tions compared to the existing models. We verified the ON-BCs biophysical model by testing our
simulations against comparable experimental recordings. Compared to previous works, our model
127
contains potassium channels at the soma, axon, and dendrites of the cell. The presence of the Na
channel in the axon and its role in the response pattern and stimulation threshold of the cell to
electrical stimulation were investigated. The model further shows that the blockage of the L-type
Ca current can suppress the active response of ON-BCs to electrical stimulation.
Notably, there is a discrepancy in the current amplitude of computational modeling and exper-
iment results (Figure 6.2). The significant differences in the resistivity of the retina reported in
the literature (Loizos et al., 2016b; Werginz and Rattay, 2016), and the potential dissimilarity in
electrode-to-cell distance/position in whole cell patch-clamp experiments compared to the modeling
approach may contribute to the current threshold difference. In this study, we mostly aimed at
determining the distributions of ionic channels for a given morphology to replicate the biophysical
response of the bipolar cells. However, morphological factors such as the length of the axon and in-
tracellular properties can play important roles in shaping the response of cells (Rattay et al., 2018).
In the future, we will incorporate morphologically different subtypes of BCs and investigate their
response to a range of electrical stimulation parameters. This sensitivity analysis of morphologically
and biophysically detailed models of BCs would help shed some light on the mechanisms underlying
thehypersensitivityofBCstolongstimuluspulsesorlowsinusoidalstimulationfrequenciesreported
in the literature (Twyford and Fried, 2016; Weitz et al., 2015). Finally, the present study illustrates
the effectiveness of the multiscale computational platform in replicating realistic cell models and
predicting their response to electrical stimulation, thereby guiding the design of efficient stimulation
strategies.
128
Chapter 7
Mechanisms Underlying Sensitivity of
Bipolar Cells to Long Stimulation Pulses
Paknahad J, Kosta P, Bouteiller JM. C, Humayun M, Lazzi G. The sensitivity of Retinal Bipolar
CellsResponsetoLongStimulusPulseDurationsinEpiretinalProstheses. Invest. Ophthalmol. Vis.
Sci. 2021;62(8):3169.
Paknahad J, Kosta P, Bouteiller JM. C, Humayun M, Lazzi G. Mechanisms Underlying Sen-
sitivity of Bipolar Cells to Long Stimulation Pulses: A Computational Study. Journal of Neural
Engineering. (Under review, 2021).
Abstract
Retinal implants have been developed to electrically stimulate healthy retinal neurons in the pro-
gressively degenerated retina. Several stimulation approaches have been proposed to improve the
visual percept induced in patients with retinal prostheses. We introduce a computational model
capable of simulating the effects of electrical stimulation on retinal neurons. Leveraging this com-
putational platform, we delve into the underlying mechanisms influencing the sensitivity of retinal
neurons’ response to various stimulus waveforms. We implemented a model of spiking bipolar cells
(BCs) in the magnocellular pathway of the primate retina, diffuse BC subtypes (DB4), and utilized
129
our multiscale Admittance Method (AM)-NEURON computational platform to characterize the
response of BCs to epiretinal electrical stimulation with monophasic, symmetric, and asymmetric
biphasic pulses. Our investigations yielded four notable results. (i) The latency of BCs increases
as stimulation pulse duration lengthens; conversely, this latency decreases as the current amplitude
increases. (ii) Stimulation with a long anodic-first symmetric biphasic pulse (duration > 8 ms)
results in a significant decrease in spiking threshold compared to stimulation with similar cathodic-
first pulses (from 98.2 µA to 57.5 µA). (iii) The hyperpolarization-activated cyclic nucleotide-gated
(HCN) channel was a prominent contributor to the reduced threshold of BCs in response to long
anodic-first stimulus pulses. (iv) Finally, extending the study to asymmetric waveforms, our re-
sults predict a lower BCs threshold using asymmetric long anodic-first pulses compared to that of
asymmetric short cathodic-first stimulation. This study predicts the effects of several stimulation
parameters on spiking BCs response while shedding some light on the underlying mechanisms in-
volved. Of importance, the effects predicted are consistent with experimental observations, thus
highlighting the capability of the methodology to predict and guide the development of electrical
stimulation protocols to generate a desired biological response, thereby constituting an ideal testbed
for the development of electroceutical devices.
7.1 Introduction
The sensitivity of BCs response to epiretinal electrical stimulation has been considered in a few
studies (Freeman et al., 2011a; Margalit and Thoreson, 2006; Walston et al., 2018). Margalit and
Thoreson have shown that long stimulus pulse durations mediate neurotransmitter release at the
terminals of BCs (Margalit and Thoreson, 2006). Recently, a photoreceptor peeling method has
been utilized to directly record the response of BCs to epiretinal stimulation of various stimulus
130
amplitude and long pulse durations in the wholemount retina (Walston et al., 2017). The BCs have
shown to be more sensitive to long pulse widths and no significant difference has been observed
between the healthy and degenerated (rd10 mice) bipolar cells.
Despite these successes, the mechanisms underlying selective excitation of BCs and the network-
mediated response of RGCs with long pulse widths are not well understood. The role of T-type and
L-type of calcium channels at the terminal of BCs in the great sensitivity of BCs to low-frequency
stimulation has been studied (Freeman et al., 2011a). The slow kinetics of calcium channels has
been suggested as a possible underlying mechanism for the high sensitivity of BCs to low stim-
ulation frequencies. Although both T-type and L-type Ca channels can play roles in regulating
neurotransmitter release at the terminals of BCs, the impact of hyperpolarization-activated cyclic
nucleotide-gated (HCN) channels on modulating the membrane potential at the BCs synaptic ter-
minals has not been investigated. A high concentration of HCN channels has been expressed at the
terminals of BCs and photoreceptors (Müller et al., 2003). Therefore, a better understanding of
the influence of HCN channels on the BCs response to electrical stimulation would allow us to gain
additional insights into the sensitivity of BCs to a range of stimulus pulse durations.
Inthiswork,weutilizedourcomputationalmodelingplatform,AdmittanceMethod(AM)/NEURON,
to better understand the response of retinal bipolar cells to electrical stimulation as a function of
various stimulation parameters. This modeling platform will enable us to capture factors affect-
ing the responsiveness of BCs through alterations of the electrical stimulation waveforms. To this
aim, we implemented computational models of bipolar cells of the primate retina that are known
to generate action potentials. Recently, the detailed model of spiking BCs incorporating the accu-
rate distribution of ion channel densities has been implemented (Rattay et al., 2017, 2018). These
spiking BCs in the magnocellular pathway are capable of generating strong synaptic activities at
131
the terminals and therefore a perfect target for evaluating their activation threshold and response
to a range of stimulus parameters. This sensitivity analysis ultimately allows us to determine the
stimulation strategies leading to the reduced activation of BCs and therefore the higher chance for
indirect activation of RGCs.
Utilizing this model, we first investigated the BCs response characteristics to epiretinal electrical
stimulation of various monophasic and biphasic symmetric charge-balanced stimulus pulses. We
determined the correlations of amplitude, pulse duration, membrane potential, and response latency
of BCs. The impact of the HCN ion kinetics on the sensitivity of BCs to modulations in pulse
durations and stimulus waveforms was examined. Our results show that the membrane voltage is
significantly affected by alterations in pulse width and current amplitude. The hyperpolarization
before the depolarization of the membrane notably influences the stimulus threshold of BCs over
a range of pulse durations. Anodic-first symmetric biphasic waveforms with long stimulus pulse
widths are found to better reduce the activation threshold of BCs compared to that of cathodic-
first biphasic pulses, thereby suggesting the greater potential for mediating synaptic release at the
pre-synaptic terminals using a lower stimulus amplitude. We further investigated the influence of
the waveform asymmetry on the stimulus threshold of BCs. The findings of our computational
modeling study and correlations with the experimental data from the literature will help us utilize
this modeling platform for designing stimulus waveforms and improving the effectiveness of current
retinal prosthetic systems.
7.2 Methods
Our multi-scale computational framework utilizes three- dimensional AM and NEURON simula-
tions to model electrical stimulation of retinal tissue and simulates the responses of retinal neurons.
132
DB4 morphology
Soma
Dendrite
Axon (SOCB)
Axon terminal
Pre-synaptic terminals
Model
(a) (b)
-100
-75
-50
-25
0
0 500 1000 1500
Voltage (mV)
Time (ms)
Na = 1000 mS/cm2
Na = 0 mS/cm2
Na & CaT = 0 mS/cm2
Experiment
L-type Ca and HCN
Passive
Na and k
T-type and k
T-type and k
(c)
Figure7.1: The verification of the developed model of spiking bipolar cells in response to intracel-
lular stimulation. (a) The morphology of the DB4 BC; (b) Experimental data showing the response
of the cell to a sinusoidal current of 10 pA in amplitude at the frequency of 20 Hz (Puthussery et al.,
2013); (c) The response of our multi-compartment model of the DB4 cell to the sinusoidal input
current. The model can closely replicate the experimentally recorded signal and the characteristics
of sodium and calcium spikes have been further shown in the figure.
First, AM is used to compute the voltage distribution inside the extracellular space. Then, this
voltage distribution is applied to the multi-compartmental models of neurons to measure spatio-
temporal activities using NEURON simulations.
7.2.1 Constructing the Retina Tissue and Electrodes
Thepropertiesoftheretinaandelectroniccomponentsareidenticaltothoseusedinourprevious
chapters. The computational model of a stimulating electrode of diameter 200 m is placed on the
top-center of the bulk retina tissue, which is discretized in 2 million computational cells and is
positioned 50 µm from the presynaptic terminals of computational models of the BCs. We applied
monophasic, symmetric biphasic, and asymmetric biphasic charge-balanced pulses of varying pulse
durations ranging from 0.1 ms to 100 ms with no interphase gap (IPG) in this study.
133
Table 7.1: Maximum ionic conductance values [mS/cm2].
Soma Dendrite Axon Synapse Terminal
g
Na
- - 1000 - -
g
Kslow
0.6 2.4 - - -
g
Kfast
- - 2 - -
g
caL
- - - 1 -
g
caT
1 1 - - -
g
HCN
- - - 3.25 -
g
l
0.033 0.033 0.033 0.033 0.033
7.2.2 NEURON: Bipolar Cells Modeling
To model the spiking BCs, we first extracted the morphology as an SWC file (Rattay et al., 2018)
and imported it into NEURON software as shown in Figure 7.1A. This multi-compartmental model
is finely compartmentalized with non-uniform distribution of ionic channels at each section and
their response characteristics to a range of electrical stimulation parameters are investigated. The
resulting DB4-BCs compartmental model consists of several ionic currents including the sodium,
slow and fast potassium, L-type and T-type calcium, and hyperpolarization-activated current. The
ability of these cells to generate spikes represents a strong release of neurotransmitters at the
terminal of BCs and a quicker signals transformation from the photoreceptor to retinal ganglion
cells. The modeling of this type of BCs enabled us to determine the activation threshold of this cell
to the electrical stimulation of various parameters. The expressions of the ionic currents including
the gating variables and rate constants for different sections (soma, dendrites, axon, terminal) are
similar to chapter 5.
The maximum ionic conductance values of each section of this BC-DB4 subtype are provided in
Table 7.1. Further details of the remaining parameters and variables can be found in Rattay et al.
(Rattay et al., 2018).
134
0
1
2
3
4
5
6
0.1 0.2 0.5 1 2 4 8 16 25
Latency (ms)
Pulse width (ms)
-100
-75
-50
-25
0
20 22 24 26 28 30
Voltage (mV)
Time (ms)
PW = 0.1 ms
PW = 0.2 ms
PW = 0.5 ms
PW = 1 ms
PW = 2 ms
PW = 4 ms
PW = 8 ms
PW = 16 ms
PW = 25 ms
(a)
(b)
Figure 7.2: The response of spiking BCs to electrical stimulation of various pulse durations using
AM-NEURON modeling framework. (a) the simulated membrane potentials as a function of time
for pulse widths (PWs) ranging from 0.1 ms to 25 ms. (b) Response latency as a function of
variations in pulse durations. Results indicate the sensitivity of BCs response to changes in pulse
durations.
7.3 Results
7.3.1 Intracellular Stimulation: NEURON Simulation
To validate the modeled DB4-BC subtype, we compared the response of the cell to intracellular
stimulation with the experimentally recorded signals of the same spiking BC types (Puthussery
et al., 2013). A sinusoidal current of 10 pA amplitude at the stimulation frequency of 20 Hz was
injected into the cell and the membrane potential was recorded from the cell body. As illustrated
in Figure 7.1B and C, the DB4-BC model can closely predict the experimentally recorded cells,
including the initial spikes after the onset of the depolarizing cycle. Similarly to the experiment,
both sodium and calcium spikes have been predicted by computational modeling (Figure 7.1c). The
absence of the Na current decreases the peak value of the depolarizing membrane potential. This
135
0
1
2
3
4
5
6
90 100 110 120 130 140 150 160
Latency (ms)
Current amplitude (uA)
-100
-75
-50
-25
0
20 22 24 26 28 30
Voltage (mV)
Time (ms)
98.2 uA 98.3 uA 98.4 uA 99 uA 100 uA 101 uA
103 uA 107 uA 120 uA 160 uA 200 uA 250 uA
(a)
(b)
Figure 7.3: Modulations in the response of BCs a function of changes in current amplitude. (a)
The response latency of BCs as a function of modulations in current amplitude. (b) The time course
of the membrane voltage for a range of current amplitudes. Data show the significant impact of
current amplitude on the response latency and the membrane potential peak.
result correlates with the electrophysically recorded signals from DB4 cells in the presence of the
Na channel blocker, tetrodotoxin (TTX) (Puthussery et al., 2013).
Our modeling has further shown the contribution of the T-type calcium channel to the small
depolarizing voltage transient measured after the blockage of the voltage-gated Na channels. Setting
the densities of Na and Ca-T channels to zero has eliminated the robust spiking in DB4 bipolar
cells as shown in Figure 7.1c.
7.3.2 Extracellular Stimulation: AM/NEURON Modeling
We aimed at better understanding the response characteristics of BCs to extracellular stimula-
tion of various parameters. Our computational modeling enabled us to capture the mechanisms for
activation of BCs and determine the sensitivity of BCs to electrical stimulation of different pulse
136
0
100
200
300
400
500
600
700
0.1 1 10 100
Amplitude (µA)
Pulse width (ms) at log scale
Cathodic monophasic
Cathodic-first biphasic
Anodic-first biphasic
Figure 7.4: Stimulation strength-duration curve of BCs for cathodic monophasic, cathodic-first
and anodic-first biphasic pulses. Our data show that stimulation amplitudes are higher for anodic-
first biphasic with shorter stimulus pulse durations. However, the presence of the anodic phase
prior to the cathode significantly reduces the threshold of BCs for longer pulse durations.
durations and waveforms. The cathodic monophasic stimulus pulses with durations ranging from
0.1 ms to 25 ms were applied and the response of BCs was investigated (Figure 7.2A). This type of
BC generates action potentials with different latencies as the pulse duration changes. At the onset
of the cathodic pulse, the membrane voltage at the soma experiences a hyperpolarization with vary-
ing durations as the pulse width is altered. These hyperpolarization events arise from the longer
distance of the soma from the stimulating electrode relative to the terminals of BCs (Rattay et al.,
2017). Therefore, with a certain delay, the signals backpropagate from the site of spike initiation,
axon with the high density of sodium channels, to the soma, leading to the depolarization events
at the soma as shown in Figure 7.2A. Figure 7.2B represents the soma spike latency as a function
of alterations in pulse duration. The latency of the evoked action potential increases as we increase
the stimulus pulse duration.
TheroleofcurrentamplitudemodulationsintheresponselatencychangesofBCswasconsidered
as shown in Figure 7.3A. For a given pulse duration of 8 ms, a rapid exponential decrease in the
137
response latency of the cell has been shown as the current amplitude increases. The latency-
amplitude curve flattens out around 130 A current amplitude having latencies of around 1.1 ms.
This indicates the significant contribution of current amplitude in the response delay of BCs to
electrical stimulation. Figure 7.3B further shows the membrane potentials of BCs for a range
of current amplitude. There is an upper limit for the peak membrane voltage as modulations
in current amplitude. Peak membrane voltage is relatively higher for the intermediate current
amplitude values. While the low current amplitude and relatively long response latency lead to a
slight reduction in the peak membrane potential, large current amplitudes with short spike latency
result in a noticeably lower membrane voltage peak at the soma. Therefore, the contribution of
currentamplitudeandpulsedurationtotheresponseofBCstoelectricalstimulationmayultimately
alter the amount of neurotransmitter release at the presynaptic terminals of BCs and thereby the
response of the downstream RGCs.
We further analyzed the stimulus thresholds of BCs for a range of pulse durations from 0.1 ms
to 100 ms in response to a single stimulus pulse of cathodic monophasic, cathodic-first, and anodic-
first biphasic pulses (Figure 7.4). We also included the cathodic monophasic pulses to isolate and
demonstrate the role of the anodic phase in the responsiveness of BCs to various electrical stimulus
pulses. Figure 7.4 shows the stimulus threshold as a function of pulse duration for these stimulus
waveforms. Thestimulusthresholdisdefinedastheminimumcurrenttogenerateanactionpotential
in the cell during the cathodic phase of the stimulation. Larger current amplitudes are required to
reach the threshold for the cathodic monophasic and cathodic-first biphasic pulses with pulse widths
less than 0.5 ms. No difference in the stimulus thresholds of BCs was observed using the cathodic
monophasic and cathodic-first biphasic pulses. This is due to the occurrence of depolarization
events and the opening of sodium gated ion channels during the cathodic phase of stimulation.
Interestingly, the longer anodic-first pulses remarkably decrease the activation threshold of BCs.
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-100
-50
0
50
20 25 30 35 40
Voltage (mV)
Time (ms)
Anodic-first biphasic
Soma
Axon
Terminal
Dendrite
-100
-50
0
50
20 25 30 35 40
Voltage (mV)
Time (ms)
Cathodic monophasic
Soma
Axon
Terminal
Dendrite
58 µA
98.2 µA
(a)
(b)
Figure 7.5: The membrane potential of spiking BCs in response to electrical stimulation of both
cathodic monophasic (top) and symmetric anodic-first biphasic (bottom) using a pulse width of
PW = 8 ms.
The simulation results indicate the role of hyperpolarization events before the depolarization in the
reduction of BCs excitation threshold to long stimulus pulses.
Figure 7.5 shows the response of BCs to electrical stimulation of 8 ms pulse duration for cathodic
monophasic and anodic-first biphasic waveforms, as a function of time. Extracellular stimulation of
cathodic pulses leads to depolarization of regions close to stimulating electrodes and hyperpolariza-
tion of compartments away from electrodes at the onset of stimulation. Therefore, as depicted in
Figure 7.5A the onset of the cathodic pulse results in the hyperpolarization of soma and dendrites
and depolarization of axon and axon terminals. With the opening of sodium channels at the axon
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initial segment (AIS), the signals backpropagate to the soma and dendrites, leading to the genera-
tion of action potentials at the soma and dendrites with a certain latency. During the anodic phase
of stimulation, the membrane potential of soma increases over time. This change in the potential
leads to the increase in the membrane voltage at the onset of the cathodic phase of the stimulation
and therefore a reduced stimulation current amplitude is required for spike generations of BCs (as
shown in Figure 7.5).
7.3.3 Role of hyperpolarization activated current (HCN)
ToexaminethefactorsinfluencingthelowstimulusthresholdofBCstolonganodic-firstbiphasic
pulse durations, we studied the contribution of the hyperpolarization-activated, cyclic nucleotide-
gated (HCN) channels at the presynaptic terminals to this sensitivity difference. We compared the
response of BCs in the presence and absence of HCN channels at the presynaptic terminals for a
range of stimulus pulse durations. Figure 7.6 shows the ratio of BCs stimulus threshold with and
without HCN channels expressions for both cathodic monophasic and anodic-first biphasic wave-
forms. HCN channels have a negligible contribution to the response of BCs to electrical stimulation
of different pulse widths for cathodic monophasic pulses (Figure 7.6A). This is expected as the HCN
channels are closed at the terminals during the depolarization. However, HCN currents are sensitive
to anodic-first biphasic pulse modulations due to the initial hyperpolarization at the presynaptic
terminals. The BCs threshold has been significantly reduced with the addition of HCNs for anodic-
first biphasic pulses with pulse widths longer than 8 ms. This indicates the role of HCN currents
in the reduction of BCs threshold required for spikes using long anodic-first biphasic pulses.
Different densities of the HCN channels were analyzed to consider the impact of the HCN
concentration difference at the terminals on the activation threshold of BCs for a given pulse width
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0
0.2
0.4
0.6
0.8
1
0.1 1 10 100
HCN/ No HCN
threshold ratio
Pulse width (ms) at log scale
Cathodic monophasic
Anodic-first biphasic
0
50
100
150
-100 -50 0 50 100
Threshold (µA)
Modulations in G_hcn density (%)
Anodic-first biphasic
Cathodic monophasic
(a)
(b)
Figure 7.6: The role of the HCN channels in response of BCs to electrical stimulation. (a)
Stimulation BCs threshold difference between simulations with and without the expression of HCN
channels. (b) The impact of HCN density on the response of BCs.
of 8 ms as demonstrated in Figure 7.6B. The cathodic monophasic pulses do not have a significant
impact on the threshold for a change in the HCN channel densities. However, for the anodic-
first biphasic pulses, reducing the expression of HCN concentration at the terminals exponentially
increases the BCs threshold (Figure 7.6B).
7.3.4 The Influence of Waveform Asymmetry
We further utilized our modeling framework to investigate the effect of asymmetric waveforms on
the response of BCs. We compared the stimulus threshold of the cell using asymmetric cathodic-first
and anodic-first biphasic pulses to symmetric cathodic-first and anodic-first biphasic stimulations
(Figure 7.7). All considered symmetric and asymmetric pulses are charge-balanced. The cathodic
pulse duration was constant and equal to 0.5 ms and the anodic pulse duration was altered. Our
computational results show that the asymmetric long anodic stimulus pulses lead to the lowest
stimulation threshold of BCs. In other words, given the modulations in both amplitude and pulse
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120 121 122 123 124 125 126
C = 0.5 ms A = 0.5 ms
A = 0.5 ms C = 0.5 ms
C = 0.5 ms A = 1 ms
C = 0.5 ms A = 2 ms
C = 0.5 ms A = 4 ms
C = 0.5 ms A = 8 ms
A = 1 ms C = 0.5 ms
A = 2 ms C = 0.5 ms
A = 4 ms C = 0.5 ms
A = 8 ms C = 0.5 ms
Cathodic stimulus threshold (µA)
Cathodic-first Anodic-first
Figure 7.7: The impact of the asymmetric biphasic pulses on the stimulus threshold of DB4-BCs.
The cathodic pulse duration is set to 0.5 ms and the anodic pulse duration is modulated from 0.5
ms to 8 ms. The asymmetric anodic-first stimulation has been shown to reduce the BCs threshold
compared to the anodic-first symmetric, and the cathodic-first symmetric and asymmetric biphasic
waveforms.
durationsofasymmetricwaveforms, thetotalchargethresholdofBCsusingasymmetriclonganodic-
firststimuluspulsesisminimum. Therefore, thisfurtherindicatestheroleofthehyperpolarizationof
membrane potential in the enhanced sensitivity of the following cathodic phase stimulation. Similar
to the results from the previous section, the HCN channels at the terminals of BCs can contribute
to the low excitation threshold of BCs using the asymmetric long anodic -first stimulation.
7.4 Discussion
In this work, we have utilized our 3D multi-scale AM/NEURON computational modeling frame-
work to gain insights about parameters affecting the response of spiking BCs to electrical stimula-
tion. The impact of pulse duration and amplitude modulations on the response of BCs including
the depolarizing membrane potential and the response latency has been investigated. An increase
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in current amplitude has been shown to reduce the spike latency of BCs. While the increase of pulse
width significantly increases the response latency of the cell at the suprathreshold current (Figure
7.2), an increase in the stimulus amplitude can decrease the spike latency and the timing associated
with the opening of the sodium channel gate (Figure 7.3A). Our computational findings correlate
with the experimental results on the response of ON BCs to epiretinal electrical stimulation us-
ing a patch-clamp technique (Walston et al., 2018). Our modeling also predicts the reduced peak
membrane potential with the huge increase in the stimulus current (Figure 7.3B).
Using this platform, we further investigated the response of BCs over a range of electrical
stimulation parameters to optimize the stimulus waveform design leading to the lowest stimulus
threshold of the cell. We found that long anodic-first biphasic stimulations can significantly reduce
the stimulus threshold of the DB4 cell. The negative membrane potential at the terminal and axon
before the onset of the cathodic stimulation can reduce the inactivation probability of the sodium
channels and, therefore, increase the sensitivity of the BCs for the spike initiation. The role of the
presence of the HCN channels is significant in decreasing the stimulus threshold of the cell. In the
presence of short stimulus pulses, we demonstrated that among various stimulus waveforms designs,
the lowest threshold is achieved using an asymmetric long anodic-first biphasic stimulation.
7.4.1 Computational Modeling of DB4-BCs
Previously, it was thought that retinal bipolar cells are passive and provide graded response only.
However, later, electrophysiological studies revealed the presence of voltage-gated ionic channels in
different types of BCs. Rat cone bipolar cells have been shown to express sodium, calcium, and
outward potassium currents (Pan and Hu, 2000). Recent patch-clamp recordings from the ON-type
BCs in the wholemount mouse retina further supports the presence of strong outward rectifying
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potassium currents. The high concentrations of HCN channels have been reported not only in BCs
of the magnocellular pathway (DB3 and DB4) of the primate retina but also in photoreceptors
and BCs terminals of the rat retina (Müller et al., 2003). The DB4-BC model implemented in the
present study incorporating different distribution and densities of ionic channels is based on the
previously published paper (Rattay et al., 2018). The Na channels have been shown to enhance the
synaptic release at the presynaptic terminals of BCs and excitatory input to parasol RGCs, thereby
increasing the potential for indirect activation of RGCs. Therefore, we centered our focus on this
particular cell type with the high-density Na channels in the AIS.
7.4.2 Sensitivity of BCs Response to Electrical Stimulation
Studies have shown that select excitation of BCs and, therefore, the network-mediated response
of RGCs can be achieved with a low stimulation frequency (Freeman et al., 2010; Twyford and Fried,
2016) and long pulse durations (Weitz et al., 2015). L-type and T-type calcium channels are known
to mediate the neurotransmitter release at the presynaptic terminals of BCs. The sensitivity of
these calcium channels to electrical stimulation of various frequencies has been previously conducted
(Freeman et al., 2011a). Furthermore, the response of DB4 spiking BCs to the intracellular and
extracellular stimulation of monophasic stimulus pulses has been investigated by Rattay et al.
(Rattay et al., 2017, 2018). Here, we compared the response of the same type of BCs to epiretinal
electrical stimulation incorporating various stimulus waveforms using the disk electrode of the Argus
II prosthetic systems (Beyeler et al., 2019). There has been no study specifically focusing on the
contribution of HCN channels to the response of BCs to electrical stimulation. We found that
the expression of HCN channels at the presynaptic terminals of BCs remarkably influences the
reduced reduction in the threshold of the cell using long anodic-first stimulus pulses (Figure 7.6).
We found that the absence of HCN channels at the presynaptic terminals of BCs increases the
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stimulus threshold of BCs. Therefore, in addition to the slow kinetics of calcium channels, HCN
channels also contribute to the higher sensitivity of BCs to long biphasic stimulus pulse and low-
frequency stimulation. Notably, the presence of the HCN current during the hyperpolarizing phase
of the sinusoidal intracellular stimulation and the role of HCN current in spike generation of the
cell during the depolarizing phase have been also demonstrated in both modeling and experimental
results (Puthussery et al., 2013; Rattay et al., 2018). Therefore, understanding the contribution
of the HCN channels to BCs response allows us to better design electrical stimulus parameters,
increase the likelihood for the indirect activation of RGCs and, therefore, help avoid the excitation
of axon bundles.
7.4.3 Asymmetric Electrical Stimulation of Retinal Neurons
Epiretinal electrical stimulation of the A2-type RGCs using asymmetric cathodic-first biphasic
waveforms with short cathodic pulses has been reported to increase the efficacy of stimulation
(Hadjinicolaou et al., 2015). A recent experiment using a calcium imaging technique has reported
the lowest threshold of RGCs using asymmetric long anodic-first stimulus pulses (Chang et al.,
2019). Therefore, we investigated these two asymmetric waveforms in addition to both symmetric
cathodic and anodic-first biphasic stimulations (Figure 7.7). This analysis allowed us to better
understand the contribution of the network-mediated response of RGCs to electrical stimulation.
The reduction of the Na inactivation probability during the hyperpolarization phase has been
shown to play a role in the reduced threshold of cells. Electrical stimulation of nerve fibers with
long anodic-first biphasic waveforms resulted in a high chance of spike generation at the onset of
the cathodic stimulation (Grill and Mortimer, 1995). The response of the RGCs model to electri-
cal stimulation indicated that the lowest stimulus threshold of the cell can be achieved using an
145
asymmetric long anodic-first stimulation with the addition of an interphase gap (IPG) (Ghaffari
et al., 2020). However, the direct activation threshold of RGCs in the absence of the IPG is the
lowest using the asymmetric short cathodic-first waveforms (Hadjinicolaou et al., 2015). Therefore,
analyzing the response of the isolated RGCs may not fully explain the calcium imaging experimen-
tal observations of the lowest threshold of the retinal network stimulation using asymmetric long
anodic-first waveforms with no IPG. In the present study, we have shown the greater sensitivity of
BCs to the asymmetric long anodic-first stimulation compared to both short symmetric (cathodic-
and anodic-first) and asymmetric cathodic-first biphasic stimulations (Figure 7.7). This indicates
the high likelihood of neurotransmitters release and excitatory inputs to RGCs, suggesting the re-
duced indirect activation threshold of RGCs. The computational findings of this study may explain
the role of the network-mediated response of RGCs as well as the presence of HCN channels at the
terminals of BCs in higher stimulation efficacy of asymmetric long anodic-first pulses.
7.4.4 Clinical Implications
Clinical testing with epiretinal implant subjects has proven the efficacy of long biphasic pulses
and low stimulation frequencies for improving the spatial resolution of these devices (Freeman et al.,
2010; Weitz et al., 2015). In this study, we have explored the role of an anodic phase following by
a cathodic phase in the reduction of activation threshold at the presynaptic terminals of BCs using
long pulse durations. This indicates the likelihood to avoid activation of RGCs axon bundles and
indirect excitation of RGCs. At a low biphasic stimulation frequency of 20 Hz and 25 ms pulse width
utilized in the subject testing, every cathodic phase is followed by an anodic phase. Therefore, the
presence of the hyperpolarizing event prior to the depolarization as well as the high concentration of
the HCN channels at terminals of both photoreceptors and BCs may reduce the threshold necessary
for indirect activation RGCs, thereby avoiding axonal activation of RGCs and better outcome of
146
currentepiretinalprostheticsystems. Thiscomputationalplatformallowedustoproposeapotential
indirect activation strategy for a more focal response of RGCs using long pulses.
RecentclinicaltestingwiththreeArgusIIsubjectshasrevealedthereducedperceptualthreshold
(on average) and great percept brightness of asymmetric long anodic-first stimulation (Ghaffari
et al., 2020). Our computational findings correlate with the clinical results, suggesting the plausible
contribution of the network-mediated response of RGCs in the reduced perceptual threshold of these
subjects. Thissupportsthepotentialofourmulti-scalepredictivemodelingframework, whichallows
us to better capture factors influencing the response of retinal neurons to electrical stimulation and
ultimately design stimulation strategies for enhancing the effectiveness of prosthetic devices.
7.4.5 Limitations and Future Work
This study is limited to BCs in the magnocellular pathway with a high density of the sodium
channels in the AIS. While there have been subtypes of BCs in mouse and rat retinas with the
expression of Na (Hellmer et al., 2015; Pan and Hu, 2000), there are many ON and OFF BCs that
do not express Na channels and their response to electrical stimulation needs to be analyzed. In the
future, we will incorporate other BCs subtypes as well as the realistic network of the retina to better
capture the response of the retinal neurons to external stimulation and improve the performance of
current epiretinal prosthetic systems. Our group is working on connectome-based retinal network
modeling of various stages of retinal degeneration (Kosta et al., 2021; Pfeiffer et al., 2019). These
models will help us understand the changes in the retinal network with the progression of the disease
and potentially help in designing better stimulation strategies.
Recently, the weakened network-mediated response of RGCs to epiretinal electrical stimulation
at the late stage of degeneration has been reported experimentally in-vitro (Yoon et al., 2020). This
147
outlines the importance of this study and designing electrical stimulus parameters for reducing the
threshold of outer retinal neurons and thereby improving the outcome of retinal implants.
7.5 Conclusion
Using our 3D multi-scale AM/NEURON computational modeling framework, we have imple-
mented the spiking BCs model and predicted its response under epiretinal electrical stimulation.
We validated our model against available computational models and experimental data from the lit-
erature. We investigated the response of BCs to different monophasic, symmetric, and asymmetric
biphasic stimulus waveform designs with various current amplitudes and pulse widths. We found
that the threshold of BCs was reduced using long anodic-first biphasic pulses compared to long
cathodic-first biphasic pulses. We further explored the role of HCN channels at the presynaptic
terminals in the reduced stimulus threshold observed using long pulses with anodic-first phases.
Further, the stimulation threshold of BCs with asymmetric long anodic-first pulses was found to
be lower relative to that of asymmetric short cathodic-first pulses. This computational platform
allowed us to gain a deeper understanding of the mechanisms underlying the excitation of retinal
neurons to different stimulation waveforms. Our predictive modeling framework will further help
design and test the stimulation strategies to enhance the effectiveness of retinal prosthetic systems.
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Chapter 8
Non-invasive Electrical Stimulation
Strategy to Slow Down the Progression
of Retinal Blindness
Invention disclosure 1: Electronic Lens (E-lens) for Retinal Neuroprotection. M. Humayun, G.
Lazzi, B. Salhia, J. Paknahad, M. Machnoor.
Invention disclosure 2: Bioelectronic Lens (E-lens) system for electrical stimulation and neuro-
protection of the retina Inventors: M. Humayun, G. Lazzi, B. Salhia, J. Paknahad, A. Gonzalez
Calle, M. Machnoor.
Abstract
Electricalstimulationofneuronscanresultintheneuroprotectiveeffectsandimprovingcellssurvival
and function. Therefore, controlled electrical stimulation can also induce epigenetic and neuropro-
tective changes in the retina to slow down the progression of retinal blindness. In this work, we
have deployed our multi-scale computational models and modeling platform to predict electric field
parameters and waveform efficacious for this purpose and to design a transcorneal electrical stim-
ulator to effectively induce epigenetic changes and slow down the progression of retinal blindness.
149
Using our three-dimensional Admittance Method (AM)/NEURON multi-scale computational mod-
eling platform, for the first time, we have analyzed the response retinal neurons to transcorneal
electrical stimulation. We designed electrical stimulation strategies including the placements of
electrodes and stimulus waveforms to better target the retinal cells such as bipolar cells that are
affected first at the early stage of retinal degeneration. Our computational findings revealed that
biphasic stimulus pulses of long pulse duration can decrease the activation threshold of BCs as well
as the differential stimulus threshold between RGCs and BCs, offering potential for targeting the
altered BCs during the early phase of degeneration. To further verify the efficacy of the designed
stimulation setup, we performed in-vivo experiments in rats applying TES over the time course of
retinal generation. Results indicate that the proposed TES strategy can slow down the deaths of
photoreceptors and reduced thickness of the retina, offering intriguing potential to translate this
work to clinics for patients suffering from prevalent retinal diseases. Further, several computational
modeling simulations were done using the segmented human head model to design the best electrode
placement and configuration for effective and safe delivery of electric fields in human tissue.
8.1 Introduction
Retinal blindness, such as retinitis pigmentosa (RP), age-related macular degeneration (AMD),
and glaucoma (POAG), is characterized by unrelenting neuronal death (photoreceptor loss in RP
and AMD and ganglion cell loss in POAG). A number of mechanisms have been identified as to
why neuronal death occurs in these different retinal blinding disorders such as genetic mutations in
RP, lipid metabolism abnormalities and inflammation in AMD, and elevated intraocular pressure
in POAG. Although treatments to ameliorate these conditions exist, there is no cure. Therefore,
approaches to prevent blindness and progressive degeneration at the very early stage of degeneration
150
would make a huge impact in lives of patients with retinal degenerative diseases. Despite significant
progress towards investigating gene and stem cell therapies to cure AMD and RP, the clinical
outcome of these approaches has been limited to specific population of patients, with the potential
tissue and retina damage.
Electrical stimulation has been shown to induce neuroprotective effects and modulations in
synaptic plasticity of neurons in the central nervous system, including the retina (Henrich-Noack
et al., 2017; Sehic et al., 2016; Yu et al., 2020). Our group has, for the first time, shown that
controlled microscale electromagnetic (EM) stimulation can lead to neuroprotective changes in the
retina. The transformational vision of this work is to use a non-invasive controlled electrical stim-
ulation to induce genetic changes in the mammalian retina to slow down the progression of retinal
blindness and perhaps even restore some level of the lost vision. The success of such an approach
would spawn a whole new area in basic science, engineering, and medicine and in doing so develop
new, innovative, cross-disciplinary educational programs critical to foster the next-generation of
researchers of bioelectronic devices to affect protective genetic changes.
There has been no systematic research conducting the most effective electrical stimulation ap-
proach for selective induction of stimulation in retinal neurons. Therefore, we have utilized a
combined AM/NEURON multiscale computational method to further our understanding of the im-
pacts of non-invasive electromagnetic stimulation on the progression of retinal degeneration and
epigenetic changes in the retina. As neurons communicate via electrical signals and neuronal ac-
tivities can indeed induce neuroprotective effects, this computational modeling framework enables
us to design electrical stimulation strategies to effectively and non-invasively stimulate and activate
certain types of retinal neurons such as retinal ganglion cells (RGCs) and bipolar cells (BCs). We
developed morphologically and biophysically realistic models of RGCs and BCs to be integrated in
151
our multi-scale computational platform in order to predict electric field distributions and response
of cells to electrical stimulation of various parameters. In parallel, we performed in vivo experiments
with Royal College of Surgeons (RCS) rats to further characterize the impacts of the proposed elec-
trical stimulation approaches from the modeling framework on retinal neurons survival and halt of
progressive retinal degeneration. This work can lead to a generalized modeling framework capable
of informing therapeutic interventions with unprecedented insights into factors affecting the survival
of retinal neurons due to electrical stimulation.
The key detailed components describing the novelty of this work include: 1) A large-scale human
and rat segmented models including the finer structures of the eye as well as micro-scale modeling
of retinal layers and connectome; 2) Analyzing, for the first time, the response of retinal neurons
to trasncorneal electrical stimulation; 3) Designing the best electrodes configuration and placement
to maximize the induce electric fields in the retina and further control the level of induced fields
in different layers of the retina; 4) Designing the most effective electrical stimulation waveform to
induce directed electric fields and better target the outer layers of the retina such bipolar cells,
which are mostly affected at the early stages of retinal degeneration; 5) In-vivo experimental results
have proven our modeling framework effective in predicting the best electrical stimulation strategy.
8.2 Method
8.2.1 Computational Modeling
WehavedeployedourAM/NEURONmulti-scalecomputationalmodelingplatformto: i)predict
the electric fields generated inside the retina tissue due to TES; ii) couple the extracellular voltages
to biophysically and morphologically realistic models of retinal ganglion cells (RGCs) and BCs; iii)
152
Retina
Vitreous humor
Lens
Cornea
Retinal layers
Rat segmented model
Retinal network
Inner
Outer
Transcorneal electrical stimulation
Figure 8.1: Multiscale Admittance Method/NEURON computational platform capable of con-
structing a large-scale rat voxel model, fine details of the eye, retinal layers, and cellular-level
modeling of retinal network including retinal ganglion cells and bipolar cells.
determine the activation threshold of these cells to different electrical stimulation parameters. This
multi-scale modeling framework allowed us to build a large-scale segmented model of a rat including
the finer structures of the eye as well as micro-scale modeling of retinal layers and connectome as
shown in Figure 8.1. In the previous chapter, we developed computational models of retinal cells,
spiking diffuse BCs (DB4) and A2 RGCs, and validated our results with the experimental data from
the literature. Here, we captured the response of these cells under the considered external electrical
stimulation to identify the greatest non-invasive electrical stimulation approach to reduce the acti-
vation threshold of BCs. We investigated the impact of electrodes configurations and placements as
well as stimulus waveforms on the excitation threshold of retinal neurons to transcorneal electrical
stimulation.
The minimum resolution of rat voxel model was set to 160 m and we applied a maximum
merged element size of 64 voxels. The final computational model is composed of approximately 400
million computational cells. We tested the stimulation waveforms of symmetric charge-balanced
biphasic and monophasic pulses over a range of pulse durations from 0.1 ms to 25 ms. The resulting
153
extracellular voltages induced in the tissue have been applied to the multi-compartment models of
neurons in the simulation platform, based on NEURON, which is integrated in our computational
multiscale simulation package.
8.2.2 In-vivo experiments
The experimental efforts consisted in non-invasive electrical stimulation performed in rats to
evaluate different electrical stimulation parameters. RCS rats were used for assessing the beneficial
effects of transcorneal electrical stimulation. The Royal College of Surgeons (RCS) rat has an
inherited retinal degeneration making them a great model to study how to preserve and restore
vision. RCS rats 20-60 days old were used for all experiments. Stimulation was performed in only
one of each animal (n = 33). Body temperature was regulated and maintained at 37 °C with an
electric heating pad. Heart rate and respiration was monitored throughout the experiment. Animals
were stimulated once a week in the right eye for two hours beginning at age of postnatal day 20
(P20). Each rat received one stimulation session weekly until reaching the age of P60 completing
a total of 6 stimulation sessions. Stimulation was performed at P21, P28, P35, P42, P49 and P56.
Animals underwent Fundus Autofluorescence (FAF) and Coherence Tomography (OCT) imaging at
P21, P35, P49 and P60 (Table 8.1). OCT imaging was used to monitor the changes in retinal layer
thickness, including the Outer Nuclear Layer. FAF imaging was used to evaluate RPE health and
disease progression by assessing the hypofluorescent and hypopigmented areas of the whole retina.
All animals were maintained on a daily 12 h light/day cycle prior experiments. All procedures
conformed to the Guide for Care and Use of Laboratory Animals (National Institute of Health).
Table 8.1 is a summary of all animals performed during the 7-week in-vivo experiment.
154
Table 8.1: The procedures performed in all animals during the 7-week experiment, according to
the designed stimulation strategy.
Weeks
1 2 3 4 5 6 7
Anesthesia x x x x x x x
OCT x x x x x
FAF x x x x x
Stimulation x x x x x x x
Euthanasia x
Histology O
X all cohorts O Half cohorts
BC
RGC
RGC axon
Retina
Ground
Stimulating ring
BC
RGC
RGC axon
Retina
Ground
Stimulating
ring
TES 1 TES 2
Figure 8.2: The two placements of the stimulating ring and ground electrodes and their configu-
rations (TES 1 & TES 2). The slide of resulting voltages from AM is shown. The extracellular
voltages were extracted from the central retina (the box in the figure) and applied to each com-
partment in multi-compartment models of RGCs and BCs as shown. A 3D interpolation function
has been utilized to count for micro-scale details of retinal cells and particularly small dendrites of
bipolar cells.
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8.3 Results
8.3.1 Computational Modeling: Segmented Rat Model
Using the developed models of retinal cells in this thesis, we have utilized our multi-scale compu-
tational modeling framework to determine the best electrode placements and electrical stimulation
parameters to focalize the induced electric fields to the eye and effectively activate and target the
outer retinal neurons such as bipolar cells. Figure 8.2 represents the two placement and configura-
tion of the stimulating and ground electrodes for TES of the rat model. Figure 8.2 shows the TES 1
electrical stimulation set up where the stimulating ring is placed on the temporal side and the return
electrode on the nasal region. The second stimulation setup (TES 2) is proposed with the stimu-
lating ring on the sclera and the ground system with a ring wrapped around the neck and a wire
on the nose. Resulting extracellular voltages induced in the retina tissue from the AM model were
applied to multi-compartment models of neurons using NEURON software to analyze the neuronal
responses of the developed RGCs and BCs. Morphological sizes of retinal neurons and particularly
bipolar cells as one of the smallest neurons in the nervous system are in the order of 10 µm to 400
µm. Therefore, to save the computation time of NEURON simulations and increase the spatial
resolution of the resulting voltages, we analyzed only a section of the central retinal as indicated
in Figure 8.2. We used a 3D interpolation function to achieve a finer resolution of the AM volt-
age distribution and apply as an extracellular voltage to each compartment of multi-compartment
models of RGCs and BCs. As illustrated, the two stimulation setups lead to different generated
voltage gradients along the two retinal neurons. To slow down the progression of retinal blindness
in patients at early stage of the diseases, BCs should be the main target of electrical stimulation as
they are affected first compared to RGCs. Therefore, the TES setup with the maximum induced
electric field along the axon of BCs is desired, leading to the enhanced likelihood of voltage-gated
156
ion channels opening and reduced threshold of BCs. As shown in Figure 8.2, TES 2 setup results in
the largest generated voltage gradient along the retinal thickness and further focalizing the voltage
distribution to the eye. To better examine the influence of electrode placement and configuration on
the response of retinal neurons, we further compared the stimulation threshold of RGCs and BCs
to electrical stimulation of TES 1 and TES 2. The ratio of retinal neurons stimulation thresholds
of TES1 to TES2 setups for a range of stimulus pulse durations is shown in Figure 8.3. While the
TES1 setup can significantly reduce the stimulation threshold of RGCs, it appears to be ineffective
for electrically stimulating BCs as BCs threshold is almost 10 folds higher than RGCs threshold.
However, the TES 2 stimulation strategy allows us to better target BCs as the stimulation threshold
of this cell type is significantly reduced compared to TES 1. Therefore, generating voltage gradient
and therefore current along the direction of BCs axons and retinal thickness has shown effective for
the purpose of this study.
An alternative ground configuration and placement have been proposed as well to achieve similar
induced electric fields in the retina. Figure 8.4A illustrates the trancorneal electrical stimulation
setup (TES 3) placing the needle ground electrode on the temporal site of the stimulating ring
placed on the cornea. This ground placement with a relatively simpler implementation for elec-
trophysiological and clinical experiments has been shown to induce electric fields along the retinal
thickness similarly to the previous ground configuration (TES 2) of Figure 8.3B. This alternative
set up also allows us to more effectively target the outer retinal neuron due to the increased voltage
gradients along the thickness of the retina and therefore greater chance for neuroprotective effects
and preserving the healthy retinal neurons.
Utilizing the TES 3 setup, we applied both monophasic and biphasic stimulus waveforms of
various pulse durations and computed the stimulation thresholds of the cells. The strength-duration
157
Ground
Stimulating
coil
Ground
Stimulating
coil
0.1
1
10
100
0.01 0.1 1 10 100
TES1/TES2 Stimulus
threshold ratio
Pulse width (ms) at log scale
BCs
RGCs
TES 1 setup results in 10-fold higher
threshold of BCs compared to TES 2
setup.
TES 1 voltage gradient results in lower
threshold of RGCs compared to TES 2.
TES 1 TES 2
Figure 8.3: The ratio of RGCs and BCs stimulation thresholds of TES1 to TES2 setups for a
range of stimulus pulse durations.
curves of both stimulus waveforms are plotted in Figure 8.4B. Our initial computational findings
show that the activation threshold of bipolar cells is higher relative to retinal ganglion cells. This
arises from the smaller diameter of axons in BCs compare to RGCs. However, our modeling reveals
that using biphasic stimulus pulses with long pulse duration can reduce the activation threshold
of BCs as well as the differential stimulus threshold between the RGC and BC as shown in the
figure. Congruent to our simulation results, experimental data from the literature indicate that
long pulse duration increases the likelihood for activation of BCs and therefore indirect activation
of RGCs. Further, Walston et al. has shown experimentally using the wholemount mouse retina
that the response of ON-type BCs is desensitized as the stimulation frequency increases (Walston
et al., 2018). The response of BCs was shown to be stable at a low stimulation frequency of 6 Hz.
Therefore, the symmetric charge-balanced biphasic stimulation with pulse duration of 10 ms and
stimulus frequency of 6 Hz were selected for the initial in-vivo experiments.
158
0
50
100
150
200
0.01 0.1 1 10 100
Stimulus subthreshold (mA)
Pulse width (ms) at log scale
RGC
BCs
monophasic stimulus pulses
0
50
100
150
200
250
0.01 0.1 1 10 100
Stimulus subthreshold (mA)
Pulse width (ms) at log scale
RGC
BCs
biphasic stimulus pulses
BC
RGC
RGC axon
Retina
Stimulating
coil
ground
Stimulating ring
Ground
Electrical stimulation setup
Stimulus waveforms
TES 3
A B
Figure 8.4: (A) The placements of the stimulating ring on the sclera and the ground needle
electrode on the temporal region (TES 3). The slice of resulting voltages as well as the extracellular
electric potential generated in the retina are shown. (B) The strength-duration curves plotted for
a range of pulse durations from 0.1 ms to 25 ms for both monophasic and biphaisc stimulus pulses;
Computational results show that long biphasic pulse durations can augment the chance for the
excitations of retinal bipolar cells and further reduce the differential stimulation threshold of RGCs
and BCs.
Table 8.2: The electrical stimulation parameters and the number of animals that were included
for each set of stimulation parameter.
Number of
Animals
Frequency (Hz) Pulse
width (ms)
Amplitude (µA)
8
6 10
20
8 50
8 100
9 NA NA Sham
159
Electrical stimulation setup
Stimulating ring
Ground
Figure 8.5: In-vivo electrical stimulation setup.
8.3.2 In-vivo experimental results
A ring-shaped electrode similar to the embodiment of Figure 8.4A (4 mm in diameter) was
placed on the cornea (right eye) and used as the stimulating electrode. An electrode was placed
temporally of the stimulated eye as a ground electrode. Charge-balanced, cathodic first, biphasic
pulses with a pulse width of 10 ms and no interphase gap were used for all stimulating groups.
Table 8.2 is describing the selected electrical stimulation parameters. The frequency was set at 6
Hz and the current amplitudes of 20 µA (n = 8), 50 µA (n = 8), and 100 µA (n = 8) were tested.
Sham group (n = 9) had the ring-shaped electrode placed on the right cornea and kept in place for
2 hours without any stimulation given (Table 8.2). The experimental setup including tested rats,
the electrodes, oscilloscope for recording the input voltage, and the stimulus waveform generator is
shown in Figure 8.5. Lastly, histology was performed using Hematoxylin and Eosin stain (H & E)
and photoreceptor count (PR) was done in both treated and untreated eyes.
160
Figure 8.6: Fundus Autofluorescence image of one animal treated in the 100 uA group. Image
A shows the non-treated eye where hypopigmentations are observed (inside dotted circle). Image
B shows the treated eye where early stages of degeneration are observed as sparse hyperpigmented
spots (blue arrow). (Figure from Alejandra Gonzalez-Calle)
8.3.2.1 OCT and FAF Imaging
FAF imaging was evaluated in order to assess the health of the whole retina and the disease
progression. Progression of the disease can be evaluated by monitoring the amount of hyperpig-
mentations and hypopigmentations covering the retinal area. The first stages of degeneration can
be observed with hyperpigmented spots (see Figure 8.6; arrow in image), but while the diseases
progress, hypopigmentations can be observed (dotted circle in image). The more hypopigmenta-
tions covering the area, the more advanced is the disease. FAF images were visually analyzed. It
was observed that for the sham and 20 µA groups the disease progressed at a similar and steady
rate in both treated and non-treated eyes. On the contrary, at 50 µA and 100µA the rate at which
the disease was progressing was reduced in the treated eye compared to the untreated eye (Figure
8.6).
OCT imaging was used to monitor the changes in retinal layer thickness. Volume scans are
taken every 30 ums and consists of 60 consecutive single scans. Volumes scans were images using
161
160
165
170
175
180
185
190
195
200
Non Treated Treated Non Treated Treated Non Treated Treated
100 uA 50uA 20 uA
Retinal Thickness (µm)
Animals Age (Days Old)
Retinal Thickness
Figure 8.7: Summary of the retinal thicknesses from the three stimulation groups stratified as
non-treated vs. treated eyes. The grey bars represent the mean per group (n = 8) and the error
bars denote the standard error of the mean. (Figure from Alejandra Gonzalez-Calle)
the optic nerve as a landmark to ensure that the same area was analyzed for all animals. Retinal
thickness was analyzed for both treated and non-treated eye. Data was analyzed using MATLAB.
A parametric paired t-test was performed to assess if the mean difference between treated and non-
treated eye at p60 was significant. The observed differences between treated and non-treated within
the sham and one stimulated at 20 µA was not statistically different (p = 0.806 and p = 0.242,
respectively). However, the groups that were stimulated at 50 and 100 µA revealed a difference in
retinal thickness that was statistically different between the treated and the non-treated eyes (p =
0.005 and p = 0.001, respectively) (Figure 8.7).
8.3.2.2 Histology
Hematoxylin and eosin (HE) staining was performed in half of the animals from each tested
group (n = 4). Histological slides were scanned, and photoreceptor counts were acquired from a 1
mm section located 1 mm away from the optic nerve in the inferior area of the retina (Figure 8.8).
Photoreceptor counts were acquired from both treated and non-treated eyes.
162
Figure 8.8: Cross section of histological slides comparing the treated vs the non-treated eye of
an animal stimulated from the 100uA group. Image A shows loss and disorganization of the ONL
layer while treated eye shows preservation of the ONL layer compared with the non-treated eye.
GCL: Ganglion Cell Layer. INL: Inner Nuclear Layer. ONL: Outer Nuclear Layer. (Figure from
Alejandra Gonzalez-Calle)
Table 8.3: Summary of the photoreceptor counts acquired from all stimulated and sham groups.
(Figure from Alejandra Gonzalez-Calle)
The improvement was defined as the percent increase in photoreceptor count when comparing
treatedvsnon-treatedeyes. Aparametricpairedt-testwasperformedtoassessifthemeandifference
between treated and non-treated eyes at p60 was significant. The mean photoreceptor count of
treated vs non treated from the sham group did not show an increase in photoreceptor count
when comparing both eyes, while the 20 µA group showed an improvement of 4.95%. Both of the
aforementioned statistical tests did not show significant differences (p = 0.2036 and p = 0.6794,
163
Ground
Stimulating ring
Stimulating ring
Ground
Stimulating ring
Ground
A B C
Figure 8.9: Coarse human head models: Three different placements and configurations of the
ground electrode.
respectively). However, the 50 µA and 100 µA groups showed an improvement of 20.8% and 38.2%
in photoreceptor count respectively, when comparing non-treated vs treated eyes, and the results
proved to be nearly statistically significant for the former (p = 0.0548) and statistically significant
for the latter (p = 0.0091) (See Table 8.3).
8.3.3 Computational Modeling: Segmented Human Head Model
While simulating the segmented rats and mice models consist of fine details of the retina and
morphometric and biophysical feature are significantly critical for identifying effective electrical
stimulation approach, the structure of the human head is entirely different from animal models and
furtherinvestigationsarerequiredtobetterunderstandtheinducedelectricfieldsduetotranscorneal
electrical stimulation. Therefore, we further utilized our multi-scale computational modeling plat-
form to determine the best non-invasive transcorneal electrical stimulation strategy in clinics for
patients suffering from various retinal degenerative diseases.
164
Ground Ground
B C
Ground
A
Figure 8.10: The slices of the current density magnitude distribution for the three ground con-
figurations.
8.3.3.1 Coarse Resolution Human Head Model
The segmented human head model is extracted from the Visible Human Project (Cela:45).
The resolution of the original coarse model is 1 mm, and the size of the human head model is
250× 340× 350 voxels. This coarse resolution is not very computationally expensive and allows
to predict the electric field distribution in the eye and the brain due to TES of varying electrode
placements and configurations. Figure 8.11 illustrates the three different configurations of return
electrodes for a given stimulating ring on the sclera. Figure 8.9A shows the placement of large metal
ground sheet on the back of the head. Another ground electrode configuration on the orbital regions
is illustrated in Figure 8.9B. Finally, a small disk electrode is placed on the temple region as a return
electrode (Figure 8.9C). This multiresolution AM approach allows us to predict the current density
and electric field distributions generated due to different TES setups. This modeling framework
further enables us to determine the best stimulation technique for both safe and effective delivery
of electrical stimulation.
Figure 8.10 compares the current density distributions from the three placements of ground
electrodes. As shown, the ground placement on the back of the eye leads to induced current density
165
12
B C A
Figure 8.11: The slices of the electric field magnitude distribution for the three ground configu-
rations.
to the brain which is desired for this therapeutic application. While the small disk ground electrode
on the temporal site may effectively apply current to the eye and optic nerve, the undesired current
density on the temple is shown to be inevitable which may cause discomfort for patients. The
TES stimulation strategy of Figure. 8.9B has been shown effective in both eliminating the current
distributed in the brain and high current density on the temporal region as illustrated in Figure
8.10B. The high current density indicates high charge density and therefore great likelihood of
charge accumulation and tissue damage. The stimulation setup leading to the minimum induced
current density in undesired regions while effectively stimulating the eye is certainly important.
The proposed TES approach of Figure 8.9B has proven effective for this purpose. The electric field
strengths of the three TES systems are shown in Figure 8.13. As expected, the electric fields directly
correlate the distributed current density. The great electric field strength generated in the brain is
illustrated in Figure 8.11A.
166
Stimulating electrode
Ground
DTL electrode on
the sclera
DTL electrode on
the eyelid
Stimulating electrode
Ground
B A
Figure 8.12: The placement of the stimulating DTL electrode: A) on the sclera; B) on the eyelid.
8.3.3.2 High Resolution Human Head Model
To predict the field distribution more accurately near the orbital region and eye, a higher resolu-
tion of human head incorporating finer structure of the eye as well as nearby tissues was constructed.
This highly detailed model with high resolution allows us to model the size of bioelectronic compo-
nents and compute the distributed electromagnetic fields more precisely. To save the computation
time the human head model is trimmed to incorporate only a quarter of the head. The resolution
of the new model is 250 µm with the dimension of 370× 500× 290 voxels.
8.3.3.3 The DTL Stimulating Electrode
This high-resolution model further enables us to compare different stimulating electrode configu-
rations as well as the influence of placing the electrode on the eyelid/sclera on the generated current
and electric fields. Figure 8.12 compares the placements of the DTL stimulating electrode on the
sclera and eyelid with the common disk ground electrode of 15 mm in diameter on the temporal
region. The model is manually modified to include 1 mm thin eyelid as shown in Figure 8.12B. The
167
Higher current
density on the eyelid
DTL electrode on
the sclera
DTL electrode on
the eyelid
B A
Figure 8.13: The slices of the current density magnitude distribution. A) DTL stimulating
electrode on the sclera; B) DTL stimulating electrode on the eyelid.
thickness of the stimulating DTL electrode is 250 µm with the length of 1 cm. The current density
and electric field distribution of the two TES systems is shown in Figure 8.13. While both electrode
placements result in a similar induced current density on the eye and surrounding tissues, the great
current density on the eyelid is detected placing the stimulating on top of the eyelid. This may
lead to discomfort and unpleasant tingling sensation for patients during TES. Figure 8.14 plots the
voltage distribution of the two systems, indicating the greater peak electric potential of the case
with the DTL electrode on the eyelid (38 V vs. 19 V). This high input impedance can possibly
limit the delivered current to the load from stimulators. Therefore, the placement of the stimulating
electrode on the sclera outweighs the TES setup with the electrode on the eyelid.
8.3.3.4 The Ring Stimulating Electrode
The DTL-Plus electrode has been widely used for clinical electroretinography including the
trans-corneal electrical stimulation for RP patients. In this section, we compared the efficacy and
safety of the DTL electrode with the ring stimulating electrode on the sclera as illustrated in Figure
168
Peak voltage = 19 V Peak voltage = 38 V
High voltage on the
eyelid
DTL electrode on
the sclera
DTL electrode on
the eyelid
B A
Figure 8.14: The slices of the electric potential distribution. A) DTL stimulating electrode on
the sclera; B) DTL stimulating electrode on the eyelid.
Stimulating electrode
Ground
DTL electrode on
the sclera
Stimulating ring
Ground
Ring electrode on the
sclera
1 mm
B A
Figure 8.15: Comparison of two stimulating electrode configurations. A) DTL electrode; B) Ring
electrode.
169
Higher current density on
the cornea
B A
Figure 8.16: The slices of the current density magnitude distribution for the two stimulating
electrode configurations.
higher electric fields
on the cornea
B A
Figure8.17: Theslicesoftheelectricfieldmagnitudedistributionforthetwostimulatingelectrode
configurations.
170
Wire ground
electrode on the
temple
Frontal region
Infraorbital
region
Figure 8.18: The configuration of the proposed ground electrode for delivering more effective and
safe TES.
8.15. The width of the ring electrode is set to be 1 mm and the inner diameter of the ring is 1.5 cm.
The distributed current density and electric field magnitude of the two TES systems of Figure 8.15
are shown in Figures 8.16 and 8.17, respectively. While the generated current density and electric
field strength on the back of the eye and the retina are almost similar using the two TES techniques,
the proposed stimulating ring can significantly reduce the current density and electric field on the
cornea compared to the DTL stimulating electrode. This indicates the safer delivery of TES to the
eye using the ring electrode of Figure 8.15B relative to the DTL electrode of Figure 8.15A.
8.3.3.5 The Proposed Return Electrode Configuration
We have so far determined the best stimulating electrode placement and configurations for both
safe and effective stimulation of the eye in human voxelized model for translating this modeling
simulation results to clinics. Small return electrodes have been widely used in the literate for TES
applications. However, our simulation results in the previous sections indicate that the generated
current density and electric field strength in the proximity of the small disk ground electrode can
171
High current density
near the temple
Current density is
significantly reduced on
the temporal side
B A
Figure 8.19: The slices of the current density magnitude distribution. A) The proposed ground
system of Figure 8.18; B) The disk ground electrode on the temple.
Reduced electric fields
on the temporal side
B A
Figure 8.20: The slices of the electric field magnitude distribution. A) The proposed ground
system of Figure 8.18; B) The disk ground electrode on the temple.
172
Peak voltage = 12 V Peak voltage = 37 V
B A
Figure 8.21: The slices of the voltage distribution. A) The proposed ground system of Figure
8.18; B) The disk ground electrode on the temple. The reduced peak voltage of the proposed system
compared to the common small ground electrode on the temporal region is shown in the figure.
be relatively high (Figures 8.16 and 8.17) and mat raise the safety concern for clinical applications.
Figure 8.18 shows the proposed ground electrode configuration covering the orbital region. A thin
and long metal wire is placed on the frontal, infraorbital, and temple regions of the human head
with the same stimulating ring on the sclera (Figure 8.16). The proposed ground electrode system
significantly reduces the current density and electric field magnitude on the temple compared to the
system with small ground electrode on temporal site as shown in Figures 8.19 and 8.20. Last but
not least, comparing the voltage distribution of the two TES systems, the peak voltage is relatively
lower with the proposed ground of Figure 8.21 that of the small disk ground electrodes (Figure
8.21).
8.4 Conclusion
Given thefact that controlledelectricalstimulation can induce neuroprotective effects in neurons
and in particular retinal cells, we have, for the first time, developed a multi-scale computational
173
method capable of analyzing the response of retinal neurons to transcorneal electrical stimulation.
We deployed this modeling framework to design electrical stimulation setups for effectively inducing
electric fields in the retina for therapeutic approaches. We further designed electrical stimulus
waveforms to selectively stimulate retinal cells such as bipolar cells that are influenced first at the
early stage of retinal degeneration to induce protection to the damaged cells and therefore slow
down the progression of retinal blindness. We found that retinal bipolar cells are more sensitive to
long stimulus pulses of TES, offering intriguing potential to induce epigenetic and neuroprotective
changes to primarily affected bipolar cells.
Utilizing the designed stimulation strategy from this computational modeling platform, we per-
formed in vivo experiments in RCS rats. Our results including FAF, and OCT imaging indicate
that the progression of retinal degeneration is reduced in the treated eye compared to the non-
treated eye. Further, the application of the proposed TES approach has preserved the number of
healthy photoreceptors relative to the control group. These preliminary findings have proven our
computational modeling approach powerful in predicting the best stimulation technique for effec-
tively inducing electric fields in the retina and stimulating retinal cells preferentially. Further animal
testing needs to be carried out to better confirm the outcome of the current study and non-invasive
TES approach for treating retinal blindness.
While simulating the segmented rat model consists of fine details of the retina and morphometric
and biophysical features are significantly critical for identifying an effective electrical stimulation
approach, the structure of the human head is entirely different from animal models and therefore
further investigations are required to better understand the induced electric fields due to TES.
Therefore, we further utilized our multi-scale computational modeling platform to determine the
best non-invasive TES strategy in clinics for patients suffering from retinal degenerative diseases
174
such as RP. We proposed a novel ground configuration and placement of electronic components to
effectively and safely induce the electric fields in the human retina. The TES system using the
segmented human head model supports the possibility pf proposing a novel electrical stimulation
strategy to slow down relentless and aggressive retinal degeneration in clinical studies.
175
Chapter 9
Summary and Future Steps
In this thesis, we have focused on the two common electrical stimulation therapeutic approaches
to treating retinal degenerative diseases: i) Retinal prosthetic devices; ii) non-invasive transcorneal
electricalstimulation(TES)techniques. Retinalprosthesesaimattargetingandstimulatingthesur-
viving retinal neurons by placing the stimulation electrodes in the close vicinity of functional retinal
neurons. This stimulation technique mostly helps patients at the late phase of retinal degeneration,
which allows for the implantation of electronic devices into the eye. In this work, we particularly
centered our focus on epiretinal prosthetic devices (Argus II, Second Sight Medical Product, Inc). In
regard to the second treatment approach, the non-invasive TES stimulator mostly aims at inducing
neuroprotective effects in the retina, preserving the function of retinal cells, thereby slowing down
the retinal degenerative progress. Therefore, this therapeutic method provides intriguing potential
for treating prevalent retinal blindness among patients (such as RP patients) at the early stage of
retinal degeneration.
To increase the performance of these two therapeutic techniques, electrical stimulation strategies
must be designed to stimulate retinal neurons selectively, effectively, and safely. In fact, not only
176
the ability to selectively target retinal neurons is essential, but also preferential activation of the
subtypes of specific retinal neurons significantly enhances the efficacy of current prosthetic devices.
This can also increase the outcome of non-invasive stimulation approaches to inducing neuroprotec-
tive changes, therefore slowing down or halting the progression of retinal blindness. Computational
modeling framework provides a means to better understand the response of retinal neurons to elec-
trical stimulation of varying types and design stimulation techniques for improving the efficacy of
electrical stimulation. Modeling platforms further enable researchers to capture mechanism under-
lying the response of neurons to electrical stimulation as well as neuroprotective effects of electrical
stimulation on retinal neurons.
We have deployed our multiscale computational modeling platform to: i) develop morphologi-
cally and biophysically detailed models of retinal neurons; ii) predict the response of retinal cells
to epiretinal electrical stimulation and compare the results with both experimental and clinical
studies; iii) utilize this predicative model to enhance our understanding of mechanism underlying
response behavior of retinal cells and their neuronal functionality; iv) deploy this knowledge to fur-
ther address challenges associated with retinal prosthetic systems and minimally invasive electrical
stimulators; v) design novel stimulation strategies to increase the outcome of the two stimulation
techniques for treating retinal blindness.
Towards this, realistic models of the two subtypes retinal ganglion cells and bipolar cells were
developedinthisworkandverifiedwithexperimentaldatafromtheliterature. Regardingtheretinal
prosthetic devices, we first focused on stimulation waveforms design for: i) selective activation of
RGCscellbodiestoavoidaxonalactivationandelongatedphosphenesreportedbyArgusIIsubjects;
ii) preferential stimulation of functionally different subtypes of RGCs, and particularly those that
carry information such as color and contrast; iii) enhanced chance for selective activation of bipolar
177
cells for indirect stimulation of RGCs, therefore preventing axonal excitation and improving spatial
resolution of current devices. Through this developed predictive computational tool, we have been
able to identify stimulation parameters to selectively target small bistratified RGCs, which have
been shown to contribute to “blue-yellow” color opponency in the retinal circuitry. This platform
allowed us to further investigate mechanisms of color encoding in electrical stimulation of the retina,
which could prove pivotal for the design of advanced retinal prosthetics that elicit both percept and
color. These findings were validated in clinical testing, where studies in blind subjects affected by
Retinitis Pigmentosa (RP) and received an artificial retina demonstrated that color sensation could
be elicited and the perceived colors may be shifted by the stimulation frequency. We also identified
the role of the hyperpolarization-activated cyclic nucleotide-gated (HCN) channel in high sensitivity
of spiking retinal bipolar cells to long stimulus pulse durations. This finding and the application
of varying stimulus waveforms also enabled us to delve into the missing puzzles of experimental
observations from the literature and find out potential explanations and solutions utilizing this
modeling framework.
In the future, this multiscale modeling strategy will be used to incorporate a highly detailed
model of retinal network and connectomes including morphological and physiological properties.
The response of the retinal neurons in the healthy network to electrical stimulation will be compared
to that of patho-connectome models, or connectomics volumes constructed from pathological or
neurally degenerating retina tissue for various stages of retinal degeneration. We will characterize
the impact of the retinal degeneration on neural activation induced by stimulating electrodes and
compare it with previously obtained results with the healthy or synthetically degenerated retina.
Anatomical and electrophysiological studies will be performed to predict more closely the natural
signaling patterns and features of retinal neurons in response to electrical stimulation for further
improving implanted retinal prosthetic devices.
178
In addition to applications of neuroprosthetic devices, we utilized this multiscale computational
modeling framework to design safer and more effective TES neurostimulators. This predictive
numerical toolset and the developed retinal neurons in the present work allowed us to propose
electrical stimulation setup to effectively induce of electric fields in the retina for therapeutic effects.
Our preliminary results in rats indicated the effectiveness of the proposed stimulation strategy to
rescue retinal neurons and slow down the blindness progression. For the future studies, the design
electronic components and configuration will be tested in clinics to demonstrate the short-term and
long-term safety and efficacy of the TES stimulator.
179
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Abstract (if available)
Abstract
Retinal diseases, such as retinitis pigmentosa (RP), age-related macular degeneration (AMD), and glaucoma (POAG), are characterized by unrelenting neuronal death. Although treatments to ameliorate these conditions exist, there is no cure. Therefore, attempts have been made to restore partial sight to the blind or slow down the progression of retinal blindness. For instance, epiretinal prosthetic devices have been developed to electrically stimulate the surviving retinal neurons and restore some forms of visual function. While these devices have had a significant impact on the lives of totally blind patients, several challenges - such as limited spatial resolution and the inability of subjects to perceive color and contrast - have yet to be addressed. In this dissertation, we applied a three-dimensional Admittance Method (AM)-NEURON multiscale computational modeling platform to gain an understanding of the mechanisms underlying the response of retinal neurons to electrical stimulation, and their functional implications. The AM-NEURON computational platform is capable of modeling complex, large-scale, heterogeneous biological tissues as well as micro-scale modeling of biophysically and morphologically realistic models of neurons; its multiphysics nature enables us to design electrical stimulation strategies for enhancing the efficacy of current epiretinal prosthetics systems, with the ultimate goal of developing the next generation of retinal prostheses. While current retinal prosthetic systems are intended for blind patients that are at late stages of retinal degeneration, approaches to delaying the onset of blindness and progressive retinal degeneration at the early stage of degeneration would make a significant impact in the lives of patients suffering from these conditions. We introduce in this dissertation a strategy that relies on controlled electromagnetic (EM) retinal stimulation to induce neuroprotective changes in the retina. Toward this goal, our computational modeling platform was utilized to design a non-invasive electrical stimulator to maximize the induced electric fields in the retina, thus likely increasing the potential for neuroprotective effects and potentially opening avenues to slow down the progression of retinal blindness.
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Asset Metadata
Creator
Paknahad, Javad
(author)
Core Title
Electrical stimulation approaches to restoring sight and slowing down the progression of retinal blindness
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Electrical Engineering
Degree Conferral Date
2022-05
Publication Date
07/28/2022
Defense Date
10/28/2021
Publisher
University of Southern California
(original),
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Tag
admittance method,color perception,computational modeling,neuron,OAI-PMH Harvest,retinal diseases,retinal implants,sight restoration
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English
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Lazzi, Gianluca (
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javadpaknahad@gmail.com,paknahad@usc.edu
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Tags
admittance method
color perception
computational modeling
neuron
retinal diseases
retinal implants
sight restoration