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University of Southern California Dissertations and Theses
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Therapeutic electrical stimulation strategies for neuroregeneration and neuroprotection of retinal neurons
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Therapeutic electrical stimulation strategies for neuroregeneration and neuroprotection of retinal neurons
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Content
THERAPEUTIC ELECTRICAL STIMULATION STRATEGIES FOR NEUROREGENERATION
AND NEUROPROTECTION OF RETINAL NEURONS
by
Ege Iseri
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
(BIOMEDICAL ENGINEERING)
May 2024
Copyright 2024 Ege Iseri
Acknowledgements
I would like to express my sincere gratitude to my advisor, Professor Gianluca Lazzi, for providing me
with the opportunity to be a part of his lab and for his unwavering support during challenging times. I
am grateful for the privilege of collaborating with numerous other groups during my Ph.D., and I extend
my heartfelt thanks to Professor Kimberly Gokoffski and Professor Mark Humayun for their invaluable
mentorship during my research.
I am appreciative of all my colleagues and mentors whom I have had the privilege of working with
over the years; their guidance has been invaluable.
I owe a debt of gratitude to my dear parents, Verda and Haluk, whose support and encouragement of
independence from a young age have been instrumental in my journey.
Lastly, I want to express my profound appreciation to my dear love, Dilara, who has stood by me
throughout my academic journey, giving me all the support I could ask for.
ii
Table of Contents
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi
Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Neuromodulation Through Direct Electrical Stimulation . . . . . . . . . . . . . . . . . . . 1
1.1.1 Neuroregeneration and Electrotaxis . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Neuroprotection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.3 Neural Stimulation Protocols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.3.1 Electrode Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.3.2 Waveform Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 The Retina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 Retinal Ganglion Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.2 Photoreceptors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.3 Retinal Degeneration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3 Computational Modeling and Simulation Methods . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.1 NEURON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.2 Admittance Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4 Significance and Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Chapter 2: Electrotaxis and Target-Specific Migration of Axons Using Asymmetric ChargeBalanced Waveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.1 Cell Culture Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.2 Stimulation Parameters and Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.3 Purity and Viability Assays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.4 Quantification and statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.4.1 RGC growth in vitro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
iii
2.7 Data availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Chapter 3: In Vivo Neuroregenerative Electrical Stimulation Therapy Using Asymmetric ChargeBalanced Waveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.1 Animal Surgical Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.2 Stimulation Parameters and Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.3.3 Computational Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3.4 Anatomical Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.3.5 Functional Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.3.6 Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.4.1 Viability Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.4.2 Long-term Assessment of Equivalent Tissue Impedance . . . . . . . . . . . . . . . 54
3.4.3 Target-Specific Regeneration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.4.4 Partial Recovery of Electrophysiology . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.4.5 Recovery of Pupillary Function and Visual Behavior . . . . . . . . . . . . . . . . . 61
3.4.6 Prediction of RGC Response to Employed Waveforms . . . . . . . . . . . . . . . . 62
3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Chapter 4: A Transcorneal Electrical Stimulator to Induce Neuroprotection and Prolong Photoreceptor Survival in the Degenerating Retina . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.3.1 Computational Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.3.2 Animal Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.3.3 Electrode Connection and Stimulation Parameters . . . . . . . . . . . . . . . . . . 77
4.3.4 Calculation of the Current Density . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.4.1 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.4.2 In vivo and Ex vivo Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 81
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Chapter 5: A Connectome-Based Computational Model of Early-Stage Retinitis Pigmentosa . . . . 92
5.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.3 Methods and Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.3.1 Data Extraction and Simulation Framework . . . . . . . . . . . . . . . . . . . . . . 96
5.3.1.1 Morphology and Topology . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.3.1.2 Pre-processing and Simulation in NEURON . . . . . . . . . . . . . . . . 97
5.3.1.3 Pre-processing and Simulation in NEURON . . . . . . . . . . . . . . . . 98
5.3.2 Cell Biophysical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.3.2.1 Rod Photoreceptor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
iv
5.3.2.2 Cone Photoreceptor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.3.2.3 Rod Bipolar Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.3.2.4 ON-Cone Bipolar Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.3.2.5 Aii Amacrine Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.3.2.6 ON-Retinal Ganglion Cell . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.3.3 Synaptic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.3.3.1 Rod Photoreceptor - Rod Bipolar Cell . . . . . . . . . . . . . . . . . . . . 106
5.3.3.2 Cone Photoreceptor – ON Cone Bipolar Cell . . . . . . . . . . . . . . . . 106
5.3.3.3 Cone Photoreceptor – Rod Photoreceptor . . . . . . . . . . . . . . . . . . 106
5.3.3.4 ON Cone Bipolar Cell – Aii Amacrine Cell . . . . . . . . . . . . . . . . . 107
5.3.3.5 Aii Amacrine Cell – Aii Amacrine Cell . . . . . . . . . . . . . . . . . . . 107
5.3.3.6 ON Cone Bipolar Cell – Ganglion Cell . . . . . . . . . . . . . . . . . . . 108
5.3.3.7 Rod Bipolar Cell – Aii Amacrine Cell . . . . . . . . . . . . . . . . . . . . 108
5.3.3.8 Cone Photoreceptor – Rod Bipolar Cell . . . . . . . . . . . . . . . . . . . 109
5.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.4.1 Baseline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.4.2 Early-Stage Degeneration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.4.2.1 Photopic Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.4.2.2 Mesopic Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.4.2.3 Scotopic Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.4.3 Model Parameter Sweep and Impact on the Output . . . . . . . . . . . . . . . . . . 117
5.4.3.1 Number of Rod Inputs per RodBC . . . . . . . . . . . . . . . . . . . . . . 117
5.4.3.2 Gap Junction Blockage and Conductance . . . . . . . . . . . . . . . . . . 118
5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
Chapter 6: An External Circuit Technique for Improving Neurostimulation Tolerance In Vivo . . . 127
6.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.3.1 Approaches for Improving Stimulation Tolerance and Efficacy . . . . . . . . . . . . 130
6.3.1.1 Electrode Equivalent Circuit Model . . . . . . . . . . . . . . . . . . . . . 130
6.3.1.2 Stimulation Waveform Design . . . . . . . . . . . . . . . . . . . . . . . . 132
6.3.1.3 Proposed Circuit Design for Improving Stimulation Tolerance . . . . . . 134
6.3.1.4 Active Circuit Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.3.1.5 Passive Circuit Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.3.2 Electrodes, Waveform and Polarity . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
6.3.3 Circuit Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
6.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6.4.1 Circuit Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6.4.2 In Vivo Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
6.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
Chapter 7: Summary and Future Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
v
List of Tables
2.1 Decreased maximum length of anodically-oriented axons in DC treated cultures compared
to control and monophasic treated cultures. Purified RGC cultures were exposed to direct
current or monophasic pulse stimulation. Axon length was quantified as described in
METHODS. The longest anodically-oriented axon was significantly shorter in 2 V/cm
DC treated cultures over control and monophasic treated cultures. *** p < 0.001, ANOVA
followed by Tukey’s multiple comparisons. Control n = 251 axons over 4 cultures; 2 V/cm
DC n = 270 axons over 4 cultures; 2 V/cm monophasic n = 351 axons over 3 cultures; 4
V/cm monophasic n = 288 axons over 3 cultures. . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1 Target stimulation parameters for each waveform. . . . . . . . . . . . . . . . . . . . . . . . 45
3.2 Average percent of regenerated RGCs at various distances from the crush site. Error
represents SEM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.3 Biphasic stimulation with ACB 1:4 mediates partial recovery of RGC function. Baseline:
One week after crush and electrode placement but before initiation of stimulation. Mean
normalized N95 amplitude on PERG testing over time in each stimulation group (error
bars, SEM). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.1 List of Resistivity Values for the Tissue Types Used in the Rat Head Model . . . . . . . . . 75
4.2 Maximum and average induced current densities at the retina and the off-target voltage
induced in the brain for three configuration of TES . . . . . . . . . . . . . . . . . . . . . . 81
5.1 The cells IDs extracted from the RPC1 dataset and plotted in Fig. 5.1 . . . . . . . . . . . . . 96
5.2 Voltage-Gated Ionic Channel Distribution for Retinal Cells . . . . . . . . . . . . . . . . . . 105
5.3 Synaptic distribution in the network model between neighboring cells. (Rg): metabotropic
graded ribbon, (−Rg): ionotropic graded ribbon, (Re): excitatory exponential ribbon, (G):
gap junction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.4 The impact of blocking different gap junction groups and increasing the conductance
on the RGC firing rate peri-stimulation (cone photocurrent active, 2 s < t < 2.5 s) and
post-stimulation (cone photocurrent zero, t > 2.5 s). . . . . . . . . . . . . . . . . . . . . . . 120
vi
6.1 Parameters for the simulated systems shown in Fig. 6.5. Same components for the NIC
and RC systems were also used in the in vivo experiments. . . . . . . . . . . . . . . . . . . 142
6.2 The total charge tolerated during the anodic phase by each animal between standard, NIC
and RC systems. The total charge is the area under the curve, calculated using trapezoidal
integration of the anodic phase from t = 0.1 ms to t = 0.5 ms (Fig. 6.8). . . . . . . . . . . . . 148
vii
List of Figures
1.1 Typical waveforms used in neurostimulation. While the total charge balance in maintained
in all three cases, the rate of charge injection is different, which can have an influence on
the physiological effect. Figure modified from [19]. . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Illustration of the visual pathway from the retina to the optic nerve. Light stimulation
is converted to a change in the electrical potential across the cell membrane through
phototransduction. This signal propagates downstream from photoreceptors to retinal
ganglion cells and towards the visual cortex via the optic nerve. . . . . . . . . . . . . . . . 6
1.3 The three phases of remodeling during retinal degeneration. An early intervention timing
falls between phases one and two, when the photoreceptors partially alive and functional.
Therapeutic interventions at this stage will aim to prolong photoreceptor survival and
delay disease progression. After a complete loss of photoreceptors in phase three, the
intervention will aim to create artificial vision through direct electrical stimulation of the
retina or visual cortex. Figure modified from [29]. . . . . . . . . . . . . . . . . . . . . . . . 9
1.4 A two-cell network in the retina represented in 3D space as .swc files. The cells are
made up of small compartments in the order of 103
to capture morphological realism.
Each compartment can have unique biophysical properties to model the soma, axon
or dendrites. The equivalent circuit model of a compartment is shown, which includes
voltage-gated ionic channel conductances (g), equilibrium potentials (E), membrane
capacitance (C) and axial resistance that connects the compartments (Ra). . . . . . . . . . 11
1.5 The bulk tissue model in AM combined with the two-cell network of Fig. 1.4. The 3D space
can be segmented into voxels of sufficient resolution to solve the membrane potential
response of different compartments. Each node of the voxels are connected by equivalent
resistances reflecting the tissue properties. The computed voltages at these nodes are
applied as the extracellular potential to the equivalent circuit model of the compartment
in NEURON simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
viii
2.1 Schematic of Electrotaxis Chamber and Waveforms Tested. (A) An electrotaxis chamber
was built onto a 100 mm tissue culture plate previously coated with Matrigel. Purified
RGCs (yellow) were seeded onto the plate and agarose salt bridges were used to deliver
current to the electrotaxis chamber. (B) Representative schematic of DC, AC, ACB
waveforms and monophasic pulse. (C) An example of voltages recorded across an
electrotaxis chamber (Va-Vb) stimulated with ACB waveform 1:2. The left plot was
recorded at the start of stimulation while the right plot was recorded after four hours of
stimulation. Modified from [51]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 Larger pulse amplitudes direct more avid cathodic growth of RGC axons. Purified RGC
cultures were exposed to direct current (A) or monophasic EF stimulation (B). Increases
in pulse amplitude led to increases in cathodic-directed growth of RGC axons. * p <
0.05; ** p < 0.01; *** p < 0.001; **** p < 0.0001; ANOVA followed by Tukey’s multiple
comparisons. Control n = 251 axons over 4 cultures; 0.5 V/cm DC n = 559 axons over
3 cultures; 1 V/cm DC n = 368 axons over 3 cultures; 2 V/cm DC n = 270 axons over 4
cultures; 1 V/cm monophasic n = 510 axons over 3 cultures; 2 V/cm monophasic n= 351
axons over 3 cultures; 4 V/cm monophasic n = 288 axons over 3 cultures. As published in
[51], supplementary figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3 Larger pulse amplitudes direct more avid cathodic growth of RGC axons. Purified RGC
cultures were exposed to direct current (A) or monophasic pulse stimulation (B). Increases
in pulse amplitude led to increases in cathodic-directed growth of RGC axons (*p < 0.05
comparing cathodic growth; ANOVA followed by Tukey’s multiple comparisons). Tissue
culture experiments were performed concurrently and only segregated into separate
charts to facilitate flow of the paper. (C) Stills of time lapsed recordings of RGC axon
growth in control and 2 V/cm DC treated cultures. Black numbers label axons that grew
towards the cathode, red numbers label axons that grew towards the anode, while yellow
numbers label axons that grew perpendicular to the EF. Scale bar 100 µm. As published in
[51]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4 Longer pulse width duration is more effective at directing axon growth. Purified RGC
cultures were exposed to monophasic EF stimulation. (A) Fewer RGC axons grew
towards the cathode with shorter pulse widths. (B) Increasing voltage amplitude or (C)
experimental duration did not increase the effectiveness of a short pulse width waveform.
(D) Decreasing interpulse interval did not increase the effectiveness of a short pulse
width waveform. (E) Increasing interpulse interval did not neutralize the effectiveness
of a longer pulse width waveform (*p < 0.05; ANOVA followed by Tukey’s multiple
comparisons) As published in [51]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.5 (A) 2 V/cm 25% duty cycle n = 396 axons over 3 cultures; 37.5% duty cycle n = 316 axons
over 3 cultures; 50% duty cycle n = 351 axons over 3 cultures; 100% duty cycle n = 270
axons over 4 cultures. (B) 2 V/cm n = 458 axons over 3 cultures; 4 V/cm n = 288 axons
over 3 cultures. (C) 4 hours n = 458 axons over 3 cultures; 8 hours n = 508 over 3 cultures.
(D) 400 mHz n = 396 axons over 3 cultures; 800 mHz n = 444 axons over 4 cultures (E) 400
mHz n = 351 axons over 3 cultures; 200 mHz n = 611 axons over 4 cultures Modified from
??, supplementary figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
ix
2.6 ACB waveforms directed more avid cathodic growth of RGC axons than symmetric
waveforms. Purified RGC cultures were exposed to ACB waveforms with different
cathodic:anodic pulse width and pulse amplitude ratios. (A) Increased anodic pulse
width duration was associated with increases in cathodic-directed growth of RGC axons
(unstimulated n = 4; AC 1:1 n = 4; ACB 1:2 n = 6; ACB 1:2 (2X-amplitude) n = 6; ACB 1:4
n = 5; * p < 0.05; ANOVA followed by Tukey’s multiple comparisons). (B) Stills of time
lapsed recordings of RGC axon growth in AC 1:1 (phase contrast microscopy) and ACB
1:4 (DIC microscopy) treated cultures. Black numbers label axons that grew towards the
cathode, red numbers label axons that grew towards the anode, while yellow numbers
label axons that grew perpendicular to the EF. Scale bar 100 µm. As published in [51]. . . . 31
2.7 Increasing anodic pulse width duration was associated with increases in cathodic-directed
growth of RGC axons (control n = 251 axons over 4 cultures; AC 1:1 n = 403 axons over
4 cultures; ACB 1:2 n = 696 over 6 cultures; ACB 1:2 (2X-fold amplitude) n = 579 axons
over 6 cultures; ACB 1:4 n = 467 axons over 5 cultures; * p < 0.05; ** p < 0.01; *** p < 0.001;
**** p < 0.0001; ANOVA followed by Tukey’s multiple comparisons). As published in [51],
supplementary figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.8 Preserved RGC viability with ACB 1:4 stimulation compared to DC EF treatment. Purified
RGC cultures were exposed to ACB 1:4 or 2 V/cm DC stimulation for 4 h. (A) 2 V/cm
DC stimulation was associated with 19% decrease in cell viability compared to controls.
No significant difference was detected with ACB 1:4 stimulated cultures. (B) Images of
LIVE/CELL viability assay. Green, living cells; red, dead cells (control n = 6533 cells over 7
cultures; 2 V/cm DC n = 5394 cells over 5 cultures; ACB 1:4 n = 2783 cells over 5 cultures;
*p < 0.05, ***p < 0.001; ANOVA followed by Tukey’s multiple comparisons). As published
in [51]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1 Schematic of experimental timeline, stimulation system, and stimulation waveforms.
(A) Adult Long-Evans rats underwent concurrent electrode placement and optic nerve
crush on Day 0. Five to seven days later, optic nerves were stimulated with various
waveforms for five hours a day every weekday for 6 weeks. Schematic of orientation
of electric gradient during anodic and cathodic phases. Three to four days before
euthanasia, rats underwent intravitreal injection with CTB-647. Schematic of orientation
of electric gradient during anodic and cathodic phases. (B) Rats were attached to a
stimulation generator via a tether on a ball joint, allowing for continuous stimulation in
an unanesthetized, mobile rat. Continuous waveform monitoring with an oscilloscope
was performed to assure that rats were being stimulated appropriately. (C) The current
stimulation pulses of various waveforms recorded across a 1 kΩ resistor connected in
series to the return electrode and the resulting voltage transient measured across the
platinum needle electrodes. Eipp is the electrode potential at the onset of the current
pulse (interphase), ∆V is the total polarization of the electrode during the stimulation
phase, VOhmic is the near-instantaneous potential change at the onset/termination of
the current pulse following the characteristics of a purely resistive load, and ∆Ep is the
steady state potential following the characteristics of a reactive (capacitive) load. SCB,
symmetric charge balanced; ACB, asymmetric charge balanced. Numbers represent the
relative cathodic:anodic pulse width ratios. . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
x
3.2 Preserved RGC viability with biphasic electrical stimulation. Whole mount retinas
processed for RBPMS immunohistochemistry demonstrated no significant difference
in RGC density in crushed, EF treated animals compared to crushed, untreated (UnTx)
controls. One way ANOVA with Tukey’s multiple comparisons test. Scale bar, 20 µm. . . . 53
3.3 Biphasic stimulation with ACB 1:4 directs full-length regeneration of crushed RGC
axons. (A) Optic nerves underwent crush injury followed by 6 weeks of stimulation
with various biphasic waveforms and CTB labeling of RGC axons. Regenerated axons
observed past the crush site (asterisk) with ACB 1:4 treatment. (B) Decussating (blue
arrow) and non-decussating (blue arrowhead) RGC axons seen in the optic chiasm of an
ACB 1:4 treate animal. (C) Pre- and post-crush RGC axons (pink arrow and arrowheads,
respectively observed projecting back towards the eye in an ACB 4:1 treated animal. (D)
Quantification of RGC axon density at increasing distances from the crush site (error
bars, SEM; * p < 0.05, ** p < 0.01, *** p < 0.001; two-way ANOVA with Tukey’s multiple
comparisons test). (E) Whole optic nerve of an ACB 1:4 treated animal demonstrating
long-distance RGC axon regeneration past the crush site (asterisk) and through the optic
chiasm. Scale bars 250 µm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.4 Biphasic stimulation with ACB 1:4 mediates target specific regeneration. In ACB 1:4
treated animals, CTB-labeled RGC axons (green) can be seen projecting to subcortical
visual targets including bilateral SCN and contralateral vLGN, IGL, dLGN, OPN, NOT,
MPT, PPT, and SC. SCN, suprachiasmatic nucleus; vLGN, ventral lateral geniculate
nucleus; IGL, intergeniculate leaflet; dLGN, dorsal lateral geniculate nucleus; OPN, olivary
pretectal nucleus; NOT, nucleus of the optic tract; MPT, medial pretectal nucleus; PPT,
posterior pretectal nucleus; SC, superior colliculus. . . . . . . . . . . . . . . . . . . . . . . 58
3.5 Biphasic stimulation with ACB 1:4 mediates partial recovery of RGC function. Serial PERG
recordings were performed in animals after optic nerve crush injury. (A) Representative
PERG recordings with a 15-point smoothing filter applied. Baseline: one week after
electrode placement and crush injury but before initiation of electrical stimulation. (B)
Mean normalized N95 amplitude (left eye: right eye) over time in each stimulation group
(error bars, SEM). * p < 0.05; ** p < 0.01. (Two-way ANOVA with Tukey’s multiple
comparisons test). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.6 Biphasic stimulation with ACB 1:4 mediates partial recovery of light-evoked LFP
recordings in the SC. Stereotactic-guided LFP responses to full-field light stimulation
were measured in the contralateral SC. (A) Sample recordings. (B) Average percent of
sites demonstrating a response. Baseline: one week after electrode placement and crush
injury but before initiation of electrical stimulation. Error bars, SEM. One-way ANOVA
with Tukey’s multiple comparisons test. ** p < 0.01, *** p < 0.001. (C) 3D rendering of the
distribution of positive responses in the SC of representative animals. . . . . . . . . . . . . 61
3.7 AM admittance method was used to generate a 3D computational model of the electric
gradient along the optic nerve. Inset shows “J” shaped source electrode wrapped around
the optic nerve while the ground electrode pierces the contralateral optic tract. . . . . . . . 63
xi
3.8 Biphasic stimulation elicits action potentials in RGCs. Time course of the membrane
potential response for two RGC subtypes when stimulated with all three waveforms.
The extracellular potential generated near the soma is computed using AM and the cell
membrane response is computed in the NEURON simulation environment. While the D1
cells can better sustain repetitive firing at high frequencies, both RGC subtypes can fire
very fast at these amplitudes, across all waveforms. However, the simulations suggest a
preferential activation in the D1 subtype when using SCB 1:1 and ACB 1:4 over ACB 4:1,
with over 120 % increase in the sustained firing rate. . . . . . . . . . . . . . . . . . . . . . . 64
4.1 (a) A slice of the 3D segmented rat model with the ring electrode (shown in red) (b) The
eyeball model with retina (orange) and stimulating ring electrode (red). (c) An inset shows
the zoomed in view of the eyeball with structures of vitreous humor, lens, cornea, inner
and outer eyelids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.2 (a) Schematic representation of the different TES setups with three return electrode
configurations tested in vivo. (b) Illustration of the TES setup shows the stimulating ring
electrode on the cornea and the disk-shaped return electrode positioned retro-orbitally
adjacent to the optic nerve. Two insulated W needle electrodes with exposed tips
were inserted in the vitreous humor and the base of the optic nerve to measure the
voltage across the retina, at a separation of ∆S = 2 mm, which is used to estimate the
current density generated between them. (c) The symmetric biphasic stimulation current
waveforms at increasing amplitudes and the resulting potential difference Vab between
the two measuring electrodes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.3 Simulation results of various placements for the ground electrodes. Row (a): the voxelized
rat head model with stimulating and return electrodes. Row (b): The voltage distribution
across a 2D slice in the xy plane (passing through z = center of the stimulating ring). Row
(c): the current density distribution inside the retina in the xyz plane. The left side is
medial, right is lateral, top is superior and bottom is inferior direction. . . . . . . . . . . . 80
4.4 The maximum voltage difference Vab (blue) and the voltage offset during the interpulse
time (orange) recorded across 10 rats for different return electrode configurations. The
closer the electrode is to the target (retina), the smaller the range of values and the offset
voltages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.5 The potential generated across the electrodes and the voltage measured across the pig’s
retina using the same stimulation waveform from Fig. 4.2 but with higher amplitudes. . . 86
4.6 (Top Row) The TES was set up on the right eye while the voltage difference was measured
across the sclera of the right eye (blue arrow), halfway between the two eyes (orange
arrow) and across the sclera of the left eye (yellow arrow). The Vab approaches zero
sharply moving away from the right eye, indicating that the current density generated
outside the target area is negligible. (Bottom Row) The Vab was measured across the
perpendicular axes to determine the directionality of the electric field generated in the eye
tissue. The vertical Vab between the cornea and the optic nerve was significantly higher
than the horizontal Vab between medial and lateral sides, indicating that the induced fields
cross the retina perpendicularly. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
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5.1 (a) 3-D plot of the RPC1 cell network, showing the morphology and topology captured
by the TEM imaging. The size and coordinates of the cells are stored in .swc files and
plotted with a 3-D visualization software. Rod and cone photoreceptors are partially
represented in the image because of their large number. (b) Signal flow illustration in the
ON-type network of RPC1. Green connections are normally found in the healthy retina.
Red connections are observed only in RPC1. Empty circles represent ribbon synapses with
metabotropic mGluR6 channels solid circles represent ionotropic channels and resistors
represent gap junctions. Legend: subscript H - healthy, subscript D - degenerated. . . . . . 97
5.2 Changes in photoreceptor membrane potentials following the generated photocurrent due
to a flash of light input. Cells begin at rest (dark-adapted) and the input is applied at the
2-second mark. The photocurrent amplitude scale is shifted to rest on 0 for convenience
(in the actual simulation, the “dark current” during absence of stimulation is accounted
for and the resting potential of the photoreceptors reflect it). . . . . . . . . . . . . . . . . . 102
5.3 Changes in membrane potentials of the main cell types following a saturating flash of
light input shown in Fig. 3 at the 2-second mark. Left column: cell responses in the
baseline network. Right column: cell responses in the degenerated network with aberrant
cones and GJs added. Notable differences are: (a) Increased RodBC resting potentials,
(b) suppressed transient component of the Aii GAC as well as an increased difference
between resting and steady-state voltages, (c) suppressed initial peak of the ConeBC and
(d) rhythmic firing at the RGC after stimulation is turned off. Some of the overlapping
RodBCs were not plotted for visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.4 (a) Comparison of RGC firing rate at varying degrees of degeneration. The firing rate
saturates with increasing cone input strength. (b) Percentage difference in the RGC firing
rate compared to the baseline (x = 0). Ten percent saturation corresponds to 2 pA of cone
photocurrent amplitude. The contribution from gap junction degeneration to the RGC
firing rate is independent from cone input strength and the relative contribution is less
pronounced at stronger light levels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.5 EPSPs in the baseline (top) and gap junction degenerated (bottom) networks while the
cone photocurrent is zero. Aii GACs in the healthy network generate a strong transient
that repolarizes to resting state from rod-only input. This is reflected as a high-frequency
burst on the ganglion cell for the duration of the transient. The degenerated case leads
to a suppressed transient on the Aii GACs and a more depolarized steady state after the
transient. This causes oscillatory firing at the RGC. . . . . . . . . . . . . . . . . . . . . . . 115
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5.6 Left: The RGC membrane potential in the degenerate retina plotted when (a) 7 rods were
connected to each RodBC, (b) 30 rods were connected to each RodBC and (c) 100 rods
were connected to each RodBC. A sustained post-stimulation firing was observed for 30
and 100 rods per RodBC whereas dampening was observed before t = 4 s when 7 or less
rods per RodBC were connected. The duration of the oscillations depend on that of the
rod photocurrent. Right: The peri-stimulation (saturated cone photocurrent) RGC firing
rate remained at 190 Hz whereas the post-stimulation RGC firing rate (between t = 3 s
and t = 4 s) followed a logarithmic relationship with respect to the number of rods per
RodBC. The cut-off for characterizing the rhythmic firing is set to be 7 rods per RodBC
due to the dampening where its rate was assumed zero for less. The minimum firing rate
characterized as aberrant rhythmic was 6 Hz and a saturation towards 20 Hz was observed
as the rod number increased. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.7 The effect of blocking the gap junctions between different cell types on the RGC output.
(a) Aii GAC and RGC responses do not change significantly when the Aii GAC-Aii GAC
GJs are blocked compared to the simulations of Fig 5.3(b). (b) Blocking Aii-ConeBC GJs
severs the connection to the rod pathway and eliminates the rhythmic firing of the RGC
after t = 3 s. The Aii GACs lose their sustained depolarization response from ConeBC
coupling. This also brings the resting EPSPs of the Aii GACs near the same resting
potential compared to (a), except Aii GAC 69, which does not have GJs with other Aii
GACs. This suggests that the GJs between Aii GACs help regulate their resting EPSPs. (c)
Blocking the RodBC-Aii GACs eliminates the rhythmic firing of the RGC while coupled
to the rod pathway through the Aii-ConeBC GJs. The resting EPSPs of the Aii GACs are
compact like in (b), while significantly more hyperpolarized at rest. Combined results
suggest that the aberrant RodBC-Aii GAC GJs are the source of the aberrant oscillations
at the RGC in this model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.1 A neurostimulator setup typically demonstrates the characteristics of an RC circuit. (A)
An example of the potential that develops across the electrodes and the resulting current
flow when stimulating with a voltage-controlled charge-balanced asymmetric biphasic
pulse. The potential across the resistor R1 is equivalent to the input current of the system
when divided by 1 kΩ. (B) The equivalent circuit model of the stimulator. Tissue resistance
Rs can be approximated through voltage divider calculation at t = 0, when the reactance
of the capacitor is zero. Next, double layer capacitance Rp can be approximated the same
way when the reactance becomes large approaching the low-frequency limit (roughly
at t = 1 ms). Double layer capacitance Cp can be approximated by first measuring the
time constant τ of the current waveform during discharge, shown in (A). The Thevenin
equivalent resistance can then be calculated to solve for Cp through τ = Rth × Cp. . . . . 131
6.2 Schematic of a typical NIC circuit. Conditions necessary to achieve a negative input
impedance are described. The simulations demonstrate that the NIC is equivalent to a
series negative resistor, where the input current between the standard system with Rs = 1
kΩ is the same as the NIC system with Rs = 2 kΩ and Rload = 1 kΩ. The same resistance
value Rf = 12 Ω was used for R1 and R2 to satisfy the conditions of equation 6.6. . . . . . 135
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6.3 The connection setup along a rat’s optic nerve. The stimulating electrode is hooked on
the nerve while the ground electrode is inserted in the optic chiasm. An ACB waveform
with 1:4 phase width ratio is delivered using a VC waveform generator. The input current
is measured across a 1 kΩ series resistor at the input terminal. . . . . . . . . . . . . . . . . 139
6.4 The equivalent circuit model of the micro-electrode neurostimulator, plotted for one of
the rats tested. The circuit elements are approximated using the measurement waveform
and the method outlined in Fig. 6.1. The values of the elements are setup dependent and
must be computed for each subject. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6.5 The schematics for the three configurations. These circuit models contain ideal elements
and are an approximation of the real system. . . . . . . . . . . . . . . . . . . . . . . . . . 141
6.6 Time domain simulation of the input current between the three systems. Total charge is
the area below the curve. The normalized charge for the standard, NIC and RC systems
were 1, 1.165 and 1.16 respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
6.7 A linear analysis of Vin/Iin shows the differences in the frequency response of the
three systems. The magnitude response of both NIC and RC systems is greater in the
high-frequency regime while the same in the low-frequency as the standard system.
The phase response confirms a shift towards the more capacitive region, signifying the
change in the time constant. Either domain can be emulated by manipulating the standard
system’s parameters, where reducing Rs yields the same response as the NIC and reducing
Cp yields the same response as RC. One discrepancy with the RC system is the necessity
of using an additional resistor, which leads to a smaller magnitude and greater phase
response in the low-frequency regime than reducing the Cp of the standard system. . . . . 144
6.8 The input current waveform recorded across the series 1 kΩ resistor for rat #1 at the point
of discomfort (Table 6.2). (a) Both the NIC and RC enhancement techniques lead to greater
tolerance levels. (b) A gain of about 13% over the standard system was observed during
the anodic phase in either approach. This occurs during the initial 0.2 ms of the phase and
later decays to the level of the standard system, signifying that the enhanced tolerance
corresponds to the high-frequency regime. . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
6.9 Principal of operation for the NIC system illustrated. When Rload = 0, the input current
is the same as the standard system, where node B is grounded. When Rload = 450 Ω, the
NIC becomes active and reverses the polarity of node while maintaining the current flow
direction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
6.10 The simulation parameters are tuned to obtain a better fit of the experimental data (Fig.
6.8). This is achieved when the interface capacitance Cp, which normally shouldn’t
change, is increased. These results suggest a possible shift in Cp in reality when an
external circuit is connected. A greater interface capacitance is desirable in terms of safety
as it reduces the capacitor reactance, extending the interval of capacitive conduction. . . . 147
xv
Abstract
The human nervous system is vulnerable to irreversible damage which may result from physical trauma
or degenerative disorders, culminating in the loss of neurological functions. Recovery from damage to the
central nervous system (CNS) is challenging, given its inherent incapability for regeneration. Conversely,
while the peripheral nervous system (PNS) can regenerate itself, severe damage may still result in permanent loss or distorted regeneration, leading to functional deficits. In such scenarios, external interventions
are necessary to stimulate cellular responses to activate growth factors and overcome inhibitory cues to
facilitate complete regeneration. The field of electrotherapy has evolved considerably, offering promising
avenues for addressing neurological impairments. The application of externally induced electric fields has
demonstrated remarkable potential across various domains, ranging from treating neuronal damage to replacing impaired neural function through prosthetics. These advancements stand as pivotal breakthroughs
in unraveling the complexities of the human nervous system and the development of neural prostheses.
While electrical stimulation has found widespread application in stimulating tissues at easily accessible sites and yielding straightforward functional outcomes for some neural implants, challenges persist
when attempting to target tissues with limited accessibility and evoke desired functional responses within
complex neuronal networks. This dissertation introduces innovative approaches in neuroregeneration and
neuroprotection using electrical stimulation, specifically tailored for the visual system—from the retina to
the optic nerve. Distinct stimulation strategies involving electrode and waveform designs for each application are presented, supported by rigorous computational models and experimental validations. The
xvi
three-dimensional Admittance Method (AM) computational platform developed for solving large scale bioelectromagnetic models is used in conjunction with the NEURON simulation environment for simulating
responses of individual neurons to an induced extracellular electric field. Moreover, the study employs
a connectome-based network model of the degenerating retina, leveraging the AM-NEURON simulation
platform to decipher underlying signaling patterns during retinitis pigmentosa. The primary goal is to
gain insights for optimizing therapeutic interventions during the early-stage of the disease. Lastly, this
work explores an innovative external circuit design aimed at enhancing the tolerance to electrical stimulation. The proposed design optimizes the mechanism of charge injection, holding significant promise in
improving the effectiveness and safety of stimulation protocols.
xvii
Chapter 1
Introduction
ch:introduction
1.1 Neuromodulation Through Direct Electrical Stimulation
The generation of a potential gradient across a neuron can be achieved by employing electrodes that make
direct contact with the target area. Typically, the setup involves bipolar stimulation using two electrodes
to regulate the potential gradient across the tissue of interest. The research outlined in this dissertation
employs the bipolar stimulation approach, where an electric field (EF) is established between a working
electrode and a return electrode. This method facilitates localized activation or inhibition of the target
cells. The resulting neuromodulation outcome is contingent upon various factors, including cell types and
waveform parameters. Our study concentrates on two aspects of neuronal control via electrical stimulation: i) fostering re-growth and directing the migration of damaged axons, and ii) inducing neuroprotective
effects in retinal cells to enhance their resilience during degenerative diseases. Each of these approaches
demands distinct strategies concerning threshold amplitude, pulse duration, and electrode placement. Optimizing these parameters is pivotal in ensuring both the efficacy and safety of the interventions. This
section provides a summary of considerations specific to each approach.
1
1.1.1 Neuroregeneration and Electrotaxis
The existence of electrical currents in healing tissue and their role in initiating regeneration has been
documented and quantified [1]. There is significant interest in understanding the role of bioelectricity in
regulating cellular growth mechanisms such as proliferation, migration, and differentiation, and how extracellular electrical stimulation can be utilized in achieving control over cell behavior [2, 3]. Regeneration
and electrotaxis are interconnected in the context of repair within the nervous system. Electrotaxis, the
directed movement of cells in response to EFs, plays a significant role in helping neurons rebuild their connections during neuroregeneration by guiding their growth cone towards specific targets or along desired
paths. Direct current (DC) electrical fields has been shown to enhance wound healing processes and provide guidance cues towards the intended target [4]. Others have shown that EFs can influence the direction
of axonal growth, aiding in the target-specific regeneration of hippocampal neurons [5, 6]. Overall, the
relationship between neuroregeneration and electrotaxis demonstrates how EFs can serve as navigational
cues, assisting regenerating neurons in finding their paths and reconnecting with specific targets, thereby
facilitating the process of nerve repair and reconstruction of neural circuits. [7].
1.1.2 Neuroprotection
EF-induced neuroprotection involves the utilization of electrical stimulation to mitigate neuronal damage
or enhance the resilience of neural cells against various pathological conditions. Studies have elucidated
the potential of electrical fields in promoting neuroprotection through various mechanisms. The capacity
of electrical stimulation to enhance neuronal cell survival and activity was demonstrated on various cell
types. Exposing cell cultures in vitro to electrical fields stimulated the expression of neurotrophic factors
by Schwann cells [8], induced Muller Cell proliferation and production of neurotrophic factors [9], improved photoreceptor survival in rodent specimens with light-induced damage or inherited degeneration
[10, 11, 12], rescued or increased survival rate of injured retinal ganglion cells [13, 14, 15]. These studies
2
collectively suggest that electrical stimulation holds promise in promoting neuroprotection by enhancing
cell survival, reducing oxidative stress and inflammation, and increasing expression of neurotrophic factors. EF-induced neuroprotection offers potential avenues for post-trauma rescue of neural functionality
or managing neurodegenerative conditions such as retinitis pigmentosa.
1.1.3 Neural Stimulation Protocols
Neural stimulation protocols utilizing EFs encompass a diverse array of techniques aimed at modulating
neuronal activity and inducing specific neural responses. Electrodes are strategically positioned based on
the target tissue and deliver precise electrical waveforms in accordance with predefined protocols. These
protocols manipulate various parameters such as amplitude, frequency, duration, and phase sequencing
to selectively target distinct neural populations or evoke specific physiological effects. The method of
charge delivery, achieved through either a current-controlled (CC) or voltage-controlled (VC) stimulator,
influences the rate and mechanism of charge transfer between the electrode and tissue. Our experimental
framework incorporates both approaches, recognizing their distinct considerations and advantages for
different experimental setups. Critical design components include electrode configuration and waveform
parameters, demanding optimization for a safe and effective stimulation protocol.
1.1.3.1 Electrode Design
The electrode configuration is a crucial aspect of neuromodulation for efficacy. Precise positioning of
electrodes is essential for accurate delivery of the EF to the intended area. The size and shape of electrodes affect the distribution and penetration of the EF within the tissue. Different shapes (e.g. needle,
circular) may influence current density and field distribution. Chapter 4 delves into how electrode shape
manipulation can concentrate field density within the target area, optimizing its impact. The spacing between electrodes is another critical factor, determining the spatial distribution of the EF. Optimal spacing
3
minimizes unintended excitation of the peripheral tissues and maximizes current density near the targeted
neurons. Arrays with multiple electrodes may enable complex stimulation patterns like monopolar, bipolar
and multi-contact. In our research, we adopted a two-electrode bipolar configuration to maximize current
density in a singular direction. Furthermore, the choice of electrode material profoundly affects its performance and safety. An ideal material for use as a stimulating electrode should be biocompatible, maintain
mechanical integrity, inject sufficient charge for efficacy, minimize the generation of toxic byproducts
resulting from faradaic reactions and maintain material/elecrochemical stability for the duration of stimulation [16]. For our long-term chronic implants, we utilized pure platinum (Pt) due to its favorable electrical
properties and excellent biocompatibility [17, 18], aligning with our experimental requirements.
1.1.3.2 Waveform Design
Typically, stimulation protocols involve a series of biphasic current pulses, each consisting of cathodal and
anodal phases. During the cathodic phase, the working electrode is driven with a negative potential, causing current flow from the electrode to the tissue. Conversely, in the anodic phase, the working electrode
is driven with a positive potential, resulting in current flow from the tissue back to the electrode. The
total charge delivered is calculated as the time integral of the current waveform, with the areas of cathodal
and anodal phases kept equal to prevent charge accumulation. It’s essential to balance the amplitude and
duration of these phases to maintain an overall neutral charge. Charge-balancing can be achieved using
different waveform shapes and phase sequencing, which commonly involves symmetric biphasic, asymmetric biphasic or capacitor-coupled monophasic setups (Fig. 1.1) [19]. Depending on the application, one
phase is designated as the working phase, inducing the desired electrophysiological effect, while the opposite phase counter-balances the injected charge for safety and charge neutrality. For most applications,
the leading phase is set to be cathodal, as it primes the neural cells for activation during the anodal phase.
However, the phase sequencing may be reversed for selective activation of certain neuronal cell types [20].
4
Figure 1.1: Typical waveforms used in neurostimulation. While the total charge balance in maintained in
all three cases, the rate of charge injection is different, which can have an influence on the physiological
effect. Figure modified from [19].
The parameters and variations on the biphasic waveforms vary widely depending on many factors,
including the desired physiological effect, tissue properties, electrode properties and implant duration.
The work presented in this dissertation considers a phase width range of 0.1 - 10 ms and an amplitude
range of 0.1-0.4 mA for direct electrical stimulation on rats. Both symmetric and asymmetric biphasic
waveform are utilized for neuroprotective and neuroregenerative therapies, respectively. While maintaining charge neutrality is crucial for safe stimulation, manipulating the ratios of amplitude to duration can
be used to achieve specific physiological effects. Chapter 3 describes our approach involving asymmetric
charge-balanced waveforms tailored to provide directional growth cues for retinal ganglion cell axons. Furthermore, it demonstrates that a slight imbalance may in fact be necessary to achieve directional growth,
and a perfectly balanced waveform fails at this task despite having a comparable phase width.
1.2 The Retina
ch1:sec
The retina serves as a complex neuronal network responsible for converting light signals into electrical impulses, subsequently transmitting them to the brain’s visual cortex. It comprises specialized layers of cells,
including photoreceptor cells located at the back of the retina and ganglion cells transmitting information
to the brain via the optic nerve (Fig. 1.2). Supporting cells such as bipolar cells, horizontal cells, amacrine
5
Figure 1.2: Illustration of the visual pathway from the retina to the optic nerve. Light stimulation is converted to a change in the electrical potential across the cell membrane through phototransduction. This
signal propagates downstream from photoreceptors to retinal ganglion cells and towards the visual cortex
via the optic nerve.
cells, and Müller cells contribute to signal processing and maintain the retinal environment. Therapeutic
strategies using electrical stimulation often target two distinct types of retinal neurons: the photoreceptor
(PR) and the retinal ganglion cell (RGC). This dissertation evaluates two different stimulation approaches:
neuroregeneration of the RGC axons (Chapters 2, 3) and neuroprotection of the PRs (Chapter 4).
1.2.1 Retinal Ganglion Cells
RGCs collect visual information from the retina, transmitting electrical impulses through their axons along
the optic nerve to the brain’s visual centers, resulting in vision perception. Encoding this information as
a sequence of action potentials, RGCs are influenced by stimulation intensity, color, contrast [21], and
6
receptive field properties [22]. Various direct stimulation approaches aim to target RGCs for artificial vision, either through electrodes on the retinal surface (epiretinal stimulation) or indirectly within the retina
(subretinal stimulation). Ongoing efforts focus on optimizing implant stimulation parameters, with recent
research demonstrating tailored waveform usage for selective activation of RGC subtypes [23] or color
selectivity [24] in epiretinal implants. This dissertation explores direct stimulation of the optic nerve,
an extension of RGCs, albeit with different biophysical mechanisms. Chapter 3 details a neuroregenerative stimulation approach for a crushed optic nerve, providing directional cues for regrowing RGC axons
toward the lateral geniculate nucleus. Additionally, the computational model of the degenerate retina presented in Chapter 5 employs the firing rate of an RGC as the metric to validate the electrophysiological
recordings of RP animal models.
1.2.2 Photoreceptors
PR cells consist of rods and cones, which generate electrical signals from incident photons in a process
called phototransduction. Once light stimulates the PRs, it initiates a series of neural signals across the
retina’s layers that are collected by the RGCs. Rods, predominantly in the peripheral retina, support dimlight vision, while cones, concentrated in the macula’s fovea, contribute to color vision and visual acuity
in brighter conditions [25]. The functionality of a PR is correlated to its sensitivity, where rods are capable
of single-photon detection whereas cones require a stimulus of higher intensity to generate a signal. The
loss or dysfunction of PR cells is a common feature in various retinal degenerative conditions. The modeling and therapeutic approaches presented in this dissertation aim to understand the cellular mechanisms
involved in these conditions and develop potential treatments. A neuroprotective electrical stimulation
strategy to promote the expression of neurotrophic factors and prolong neuronal function is the focus of
the therapies directed towards PR cells.
7
1.2.3 Retinal Degeneration
Retinal degeneration typically falls into two categories that commence with the loss of PRs. Retinitis pigmentosa (RP) is an inherited neurodegenerative disease that primarily affects rod PRs, beginning at the
peripheral regions of the retina. This is followed by rewiring and remodeling of the innermost layers,
where bipolar and amacrine cells are located [26]. As the disease advances, night vision and peripheral vision deteriorate, ultimately leading to the loss of central vision and complete blindness. On the other hand,
age-related macular degeneration (AMD) commonly impacts individuals aged 50 and older. In contrast to
RP, AMD causes the deterioration of cone PRs in the macula, resulting in the loss of central vision. This
thesis primarily focuses on disease models and transgenic animals exhibiting progressive photoreceptor
degeneration. RP stands out as an exemplary model for studying neurodegenerative diseases because the
fundamental pathogenic process in RP, involving PR atrophy, is applicable to other forms of retinal degenerative diseases, such as AMD [27]. The timeline of RP degeneration has been defined from a remodeling
perspective and categorized into three phases [26, 28, 29]. Phase one is characterized by the early markers
photoreceptor stress, phase two is characterized by PR loss and glial remodeling of the outer nuclear layer
and phase three is characterized by aggressive remodeling and subsequent death of the retinal neurons
(Fig. 1.3).
The therapeutic approach depends on the stage of the disease. Invasive intervention methods such as
the epiretinal implant are considered for the later stages of degeneration, when complete photoreceptors
loss leads to blindness. Because of the innate complexity of creating useful artificial vision through direct
stimulation of the RGCs, as in the case of epiretinal prostheses, efforts are increasingly directed towards
preserving the photoreceptors and natural visual acuity as long as possible through early intervention.
The prolonged synaptic integrity of the PRs is critical as RP modeling is believed to progress differently
depending on the degree of cone survival, where the survivor cones may delay remodeling and cell death
[29]. Chapter 4 discusses a neuroprotective strategy using transcorneal electrical stimulation to induce a
8
Figure 1.3: The three phases of remodeling during retinal degeneration. An early intervention timing
falls between phases one and two, when the photoreceptors partially alive and functional. Therapeutic
interventions at this stage will aim to prolong photoreceptor survival and delay disease progression. After
a complete loss of photoreceptors in phase three, the intervention will aim to create artificial vision through
direct electrical stimulation of the retina or visual cortex. Figure modified from [29].
threshold current density in the degenerating retina. Chapter 5 describes a computational model of the
early-stage degenerate retina to evaluate the differences in signaling compared to a healthy baseline.
1.3 Computational Modeling and Simulation Methods
modeling
Computational modeling serves as a pivotal tool for anticipating the effectiveness of neuroprosthetic electrodes by computing the distribution of EFs within bulk tissue. It employs mathematical techniques to
simulate and unravel the interactions between electrodes and neural tissues, offering invaluable insights
into the outcome of neural prostheses. Most importantly, they offer flexibility in parameter tuning and
serve as a guide for designing experiments, which might otherwise be challenging to investigate solely
through experimentation. Computational models and techniques continue to evolve as neural tissues are
9
characterized in greater detail and computational ability increases that confers the ability to run simulations at greater resolutions. Modeling methodologies can be categorized based on spatial scales. For
micrometer-scale resolutions or lower, numerical techniques in bioelectromagnetics, such as various finite
difference methods, impedance or the admittance method, are commonly employed [30]. These techniques
compute EFs and current densities in complex geometries and dielectric properties of bulk tissue models,
suitable for low-frequency or quasistatic approximations. However, exploring neural activity at a cellular
level necessitates a different approach, specifically the biophysical modeling of the membrane properties
of stimulated neurons. Computational neuron models, such as the Hodgkin-Huxley models [31], simulate individual neuron behavior by considering cellular biophysics and ion channel kinetics, thus aiding
in comprehending neuronal responses to electrical stimuli. An activating function to estimate the neural activity resulting from the change in extracellular potential was derived from this method [32, 33,
34]. To simulate neuronal network activity, integrating nanometer-scale resolution components, such as
synaptic structures, is crucial. Tools capable of modeling non-linear dynamics and incorporating diffusion
functions into synapse and cellular network models are needed at this finer scale. Cellular models, aligning closely with experimental studies and often utilizing the patch clamp recording method, assume an
isotropic space independent of the extracellular EFs that drive neuronal responses. For a comprehensive
simulation of neural prosthesis interactions with target tissues across varying spatial scales, a multi-scale
modeling approach becomes imperative. This study utilizes both the Admittance Method (AM) [30] for
approximating current density mapping in a 3D bulk tissue model and the NEURON simulation environment [35, 36] for modeling individual retinal neuron responses to light and extracellular EF stimuli. These
approaches are integrated into the multi-scale AM-NEURON computational platform. This framework is
applied to simulate responses of retinal neurons during electrical stimulation therapies, facilitating a better
understanding of the contributing factors to neuroregeneration and neuroprotection.
10
Figure 1.4: A two-cell network in the retina represented in 3D space as .swc files. The cells are made
up of small compartments in the order of 103
to capture morphological realism. Each compartment can
have unique biophysical properties to model the soma, axon or dendrites. The equivalent circuit model
of a compartment is shown, which includes voltage-gated ionic channel conductances (g), equilibrium
potentials (E), membrane capacitance (C) and axial resistance that connects the compartments (Ra).
1.3.1 NEURON
The NEURON software is used to simulate the response of a neuronal network to an external stimulus,
which is either light or extracellular electrical field. In NEURON, cellular segments can be compartmentalized to facilitate the solution for localized membrane and axial properties. These compartments are based
on neuronal branch types (soma, axon or dendrite) and can have varying dimensions to model complex
morphology, such as dendritic branching. Each compartment is defined as a tapered cylinder, incorporating a cable circuit model that characterizes intracellular and membrane properties as circuital elements
(Fig. 1.4). The equivalent circuit Users have the flexibility to define equivalent membrane conductance,
resistance, and capacitance values for each compartment. Additionally, synaptic properties between cells
can be specified.
11
1.3.2 Admittance Method
Estimating the electric field distribution in a bulk tissue model is essential for designing and optimizing in
vivo experimentation. A numerical electromagnetic method named the AM is used to partition the problem
space in terms of an admittance network created from the material properties of the intervening tissues
[30]. The response of this equivalent 3D electrical network in the presence of electromagnetic stimulation
can be approximated at a cellular level.
First, the three dimensional bulk tissue model is partitioned into cuboid voxels, size of which depend
on the required resolution. Network nodes are placed on the vertices of each voxel to define their boundaries. Then, an equivalent lumped admittance at each node is calculated from the conductivity of the
voxels sharing boundaries. Each voxel is treated as a volume with homogenoues electrical properties and
assigned a material index with the corresponding dielectric properties. Finally, external stimulation is applied by means of an ideal current source and the resulting node voltage is solved across the network.
This approximation is valid under quasistatic conditions, where the model size must be small compared
to the wavelength of the electrical stimulation. Quasistatic approximations are useful for low frequency
problems in neurostimulation such as those encountered in this dissertation.
Once extracellular voltages induced from the current source of the AM model are computed in each
voxel, they can be applied to the simulation environment of NEURON. The coordinates of the 3-D space
between AM and NEURON are synchronized using a MATLAB script that superimposes the node voltages
within the tissue volume onto the NEURON model using its built-in "extracellular" mechanism. This mechanism defines the extracellular potential experienced by the neuronal compartment (Fig. 1.5). NEURON
then simulates the membrane response for of each compartment, which allows for a detailed examination
at a high temporal resolution. A large-scale model involving many neurons with synaptic connections can
provide insight on the impact of external stimuli at a network level. Combining the two simulation environments, this method is conveniently named as the AM-NEURON computational platform and utilized
12
Figure 1.5: The bulk tissue model in AM combined with the two-cell network of Fig. 1.4. The 3D space
can be segmented into voxels of sufficient resolution to solve the membrane potential response of different
compartments. Each node of the voxels are connected by equivalent resistances reflecting the tissue properties. The computed voltages at these nodes are applied as the extracellular potential to the equivalent
circuit model of the compartment in NEURON simulation.
here for simulating the response of retinal neurons to external electric fields. The AM-NEURON method
has been extensively used and verified throughout multiple works investigating computational models of
both the retina and hippocampus [37, 38, 39], and is a valuable tool for estimating cellular responses to
extracellular fields during electrical stimulation.
1.4 Significance and Outline
This dissertation presents neuromodulation strategies using implantable electrodes designed to evoke specific physiological responses in the visual pathway while ensuring safety and tolerance. Each stimulation
approach begins with developing a computational model of bulk tissue, which is essential for testing various electrode and waveform configurations. This phase aims to determine optimal electrode placement and
13
surface areas, crucial for achieving the necessary electric field and current density across target cells. Utilizing the 3D Admittance Method and NEURON computational modeling platforms, the research predicts
electric field distribution within bulk tissue and characterizes the subsequent response of retinal neurons.
These predictive models then undergo validation through ex vivo and in vivo trials, enabling iterative
refinements until optimal functional efficacy is achieved.
Chapter 2 explores the effectiveness of various waveforms in directing axon growth. Past studies on
electrotaxis of RGCs are experimentally validated, and a new waveform suitable for long-term in vivo stimulation is introduced. This chapter demonstrates that an asymmetric charge-balanced waveform can be a
safe and effective design for driving directional axon growth. In Chapter 3, the focus shifts to regenerating
damaged axons utilizing external electric fields and harnessing the mechanism of electrotaxis. This innovative approach involves using charge-balanced and safe waveforms to provide directional guidance cues for
axons in the crushed optic nerve to grow toward the lateral geniculate nucleus. While prior studies demonstrated electrotaxis using direct current or charge-imbalanced stimulation, our work represents the first
successful demonstration of conscious animal-directed neuroregeneration via safe stimulation waveforms.
Chapter 4 explores the optimal electrode configuration to achieve maximum current density in the retina
during transcorneal electrical stimulation. Through a computational study supported by animal experimentation, a proposed electrode design aims to generate a threshold current density in the retina, serving
as a neuroprotective measure during early-stage retinal degeneration. This research outcome provides
valuable data on electrode design requirements for effective stimulation and establishing an input-output
relationship between stimulation amplitude and current density generated in the retina, which is validated
by in vivo measurements. Chapter 5 delves into modeling the signaling characteristics of the retinal neuronal network, shedding light on how synaptic rewiring during early-stage retinitis pigmentosa can alter
these signals. The unique connectome-based computational model captures a morphologically and topologically realistic network of degenerating retinal cells from the photoreceptor layer to the ganglion cell
14
layer within a 70 µm diameter cylindrical volume. Leveraging this high-resolution model of the degenerate
retina enables predictions of signal evolution at various degeneration stages. Integration with multi-scale
computational methods aims to optimize waveform patterns for specific functions, such as suppressing
aberrant firing of the observed retinal ganglion cells in our model. Finally, Chapter 6 concludes the dissertation by proposing a generalized enhancement technique for neurostimulators using external circuit
components. This approach targets implantable microelectrodes with stricter stimulation amplitude limits
due to high charge density formation on their small surfaces. Our enhanced stimulator, compared to standard electrode configurations, demonstrated an average delivery of 20% greater charge within tolerance
limits when tested on the rats discussed in Chapter 3.
The combined computational and experimental investigations detailed in this dissertation have culminated in the development of clinically applicable neuromodulation methodologies. These methodologies,
having shown to be effective in animal studies, hold promise for translation into human trials, offering
new avenues for therapeutic interventions involving neuroprosthetics. The computational and experimental findings significantly contribute to our understanding of both tissue-level responses to extracellular electrical stimulation and the network-mediated reactions of degenerating retinal neurons. Modeling
an input-output relationship for neurostimulation, supported by an in-depth understanding of the neuronal response at the intracellular level, is vital in fine-tuning the stimulation parameters for effective
therapeutics.
The work presented in this dissertation is the outcome of interdisciplinary collaboration among several groups with different specializations. The principal contribution of Ege Iseri involves the design and
optimization of electrical stimulation methods and systems, data processing, building application-specific
computational models, and running predictive simulations of experimental outcomes. The cultivation and
setup of tissue cultures and animal-related procedures described in Chapters 2, 3, 4, and 6 are credited to
15
authors from the collaborating groups. Additionally, imaging/quantification techniques and the acquisition of electrophysiology data in Chapters 2 and 3 are credited to the collaborating authors.
16
Chapter 2
Electrotaxis and Target-Specific Migration of Axons Using Asymmetric
Charge-Balanced Waveforms
Chapter 2
M. G. Peng, E. Iseri, A. Simonyan, P. Lam, T. Kim, S. Medvidovic, J. Paknahad, M. Machnoor, G. Lazzi
and K. K. Gokoffski. Asymmetric charge balanced waveforms direct retinal ganglion cell axon growth.
Scientific Reports (2023)
2.1 Abstract
Failure to direct axon regeneration to appropriate targets is a major barrier to restoring function after
nerve injury. Development of strategies that can direct targeted regeneration of neurons such as retinal ganglion cells (RGCs) are needed to delay or reverse blindness in diseases like glaucoma. Here, we
demonstrate that a new class of asymmetric, charge balanced (ACB) waveforms are effective at directing
RGC axon growth, in vitro, without compromising cell viability. Unlike previously proposed direct current stimulation approaches, charge neutrality of ACB waveforms ensures the safety of stimulation while
asymmetry ensures its efficacy. Furthermore, we demonstrate the relative influence of pulse amplitude
and pulse width on the overall effectiveness of stimulation. This work can serve as a practical guideline
for the potential deployment of electrical stimulation as a treatment strategy for nerve injury.
17
2.2 Introduction
The approach to bolster nerve regeneration in the CNS using electric field (EF) stimulation stems from
research indicating the natural occurrence of EFs in the body, which play a crucial role in orchestrating
tissue development [40] and facilitating wound healing post-injury [41]. In a study concerning the optic
nerve, immediate application of EFs after nerve transection notably increased the survival rate of RGCs
by 1.5 times compared to untreated controls [42]. It has been demonstrated that extracellular electrical
activity can augment RGC axon growth when stimulated by brain-derived nerve factor (BDNF) in vitro
[43]. Further in vitro studies on RGCs has shown that EFs not only foster axon growth but also exert
control over the directional growth [44]. When exposed to an EF ranging between 1 and 2 V/cm, RGC
axons exhibit a tendency to project towards the negatively driven electrode. Altering the location of the
negative electrode readily manipulates the direction of RGC axon growth, suggesting the potential utility
of EFs in steering target-specific axon growth, which may be a crucial consideration for devising therapies
tailored to intricate tissues such as the CNS.
Despite these promising findings indicating the potential of EFs in guiding axon regeneration, clinical
translation of electrical stimulation has faced challenges primarily due to reliance on direct current (DC).
DC stimulation often leads to charge accumulation, resulting in tissue damage upon exposure to high voltage or extended durations [45]. Alternating current (AC) has emerged as a safer alternative by coupling
positive pulses with symmetric negative pulses, ensuring a net charge of zero. However, AC application in
clinical settings has demonstrated limited visual improvements [46] and lacks the ability to promote directional growth [47]. A promising avenue lies in hybrid currents or ACB waveforms, where anodic (positive)
pulses are paired with cathodic (negative) pulses. Unlike AC, ACB waveforms feature asymmetric amplitudes and pulse durations for anodic and cathodic pulses. This asymmetry holds potential for driving axon
growth effectively. Nevertheless, the design of ACB waveforms is currently hindered by our limited understanding of the impact of various waveform parameters, including pulse amplitude, width, and stimulation
18
frequency, on controlling cellular behavior. To address this, we conducted a systematic investigation to
determine the optimal level of asymmetry in pulse duration and amplitude per phase required to effectively steer directional RGC axon growth in vitro. Our findings underscore that pulse duration exerts a
more significant influence on RGC axon growth compared to pulse amplitude. Moreover, our experiments
revealed that ACB waveforms with higher asymmetry are more successful in guiding axon growth than
those with lower asymmetry. Symmetric pulses, however, were ineffective in directing electrotaxis.
2.3 Methods
2.3.1 Cell Culture Preparation
The use of animals was in accordance with the ARRIVE guideline and the Association for Research in
Vision and Ophthalmology (ARVO) Statement on the use of animals for research and was approved by the
Ethical Committees at the University of Southern California [48]. CD1 mice were obtained from Charles
River Laboratories. Post-natal day 0–1 (P0-P1) CD1 pups were euthanized according to institutional board
protocol. Globes were enucleated and placed in ice cold DMEM:F12 media (Gibco, Langley, OK, 11320-
082). Retinas were isolated and RGCs were purified using a magnetic-bead separation method that has
been previously described [49]. Briefly, retinas were digested for 4–5 min at 37◦C in Hanks Balanced Salt
Solution (HBSS; VWR, Radnor, PA 45000-458) containing 20 U/ml papain and 0.005% DNase I (Worthington
Biochemicals, Lakewood, NJ). Digestion was neutralized with ovomucoid and 0.005% DNase I; the retina
was then triturated. Dissociated cells were coated with rabbit anti-mouse Thy1.2 antibody conjugated
to micrometal beads (130-049-101, Miltenyi Biotech, Auburn, CA) for 15 min at room temperature (RT)
in MACS buffer (phosphate-buffered saline with 0.5% bovine serum albumin and 2 mM EDTA; Miltenyi
Biotech, Auburn, CA). RGCs were then purified from the cell suspension using a single metal column
with and without a magnetic field, sequentially. Purified RGCs were then quantified and then diluted to
19
0.3 × 106 RGCs/ml in media. A cell volume of 1 ml was then plated onto an electrotaxis chamber then
incubated at 37◦C overnight for 12 h. Culture purity was assessed by quantifying the percentage of total
cells that stained positive for (+) RBPMS at 10x magnification (see below). RGC purity was found to be
85%±3% (n=3 separate cultures, 5030 total cells counted), slightly lower than Gao et al. who passaged cells
through two columns sequentially [50].
Tissue culture media was made with 500 ml Neurobasal A medium (Thermoscientific, 10888022), 2.5 ml
100x l-glutamine (Thermoscientific, 25030081), 10 ml B27 (Gibco, 17504044), and 5 ml of penicillin–streptomycin. 45 ml of this media was combined with 5 ml of 2.75% methylcellulose in 1 × IMDM and 10 mM
HEPES. Media was supplemented with 50 ng/ml BNDF (Peprotech, Rocky Hill, NJ 450–02), 50 ng/ ml CTNF
(Peprotech, 450–13), 5 µM Forskolin (StemCell Technologies, Cambridge, MA, 72114) and 5 µg/ml insulin
(Sigma, St. Louis, MO 91077C). 100 mm tissue culture plates (Genesee San Diego, CA 25-202) were UV
sterilized for 20 min. A sterile glass tissue culture insert was placed in the center of the plate (Fig. 2.1 and
Fig. 2.2). Plates were then coated with Matrigel (VWR, Radnor, PA RBD354277). Matrigel was allowed to
settle for 60 min in a 37◦C incubator. Residual, unbound matrigel was then removed and purified RGCs
were seeded onto the plates and incubated overnight at 37◦C. The next day, the tissue culture insert was
removed and vacuum grease was applied to the plate to attach sterile cut glass coverslips to build the
walls of the electrotaxis chamber, centered around the seeded cells. Pre-cut Linbro plate sealer was then
placed over the RGCs and attached to the chamber walls, serving as the roof of the chamber. When fully
assembled, the dimensions of the chamber through which current was passed measured 30 mm × 10 mm
× 0.5 mm.
2.3.2 Stimulation Parameters and Setup
Tissue culture plates were placed in a gas/temperature chamber-controlled inverted Axio Observer 7 microscope (Carl Zeiss, Oberkochen, Germany). Agarose salt bridges were used to connect silver electrodes
20
in beakers of Steinberg’s solution to pools of culture media on either side of the electrotaxis chamber to
prevent diffusion of electrolysis byproducts in to the culture media (Fig. 2.1). RGCs were stimulated at
37◦C and 5% CO2 for 4 h continuously. Electrical stimulation was applied using an Arbitrary Waveform
Generator (RIGOL DG 822 2-Channel AWG, Portland, OR, 97,223) with a Dual-Channel High-Voltage Wideband Amplifier (TEquipment, Long Branch, NJ, 9200ADST). Two tungsten needle electrodes were placed at
the edges of the roof of the electrotaxis chamber to continuously measure the voltage gradient generated
across the chamber. These values were recorded in MATLAB (MathWorks, Natick, MA) at 15-min intervals
for the duration of the experiment using a Keysight DSOX2014A oscilloscope. To ensure that our biphasic
waveforms were charge balanced, total injected charge (area under the plot, Fig. 2.1C) was calculated from
the first and last recordings of each experiment. The total charge of the cathodic phase was divided by that
of the anodic phase to obtain a charge balance ratio. Experiments with a charge balance ratio < 0.9 or >
1.1 were discarded. We found the ratio of the cathodic to anodic area to be 0.95 on average at the start of
the experiment (± 0.05) and 0.93 at the end of the experiment (± 0.04), suggesting a slight shift in balance
towards the anodic phase over time. In addition to charge balance, voltage gradient drift during the duration of the experiment was calculated from the aforementioned waveform plots and compared over time.
Time lapse images were captured with a CCD camera and the SimplePCI 5.3 imaging system (Hamamatsu
Photonics, Hamamatsu City, Japan). Only axons that demonstrated active growth/elongation during the
timelapse videos were quantified. Axons that had formed synapses with other cells in the culture during
the overnight incubation were excluded.
2.3.3 Purity and Viability Assays
After overnight incubation, cells were fixed with 4% paraformaldehyde for 30 min at room temperature.
Cells were washed with 0.3% Triton X-100, then blocked with 5% horse serum for 30 min. Following this,
cells were incubated overnight at 37◦C with anti-RBPMS antibody (1:500; Millipore). Cells were then
21
Figure 2.1: Schematic of Electrotaxis Chamber and Waveforms Tested. (A) An electrotaxis chamber was
built onto a 100 mm tissue culture plate previously coated with Matrigel. Purified RGCs (yellow) were
seeded onto the plate and agarose salt bridges were used to deliver current to the electrotaxis chamber. (B)
Representative schematic of DC, AC, ACB waveforms and monophasic pulse. (C) An example of voltages
recorded across an electrotaxis chamber (Va-Vb) stimulated with ACB waveform 1:2. The left plot was
recorded at the start of stimulation while the right plot was recorded after four hours of stimulation.
Modified from [51].
22
Figure 2.2: Larger pulse amplitudes direct more avid cathodic growth of RGC axons. Purified RGC cultures
were exposed to direct current (A) or monophasic EF stimulation (B). Increases in pulse amplitude led to
increases in cathodic-directed growth of RGC axons. * p < 0.05; ** p < 0.01; *** p < 0.001; **** p < 0.0001;
ANOVA followed by Tukey’s multiple comparisons. Control n = 251 axons over 4 cultures; 0.5 V/cm DC
n = 559 axons over 3 cultures; 1 V/cm DC n = 368 axons over 3 cultures; 2 V/cm DC n = 270 axons over
4 cultures; 1 V/cm monophasic n = 510 axons over 3 cultures; 2 V/cm monophasic n= 351 axons over 3
cultures; 4 V/cm monophasic n = 288 axons over 3 cultures. As published in [51], supplementary figures.
washed and incubated for one hour at RT with Alexa Fluor 488–conjugated goat anti rabbit IgG (1:200;
Jackson ImmunoResearch). Cells were then washed and incubated with Hoechst (94403; Sigma) for 10 min
at RT. Images were taken using the Keyence Live Cell Imaging system BZ-X800E using a 10x objective.
Percent of (+)-RBPMS cells of total cells was quantified; cultures were found to consist of 85%±3% (+)-
RBPMS RGCs (n=3, 5030 total cells quantified). Upon termination of stimulation, the Linbro plate sealer
and media were carefully removed. Cells were washed twice with PBS, then stained using the LIVE/DEAD
Viability/ Cytotoxicity Assay Kit (Thermo Fisher, L3224). The staining reagent was made by adding 1 µl
of 4 mM calcein AM and 4 µl of 2 mM EthD-1 to 2 ml of PBS. 150 µl of solution was added to the cells and
incubated in the dark at RT for 30–45 min. Images were taken using the Keyence Live Cell Imaging system
BZ-X800E using a 10x objective. Total number of live and dead cells were quantified from 10 images from
each culture.
23
2.3.4 Quantification and statistics
The electrotaxis chamber was aligned so that the EF was parallel to the horizontal axis of the image,
with the cathode to the left and the anode to the right of each image. All data were collected from timelapse videos. Images were taken at 15-min intervals and recorded for a minimum of four hours. Images
were analyzed using ImageJ (NIH) or Zen (Zeiss International). Direction and speed of axon growth were
quantified by tracing the movement of its growth cone from the time-lapsed videos as previously described
[44, 52]. As measured by the angle function on Zen, an axon was deemed to be growing towards the cathode
if its observed growth was within 120 degrees of the negative electrode, and towards the anode if within
120 degrees of the positive electrode. The remaining axons were deemed to be growing perpendicular
to the EF. Because growing axons extend, retract, and “wobble” by approximately 10°, directionality was
assigned as the average angle of growth that was observed during the 4 hours of videography (e.g., if an
axon wobbled between 140° and 150°, an angle of 145° was assigned). Axon length was measured by tracing
the segment of each axon demonstrating active growth during the experiment, which is from the location
of the growth cone at the beginning of the video to its final position at the end. Total length was divided
by the total amount of time active growth observed. Results are reported from at least three independent
tissue culture experiments performed with pups born from at least three separate litters and from different
mating pairs. The percentage of total axons growing towards the cathode, anode, and perpendicular to the
EF, and average axon speed (± standard deviation (SD)) are reported unless otherwise stated. Significant
differences between cultures were determined using one-way analysis of variance (ANOVA) followed by
Tukey’s post hoc test for multiple comparisons using GraphPad Prism 7 (San Diego, CA). P<0.05 was
considered to indicate a statistically significant difference. Investigators were blinded to experimental
conditions when quantifying the results.
24
2.4 Results
2.4.1 RGC growth in vitro
1) RGC axons exhibit cathode-directed growth in the presence of DC
Previously, we demonstrated that RGC axons grow towards the negatively-driven electrode (cathode)
when DC was applied, corresponding to EFs of 1 V/cm or 2 V/cm in amplitude [44]. However, these
previous experiments were performed on full thickness retinal explants which contain a heterogeneous
collection of cells including RGCs, photoreceptors, and bipolar neurons. To isolate the effect of electrotaxis
on RGCs, we exposed purified RGCs to DC EFs. RGCs were isolated from post-natal day 0 to 1 mouse retina
as these RGCs more readily sprout new axons in culture. In the cultures exposed to 1 V/cm or 2 V/cm DC,
we observed significantly more cathode-directed growth compared to unstimulated controls (Fig. 2.2A),
similar to our prior retinal explant experiments [44]. Notably, no significant difference was noted between
control cultures and cultures exposed to 0.5 V/cm DC, indicating a threshold stimulation amplitude is
needed to drive axon growth.
2) RGCs exhibit cathode-directed growth in the presence of monophasic pulse stimulation
Although effective at directing axon growth, DC cannot be applied to living organisms at high voltages
or for prolonged periods of time without inducing tissue or electrode damage from charge accumulation
and irreversible chemical reactions [45]. A safer alternative is AC, which pairs a positive electrical pulse
with a symmetric negative pulse. Although AC is charge balanced and thus safer for clinical applications,
previous work by us has shown that retinal axons acutely redirect their growth towards the “new” cathode
when EF polarity is switched [44]. In other words, the symmetry of the cathodic and anodic pulses in AC
waveforms “cancel out” their electrotaxis effect and lead to net zero directional growth. Given this, we
hypothesized that a hybrid waveform in which the cathodic pulse is paired with an asymmetric anodic
pulse could be both (i) safe, if charged balanced, and (ii) effective at directing axon growth, if the right
25
amount of asymmetry is maintained between the amplitudes and pulse widths of each pulse (Fig. 2.1B).
To determine the optimal asymmetry needed for directional axon growth, we first performed monophasic
pulse stimulation experiments to determine effective stimulation parameters.
Previously, we demonstrated that neural progenitor cells migrate towards the cathode in the presence
of a monophasic pulse with a 1-second pulse width, 50% duty cycle (DTC) [53]. Given this, we exposed
purified RGCs to a monophasic waveform of similar duration and amplitude (2 V/cm, 400 mHz, 50% DTC
or pulse width/period). As seen in Fig. 2.2B and 2.3B, RGC axons exhibited cathode-directed growth with
monophasic pulsed stimulation. However, doubling the stimulation amplitude to 4 V/cm did not result in a
proportional doubling in the percentage of axons that grew towards the cathode. This suggests that above
a certain threshold, increasing stimulation amplitude does not have a linear additive effect on directing
axon growth. Monophasic pulse stimulation appeared to be less effective at directing axon growth in
comparison to DC of the same amplitude. While axonal electrotaxis was observed with DC of 1 V/cm (Fig.
2.2A, Fig. 2.3A), this was not observed with monophasic pulse stimulation of the same amplitude (Fig. 2.2B,
Fig. 2.3B). These experiments suggest that in addition to amplitude, pulse width or total injected charge
may also influence the efficacy of EFs at directing axon growth.
3) Minimal pulse width is necessary to direct axon growth
To understand the impact of pulse width or cycle duration on directing axon growth, we exposed
purified RGCs to waveforms with successively shorter pulse widths. While maintaining a stimulation
amplitude at 2 V/cm, decreasing the pulse width below 1.25 s was associated with proportional decrease
in % axon growth towards the cathode (Fig. 2.4A, Fig. 2.5A). Interestingly, doubling the amplitude (from
2 V/cm to 4 V/cm) while maintaining a pulse width duration of 0.625 s did not compensate for the short
and ineffective pulse width (Fig. 2.4B, Fig. 2.5B). Doubling the experimental time length (Fig. 2.4C, Fig.
2.5C) or decreasing the interpulse interval (Fig. 2.4D, Fig. 2.5D) so that the total charge injected into the
system was equivalent to the previously effective stimulation parameters (2 V/cm, 400 mHz, 50% DTC)
26
Figure 2.3: Larger pulse amplitudes direct more avid cathodic growth of RGC axons. Purified RGC cultures
were exposed to direct current (A) or monophasic pulse stimulation (B). Increases in pulse amplitude led
to increases in cathodic-directed growth of RGC axons (*p < 0.05 comparing cathodic growth; ANOVA
followed by Tukey’s multiple comparisons). Tissue culture experiments were performed concurrently and
only segregated into separate charts to facilitate flow of the paper. (C) Stills of time lapsed recordings of
RGC axon growth in control and 2 V/cm DC treated cultures. Black numbers label axons that grew towards
the cathode, red numbers label axons that grew towards the anode, while yellow numbers label axons that
grew perpendicular to the EF. Scale bar 100 µm. As published in [51].
were insufficient to compensate for the ineffective shorter pulse width. Conversely, maintaining a pulse
width at 1.25 s, an effective pulse width length, and tripling the interpulse interval (from 1.25 to 3.75 s) did
not significantly neutralize the electrotaxis effect of the waveform on directing RGC axon growth (Fig. 2.4E,
Fig. 2.5E). These experiments demonstrate that the pulse width duration, in addition to pulse amplitude,
are important stimulation parameters that control cellular behavior. In fact, increasing the pulse width
for ineffective amplitudes (e.g. 1 V/cm 50% DTC vs. 1 V/cm DC in Fig. 2.3) rendered them effective while
27
increasing amplitude for ineffective pulse widths (Fig. 2.4B, Fig. 2.5B) did not rescue their activity. This
argues that pulse width duration exerts a stronger influence on EF-directed cellular behavior than pulse
amplitude.
Figure 2.4: Longer pulse width duration is more effective at directing axon growth. Purified RGC cultures
were exposed to monophasic EF stimulation. (A) Fewer RGC axons grew towards the cathode with shorter
pulse widths. (B) Increasing voltage amplitude or (C) experimental duration did not increase the effectiveness of a short pulse width waveform. (D) Decreasing interpulse interval did not increase the effectiveness
of a short pulse width waveform. (E) Increasing interpulse interval did not neutralize the effectiveness of a
longer pulse width waveform (*p < 0.05; ANOVA followed by Tukey’s multiple comparisons) As published
in [51].
4) Biphasic stimulation with ACB directs cathodic growth of RGC axons
We hypothesized that pairing monophasic pulses that are effective at directing axon growth with pulses
of the opposite phase that are ineffective, would allow us to develop ACB waveforms capable of directing
“net” RGC axon growth. As we are constrained by the need to develop charge balanced waveforms, the
ratio of the pulse amplitude to pulse width of the cathodic pulse must be mirrored in the anodic pulse.
28
Figure 2.5: (A) 2 V/cm 25% duty cycle n = 396 axons over 3 cultures; 37.5% duty cycle n = 316 axons over 3
cultures; 50% duty cycle n = 351 axons over 3 cultures; 100% duty cycle n = 270 axons over 4 cultures.
(B) 2 V/cm n = 458 axons over 3 cultures; 4 V/cm n = 288 axons over 3 cultures.
(C) 4 hours n = 458 axons over 3 cultures; 8 hours n = 508 over 3 cultures.
(D) 400 mHz n = 396 axons over 3 cultures; 800 mHz n = 444 axons over 4 cultures
(E) 400 mHz n = 351 axons over 3 cultures; 200 mHz n = 611 axons over 4 cultures
Modified from ??, supplementary figures.
Given that our results above demonstrated that pulse width has a stronger influence on controlling axon
growth than amplitude, we prioritized longer pulse widths for our “working” pulse. With this paradigm,
our “recharging” pulse has a relatively shorter pulse width but higher amplitude than our “working” pulse.
In designing our biphasic waveforms, we had the option of using cathodic-first versus anodic-first configurations. We chose to implement cathodic-first waveforms over anodic-first waveforms because prior
work showed that RGC stimulation thresholds are lower with cathodic-first pulses [54]. This way, less
current would be needed to elicit a biological effect with cathodic-first waveforms.
To test whether ACB waveforms can direct the growth of RGC axons, we paired an “effective working”
(2 V/cm, 400 mHz, 50% DTC) anodic pulse with an “ineffective recharging” (-4 V/cm, 400 mHz, 25% DTC)
cathodic pulse. This 1:2 ratio ACB waveform directed significantly more cathodic growth over unstimulated controls (Fig. 2.6, Fig. 2.7). A similar proportion of cathodic growth was also observed when we
29
doubled the pulse amplitude of both the cathodic and anodic pulses but maintained the 1:2 cathodic:anodic
ratio (a 4 V/cm, 400 mHz, 50% DTC anodic “working” pulse paired with an -8 V/cm, 400 mHz, 25% DTC cathodic “recharging” pulse), what we termed 1:2 ratio waveform with 2X-amplitude. This indicates the ratio
of asymmetry rather than the absolute amplitude directs axon growth. In support of this, increasing the
ratio of waveform asymmetry to 1:4 (e.g. 2 V/cm, 400 mHz, 50% DTC anodic “working” pulse paired with
an -8 V/cm, 400 mHz, 12.5% DTC cathodic “recharging” pulse) was significantly more effective at driving
cathodic growth than the ACB 1:2 waveform (Fig. 2.6A,B, Fig. 2.7). Conversely, when the amplitude to
pulse width ratio was maintained at 1:1 (i.e., a traditional AC current), no directional growth of RGC axons
was detected over unstimulated controls. These experiments demonstrate that the driving force behind
axonal electrotaxis is the asymmetry in the duration of “working” vs. “recharging” components rather
than just the presence of injected current.
5) Maximum length of anodic RGC axons is shorter than cathodic RGC axons with DC stimulation
One method by which EFs could influence the direction of axon growth is by influencing the rate of
neurite growth: Xenopus dorsal root ganglia neurites which faced the cathode were measured to grow
faster than those that faced the anode [52]. Although there appeared to be a trend towards more rapid
growth of cathode-oriented RGC axons and slowed growth of anode-oriented RGC axons treated with 2
V/cm DC stimulation, a statistically significant difference was not observed (42.6 ± 6.5 µm/h versus 25.6 ±
4.5 µm/h; p>0.05; ANOVA followed by Tukey’s multiple comparisons; Fig. S5). The mean maximum length
of anode-directed axons, however, was significantly shorter in 2 V/cm DC treated cultures compared to
untreated and monophasic pulse treated cultures (Table 2.1; p<0.001, ANOVA followed by Tukey’s multiple
comparisons). This suggests that 2 V/cm DC stimulation negatively affects growth of anodically-oriented
RGC axons without affecting growth rate.
30
Figure 2.6: ACB waveforms directed more avid cathodic growth of RGC axons than symmetric waveforms. Purified RGC cultures were exposed to ACB waveforms with different cathodic:anodic pulse width
and pulse amplitude ratios. (A) Increased anodic pulse width duration was associated with increases in
cathodic-directed growth of RGC axons (unstimulated n = 4; AC 1:1 n = 4; ACB 1:2 n = 6; ACB 1:2 (2Xamplitude) n = 6; ACB 1:4 n = 5; * p < 0.05; ANOVA followed by Tukey’s multiple comparisons). (B) Stills
of time lapsed recordings of RGC axon growth in AC 1:1 (phase contrast microscopy) and ACB 1:4 (DIC
microscopy) treated cultures. Black numbers label axons that grew towards the cathode, red numbers label
axons that grew towards the anode, while yellow numbers label axons that grew perpendicular to the EF.
Scale bar 100 µm. As published in [51].
6) Preserved RGC viability with 1:4 ACB waveform stimulation
We performed LIVE/DEAD cell assays to assess the effect of EF stimulation on RGC viability. As
expected, after 4 h of stimulation, DC treated cultures were associated with a significant 19% decrease
in RGC cell viability compared to untreated controls (viability: 63% ± 11% DC treated cultures versus
79% ± 5% in untreated controls; p<0.001; ANOVA followed by Tukey’s multiple comparisons; Fig. 2.8).
31
Figure 2.7: Increasing anodic pulse width duration was associated with increases in cathodic-directed
growth of RGC axons (control n = 251 axons over 4 cultures; AC 1:1 n = 403 axons over 4 cultures; ACB 1:2
n = 696 over 6 cultures; ACB 1:2 (2X-fold amplitude) n = 579 axons over 6 cultures; ACB 1:4 n = 467 axons
over 5 cultures; * p < 0.05; ** p < 0.01; *** p < 0.001; **** p < 0.0001; ANOVA followed by Tukey’s multiple
comparisons). As published in [51], supplementary figures.
Remarkably, cultures stimulated with ACB 1:4 were not associated with a significant decrease in RGC cell
viability compared to untreated controls. These results demonstrate that the 1:4 ACB waveform, like DC
stimulation, is effective at directing RGC axon growth but, unlike DC stimulation, does not compromise
RGC viability.
7) DC stimulation induces larger changes in impedance than ACB 1:4 stimulation
A possible source for the decreased viability observed with DC trials is the excessive charge accumulation produced by charge-unbalanced stimulation. Continuous injection of anodic current, such as
occurs with DC stimulation, leads to production of oxidative species at the electrode surface and within
the electrotaxis chamber [45]. A changing voltage profile can be used as a surrogate marker of the number of electrochemical reactions that occur from electrical stimulation and is dependent on the ionization
level of the electrolyte. To compare the change in electrolyte conductivity between our different stimulation waveforms, we measured the changing voltage profile or voltage difference drift that occurred
within the electrotaxis chamber over four hours of stimulation. As expected, cultures stimulated with DC
32
Table 2.1: Decreased maximum length of anodically-oriented axons in DC treated cultures compared
to control and monophasic treated cultures. Purified RGC cultures were exposed to direct current or
monophasic pulse stimulation. Axon length was quantified as described in METHODS. The longest
anodically-oriented axon was significantly shorter in 2 V/cm DC treated cultures over control and
monophasic treated cultures. *** p < 0.001, ANOVA followed by Tukey’s multiple comparisons. Control n = 251 axons over 4 cultures; 2 V/cm DC n = 270 axons over 4 cultures; 2 V/cm monophasic n = 351
axons over 3 cultures; 4 V/cm monophasic n = 288 axons over 3 cultures.
Avg. axon
length
Max. axon
length
Min. axon
length
Control 43.7 ± 7.4 146.9 ± 34 13 ± 4.4
All 2 V/cm DC 50.6 ± 7.3 149 ± 34.4 11 ± 1.1
axons 2 V/cm 400 mHz 50.3 ±2.5 127 ±6.8 15± 2.2
4 V/cm 400 mHz 53.6± 9.2 151.8 ±36.1 18.6± 7.4
Control 48 ±7.6 145.7 ±35.6 17.3 ±7.2
Cathodic 2 V/cm DC 55.5 ±10 148.9 ±34.4 11.8 ±2.5
axons 2 V/cm 400 mHz 50.4 ±6.7 127 ±6.8 17.3 ±2.1
4 V/cm 400 mHz 52.9 ±8.4 143.5 ±47.4 19.2± 8.5
Control 38.8± 5.5 105.7 ±15 14.8± 4.7
Anodic 2 V/cm DC 26.9 ±4.9 45.1 ±29.2 17.3 ±4.7
axons 2 V/cm 400 mHz 46.1± 7.4 86.8± 5.8 23.2 ±8.2
4 V/cm 400 mHz 52.2 ±9.3 94 ±9.8 29.7 ±6.9
Control 43.4 ± 11.1 94.4 ± 47.2 16 ± 1.4
Perpendicular 2 V/cm DC 37.2 ± 7 81.3 ± 23.7 13.9 ± 1.1
axons 2 V/cm 400 mHz 49.1 ± 4.4 110 ± 13.5 16.3 ± 4.4
4 V/cm 400 mHz 58.4 ± 16 106.8 ± 13.3 26.4 ± 8.8
demonstrated a large drift in voltage difference, with an average change of -46% ± 13.5% (n = 5). This was
significantly higher than the -10.5% ± 6.6% (n = 5) drift seen in unstimulated cultures. Cultures stimulated
with the 1:4 ACB waveform demonstrated an average of -15.7% ± 7.1% (n = 9) drift which did not differ
significantly from the drift measured in untreated control cultures. Together, our measurements demonstrate that ACB waveforms lead to less charge accumulation and byproducts from electrolysis than DC,
which may account for the improved viability seen in ACB versus DC stimulation.
33
Figure 2.8: Preserved RGC viability with ACB 1:4 stimulation compared to DC EF treatment. Purified
RGC cultures were exposed to ACB 1:4 or 2 V/cm DC stimulation for 4 h. (A) 2 V/cm DC stimulation was
associated with 19% decrease in cell viability compared to controls. No significant difference was detected
with ACB 1:4 stimulated cultures. (B) Images of LIVE/CELL viability assay. Green, living cells; red, dead
cells (control n = 6533 cells over 7 cultures; 2 V/cm DC n = 5394 cells over 5 cultures; ACB 1:4 n = 2783 cells
over 5 cultures; *p < 0.05, ***p < 0.001; ANOVA followed by Tukey’s multiple comparisons). As published
in [51].
2.5 Discussion
Development of electric field application into a technology to enhance endogenous repair mechanisms
within the CNS to direct target-specific axon regeneration will likely require the use of biphasic waveforms
that are charge balanced but also effective at directing axon growth. Towards this goal, we systematically
tested monophasic waveforms with different amplitudes and pulse widths to ascertain minimal thresholds
needed to design an effective ACB waveform. Our results show that although both pulse amplitude and
pulse width thresholds must be met for electrical stimulation to be effective at directing RGC axon regeneration, pulse width exerts a stronger influence on axonal growth than pulse amplitude. While monophasic
waveforms with amplitudes just below threshold could be rendered effective if the pulse width was increased (e.g. monophasic stimulation with a 1 V/cm amplitude, 1.25 s pulse width, and 50% duty cycle was
ineffective at directing RGC axon growth while 1 V/cm DC stimulation was effective), increasing pulse
amplitude did not rescue ineffective short pulse widths (e.g. doubling the amplitude of an ineffective 0.625
s pulse width, 50% duty cycle waveform did not render it effective). Our findings were confirmed when the
system was challenged with biphasic stimulation. Axonal electrotaxis was observed towards the cathode
during the anodic phase with a longer pulse width rather than towards the cathode during the cathodic
34
phase with the higher amplitude. No net directional growth was observed with symmetric biphasic waveform stimulation. Importantly, our work shows that ACB waveforms are effective at directing RGC axon
growth without compromising viability, a problem associated with DC stimulation. Improved viability is
likely a result of ACB waveforms inducing less charge accumulation than DC. Our finding that RGC axons
grow towards the cathode during the anodic phase with ACB waveform stimulation differs from those of
Babona-Pilipos et al. who demonstrated that differentiated neural progenitor cells (NPCs), of which RGCs
resemble, did not exhibit electrotaxis with biphasic stimulation [55, 56]. A possible explanation for our
different observations is that Babona-Pilipos et al. experiments were performed to assess for cell migration of NPCs, not axon growth of mature neurons as in our experiments. The hypothesis that different
waveforms may elicit different cellular responses in different cell types or that EFs of varying amplitudes
can elicit different cellular responses in the same cell type has been documented previously by others [57].
Whether this finding could be exploited for clinical application, whereby different cells and different biological behaviors are targeted and activated by different stimulation frequencies, depending on need, is
being actively investigated by our group and others. The exact mechanism through which cells translate
voltage gradients into directional cues and stereotypic behavior is largely unknown. Prior work suggests
that extracellular EFs activate voltage-gated calcium membrane channels in a graded manner along the cell
surface, translating the extracellular electrical gradient into an intracellular calcium gradient [41]. Along
similar lines, our group has shown dependence of RGC axonal electrotaxis on the signaling activity of Rac
Family Small GTPase 1 (Rac1), a calcium activated Rho-GTPase [44]. Activation of Rac1 in cathodicallyoriented neurites, in turn, activates the actin polymerization needed for neurite elongation. Therefore, EF
mediated activation of Rac1 is one possible explanation for how EFs drive and direct axon growth. Conversely, lower intra-calcium levels in anodically-oriented neurites leads to activation of Ras homolog A
(RhoA), another member of the calcium dependent GTPases [52]. Unlike Rac1, RhoA induces actin depolymerization, leading to retraction of anodic neurites. It will be interesting to see if future work is able
35
to correlate RhoA activation with a decrease in maximum neurite length of anodically-oriented axons observed in DC treated cultures (Table 2.1). EFs have also been shown to redistribute charged membrane
proteins including acetylcholine receptors (AchRs) and epidermal growth factor receptors on cell surfaces
[41]. As AchRs are an alternative avenue for extracellular calcium can influx into a cell, this clustering
of receptors may serve as an additional mechanism through which EFs can induce intracellular gradients of calcium. Regardless of the ion channel, intracellular calcium gradients likely play a major role in
translating electrical gradients into directed axon growth.
2.6 Conclusion
Although exploiting natural cellular responses to EFs is an attractive approach to engineering tissue regenerative treatments, clinical translation is dependent on the development of safe stimulation strategies.
Ultimately, biphasic stimulation will play a central role in electrical stimulation strategies aimed at promoting endogenous neurorepair. The outcome of this chapter will be relevant choosing the optimal parameters
in EF therapeutics for electrotaxis of RGC axons. The follow-up in vivo study will be presented in the next
chapter.
2.7 Data availability
Raw data can be downloaded from the following links:
https://drive.google.com/drive/folders/15MlKDETd2LVUcCih5iwk0XcPmWvEhiHF?usp=share_link,
https://osf.io/pa7fv/?view_only=206bd04cb3fb42da9b94112123cf9ea7.
Tissue culture files are in a czi format which can be opened with Zen Black which is a freely available software produced by Carl Zeiss. The stimulation parameters and our counts for each culture are catalogued
36
in the attached Excel sheets. The waveform measurements are in .txt format and can be processed using
the MATLAB software.
37
Chapter 3
In Vivo Neuroregenerative Electrical Stimulation Therapy Using
Asymmetric Charge-Balanced Waveforms
Chapter 3
T. Kim, E. Iseri, M G. Peng, S. Medvidovic, T. Siliman, P. Pahlavan, G. Niu, C. Huang, A. Simonyan, P.
Yao, P. Lam, M. Shahidi, M. S. Bienkowski, D. J. Lee, B. Thomas, G. Lazzi, K. K. Gokoffski. Electric Field
Stimulation Directs Target Specific Axon Regeneration and Partial Restoration of Vision with After Optic
Nerve Crush Injury. Experimental Neurology (Under review, 2024)
3.1 Abstract
Injuries to the neurons within the central nervous system (CNS) often result in permanent disability due
to the lack of innate regenerative capabilities. While several molecular neuroregenerative strategies have
been proposed as potential treatments, they often lack the necessary guidance cues required to direct specific axon regeneration. To achieve functional recovery in these damaged systems, it’s essential for axons
to grow toward their appropriate target sites to restore broken synapses. Our methods from Chapter 2
were extended to adult rats after optic nerve crush injury, where the application of ACB waveforms acted
as an external guidance cue, directing long-distance, target-specific regeneration of RGC axons to their
native targets in the diencephalon. Notably, besides achieving partial anatomical restoration, ACB waveforms facilitated partial recovery of visual function, as evidenced by pattern electroretinogram (PERG)
38
recordings, local field potential (LFP) recordings in the superior colliculus, and pupillary light reflex measurements—without necessitating genetic manipulation. These results highlight the potential of exogenous
electric field (EF) application to overcome intrinsic and extrinsic barriers to axon regeneration. Moreover,
our study underscores the efficacy of electrical stimulation using specific ACB waveforms as a promising
strategy for anatomical and functional restoration following CNS injury.
3.2 Introduction
Failure of neurons to regenerate after injury in the CNS is a consequence of diminished intrinsic growth
capacity of adult neurons (cell-intrinsic barriers) and inhibitory signals in the extracellular environment
(cell-extrinsic barriers) [58, 59]. To date, most approaches to drive long-distance axon regeneration focus
on overcoming cell-intrinsic barriers—via upregulation of dormant signaling pathways that were active
during development to revert cells to a developmental or growth state. In the case of the optic nerve,
a screen for evolutionarily conserved signaling pathways that control cellular growth identified mTOR
(mammalian target of rapamycin) suppression as a major barrier to RGC axon regeneration in mice. Deletion of phosphatase and tensin homolog (PTEN), a negative regulator of mammalian target of rapamycin
(mTOR), led to long-distance RGC axon regeneration after optic nerve crush injury [60]. Since then, RGC
axon regeneration has been reported with genetic modulation of other signaling pathways including suppressor of cytokine signaling (SOCS3) and the Yamanaka genes [61, 62]. Increased gains were reported
when these neuro-regenerative strategies were combined with overexpression of neurotrophic factors such
as ciliary neurotrophic factor (CNTF), erythropoietin, intraocular injection of pro-inflammatory molecules
like zymosan, or chelation of zinc [63, 64, 65, 66, 67]. Although these strategies have significantly advanced
the field of optic nerve regeneration, they do not address the need to provide growing axons with navigational cues. As a result, regenerating RGC axons were found to stall at the optic chiasm [60, 62]. In
39
PTEN/SOCS3 knock out (KO) mice and PTEN KO/zymosan/cAMP treated mice, 10-20% of axons exhibited premature branching and 40% of axons regenerated aberrantly, making U-turns and extending back
towards the eye or growing into the contralateral optic nerve [68]. Of those animals that demonstrated
retrochiasmal growth, RGC axons projected to bilateral suprachiasmatic nuclei (SCN) but essentially no
RGC axons were found to project to distal structures including the superior colliculus (SC) or lateral geniculate nucleus (LGN) [68, 69].
Restoration of function in the CNS requires targeted axon regeneration. However, development of
strategies that can recapitulate the guidance cues that directed axon growth during development have
been limited by the need to not only express these cues in spatial but also temporal gradients [70]. For
example, in the developing Drosophila CNS, axon decussation requires neurons to exchange Fasciclin II
(FasII) surface receptors for FasI. Once decussation is complete, neurons must then switch back to express
only FasII [71]. Successful recapitulation of these gradients using current molecular techniques has been
limited. EFs serve as a unique solution to this problem. Electric potentials are naturally generated in
the body, and EFs have been shown to direct tissue pattern during development and wound healing after
injury [72]. In regard to the optic nerve, we and other groups have shown that EFs confer both prosurvival and pro-regenerative benefits on RGCs. Immediate application of EFs after optic nerve transection
promoted 1.5-fold more RGC survival over controls after optic nerve transection [73]. EF stimulation
in vitro enhanced RGC axon growth in response to neurotrophic factors including BDNF (brain derived
neurotrophic factor) [74]. Notably, we have demonstrated that EFs not only promote RGC axon growth,
but also control the direction of growing axons [75]. RGC axons acutely responded to changes in charge
orientation by turning and redirecting their growth cones towards the cathode, the electrode with the
more negative potential, in vitro. Here, we exploit these findings to show that in vivo EF stimulation can
direct full-length, target-specific RGC axon regeneration in adult rodents after optic nerve crush injury,
without evidence of aberrant regeneration. In addition to anatomical restoration, EF stimulation partially
40
restored electrophysiologic function, and did so without the need for concurrent genetic manipulation.
Our findings illustrate the potential of exogenous EF application to provide the missing link, directing
target-specific regeneration in the mature CNS.
3.3 Methods
To test whether in vivo stimulation of the optic nerve can direct RGC axon regeneration after crush injury, we developed an apparatus that would enable for continuous stimulation of the optic nerve in an
unanesthetized rat (Fig. 3.1A-B).
3.3.1 Animal Surgical Procedure
The use of animals was in accordance with the ARRIVE guideline, the Association for Research in Vision
and Ophthalmology (ARVO) Statement on the use of animals for research and was approved by the Institutional Animal Care and Use Committee at the University of Southern California [76]. After sedation with
isoflurane, adult male Long-Evans rats (300-500 g; Charles River; Wilmington, MA) underwent a midsagittal scalp incision to expose the bregma and lambda followed by a left lateral canthotomy and cantholysis
to expose the left optic nerve. Blunt dissection was performed under the frontalis muscle to create a tunnel
between the orbit and the scalp incision. A 25 mm long platinum (Pt) “J-shaped” source electrode (250 µm
diameter; P1 Technologies; Boerne, TX) with 5 mm of its insulation coating removed was tunneled from
the scalp incision into the orbit, under the lateral rectus, and then wrapped around the left optic nerve
at the base of the globe. A straight 16 mm long Pt ground electrode with 1 mm of its insulation coating
removed was placed stereotactically (2.43 M-L, -1.00 A-P, -9.65 D-V at 10°; Stoelting 51900; Wood Dale, IL)
into the contralateral optic tract (Fig. 3.1A). Both source and ground electrodes were made of Pt [77, 78].
The source electrode was made into a “J-shape” to maximize contact with the optic nerve, which was assumed to move and distort with eye movement. During the same surgery, rats then underwent optic nerve
41
crush injury for 10 seconds using cross-action #5 Dumont forceps (World Precision Instruments; Sarasota,
FL). The electrodes were then secured into place with dental acrylic (Patterson Dental; El Segundo, CA)
and a plastic pinwheel pedestal (P1 Technologies; Boerne, TX). The lateral canthus was repaired and dexamethasone/neomycin sulfate/polymyxin B ophthalmic ointment (MWI Veterinary Supply 044523; Boise,
ID) applied to the eye. Rats underwent subcutaneous injection of extended-release buprenorphine (0.65
mg/kg, Ethiqa XR, MWI Animal Health, Boise, ID).
3.3.2 Stimulation Parameters and Setup
Rats were stimulated with three different waveforms. We hypothesized that stimulation with charge balanced, biphasic waveforms that pair a positive pulse with a negative pulse would be a safer alternative
to DC as they minimize charge accumulation and irreversible deleterious chemical reactions [77]. Not all
biphasic waveforms, however, are likely to be equally effective at directing RGC axon growth. For example,
prior work showed that RGC axons can sense acute changes in EF polarity and react by redirecting their
growth towards the “new” negative electrode [75]. This suggests that symmetric charge balanced waveforms (SCB 1:1, Fig. 3.1C), in which the anodic pulse is paired with an identical cathodic pulse of opposite
polarity, would be ineffective at directing RGC axon growth. With symmetric waveforms, the anodic and
cathodic pulses would “cancel out” and direct net zero axon growth. ACB waveforms (Fig. 3.1C), on the
other hand, could be both safe and effective at directing RGC axon growth. ACB waveforms are similar to
SCB in that they are charge balanced [79] but have different anodic phase amplitude and width ratios (Fig.
3.1C). It is this asymmetry that was hypothesized to generate the directional fields needed to drive axon
growth. Indeed, our in vitro work showed that not only are ACB waveforms effective at directing RGC
axon growth, but that the greater the asymmetry, the more effective the waveform 2.
Rats underwent optic nerve crush injury concurrently with electrode placement. However, to mimic
clinical scenarios of acute optic nerve injury more closely, electrical stimulation was not initiated until
42
5 to 7 days after crush injury. Rats were stimulated with ACB 1:4 (cathodic:anodic pulse width ratio), a
waveform in which the pulse duration of the anodic phase (working phase) was 4 times longer than that of
the cathodic phase (rebalancing phase; Fig. 3.1C). To maintain charge balance, the pulse amplitude of the
cathodic phase was set to be four times higher than that of the anodic phase. Other rats were treated 1 with
either a symmetric charge balanced waveform (SCB 1:1) or ACB 4:1 (the inverse of ACB 1:4; Fig. 3.1C).
Rats were continuously stimulated for 5 hours each weekday for 6 weeks (30 days of total stimulation).
Measurements of total injected charge across a 1 kΩ resistor indicated that our biphasic waveforms are
charge balanced. The cathodic to anodic area was 0.98, 0.98, and 1.01 for ACB 1:4, SCB 1:1, and ACB 4:1
stimulated rats, respectively.
Electrical stimulation was delivered across the optic nerve using a two-electrode configuration, where
the working source electrode was placed around the left optic nerve and the return ground electrode within
the contralateral optic tract (Fig. 3.1A). A current-controlled stimulus generator (STG 4008, Multi-Channel
Systems, Harvard Bioscience, Inc.) was connected to the source and ground electrodes via a wire tether
that was attached to a commutator with a ball joint (P1 instruments; Fig. 3.1B). This allowed the unanesthetized rat to roam freely within the cage during stimulation. Constant current mode was selected to
ensure the delivery of a stable current between the electrodes independent of changes in the electrode or
tissue properties that might affect impedance during the stimulation period. This configuration has been
shown to generate linear voltage gradients along the optic nerve [78]. Three custom waveforms were used
in the trials: 1) symmetric biphasic, 2) asymmetric biphasic, anodically-driven, and 3) asymmetric biphasic, cathodically-driven, all at 50% duty cycle (Fig. 3.1C). The waveform parameters are provided in Table
3.1. Each custom waveform was programmed using the MC Stimulus II software (Harvard Biosciences,
Germany). On day 1 (one week after surgery), stimulation was initiated at 100% amplitude and 5% duty
cycle. Duty cycle was increased every hour as tolerated until 50% duty cycle was reached. Rats were
43
Figure 3.1: Schematic of experimental timeline, stimulation system, and stimulation waveforms. (A) Adult
Long-Evans rats underwent concurrent electrode placement and optic nerve crush on Day 0. Five to seven
days later, optic nerves were stimulated with various waveforms for five hours a day every weekday for 6
weeks. Schematic of orientation of electric gradient during anodic and cathodic phases. Three to four days
before euthanasia, rats underwent intravitreal injection with CTB-647. Schematic of orientation of electric
gradient during anodic and cathodic phases. (B) Rats were attached to a stimulation generator via a tether
on a ball joint, allowing for continuous stimulation in an unanesthetized, mobile rat. Continuous waveform
monitoring with an oscilloscope was performed to assure that rats were being stimulated appropriately.
(C) The current stimulation pulses of various waveforms recorded across a 1 kΩ resistor connected in series
to the return electrode and the resulting voltage transient measured across the platinum needle electrodes.
Eipp is the electrode potential at the onset of the current pulse (interphase), ∆V is the total polarization
of the electrode during the stimulation phase, VOhmic is the near-instantaneous potential change at the
onset/termination of the current pulse following the characteristics of a purely resistive load, and ∆Ep
is the steady state potential following the characteristics of a reactive (capacitive) load. SCB, symmetric
charge balanced; ACB, asymmetric charge balanced. Numbers represent the relative cathodic:anodic pulse
width ratios.
44
considered to be intolerant to the stimulation if they displayed physical behaviors such as eyelid fasciculations, or ceased expected behaviors such as grooming, sleeping, or exploration of their cage. To ensure
that rats were receiving the correct stimulation, the voltage waveforms of the electrodes were monitored
continuously with an oscilloscope. As the compliance voltage of this stimulation system was an order
of magnitude larger than the voltage necessary to pass the target current through the impedance of the
electrode-tissue interface, the rats were guaranteed to receive the full input current for the entire duration
of the experiment. The stability of the current delivery was verified by connecting a 1 kΩ series resistor to the ground terminal and measuring the voltage drop across it. The voltage generated between the
electrodes was periodically measured to assess for changes in the stimulation tissue or electrode-tissue
interface over time.
Waveform
Type
Cathodic
Amplitude
(µA)
Anodic
Amplitude
(µA)
Cathodic
Duration
(µs)
Anodic
Duration
(µs)
Duty
Cycle
(%)
SCB 1:1 -400 400 400 400 50
ACB 1:4 -400 100 100 400 50
ACB 4:1 100 400 400 100 50
Table 3.1: Target stimulation parameters for each waveform.
3.3.3 Computational Modeling
The Admittance Method (AM) developed by our group was used to predict the voltage distribution along
the rat optic nerve and the retina by our stimulation setup 1.3. Briefly, a high resolution 3D image of the
rodent head and orbital structures was obtained using computed tomography performed on a CD1 adult
mouse. This image was then discretized and imported into the AM computational platform. The size of
the head, and the length and angle of the optic nerve were then adjusted according to the measurements
taken in an adult Long-Evans rat. This generated a model consisting of 912, 900, and 504 voxels in the x,
45
y, and z directions respectively, each voxel being a cube with a length of 83 µm. Resistivity of different
tissues within the rat head was assigned according to prior work [80, 81, 82]. The optic nerve was modeled
as a cylinder with a diameter of 500 µm, starting from behind the eye and extending to the optic chiasm.
The optic nerve was surrounded by a thin layer of cerebrospinal fluid during its course within the orbit,
surrounded by a large layer of fat, a thin discrete layer of muscle to represent the recti muscles, and finally
enclosed in bone. Electrode size and position were modeled according to the surgical positions described
above. To predict how individual RGCs may respond to stimulation, we generated a realistic morphological model of a RGC cell as a .swc file and assigned membrane properties specific to its subtype [83]. The
extracellular voltage mapping was interpolated onto the RGC morphologies in the NEURON simulation
environment to calculate the change in their membrane potentials at every time step as previously described [84]. We modeled the extracellular potential that the RGCs are exposed to depending on these
waveform characteristics.
3.3.4 Anatomical Assessment
1) RGC axon labeling and quantification
Three to four days before euthanasia, cholera-toxin subunit-B (CTB) conjugated to Alexa-Fluor-647
(CTB-647; C34778, Thermofisher, Waltham, MA) was injected intravitreally to label RGC axons. Briefly,
rats were sedated with inhaled isoflurane (2-4%). Pupils were dilated with 0.5% tropicamide and 2.5%
phenylephrine. Using a 30G syringe, an anterior chamber tap was performed to lower intraocular pressure. The same needle was used to generate a tunnel through the sclera at the level of the ora serrata.
Through this hole, 2 µL of 2 mg/ml CTB-647 was injected intravitreally using a 33G Hamilton syringe
(NANOFIL10, World Precision Instruments, Sarasota, FL). Visible filling of the vitreous was confirmed directly under a surgical microscope. Rats were euthanized and subsequently perfused with PBS followed
46
by 4% paraformaldehyde (PFA). Optic nerves were dissected out whole and cleared using a modified version of a previously described protocol [85]. Briefly, the nerves were rinsed twice in PBS for 5 minutes
then dehydrated in ascending ethanol series (50%, 80%, 95%) for 1 hour each under gentle agitation and in
100% ethanol overnight at room temperature (RT). The nerves were further dehydrated in hexane (EM-131
HX0304-6, VWR, Radnor, PA) overnight at RT, then transferred into a clearing solution (BABB) of 1 part
benzyl alcohol (103514-446, VWR, Radnor, PA) in 2 parts benzyl benzoate (200000-094, VWR, Radnor, PA)
and left overnight at RT under agitation. Optic nerves were then placed in a 35 mm glass bottom dish
(MatTek, P35G-0-20-C, Ashland, MA) in BABB solution sealed with a glass coverslip (89167-110, VWR,
Radnor, PA). A confocal laser scanning microscope (LSM 800, Zeiss, Germany) was used to image the optic
nerves at 20x magnification in longitudinal optical sections of 20 µm increments, with tiling set to 512 px
x 512 px, 16-bit, and 221 µm pinhole. All optical sections per nerve were saved in a single .czi file for analysis. Axon quantification was performed as previously described [85]. Briefly, a semi-automated method
was used. The fluorescent intensity of individual pixels from CTB labeling served as a surrogate for axon
density in specific regions of interests (ROIs) drawn perpendicular to the long axis of the nerve. Optic
nerve images were opened in ImageJ/FIJI at the highest resolution and the nerves straightened. ROIs were
designated at the pre-crush site (ie, the region of the optic nerve between the globe and crush site), and up
to 2000 µm past the crush site in 250 µm increments (collectively, the post-crush ROIs). Threshold pixel
intensity was determined to exclude background noise from subsequent analysis using AxonQuantifier,
a freely available ImageJ plugin. AxonQuantifier was run to quantify the fluorescence intensities of each
post crush ROI throughout its longitudinal optical sections and normalized to the fluorescence intensity
of the pre-crush ROI, and thereby determine the percent of RGC axon density at specified distances from
the crush site.
47
2) Immunohistochemistry and RGC quantification
Eyes were immersed in 4% PFA for 45 minutes at RT then transferred to 0.3% Triton X-100 (VWR,
Radnow, PA) and stored at 4℃overnight. The retinas were dissected and cut in four corners and then
washed for 5 minutes three times with 0.3% Triton X-100 followed by blocking with 3% horse serum (VWR,
Radnow, PA, USA) and 1% Triton X-100 for 30 minutes at RT. The retinas were then incubated with rabbit anti-RBPMS (1:500, GenTex, Irvine, CA) polyclonal antibody for 5 days at 4℃[86]. The retina was
washed repeatedly and then incubated with Alexa Fluor 488-conjugated goat anti-rabbit IgG (1:200; Jackson ImmunoResearch, West Grove, PA) secondary antibody overnight at 4℃. After repeating the washing
step, retinas were flat mounted on glass slides and sealed with 1.5-mm coverslips with antifade mounting
medium (ProLong Diamond; Life Technologies, Eugene, OR) and dried overnight before imaging.
An upright fluorescence microscope (Axio Observer 7, Zeiss, Germany) 1 was used to obtain images
using a 20x objective. Images were captured with a charge-coupled device camera and the SimplePCI 5.3
imaging system (Hamamatsu Photonics, Hamamatus City, Japan). The number of RBPMS-positive cells
and area of the image were quantified. At least three images from the center, middle, and peripheral area
of each quadrant (minimum 12 per retina) were analyzed per rat, totaling at least 1.7 mm2 of retina per
animal.
3) Brain Histology
Brains were fixed in 4% PFA, cryoprotected in graded sucrose series (10%, 20%, 30%), and then embedded in OCT (Sakura Finetek, Torrance, CA) before storage at -80℃. Brains were cryosectioned (QS12
Cryostat, Avantik, Pine Brook, NJ) at 25 µm thickness in the coronal plane. Sections were rinsed in PBS,
counterstained with 0.15 µg/ml Hoechst (33342, Enzo Life Sciences, Farmingdale, NY) and rinsed again
in PBS prior to mounting. The samples were then sealed with 1.5-mm coverslips and antifade mounting
medium (ProLong Diamond; Life Technologies, Eugene, OR) and dried overnight. Subcortical targets of
48
the retinofungal pathway were imaged with a Andor Dragonfly spinning disk confocal microscope (Oxford Instruments, United Kingdom) equipped with a 25x Nikon silicon oil objective. All images are MIP
imaged with 1 µm Z step through the tissue section.
3.3.5 Functional Assessment
1) Pattern electroretinogram recordings
Pattern electroretinogram (PERG) recordings were performed with a UTAS Visual Electrodiagnostic
System (LKC, Gaithersburg, MD), using DTL-plus electrodes (M019258 and M014764, Jorvec, Miami, FL).
Rats were sedated with inhaled isoflurane followed by an intraperitoneal injection of a ketamine/xylazine
cocktail (5/37.5 mg/kg, respectively). Rats were then placed on the system’s thermostatically controlled
heating pad and positioned such that the projection of the pupil was aligned to the center of the pattern
monitor 20 cm away. The eyes were not dilated, in keeping with prior publications [87]. The ground
and reference electrodes were superficially inserted into the base of the tail and snout, respectively, while
recording electrodes were placed on the corneal surface with careful attention to not block the pupil. The
cornea was kept moist with lubricating eye drops. Impedance was checked three times prior to running the
experiment. Rats were evaluated without dark adaptation to limit the possibility of direct photoreceptormediated evoked responses [88]. The pattern stimuli were displayed on an RGB monitor (model Dell
M933S; Dell, Inc., Round Rock, TX). Stimuli consisted of 0.05 cyl/deg horizontal black and white bars
reversing at 1 Hz, presented at 100% contrast and an average ambient room lighting mean luminance of
100 cd/m2
. A range of 992 to 1488 signals were obtained and averaged per rat at each timepoint to isolate
the response from background noise. The amplitude was measured from the P1 peak to the N2 trough.
The peak time was measured as the time to the peak of the positive response. Normalized amplitudes are
reported as left eye amplitude divided by the corresponding right eye amplitude. A two-way ANOVA with
Tukey’s test for multiple comparisons test 1 was performed on the normalized amplitudes. Responses not
49
within four standard deviations of the mean amplitude of the group were regarded as artifact and discarded
[87].
2) Local field potential recordings
Stereotactically-guided LFP recordings in the SC were performed as previously described [89]. After
dark-adaptation overnight, rats were sedated with an intraperitoneal injection of xylazine/ketamine (5/37.5
mg/kg respectively) and maintained on 1%-3% inhaled sevoflurane. Pupils were dilated with 0.5% tropicamide and 2.5% phenylephrine. The scalp was carefully separated from the dental acrylic to expose the
orbital electrode. The electrode was then cut and the dental acrylic along with the intracranial electrode
removed. Rats were placed in a stereotactic apparatus (David Kopf Instruments, Tijunga, CA), and a right
parietal craniotomy was performed with a handheld drill (Dremel, Walnut Ridge, AR). A small amount of
cortex overlying the right SC was then aspirated to directly visualize the SC. The stereotactic apparatus
was referenced from the lambda suture and used to guide placement of a single custom-made tungsten
recording electrode within the right SC. The reference electrode was placed near the exposed scalp, and
the ground electrode was placed subcutaneously in the tail region. Electrical response to a full-field flash of
1300 cd/m2
(Grass model PS 33 Photic stimulator, W. Warwick, RI) was recorded using the Powerlab data
acquisition system (ADInstruments, Mountain View, CA). Recordings were performed from 28-30 SC locations per animal ( 200-400 µm apart) covering the fullest visible extent of the SC. Based on the SC activity,
3-10 trials were performed at each recording site. Stereotactic coordinates of the electrode penetrations
were recorded at each site. Light stimulus was time locked with the recording device. LFP recordings
were analyzed using LabChart 8 Reader (ADInstruments, 1 Mountain View, CA). Visual responses to light
were defined as a clear, prolonged (>20 msec) increase (at least twofold) in the light-evoked electrical activity above background activity (determined using the 100 msec of activity recorded prior to light stimulus).
Recordings were analyzed for (1) percentage of visually responsive sites, (2) response onset latency, defined
as time from stimulus to the earliest point of visual response, and (3) peak response amplitude, defined as
50
the largest excursion peak to peak during the visual response [89, 90]. The response onset latencies and
peak response amplitudes were averaged across all trials from each recording location.
3) Pupillary response
To assess direct pupillary light reflex, rats underwent tarsorrhaphy of the uninjured eye to prevent
consensual pupillary constriction. After dark adaptation for at least 1 hour, the rats were sedated under
inhaled isoflurane and the injured eye was gently opened with manual traction. Photic stimulus was
provided by an LED lamp (GearLight, Walpole, MA) measured to deliver a high intensity light of 1500 lux
at 20 cm from the eye. Pupillary response was video recorded at 3x magnification using an iPhone 13 Pro for
at least 45 seconds. The rate and extent of pupillary constriction were quantified on ImageJ by measuring
the change in ratio of pupil to iris diameter at 0, 10, and 30 seconds after start of photic stimulation.
Measurements were performed in triplicates and averaged. During testing, rats were neither awake nor
handheld to avoid the possibility of sympathetically-driven pupillary dilation that could interfere with
measurements.
4) Optokinetic reflex testing
Optokinetic reflex (OKR) testing was performed similar to Ahmed et al [91]. All rats were dark adapted
for at least 15 minutes prior to the experiment. Rats were placed on a platform positioned 10 inches
above the ground and 4.5 inches away from two iPad tablets (5th generation, 9.7-in display) positioned
lengthwise against each other at a 155° angle to create a seamless overlap of both screens. The OKN
Stripes Visualization Web Application program was then opened and set to the lowest spatial frequency of
0.08 c/d. The spatial frequency was gradually increased from 7 to 15 stripes in increments of 2 stripes while
maintaining a constant speed of 20 seconds across the screen. Head tracking was monitored for a positive
response with either right or leftward rotating lines, respectively. A response was considered positive if
the rat was observed to perform a head tracking movement in the same direction of the stripes. The rat
51
was deemed non-responsive to the visual stimuli when no tracking movement was detected for at least 5
seconds on either side over at least two trials. Responses were recorded as able or unable to track for each
eye. OKR testing was conducted weekly.
5) Visual cliff test
The visual cliff avoidance test was performed as previously described [92]. A clear, open-top plexiglass
box (Conduct Science, Skokie, IL) measuring 82 x 82 cm was placed on a 3-foot-tall table with half of the
box protruding. A black-and-white checkerboard pattern was displayed directly underneath the box on
the counter (shallow side) and 3 feet below the protruding portion of the box on the floor (deep side). A
25 x 15 x 7.5 cm platform was stationed in the center of the box bisecting the shallow and deep sides. To
assure that responses were a result of regeneration in the lesioned eye, tarsorrhaphy was performed on the
uninjured right eye. The following day, rats were placed on the platform and scored as follows (1) failure to
dismount, which was considered as “failed depth perception” (2) correct dismount to shallow side, which
was considered “successful depth perception”, or (3) incorrect dismount to deep side, which was considered
“failed depth perception.” Rats were observed for 5 minutes, and each trial was video recorded. Only one
trial was performed to avoid the confounding influence of memory effect [92].
3.3.6 Statistical Analysis
Results are reported as either standard deviation (STD) or standard error of the mean (SEM) as specified in
the text. Significant differences were determined using one-way or two-way analysis of variance (ANOVA)
followed by Tukey’s post hoc test for multiple comparisons using GraphPad Prism 7 (San Diego, CA).
P < 0.05 was considered to indicate a statistically significant difference. Investigators were masked to
experimental conditions when analyzing the data.
52
3.4 Results
3.4.1 Viability Assessment
At baseline, 1 week after electrode placement and crush injury but before initiation of EF stimulation, whole
mount immunohistochemistry demonstrated a near 50% decrease in the number of RBPMS-positive RGCs
per area compared to uncrushed controls (Fig. 3.2). This number continued to decline over time. At 7 weeks
post crush injury (6 weeks of stimulation), the average RGC density was 2-fold higher in EF stimulated
animals compared to untreated controls. This increase, however, was not statistically significant. Similar
to our prior in vitro findings 2, this indicates that electrical stimulation does not compromise RGC viability.
Figure 3.2: Preserved RGC viability with biphasic electrical stimulation. Whole mount retinas processed
for RBPMS immunohistochemistry demonstrated no significant difference in RGC density in crushed, EF
treated animals compared to crushed, untreated (UnTx) controls. One way ANOVA with Tukey’s multiple
comparisons test. Scale bar, 20 µm.
53
3.4.2 Long-term Assessment of Equivalent Tissue Impedance
To assess the safety of electrical stimulation on the optic nerve, we measured the change in tissue resistance over time, a surrogate marker of electrically induced tissue damage [93, 94]. The near-instantaneous
voltage change at the onset and termination of the current pulse was measured to determine the approximate voltage drop across the optic nerve. The resistance value was calculated from these measurements
using a simplified version of the equation presented in Cogan et al. for calculating the voltage drop (Va)
across the electrolyte (tissue) and estimating its resistance (RT) in the Ohmic relationship Va = IRT (Fig.
3.1C) [19]. We used the same method for untreated rats by applying a transient 1:1 SCB stimulation pulse
at 25% amplitude and 10% duty cycle to minimize any unwanted stimulation effect. The average change
in the approximated tissue resistance over 6 weeks was found to be +0.7% +/- 5.4%, -11.5% +/- 6.1%, +4.9%
+/- 7.6%, and -5.7 +/- 11.4% for untreated, SCB 1:1, ACB 1:4, and ACB 4:1 treated rats, respectively. No
significant difference was detected between untreated animals or animals stimulated with any of these
waveforms (n = 4, one-way ANOVA with Tukey’s multiple comparisons test). This suggests that 30 days
of near continuous biphasic stimulation induces negligible tissue damage on the optic nerve, orbit, and
optic tract.
3.4.3 Target-Specific Regeneration
In unstimulated animals, few axons were seen extending past the crush site at 250 µm while almost no
axons were seen at 1000 µm past the crush site (Fig. 3.3A; Table 3.2), consistent with prior reports [95].
This contrasts with animals stimulated with ACB 1:4 in which 5 of 5 rats demonstrated long-distance optic
nerve regeneration. Within these animals, 25-fold and 53-fold more RGC axon labeling was noted at 250
µm and 1000 µm past the crush site compared to unstimulated controls, respectively (p < 0.001, p < 0.05;
two-way ANOVA with Tukey’s multiple comparisons test; Table 3.2). Most axons were seen decussating at
the optic chiasm while few traveled ipsilaterally (Fig. 3.3B), as occurs in developmentally normal rodents.
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Figure 3.3: Biphasic stimulation with ACB 1:4 directs full-length regeneration of crushed RGC axons. (A)
Optic nerves underwent crush injury followed by 6 weeks of stimulation with various biphasic waveforms
and CTB labeling of RGC axons. Regenerated axons observed past the crush site (asterisk) with ACB 1:4
treatment. (B) Decussating (blue arrow) and non-decussating (blue arrowhead) RGC axons seen in the
optic chiasm of an ACB 1:4 treate animal. (C) Pre- and post-crush RGC axons (pink arrow and arrowheads,
respectively observed projecting back towards the eye in an ACB 4:1 treated animal. (D) Quantification of
RGC axon density at increasing distances from the crush site (error bars, SEM; * p < 0.05, ** p < 0.01, ***
p < 0.001; two-way ANOVA with Tukey’s multiple comparisons test). (E) Whole optic nerve of an ACB
1:4 treated animal demonstrating long-distance RGC axon regeneration past the crush site (asterisk) and
through the optic chiasm. Scale bars 250 µm.
55
Importantly, only rare RGC axon labeling was observed in animals stimulated with the SCB 1:1 waveform,
indicating that the driving force behind axonal galvanotaxis is charge asymmetry rather than only the
presence of injected current. Similarly, only a few axons were noted in animals stimulated with ACB
4:1, validating our prior in vitro findings that pulse width exerts a stronger influence on axonal growth
than pulse amplitude [79]. In fact, some axons could be seen projecting back to the globe after 10 days of
stimulation with ACB 4:1, the inverse of ACB 1:4 (Fig. 3.3C). Altogether, our work suggests that electrical
stimulation with ACB 1:4 directs long-distance RGC axon regeneration after optic nerve crush injury.
Group N 250 µm 500 µm 1000 µm 2000 µm
UnTx 1:1 5 0.82 ± 0.32 0.36 ± 0.15 0.14 ± 0.1 0 ± 0
SCB 1:1 4 0.53 ± 0.23 0.38 ± 0.24 0.15 ± 0.1 0.03 ± 0.03
ACB 1:4 5 20.24 ± 3.46 9.68 ± 2.84 7.38 ± 2.89 6.1 ± 3.11
ACB 4:1 4 2.72 ± 0.88 1.38 ± 0.5 0.33 ± 0.14 0.15 ± 0.09
Table 3.2: Average percent of regenerated RGCs at various distances from the crush site. Error represents
SEM.
RGCs project to over 40 different regions in the brain to relay visual information. In the rodent brain,
most RGCs project to either the SC, which controls gaze, or to the lateral geniculate nucleus 12, which
relays visual information to the primary visual cortex. RGC fibers also project to the SCN, which controls
circadian rhythm, the olivary pretectal (OPN) nucleus which controls pupillary response, and the nucleus
of the optic tract (NOT) which initiates or maintains horizontal gaze [96, 97]. Interventions to restore
function after nerve injury must be able to direct axons accurately to these subcortical targets. Given
that animals stimulated with ACB 1:4 demonstrated long-distance axon growth past the optic chiasm, we
investigated whether these RGC axons targeted appropriate structures in the diencephalon. After 6 weeks
of stimulation with ACB 1:4, CTB-labeled RGC axons were observed projecting to bilateral SCN in one
animal, the contralateral SCN in two animals, and the contralateral SC in three of the five animals (Fig.
56
3.4). In two of these animals, RGC axons were also observed in the contralateral dorsal and ventral lateral
geniculate nucleus (dLGN and vLGN), the contralateral intergeniculate leaflet (IGL), the contralateral NOT,
and OPN (one bilateral and one contralateral). Altogether, axons were observed projecting to at least one
subcortical target in all but one of the five animals. Of note, the axons appeared to laminate to the correct
layer of the SC and there was no evidence of off-target regeneration to non-visual regions of the brain.
In contrast, no RGC axons were observed to project to subcortical targets in untreated animals (data not
shown).
3.4.4 Partial Recovery of Electrophysiology
To assess whether treatment with electrical stimulation after optic nerve crush injury restores RGC function, serial pattern electroretinogram (PERG) recordings were performed at baseline (1 week after crush
injury, before initiation of treatment), after 2 weeks of electrical stimulation, and after 6 weeks of electrical
stimulation in the same animal (Fig. 3.5). To account for variability in signal response from anesthesia,
recordings in the left eye were normalized to the right eye. Normal age-matched rats had an average N95
amplitude of 4.71 µV (+/- 0.6 SEM) in their left eye, with a left to right eye normalized ratio of 1.02 +/- 0.05
SEM (N = 4). At baseline, the normalized N95 amplitude decreased to an average ratio of 0.45 +/- 0.02 SEM
in the untreated group. No difference in baseline measurements was detected between untreated animals
and animals assigned to any of the treatment groups (Table 3.3). Two-way ANOVA detected significant
time by group interaction (p < 0.0001). Post-hoc analysis using Tukey’s multiple comparisons test demonstrated a significant decline in PERG amplitudes in the untreated group and in animals stimulated with
ACB 4:1 over time. In contrast, animals treated with ACB 1:4 demonstrated a significant 1.8-fold increase
in their normalized PERG amplitude after 6 weeks of stimulation compared to baseline (baseline 0.37 +/-
0.04 vs 6- weeks 0.68 +/- 0.07, SEM, p < 0.05). This indicates that ACB 1:4 stimulation conferred partial
57
Figure 3.4: Biphasic stimulation with ACB 1:4 mediates target specific regeneration. In ACB 1:4 treated
animals, CTB-labeled RGC axons (green) can be seen projecting to subcortical visual targets including
bilateral SCN and contralateral vLGN, IGL, dLGN, OPN, NOT, MPT, PPT, and SC. SCN, suprachiasmatic
nucleus; vLGN, ventral lateral geniculate nucleus; IGL, intergeniculate leaflet; dLGN, dorsal lateral geniculate nucleus; OPN, olivary pretectal nucleus; NOT, nucleus of the optic tract; MPT, medial pretectal nucleus;
PPT, posterior pretectal nucleus; SC, superior colliculus.
58
restoration of RGC function. Although SCB 1:1 stimulation failed to significantly increase PERG amplitudes over time (baseline 0.32 +/- 0.05 vs 6- weeks 0.52 +/- 0.11 SEM), these animals did not demonstrate
the continued loss of function seen in untreated animals and ACB 4:1 stimulated animals, suggesting a
weak neuroprotective effect.
Group N Baseline 2 Weeks 6 weeks
UnTx 1:1 5 0.45 ± 0.02 0.33 ± 0.07 0.18 ± 0.03
SCB 1:1 7 0.32 ± 0.05 0.42 ± 0.04 0.52 ± 0.11
ACB 1:4 8 0.37 ± 0.04 0.49 ± 0.06 0.68 ± 0.07
ACB 4:1 5 0.32 ± 0.04 0.38 ± 0.05 0.18 ± 0.07
Table 3.3: Biphasic stimulation with ACB 1:4 mediates partial recovery of RGC function. Baseline: One
week after crush and electrode placement but before initiation of stimulation. Mean normalized N95 amplitude on PERG testing over time in each stimulation group (error bars, SEM).
To demonstrate that visual information is being transmitted by RGC axons to target structures in the
brain, we performed stereotactic-guided, light-evoked LFP recordings in the contralateral SC [98, 89]. On
average, 2.67% +/- 1.64% (SEM) of areas in the SC demonstrated a response to full-field light stimulation
in untreated animals (Fig. 3.6). These rare responses were detected in two of five untreated animals.
Remarkably, all 8 animals that underwent 6 weeks of stimulation with 1 ACB 1:4 demonstrated a positive
response to full-field light stimulation. On average, 20.69% +/- 4% of sites (SEM) in ACB 1:4 treated animals
demonstrated a positive response, ranging from 10% to 40% sites out of an average of 31 sites tested per
animal. However, the average amplitude of 81.78 +/- 18.1 µV and the average latency of 113 +/- 31.4 msec
in ACB 1:4 treated rats were lower and longer than in normal age-matched controls (amplitude 223.7 +/-
93.7 µV; latency 31.4 +/- 3.3 msec; N = 3; mean +/- SD), respectively. Rare responses were recorded in SCB
1:1 and ACB 4:1 treated animals (1% +/- 1% and 5% +/- 3% of sites, respectively). Of note, no response was
detected in baseline animals (evaluated one week after crush but before initiation of electrical stimulation),
59
suggesting that our findings in ACB 1:4 stimulated animals represent visual restoration as opposed to
preserved function.
Figure 3.5: Biphasic stimulation with ACB 1:4 mediates partial recovery of RGC function. Serial PERG
recordings were performed in animals after optic nerve crush injury. (A) Representative PERG recordings
with a 15-point smoothing filter applied. Baseline: one week after electrode placement and crush injury
but before initiation of electrical stimulation. (B) Mean normalized N95 amplitude (left eye: right eye) over
time in each stimulation group (error bars, SEM). * p < 0.05; ** p < 0.01. (Two-way ANOVA with Tukey’s
multiple comparisons test).
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Figure 3.6: Biphasic stimulation with ACB 1:4 mediates partial recovery of light-evoked LFP recordings in
the SC. Stereotactic-guided LFP responses to full-field light stimulation were measured in the contralateral
SC. (A) Sample recordings. (B) Average percent of sites demonstrating a response. Baseline: one week
after electrode placement and crush injury but before initiation of electrical stimulation. Error bars, SEM.
One-way ANOVA with Tukey’s multiple comparisons test. ** p < 0.01, *** p < 0.001. (C) 3D rendering of
the distribution of positive responses in the SC of representative animals.
3.4.5 Recovery of Pupillary Function and Visual Behavior
Direct pupillary light reflex (PLR) testing was performed to measure recovery of pupillary function. No
significant differences in pupillary constriction were observed among the different treatment groups after
10 seconds of photic stimulation. However, after 30 seconds, ACB 1:4 treated animals demonstrated a
38.3% decrease in pupil to iris ratio versus only 12.8% in untreated animals (Two-way ANOVA with Tukey’s
multiple comparisons test; p < 0.001). This was also significantly higher than the 13.9% decrease detected in
SCB 1:1 treated animals and 21.8% decrease detected in ACB 4:1 treated animals (p < 0.01 and p < 0.05, Twoway ANOVA with Tukey’s multiple comparisons test). Given that RGC axons were found to successfully
target the OPN in ACB 1:4 treated rats (Fig. 3.4), this finding suggests that these regenerated axons are
functional and able to mediate partial recovery of the PLR response.
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To assess whether ACB 1:4 stimulation conferred recovery of visual behaviors, we challenged rats with
the visual cliff test and the optokinetic reflex testing. Two out of eight rats dismounted onto the correct
side in the ACB 1:4 stimulation group. This did not differ significantly from untreated animals or animals
treated with SCB 1:1 or ACB 4:1 (average shallow dismounts of 40%, 33.3% and 50%, respectively). Similarly,
none of our rats, stimulated or untreated, demonstrated head tracking with OKR testing (UnTx, N = 5; SCB
1:1, N = 6; ACB 1:4, N = 8; ACB 4:1, N = 4). Altogether, electrical stimulation failed to mediate recovery of
behavioral visual function.
3.4.6 Prediction of RGC Response to Employed Waveforms
We observed variability in how effective the ACB 1:4 waveform was at directing RGC axon regeneration.
A possible explanation for this variability is that the electric gradient generated along the optic nerve
is sensitive to electrode position. To interrogate this, we performed 3D computational modeling of our
stimulation system.
A 3D model of the rat head and orbit was made using the Admittance Method (AM), a numerical electromagnetic method that partitions tissue into an admittance network that then computes the EFs generated
from a current-controlled stimulation pulse [30]. To investigate the effect of electrode misplacement on
the voltage gradient generated along the optic nerve, we modeled the source and the ground electrodes as
used in the experiments (Fig. 3.7). Specifically, the source electrode was placed in direct contact with the
optic nerve for half of its circumference (1.3 mm of direct contact), and the ground electrode was placed
piercing into the optic tract.
Previously, neural activity was shown to enhance RGC axon regeneration after crush injury [95]. Given
that EFs of certain frequencies and amplitudes can activate RGCs, we employed previously developed
RGC models to simulate RGC responses to ACB stimulation [84]. Because different RGC subtypes are
sensitive to different stimulation frequencies, we modeled two types of RGCs that represent different ends
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Figure 3.7: AM admittance method was used to generate a 3D computational model of the electric gradient
along the optic nerve. Inset shows “J” shaped source electrode wrapped around the optic nerve while the
ground electrode pierces the contralateral optic tract.
of this spectrum: the D1 bistratified subtype, which has been shown to be responsive to high frequency
electrical stimulation and the A2 monostratified subtype, which is responsive to lower frequency electrical
stimulation [99]. AM-NEURON computational modeling 1.3 indicate that with SCB 1:1, ACB 1:4 and ACB
4:1 stimulation, the cathodic pulse elicits an action potential every 3.25, 3.0, and 6.8 msec in D1 and 4.85,
3.95, and 6.35 msec in A2 RGCs, respectively (Fig. 3.8). These results suggest that there may be preferential
activation for different phase sequences, as seen in the D1 subtype where over 120% faster firing rate was
observed with either SCB 1:1 and ACB 1:4 stimulation compared to ACB 4:1 stimulation [83]. However,
given that only ACB 1:4, and not SCB 1:1, stimulation conferred an appreciable regenerative response after
crush injury in adult rats, the most parsimonious conclusion is that RGC activation is not the only factor
driving ACB 1:4 mediated axon regeneration. Rather, the different regenerative responses seen between
different waveforms is more likely dependent on the polarity and imbalance of the fields generated across
the optic nerve.
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Figure 3.8: Biphasic stimulation elicits action potentials in RGCs. Time course of the membrane potential
response for two RGC subtypes when stimulated with all three waveforms. The extracellular potential
generated near the soma is computed using AM and the cell membrane response is computed in the NEURON simulation environment. While the D1 cells can better sustain repetitive firing at high frequencies,
both RGC subtypes can fire very fast at these amplitudes, across all waveforms. However, the simulations
suggest a preferential activation in the D1 subtype when using SCB 1:1 and ACB 1:4 over ACB 4:1, with
over 120 % increase in the sustained firing rate.
All of the waveforms used here were charge-balanced across the entire pulse. Regarding tolerance
of pulse asymmetry, no rat showed a visible reaction to continuous electrical stimulation. Moreover, we
detected little change in tissue resistivity over the course of 6 weeks of stimulation with any of the waveforms tested, and no significant difference was detected when compared to untreated rats (Fig. 3.1C). These
findings are strengthened by our prior work showing that ACB 1:4 stimulation does not compromise RGC
viability, in vitro 2. Together, this body of work suggests that CNS neurons may be able to tolerate longterm ACB stimulation in vivo.
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3.5 Discussion
To date, most approaches for promoting axon regeneration exploit genetic tools to selectively upregulate
dormant signaling pathways that were active during development, with the aim of reverting neurons back
to a developmental or growth state. A major limitation associated with these approaches is that they do
not provide growing axons with navigational cues. Lack of navigational cues likely explains why examples
of stalled growth at the optic chiasm or aberrant regeneration have been reported in the literature. For
highly organized structures like the CNS, restoration of function requires approaches that not only “drive”
axon growth but also “steer” axons towards intended targets. Here, we demonstrate that applying an
external guidance cue in the form of electric field stimulation was successful at directing target-specific
axon regeneration and conferring partial recovery of visual function. Notably, our approach delivered
these gains without the need for concurrent, genetic modulation. These experiments not only indicate
that providing a permissive environment for regeneration could be a viable approach for directing axonal
growth but that environmental cues can override cell intrinsic barriers to axonal regeneration. However,
recapitulating the extracellular molecular gradients that directed tissue patterning and axon growth during
development within an adult animal has been exceedingly difficult. One reason for this failure is that axons
need these extracellular guidance molecules to be expressed in not only spatial but also temporal gradients
[68, 70, 100, 101]. EF stimulation offers a unique solution to this dilemma. Not only can exogenous EFs
modulate the direction of axon growth, as has been demonstrated with many different neuronal subtypes
in tissue culture, but the strength, location, and duration of EF stimulation can be readily manipulated in
vivo by controlling the location of electrode placement and by modulating the frequency, amplitude, and
pulse width of the stimulation waveform. Stimulation duration can also be titrated to need. One major
reason why have these approaches have largely failed to translate into clinical treatments is that most
prior approaches employed DC stimulation. Although effective at directing CNS axonal regeneration in
the spinal cord of lampreys and guinea pigs [102, 103, 104], DC stimulation can only be applied at low
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amplitudes or for short intervals before charge accumulation causes tissue damage [45]. To circumvent
some of the limitations associated with DC stimulation, we employed a unique subclass of asymmetric
biphasic waveforms to guide RGC axon growth. ACB waveforms are charge balanced and thus safer than
DC but retain the ability to generate EF needed to direct axon growth. Here, we tested the efficacy of
three different charge balanced waveforms to direct RGC axon regeneration. Of these three, the greatest
regeneration and electrophysiologic recovery was conferred by the ACB 1:4 waveform. During the anodic
phase of ACB 1:4, the cathode is in the optic tract during the cathodic phase, while the anode is located
in the orbit (Fig. 1A). As prior work has shown that RGC axons consistently project towards the more
negative electrode [75], RGC regeneration seen in ACB 1:4 stimulated animals indicates that the anodic
phase in this setup drove axon growth. Given that the anodic phase of ACB 1:4 was four times longer than
that of the cathodic phase, our in vivo findings are consistent with our prior in vitro work which showed
that pulse duration exerts a stronger influence on RGC axon growth than pulse amplitude 2. Further
support for this comes from the finding that no appreciable axon regeneration was seen in SCB 1:1 or ACB
4:1 stimulated animals.
Although electrical stimulation was able to confer partial recovery of electrophysiologic function, it
failed to restore visual behaviors. Several explanations likely account for this finding. First, although
electrical stimulation with ACB waveforms did not compromise RGC viability (Fig. 3), the short phase
widths (400 µs) did not confer statistically significant increase in RGC survival either. ACB 1:4 stimulation was likely only able to drive axonal growth in RGCs that would have survived crush injury anyways—approximately 13% of the RGC population. Nevertheless, with the breakthrough discovery of neuroprotective molecules like CNTF (ciliary neurotrophic factor) and BDNF (brain derived neurotrophic factor)
[105] it would be worthwhile to investigate whether combining ACB 1:4 stimulation with these neuroprotective molecules could offer synergistic gains in function. Alternatively, different stimulation waveforms
have been reported to activate distinct signaling pathways that control different cellular behaviors [106].
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Transcorneal electrical stimulation with symmetric biphasic waveforms at 20 Hz frequency promoted 1.5-
fold more RGC survival after optic nerve transection compared to untreated controls in rodents [73]. Repetitive transorbital alternating current stimulation (rtACS) at 5Hz was also associated with increased RGC
survival in rodents [107]. In humans, rtACS between 8-25 Hz has been shown to improve visual field outcomes by, presumably, modulating brain plasticity [108]. Although our stimulation frequencies differed
from these groups, our PERG recordings detected a weak neuroprotective effect with SCB 1:1 stimulation.
It is possible that alternating stimulation with pro-regenerative waveforms, such as the ACB presented
here, with neuroprotective waveforms, such as the SCB, could lead to greater recovery of function. The
incomplete recovery of function with ACB 1:4 stimulation could also be due to regenerated axons that
are unmyelinated or form aberrant synapses with target neurons. LFP recordings in ACB 1:4 treated rats
had decreased amplitude and longer latency than age-matched normal animals. As LFP recordings are a
summation of local signaling, it is unknown whether this finding represents signaling from a few normal
functioning RGC axons or many aberrantly signaling RGC axons. Bei et al. found regenerated axons in the
optic tract to be unmyelinated, and thus we favor the latter possibility [61]. Another possible explanation
for the failure to restore visual behavior could be due to a selective RGC subtype regeneration. Performance on OKR relies on direction sensitive RGCs in the accessory optic system [109, 110, 111] while the
visual cliff relies on binocular vision and involves the dLGN and primary visual cortex [112]. Deletion of
Rbfox1, a family of ribonucleic acid binding proteins, led to loss of performance on visual cliff testing in
aged mice [113]. Prior reports have shown that αRGCs represent the majority of RGCs that regenerate
with PTEN deletion, possibly because of higher intrinsic mTOR activity [114, 115]. Although RGC axons could be observed to project to the dLGN in ACB 1:4 treated animals, the level of regeneration may
have been subthreshold compared to what is needed for functional recovery. Finally, failure to restore
visual behavior could result from failure of regenerated RGC axons to maintain retinotopy. Although LFP
recordings indicate that RGCs are transmitting information to the SC and histology shows RGC axons
67
projecting to both the SC and the LGN, it is unknown whether these cells are transmitting formed images.
Lamination-specific regeneration has been reported by others and is thought to stem from developmental
guidance cues still being present in the adult CNS [116]. Current efforts are directed at assessing whether
the retinotopic map is maintained in ACB 1:4 treated animals.
Prior work by Lim et al. demonstrated long-distance RGC axon regeneration and partial restoration of
function after optic nerve crush injury in adult mice that underwent treatment with biased visual activity
concurrently with mTOR activation [95]. They showed that reducing RGC activation prevented visualstimulation-mediated axon regeneration while increasing RGC activity promoted axon regeneration. Our
modeling suggests that unlike Lim et al., RGC neuronal activation by EF stimulation plays a minor role in
the EF-guided RGC axon regeneration presented in this paper. First, our rats did not undergo visual deprivation in their contralateral eye, a concurrent treatment without which the positive outcomes reported
by Lim et al. could not be achieved. Second, our modeling showed that SCB 1:1 and ACB 1:4 were equally
effective at inducing an action potential in RGCs. If the regenerative response seen in ACB 1:4 was solely
based on RGC activation, then a similar amount of regeneration should have been observed with SCB 1:1.
The fact that no axon regeneration was observed with SCB 1:1 indicates that electric gradients direct axon
regeneration by an alternative mechanism than through eliciting action potentials in RGCs.
3.6 Conclusion
The breakthrough discoveries of molecules that mediate neuro-protection and activate signaling pathways
that are capable of driving axon growth allow the development of approaches to guide these regenerating
axons to intended targets. Our work suggests that electrical stimulation could play an important role in
directing facilitating target-specific regeneration of CNS neurons. The trade-off between effectiveness,
which is driven by pulse asymmetry, and tissue safety, which is driven by charge balance, is an important
68
consideration when designing waveforms for neurorestoration. This work demonstrates that directional
neuronal growth can be achieved safely by using asymmetric charge balanced pulses.
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Chapter 4
A Transcorneal Electrical Stimulator to Induce Neuroprotection and
Prolong Photoreceptor Survival in the Degenerating Retina
Chapter 4
E. Iseri, P. Kosta, D. Pollalis, P. Lo, B.Y. Tew, S. Louie, B. Salhia, M. Humayun, G. Lazzi. Characterization
of Induced Current Density During Transcorneal Electrical Stimulation to Promote Neuroprotection in the
Degenerating Retina. IEEE Transaction in Biomedical Engineering (Under review, 2024)
4.1 Abstract
Transcorneal electrical stimulation (TES) is a promising approach to delay retinal degeneration by inducing extracellular electric field-driven neuroprotective effects within photoreceptors. Although achieving
precise electric field control is feasible in vitro, characterizing these fields becomes intricate and largely
unexplored in vivo due to uneven distribution in the heterogeneous body. In this paper, we investigate and
characterize electric fields within the retina during TES to assess the potential for therapeutic approaches.
We developed a computational model of a rat’s head, enabling us to generate predictive simulations of the
voltage and current density induced in the retina. Subsequently, an in vivo experimental setup involving
Royal College of Surgeon (RCS) rats was implemented to measure the voltage across the retina using identical electrode configurations as employed in the simulations. A stimulation amplitude of 0.3 mA may be
necessary during TES in rats to induce a current density of at least 20 A/m2
in the retina, which is the
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lower limit for triggering neuroprotective effects according to culture studies on neural cells. Measurement
taken from cadaveric pigs’ eyes revealed that a stimulation amplitude of 1 mA is necessary for achieving
the same current density. The computational modeling approach presented in this study was validated
with experimental data and can be leveraged for predictive simulations to optimize the electrode design
and stimulation parameters of TES. Once validated, the flexibility and low research cost of computational
models are valuable in optimization studies where testing on live subjects is not feasible.
4.2 Introduction
Neuronal loss is a defining characteristic of retinal dystrophies, encompassing conditions such as retinitis
pigmentosa, age-related macular degeneration (AMD), and primary open-angle glaucoma [117, 118, 119].
Advances in ophthalmology have introduced innovative strategies to counteract the debilitating impact
of retinal degeneration like gene therapy [120], cell therapy [121, 122, 123] and retinal prostheses [124].
Among these pioneering approaches, TES of the retina has emerged as a promising strategy for slowing
down the progression of retinal degeneration. TES has showcased its potential in preserving the integrity
of the outer nuclear layer and enhancing the functionality of electroretinography following a six-week
stimulation period in live rats [125]. Additionally, electrical stimulation can contribute to neuronal preservation, primarily through the modulation of neurotrophic factors after TES sessions [126, 127, 128]. One
of the major limitations in assessing the success of the electrical stimulation therapies in the literature
is the metric used for characterizing the stimulator setup between different trials. The effectiveness of
neuromodulation and TES trials on animal models and humans is commonly gauged with respect to the
stimulation amplitude in a current-controlled system, which ranges from 0.1 mA to 0.5 mA in rodents [129,
10] and 0.1 mA to 1 mA in humans [130]. Higher stimulation amplitudes were employed in cases of more
severe injuries such as rats with crushed optic nerves (0.5 mA) or animals with larger eyes such as rabbits
(0.7 mA) [131]. However, inconsistent outcomes have been reported for inducing neuroprotective effects in
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comparable trials. One study reported success using 0.15 mA transpalpebral stimulation in patients with
dry AMD [132], an amplitude considered to be at the low-end of the spectrum in human studies [130],
whereas another study using 0.8 mA amplitude and similar intervals on the same disease-type did not see
a statistical significance compared to the control [133]. Therefore, stimulation amplitude is not a reliable
metric to characterize the setup, as the variation between the bodies of the subjects, modality (voltageor current-controlled) and quality of the stimulation system and the design parameters of the electrodes
themselves will influence the electric field distribution inside the stimulated tissue. To overcome this limitation, our goal is to assess the current density generated within the targeted region, as we hypothesize
that it offers a more informative and encompassing metric that can ensure consistency between trials.
Here, we achieve this through a multi-scale computational method to simulate the electric fields generated in the eye during TES followed by a series of in vivo and ex vivo experiments, which are used to
validate the simulation results and help characterize the electric fields produced by various setups. We
empirically characterize the current-controlled stimulation amplitude required for generating the target
current density in the retinas of rat and pig eyes during TES.
4.3 Methods
4.3.1 Computational Modeling
The modeling efforts aim to develop and leverage multi-scale computational modeling platforms to design
the most efficient and safe electric stimulation configurations for minimally-invasive TES. To induce epigenetic changes and achieve the neuroprotective effect, we aim to maximize the induced current in the
retina while using safe stimulation current magnitudes. With the help of our AM-NEURON multi-scale
computational modeling platform 1.3, we can predict the induced electric fields inside a bulk tissue model.
This platform was previously used for predictive extracellular electrical stimulation in the retina [23, 37]
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and the hippocampus [38]. Here, we leverage this method to design electrodes and their placement locations to effectively induce the electric fields in the rat and human retina during TES. We use a large-scale
segmented model of a rat, including the finer structures of the eye, such as the sclera, cornea, lens, vitreous
humor, and eyelid layers. AM can be used to modify the stimulation parameters and predict the induced
voltage and current densities in the rat model. AM discretizes the model into cuboid voxels, and each voxel
is represented by the lumped admittances at its edges. The admittance values are calculated using the electric properties of the tissue, which are its conductivity and permittivity. As such, the admittance values
depend on the operating frequency and voxel dimensions. The 3D model is then reduced to a network of
lumped admittances, a current source is applied to a given node and the induced voltage is then computed
at each node of this network using iterative methods for solving a set of linear equations, computed in
each axis:
I = GV (4.1)
−→E =
Vn − Vn+1
∆S
(4.2)
−→J = σ
−→E (4.3)
σ =
1
ρ
+ jωϵ∗
(4.4)
where I is a vector containing stimulation current at each node, G is the admittance matrix and V is a
vector that contains induced voltage at each node. Electric field −→E is calculated from the voltage difference
between neighboring voxels Vn − Vn+1 and their separation ∆s, and the current density −→J is calculated
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Figure 4.1: (a) A slice of the 3D segmented rat model with the ring electrode (shown in red) (b) The eyeball
model with retina (orange) and stimulating ring electrode (red). (c) An inset shows the zoomed in view of
the eyeball with structures of vitreous humor, lens, cornea, inner and outer eyelids.
using the material properties of the tissue type. For this study, we consider a direct current (DC) pulse,
which negates the complex conductivity component and simplifies equation (4.4) as σ =
1
ρ
. This approach
is in tandem with the common method of stimulation in cell cultures, which uses the rectangular biphasic
waveform. Therefore, the mesh generated from the bulk tissue model is a network of resistors and the
calculated −→J reflects the equivalent resistive component of the model. The resistivity of each tissue and
electrode material type included in the model is summarized in Table 4.1. These values were obtained from
the IT’IS Foundation database of tissue properties [134].
To minimize the computational cost, the 3D rat model is truncated from the sides and mostly contains
the head. The truncated model is shown in Fig. 4.1(a) where the stimulating transcorneal ring electrode
is shown in red. The retina is represented by two voxel-thick layers, as shown in Fig. 4.1(b). The eyelids
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are modeled using two layers: an inner eyelid layer (modeled with sclera properties) and an outer layer
(modeled with wet skin properties). Fig. 4.1(c) presents the 2D slice of the bulk rat model, which highlights
the various tissues present in the model, including eye details. The model resolution is 166 µm, which is
the length of each side of the cuboid voxels.
Table 4.1: List of Resistivity Values for the Tissue Types Used in the Rat Head Model
RESISTIVITIES IN THE RAT HEAD MODEL
Material Type Resistivity (Ω.m)
Air 1*107
Muscle 4.82
Fat 64.6
Skin (dry) 5000
Bone 763
Brain 25.7
Sclera 1.99
Vitreous Humor 0.67
Lens 3.15
Cornea 2.4
Outer Eyelid 2456
Retina 1.5
Working Electrode 1*10−7
Return Electrode 1*10−7
4.3.2 Animal Procedure
Long Evans rats were used for experiments. The care and use of the rats were conducted in accordance
with the regulations and guidelines of the Institutional Animal Care and Use Committee (IACUC) of the
University of Southern California (USC) which are in adherence to the National Institutes of Health (NIH)
Guidelines for the Care and Use of Laboratory Animals, and the Association for Research in Vision and
Ophthalmology (ARVO) Statement for the Use of Animals in Ophthalmic and Vision Research. A combination of ketamine (100mg/ml) and xylazine (100mg/ml) was administered intraperitoneally to anesthetize
75
the animals before the procedure. Topical anesthesia such as 0.5% Tetracaine eye drops, was administered prior to any ocular manipulation. The three different placement configurations that were tested,
as illustrated in Fig. 4.2(a): retro-orbital disc ground electrode, retro-orbital needle ground electrode, and
subcutaneous temporal needle ground electrode. Briefly, once the rat was under anesthesia, the eye, conjunctival sac, and eyelids were cleaned using a 5% povidone-iodine solution, and topical anesthesia was
applied. Both superior and inferior eyelids were retracted using fine forceps. A small conjunctival incision
was performed using microscissors. A conjunctival pocket was created, and the ground electrode (either
disc or needle) was rested retro-orbitally. In the case of temporal placement, the ground electrode was
positioned subcutaneously in front of the rat’s ear. Then one recording electrode was positioned intravitreally and one behind the orbit. A clamp was used to fixate the measuring electrodes 2 mm apart. The
stimulated electrode was placed on the surface of the cornea. Grounding cuffs were attached on the rats’
tails to keep the noise and offset values minimal across their body. The animals were euthanized after
the experiment. Enucleated porcine eyes were employed for further investigation of the TES parameter
optimization in human studies, as their diameter is more comparable to human eyes. The porcine eyes
used had a sagittal length of 24 mm on average. First, any residual connective tissue was removed from
the scleral surface. The placement of two distinct reading electrodes was executed with the use of a micromanipulator. One electrode was positioned near the optic nerve in the sclera, while the other electrode
was positioned intra-retinally via a controlled scleral incision (Fig. 4.2(a)). Like before, a clamp was used
to fixate their positions at 2 mm apart. A disc-shaped platinum (Pt) return electrode was placed near the
base of the optic nerve. Insulated, tip-only exposed tungsten (W) needle electrodes were used to measure
the voltage difference inside the eye.
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4.3.3 Electrode Connection and Stimulation Parameters
To validate our simulation results in vivo, we designed a transcorneal electrical stimulator that could be
placed on the eyeball and developed a measurement technique for approximating the current density generated through the retina. A ring electrode with a 4 mm diameter was built using a 0.25 mm thick (30 AWG)
pure Pt wire, designated as the working electrode in a bipolar two-electrode setup. First return electrode
was built using the same material but fashioned into a disk shape that can be placed next to the optic nerve
behind the globe. Second return electrode was selected to be a monopolar 30-gauge Pt needle (F-E2-24 Subdermal Needle Electrode, Natus Medical), commonly used for subcutaneous placement in TES studies. A
current pulse was delivered using a current-controlled stimulator (STG 4008, Multi Channel Systems, Harvard Bioscience, Inc.). The stimulation waveform was a cathodic-first symmetric biphasic pulse of 1 ms
phase width and 50% duty cycle for a pulse period of 4 ms. The duty cycle was maximized while making
sure the voltage offset during rest approached zero before applying the following pulse. Two W needle
electrodes with 0.2 mm diameter (E363T/2, Protech International, Inc.) were used to pierce the eye and
measure the potential difference between two points on either side of the retina, labeled as Va and Vb (Fig.
4.2(b)). This potential was used to predict the current flow through the retinal layers, starting from the
vitreous-ganglion cell layer border up to sclera and the root of the optic nerve (Fig. 4.2(c)). Each W electrode was connected to an individual channel of a digital storage oscilloscope (InfiniiVision DSOX2014A,
Keysight Technologies) and the arithmetic difference between the channels was recorded simultaneously.
4.3.4 Calculation of the Current Density
The current density generated near the targeted cells is the standard metric in TES and other electrical
stimulation techniques such as transcranial for inducing neuroprotective effects that promote neuronal
survival. Estimation of this current density depends on the experimental setup. Using a surface area
estimation will only be accurate if the geometry of the stimulated area is well defined for the surface
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Figure 4.2: (a) Schematic representation of the different TES setups with three return electrode configurations tested in vivo. (b) Illustration of the TES setup shows the stimulating ring electrode on the cornea
and the disk-shaped return electrode positioned retro-orbitally adjacent to the optic nerve. Two insulated
W needle electrodes with exposed tips were inserted in the vitreous humor and the base of the optic nerve
to measure the voltage across the retina, at a separation of ∆S = 2 mm, which is used to estimate the
current density generated between them. (c) The symmetric biphasic stimulation current waveforms at
increasing amplitudes and the resulting potential difference Vab between the two measuring electrodes.
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integral calculation. Instead, we can approximate the generated current density from the electric field,
which is a function of the voltage difference between two points (equation 4.2). This equation relies on
the assumptions that the generated field is electrostatic, the equivalent impedance of the bulk tissue is
mostly resistive and will respond linearly to stimulation. A caveat with this approach is the sensitivity
towards variations in the tissue resistivity in the target region. In the case of a rat’s retina, the resistivity
even within the layers of the retina can vary significantly, from 1 to 4 Ω.m [25, 26]. Based on the electrode
depth vs. resistivity analysis of a degenerate rat retina [26], which is comparable to the rats used in our
experiments, we combined the values of the vitreous and retinal layers between the measuring electrodes
to average out 1.5 Ω.m to use in our calculations.
4.4 Results
4.4.1 Simulation Results
Using our computational modeling approach, we evaluated the different electrode dimensions and placements. A ring electrode placed on the cornea as the working/stimulating electrode and three return electrode configurations were tested (Fig. 4.3(a)). The needle was a hollow cylinder with a diameter of 3 mm
and a wall thickness of 0.075 mm, closest to the dimensions of a 30-gauge needle. The disc electrode diameter was set as 3 mm and thickness as 0.3 mm. The voltage mapping of the head model shows that the
greatest voltage amplitude occurs when the return electrode is needle and placed subcutaneously away
from the working ring (Fig. 4.3(b)). However, the electric field magnitude in the retina does not necessarily correspond to the voltage amplitudes generated because the electric field, and the concomitant current
density (−→J ), are functions of the change over distance (2). In fact, both the maximum and average −→J were
weakest when the return electrode was placed further from the target region (Table 4.2). The simulation
results suggested that the disk ground electrode can provide higher current density at the center of the
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retina since the area where the current density is maximized corresponds to the electrode’s spatial position
(Fig. 4.3(c)). While placing the electrode closer to the globe is more invasive, it can provide significantly
higher current in the central retina which is where the cone photoreceptors are most densely packed and
the region of interest for neuroprotective effects.
Figure 4.3: Simulation results of various placements for the ground electrodes. Row (a): the voxelized rat
head model with stimulating and return electrodes. Row (b): The voltage distribution across a 2D slice in
the xy plane (passing through z = center of the stimulating ring). Row (c): the current density distribution
inside the retina in the xyz plane. The left side is medial, right is lateral, top is superior and bottom is
inferior direction.
Bringing the needle closer to the retina resulted in both an increase in the maximum and average −→J
from 7.90 to 13.10 A/m2
and 4.32 to 6.30 A/m2
, respectively and a more localized field distribution in the
central regions (Fig. 4.3(c)). Further improvement was observed when the electrode surface was changed
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Table 4.2: Maximum and average induced current densities at the retina and the off-target voltage induced
in the brain for three configuration of TES
SIMULATED VALUES IN THE RAT HEAD MODEL
Simulated Variable Subcutaneous Needle Retro-orbital Needle Retro-orbital Disk
−→J max(retina)
(A/m2
) 7.9 13.1 18.8
−→J avg(retina)
(A/m2
) 4.32 6.30 7.35
Vof f−target(brain)
(mV ) 215 55 60
into a disk where the maximum −→J increased from 13.1 to 18.8 A/m2
and the average −→J increased from
6.30 to 7.35 A/m2
, respectively. This is because a greater ratio of the electrode surface aligns with the retina
layer and more of the field lines follow a direct path through the central retina into the return electrode.
The disc electrode configuration yielded the highest −→J values and greatest control over the areas that are
being stimulated, making it the ideal choice for TES.
4.4.2 In vivo and Ex vivo Experimental Results
Following the computational analysis on the rat head model for optimizing electrode parameters in TES, in
vivo experiments were performed on anesthetized rats to validate the simulation results. Three different
electrode configurations at three different amplitudes were tested while recording from the same locations
inside the eye (Fig. 4.2). The difference of the recorded potentials Va and Vb along with the estimated
separation (∆s) between them was used to calculate the electric field (−→E ) through the retina (equation 4.2).
The −→E was then multiplied with the conductivity (σ) of the rat’s retina to calculate the −→J (equation 4.3).
−→J is the most prevalent parameter used to assess the efficacy of electrical stimulation for neuroprotection
and several studies have shown that the range required for inducing neuroprotective effects in transcranial
stimulation is 20-50 A/m2
[19]. Aiming for these numbers in the retina, we used a TES amplitude range
of 200 µA to 400 µA to determine how large of a −→J can be sustained in the retina. Because the rat’s
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Figure 4.4: The maximum voltage difference Vab (blue) and the voltage offset during the interpulse time
(orange) recorded across 10 rats for different return electrode configurations. The closer the electrode is
to the target (retina), the smaller the range of values and the offset voltages.
eye is much smaller than a human’s and can tolerate smaller currents, the same setup was used on a
pig’s eye once we validated the simulation results on rats. The diameter of the pig eye is comparable to a
human’s, which determines how much stimulation current is needed for effective therapeutics. We aimed
for a minimum of 20 A/m2
to validate the efficacy of our stimulation protocol. According to the values
obtained from the experiments and the approximations described in the Methods section, the maximum
−→J for rat is calculated to be about 11.8 +/- 2.3 A/m2
, 14.7 +/- 4.9 A/m2
, 13.7 +/- 8.7 A/m2
for columns 1,
2 and 3 of Fig. 4.4, respectively. These range of current densities are comparable with the values computed
by our simulations, which are 18.8 A/m2
, 13.1 A/m2
, 7.9 A/m2
for the retro-orbital disk, retro-orbital
needle and temporal needle, respectively.
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1) Electrode Placement Near the Globe is More Invasive but Improves Precision
The first trade-off that needs to be considered when optimizing TES methods is choosing the grounding
location in the body for placing the return electrode. Ideally, the return electrode will be minimally invasive
while ensuring the threshold current density is generated in the target area. The simulations suggested
that while the threshold requirement could be met whether the grounding was made near or further from
the optic nerve, the high current density areas shifted towards the periphery of the retina as the electrode
was placed further away (Fig. 4.3). To verify these results, we placed the return electrode both retroorbitally, next to the optic nerve and temporally in the subcutaneous tissue. The mean of the maximum
voltage differences measured (Vab) were 39.3 mV and 47.4 mV for retro-orbital and temporal placements,
respectively (Fig. 4.4). While the maximum Vab appeared to increase as the return needle was placed
further from the working ring, contrary to the simulation results in Table 4.1, the spread of the data was
also significantly greater. The standard deviation of the measured Vab were +/- 14.7 mV and +/- 26.3 mV
when the needle return electrode was placed retro-orbitally and temporally respectively. Because we want
to establish a correlation between the input stimulation and the −→J across the retina, keeping the variation
to a minimum is critical for consistency across different trials. Even though the maximum −→J on average
was smaller when the return electrode was placed closer to the globe, the confidence margin for estimating
how much current is needed for inducing the target −→J is greater; therefore, the return electrode should
be placed as close to the globe as possible for consistent results.
2) Larger Electrode Surface Reduces the Max. Current Density but Minimizes Off-Target Stimulation
The surface area of a stimulating electrode holds importance due to its role in the charge injection
mechanism associated with double-layer formation at the electrode-tissue interface [20] and involves a
trade-off between precise targeting of a small area and maintaining the charge density vs. total charge
constant within the established safety threshold [21]. For our TES setup, the size of the return electrode
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is constrained by the physical space available around the eye for implantation and our goal is to minimize the surgical trauma. For our rat experiments, this limitation translated to a maximum diameter of 3
mm. Consequently, we opted for a disk-shaped return electrode with a 3 mm diameter and compared its
performance against the retro-orbital needle electrode configuration. One important difference between
the two configurations was the actual surface area that contacted the eye. One flat side of the disk (7.1
mm2
) came into contact with the globe, whereas the needle only engaged about one-third of its outer
surface (3.2 mm2
). Switching from the disk to the needle electrode led to an increase in the maximum
voltage from 35.4 mV to 43.9 mV on average. This increase in the maximum Vab when using the needle
electrode can be attributed to its higher equivalent impedance across the electrode-tissue interface. This
impedance primarily arises from the smaller surface area of the needle. The current-controlled stimulator
adjusts its source voltage to match the target current amplitude depending on the input impedance, which
can lead to higher recorded voltage differences when using the needle electrode. However, it’s important
to acknowledge that the standard deviation also increased from +/- 6.9 mV to +/- 14.7 mV when transitioning from disk to needle, a trend observed when the return electrode was placed further away from the
working electrode (Fig. 4.4). The circular shape of the disk maximized the contact area between the electrode and the eye, thereby further improving the confidence interval. This outcome suggests that the disk
design remains desirable, despite a slightly smaller range of −→J . Another important observation pertained
to the voltage offset, which more than doubled on average when using the needle electrode. This increase
indicated that the surrounding tissue was exposed to a higher extracellular voltage level, even when the
stimulation pulse was not active. The offset value was derived by first subtracting the DC component
from the recorded signals and then measuring the voltage immediately before a new pulse was applied
(Fig. 4.2(c)). From an electrochemical perspective, a voltage offset signifies non-ideal charge transfer between the electrodes due to a mismatch in injection and discharge rates. This phenomenon can also be
elucidated from a circuit perspective, where the equivalent impedance of the electrode-tissue interface is
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loosely modeled as a parallel RC block, often referred to as the double-layer impedance [22]. Increasing the
electrode’s surface area directly influences the properties of the passive elements where a greater capacitance increases the capacitive conduction through the double-layer, which is a charge injection mechanism
that redistributes the charges in the electrolyte but does not involve electron transfer [20]. Consequently,
this minimizes faradaic charge transfer and accumulation in the tissue, leading to a reduced voltage offset
during resting periods. Given the imperative to avoid off-target excitation in TES, it is important to have a
large sufficiently large electrodes to minimize the voltage offset generated in the surrounding areas, while
ensuring that the charge density remains at a safe level. Once again, the advantage of using a disk-shaped
electrode is emphasized as its geometry aids in maximizing the covered surface area.
3) Pig’s Eye Requires 1 mA Stimulation Amplitude to Reach 20 A/m2 Current Density at the
Retina
After successfully validating the simulation results of the rat’s eye through in vivo recordings, we
applied the same experimental setup to the pig’s eye to estimate the required stimulation amplitude for
achieving a minimum current density of 20 A/m2
in its retina. The stimulation amplitude required to
elicit the target −→J depends on the tissue volume between the electrodes and its equivalent impedance. We
selected the pig’s eye for this study due to its similarity in volume to a human eye. To accommodate a
higher charge per phase and maintain charge density, we employed a larger disk return electrode with a
6 mm diameter on the pig’s eye, in contrast to the setup used for rats. Like before, we recorded voltages
simultaneously across the two electrodes separated by 2 mm and plotted the differences using an oscilloscope (Fig. 4.5). Notably, a stimulation amplitude of 1 mA resulted in a Vab of up to 60 mV across all four
eyes tested, with an average of 56 mV and a standard deviation of +/- 4.2 mV. Assuming an average combined tissue resistivity of 1.5 Ω.m through the VH and the retina, we can approximate that the generated
current density was approximately 20 A/m2
. Similar to our observations in rat experiments, increasing
the stimulation amplitude yielded a roughly linear scaling in the Vab, where a 60% increase in amplitude
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(1 mA to 1.6 mA) led to a 53% increase (from 60 mV to 92 mV). As the equipment limit was 1.6 mA, higher
stimulation amplitudes could not be tested. These findings can be extrapolated to the adult human eye,
which is slightly larger than the pig’s eye. Consequently, they suggest that a minimum amplitude of 1 mA
should be considered for use in TES trials on human subjects.
Figure 4.5: The potential generated across the electrodes and the voltage measured across the pig’s retina
using the same stimulation waveform from Fig. 4.2 but with higher amplitudes.
4) Current Density Scales Linearly with Stimulation Amplitude
In the equivalent circuit model of an electrochemical system, the tissue component (electrolyte) is typically considered as a purely resistive series load. Assuming that the reactive component of the electrode
impedance cancels out when subtracting one potential from another (Vab), the equivalent load between
the electrodes can be represented by a resistor. Consequently, we hypothesized that the current vs. voltage
relationship must be linear adhering to Ohm’s law. To test this hypothesis, we conducted experiments at
three different stimulation amplitudes: 0.2 mA, 0.3 mA, and 0.4 mA, and plotted the resulting voltage differences (Fig. 4.2). The increase in the Vab closely followed that of the stimulation amplitude during the rat
experiments, where gains of 44% and 24.5% in the Vab were measured for 50% and 33.3% increase in the amplitude, respectively. Similarly, experiments conducted on the pig’s eye showed a 53% increase (from 60 to
92 mV) when stimulated with 60% more current (1 mA to 1.6 mA) (Fig. 4.5). Both the transitions observed
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in rat from 0.2 mA to 0.3 mA and in pig from 1 mA to 1.6 mA led to a gain in Vab vs. amplitude increase
ratio of 88%, whereas it was 73% in the case of rat going from 0.3 mA to 0.4 mA. These findings suggest the
possibility of diminishing returns with respect to increasing the stimulation amplitude concerning the −→J
generated in the target area. A plausible explanation for this pattern lies in the dynamics of charge transfer at the electrode-electrolyte interface, the equivalent circuit model of which has complex components.
This includes a capacitor realistically modeled as a constant phase element, which is non-ideal and adds
amplitude and frequency dependency to the equivalent capacitance. A changing capacitance value due to
the non-ideal dynamics may ultimately lead to a nonlinear input/output relationship.
5) Current Density Does Not Reach the Contralateral Eye
An important consideration in TES is ensuring that the induced current density remains isolated within
the target area and does not interfere with the stimulation of the contralateral eye. To assess how far the induced current density extends from the return electrode, we took voltage difference measurements across
the stimulated target eye, between the two eyes and across the contralateral eye (Fig. 4.6). A Vab of about
100 mV was measured across the stimulated right eye, consistent with the results from previous trials illustrated in Fig. 4.4. However, as the measuring electrodes were shifted away from the right eye, the Vab
dropped substantially to about 10 mV at the midpoint between the left and right eyes. When the measurement was taken across the left eye, the Vab registered as zero, indicating that the −→J near the left eye
was negligible during the stimulation of the right eye. In a related test, we measured the Vab along two
axes relative to the orientation of the ring electrode. The vertical contour extended from one electrode to
the other, while the horizontal contour ran perpendicular to the vertical contour, equidistant from either
electrode (Fig. 4.6). The Vab measurements along these contours revealed that the electric field lines predominantly followed a direct vertical path between the working and return electrodes, thereby generating
a stronger
−→J across the thickness of the retina from the ganglion cell layer towards the photoreceptor
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layer. This observation aligned with the simulations demonstrated in Fig. 4.3(c), where the −→J was most
pronounced in the center for the disk electrode and decreased sharply as it approached the peripheral regions. However, we note that both in the simulations and the experimental measurements, there remained
a non-zero difference. This discrepancy can be attributed to the placement of the return electrode, which
was located towards the left side of the optic nerve and featured a large diameter extending towards the
periphery. This pattern suggests that one half of the retina receives a stronger stimulation with the disk
return electrode design employed in our study.
Figure 4.6: (Top Row) The TES was set up on the right eye while the voltage difference was measured
across the sclera of the right eye (blue arrow), halfway between the two eyes (orange arrow) and across
the sclera of the left eye (yellow arrow). The Vab approaches zero sharply moving away from the right eye,
indicating that the current density generated outside the target area is negligible. (Bottom Row) The Vab
was measured across the perpendicular axes to determine the directionality of the electric field generated
in the eye tissue. The vertical Vab between the cornea and the optic nerve was significantly higher than
the horizontal Vab between medial and lateral sides, indicating that the induced fields cross the retina
perpendicularly.
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4.5 Discussion
Characterizing the current density generated in the retina during TES is crucial for optimizing its effectiveness in promoting neuroprotection in the targeted photoreceptors. Previous experiments on various
neural cells have shown that a minimum current density is necessary to induce neuroprotective effects
and support cell survival [125, 129]. To ensure the consistency of stimulation trials, it’s essential to establish a relationship between the input amplitude and the current density −→J in the retina. Towards this
goal, we developed a computational model for the rat’s head using the Admittance Method technique, a
methodology developed by our group. We simulated various electrode configurations in TES to optimize
the distribution of the electric field in the retina. While the position of the working ring electrode had
to remain fixed on the eye, similar to a contact lens, we had flexibility in designing the return electrode,
particularly in terms of its placement location and geometry. The simulation results suggested that an invasive approach using a large-surface disk return electrode near the globe was significantly more effective
in generating
−→J at the retina. Importantly, this approach provided greater control over the area of activation, as demonstrated in Fig. 4.3(c), making the disk return electrode positioned on the globe the most
optimal configuration for TES. Although more invasive, this approach might be a necessary trade-off to
achieve effective therapeutics and neuroprotection in the retina. The experimental data corroborated the
simulation results and validated our computational methods. On average, the measured −→J in rats was 33%
smaller than the simulations, which is expected considering the imperfections of a real system, variation
among animals and limited accuracy of the measuring electrodes. We acknowledge that the most significant source of error in estimating the −→J using equation (2) likely stems from tissue conductivity. As we
could not accurately measure the voltage difference across the individual layers of the retina, resistivity
of which can vary significantly, we relied on a combined resistivity value of the retina and the vitreous
humor obtained from the literature to calculate −→J . The large 200 µm diameter needle measuring probe
posed another limitation, as the thickness of the retinal layers in the RCS rat range from 40 µm to 100 µm
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[135]. Ideally, a high-resolution microelectrode probe, similar to the one used by Kasi et al. [136], would be
able to measure the voltage differences within a 10 µm thickness, sufficient for accurate characterization of
current density within individual retinal layers during TES. Therefore, the experimental −→J values reported
in this paper should largely be considered supportive of our simulation results of the −→J generated in the
photoreceptor layer. Overall, the data collected from the rats demonstrated the reliability of our computational model as a predictor of fields generated in the eye during TES and helped establish an input/output
relationship for a current-controlled stimulator. The values obtained from rat’s eyes suggest a minimum
stimulation amplitude of 0.3 mA whereas those obtained from pig’s eyes suggest a minimum of 1 mA for
reliably generating the target −→J of 20 A/m2
in the retina. Data from pig eyes are more relevant for translation into human studies, given their comparable dimensions. The determined threshold current amplitude
from our data falls within the range of TES human trials that have successfully slowed down vision loss in
patients with retinitis pigmentosa, who received stimulation ranging from 0.8 to 1 mA [130]. Nevertheless,
there is a practical limit to the current amplitude that can be comfortably delivered in conscious subjects. In
our experiments with rats under anesthesia, we observed extraocular muscle twitching and facial spasms
in some cases when exceeding 0.3 mA. Given the stimulation amplitude cannot be increased freely until
the target −→J is reached, optimizing electrode design remains an important component in achieving successful outcomes in TES. Similar computational work involving different tissue types using the AM has
demonstrated the potential to generate results that can be experimentally validated. Predictive simulations
of the local field potential (LFP) generated in the hippocampus due to extracellular electrical stimulation
was successfully validated through analytically estimated LFPs [38]. Additionally, the neuronal response
of two retinal ganglion cell subtypes with different frequency responses during epiretinal stimulation was
accurately simulated by using the AM-NEURON computational platform to predict the mechanisms of
color encoding [137]. Most recently, the TES approach was evaluated in tandem with the retina model
of rat and AM-NEURON computational platform to design stimulation strategies for targeting the bipolar
90
cell and photoreceptor layers affected during early-stage degeneration [138]. These computational studies
have demonstrated that AM can reliably be used for predictive analysis on induced fields and neuronal
activation in electrophysiology applications. Our future efforts will focus on developing a realistic human
head model and simulating the activation of specific cell subtypes in the retina during TES, leveraging
the stimulation parameters optimized in this study. Understanding how different retinal cells respond to
extracellular potentials generated with TES will be crucial for developing therapeutic strategies, such as
targeted activation of specific subtypes.
4.6 Conclusion
We have developed an innovative multi-scale computational method aimed at analyzing the response of a
comprehensive mouse head model to transcorneal electrical stimulation for therapeutic applications. Our
model compared stimulation thresholds for various electrode placements, providing valuable insights into
the optimal design and placement of the return electrode to maximize current density in the retina. Notably, the simulation results aligned closely with the experimental data collected in vivo from rats. The
comparison between simulated and measured voltage and current density values demonstrated that employing the Admittance Method for modeling bioelectromagnetic interactions during TES is a dependable
approach for optimization and predictive analysis. This computational tool assumes even greater importance in the context of human trials, where direct invasive measurements are not feasible, and modeling
studies become essential for predicting current densities generated in biological tissue. Future validation
studies should prioritize in vivo recordings from species with eye sizes comparable to those of humans, as
live body recordings may yield different results compared to studies conducted on severed tissue. Once
validated, computational models, such as the one presented here, can be leveraged to optimize the stimulation parameters in electrophysiology applications, thereby enhancing the success rate of neuroprotective
and regenerative therapies.
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Chapter 5
A Connectome-Based Computational Model of Early-Stage Retinitis
Pigmentosa
Chapter 5
E. Iseri, P. Kosta, J. Paknahad, J.C. Bouteiller, G. Lazzi. A Computational Model Simulates Light-Evoked
Responses in the Retinal Cone Pathway. 43rd Annual International Conference of the IEEE Engineering in
Medicine and Biology Society (Oct, 2021, Virtual, Mexico.)
E. Iseri, P. Kosta, R. Pfeiffer, C. Sigulinsky, J. Anderson, J. Yang, J. Daha, J. Garcia, J. C. Bouteiller,
B. W. Jones, G. Lazzi. A Connectome-Based Computational Model of the Degenerating Retina Simulates
Aberrant Oscillations in the rd1 and rd10 Mice Vision Research, ScienceDirect (Under review, 2024)
5.1 Abstract
Retinal degeneration due to retinitis pigmentosa (RP) occurs in multiple stages, with rewiring of the neural network preceding neuronal death. Connectomics provides a high-resolution topology of the retina,
allowing precise synaptic mapping. This computational study investigates the alterations in the signaling pattern of the rabbit’s retina during early-stage degeneration using pathoconnectomics. A natural
light-stimulation protocol is developed to simulate the electrical signaling in a healthy retina model as a
baseline. The individual cell responses to the same light stimulation are simulated in terms of the change
in their excitatory postsynaptic potential (EPSP), to understand how synaptic rewiring might affect signal
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flow during degeneration. Simulation results show changes in bipolar and amacrine cell EPSPs both during
activation and rest due to the mixing of cone signals into the rod pathway and newly formed gap junctions
in the degenerate retina. Notably, the rewiring causes rhythmic firing of the retinal ganglion cell due to
the depolarization of the network compared to baseline. These findings are consistent with patch-clamp
studies in rd1 and rd10 mice with the same disease type. We envision that computational techniques, combined with connectomics as presented in this study, can be used for predictive modeling of signaling in
early-stage retinal degeneration and can help identify windows of therapeutic opportunity. Furthermore,
a realistic network model can be combined with multi-scale bioelectromagnetic computational methods
to optimize neurostimulation parameters in therapeutic applications to delay disease progression.
5.2 Introduction
The retina is a complex, layered structure that converts light into electrical signals through phototransduction, followed by signal processing in the neural retina allowing for visual perception. Its neural network
consists of different classes of cells connected through excitatory and inhibitory chemical synapses and
electrical synapses, and modulated by glia. In retinal degenerative diseases, including RP, progressive photoreceptor loss has downstream impact upon the neural retina, including alterations in morphology and
synaptic connections, ultimately corrupting healthy retinal neuronal networks. These alterations start as
stress in the photoreceptors and gradually progress to numerous negative plasticity events, collectively
termed Retinal Remodeling [139, 140, 28, 26, 141]. Retinal remodeling eventually gives way to a full neurodegeneration phenotype leading to partial, and even complete blindness. Despite significant progress in
developing retinal prosthetics that use electrical stimulation techniques to provide partial visual restoration for the blind, there is room for improvement [142, 143]. A major challenge with the current generation
of prostheses is the complexity involved in capturing the natural light response of the retina through the
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corresponding electrical stimulation waveform representing the input image. The resolution of the electrode array is a limiting factor when selective stimulation is required, and simply decreasing the electrode’s
diameter does not solve this problem [144, 145]. Furthermore, stimulation parameters such as pulse width,
frequency, and phase balancing [146, 147, 39] need to be carefully tuned to mimic the natural light response
in target cells. One strategy to improve the effectiveness of implanted electrodes is to design waveforms
that can stimulate a local cell cluster and approximate spatiotemporal patterns to better represent the input image [148]. To achieve this, a realistic retinal network model that includes all its cell types, accurate
cell membrane properties, and precise connectivity mapping is needed. In our study, we utilized connectomics data from a degenerate rabbit retina and validated computational cell models to investigate how
retinal degeneration affects the electrical firing response of individual cells to natural light. We developed
a simulation framework that considers the morphological and topological changes that occur during retinal degeneration and how the electrical signaling pattern may be affected. Our network model is based
on the pathoconnectome dataset extracted from a serial section transmission electron microscopy (TEM)
volume of rabbit retina with early-stage RP, named Retinal Pathoconnectome 1 (RPC1) [149]. The cell
models used in our study are multi-compartmental and incorporate realistic morphologies, including the
precise locations where synapses are formed for the cells (except photoreceptors) where available in the
connectome dataset. The volume is 70 µm in diameter, so some cell classes that have a larger arbor size,
including widefield amacrine cells, full horizontal cells, and complete ganglion cells are not fully contained
in it; therefore, the dataset used here does not include a complete canonical repertoire of every cell type.
Further, annotation is the slowest part of generating connectomes and the RPC1 dataset will continue to
evolve over time. Due to these factors, some synapses are artificially generated and placed based upon
relevant literature. The imaged slice of the retina is a cylindrical volume that spans from the vitreous
to the base of the outer nuclear layer. Synaptic connections between each cell were annotated in detail,
including their type, terminal locations, and post-synaptic density. The membrane properties of each cell
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type were defined by referring to published work in the ModelDB database. We also developed an input
protocol to capture the retina’s light stimulation response, allowing us to compare our results with patchclamp recordings of individual cell types under similar conditions. The key components of early-stage
retinal degeneration covered here are aberrant connections between cone photoreceptors and rod bipolar
cells and newly formed gap junctions between Aii glycinergic amacrine cells and rod bipolar cells due to
rewiring [149]. We evaluate the impact of these topological changes on the network output measured from
depolarizing retinal ganglion cells.
5.3 Methods and Model Description
The computational model of the early-stage degenerated retina [150] includes several types of cells, namely
ON-type (depolarizing) cells such as rod photoreceptors, cone photoreceptors, rod bipolar cells (RodBCs),
ON cone bipolar cells (ConeBCs), Aii glycinergic amacrine cells (Aii GACs), and an ON-type retinal ganglion cell (RGC). Some horizontal cells and GABAergic amacrine cells are also present in the imaged volume; however, they are not included in the network because their responses to light stimulation could not
be validated using the available models in the literature database at the time of the study. Additionally, the
OFF-network is also not considered in this model; therefore, all mention of ConeBC refers exclusively to
the ON-ConeBCs. References to OFF-type cells will be made exclusively. The novelty of this computational
model lies in the use of realistic cell morphology and topology within the imaged volume of RPC1. The
RPC1 dataset used in this study was generated from a ten-month-old transgenic (Tg) P347L rabbit retina
with early-stage RP [149]. Cells captured in a cylindrical volume with a diameter of 70 µm and 70 nmthick slices were annotated to create the pathoconnectome. The cell morphologies were then translated
into .swc file format to be used in the simulation environment. The NEURON software was used to run the
simulations, which computes the membrane potential of the cells at every time step for a specified current
clamp input. The model simulates the effects of degeneration on the electrical signaling of each cell type
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in the network, specifically focusing on aberrant synaptic connections between cones, RodBCs, and Aii
GACs. Modified versions of membrane models from other studies that present computational models of
the retina with single-compartment [151, 152, 153, 154], as well as multi-compartmental cells [155] were
used in this work. The model also introduces a paradigm for light input stimulation that simulates the
photocurrent generated after a flash of light [156] and is based on the ON pathway with depolarizing cells
only.
5.3.1 Data Extraction and Simulation Framework
5.3.1.1 Morphology and Topology
The connectome data that we present here is publicly available and can be accessed using the University of
Utah’s Viking file export tool at http://websvc1.connectomes.utah.edu/Export/ [157]. All cells, except photoreceptors, are modeled as multi-compartmental models to accurately represent the soma, axon and dendritic branches. We gathered 15 rod bipolar cells, 6 ON-type cone bipolar cells, 8 Aii glycinergic amacrine
cells and 1 ON-type ganglion cell, along with their synaptic mappings from the RPC1 dataset to create the
network model (Table 5.1). The 3-D representation of the network is shown in Fig. 5.1(a), plotted using
the Vaa3D open-source visualization software.
RodBCs Aii GACs ON-ConeBCs ON-RGC
822, 933, 1001, 1069,
1223, 1232, 1242, 1243,
1258, 1537, 25001,
26167, 30692, 30804,
31982
69, 192, 262, 265, 1685,
2710, 2712, 2713
298, 430, 617, 724, 740,
1167
2612
Table 5.1: The cells IDs extracted from the RPC1 dataset and plotted in Fig. 5.1
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Figure 5.1: (a) 3-D plot of the RPC1 cell network, showing the morphology and topology captured by
the TEM imaging. The size and coordinates of the cells are stored in .swc files and plotted with a 3-
D visualization software. Rod and cone photoreceptors are partially represented in the image because
of their large number. (b) Signal flow illustration in the ON-type network of RPC1. Green connections
are normally found in the healthy retina. Red connections are observed only in RPC1. Empty circles
represent ribbon synapses with metabotropic mGluR6 channels solid circles represent ionotropic channels
and resistors represent gap junctions. Legend: subscript H - healthy, subscript D - degenerated.
5.3.1.2 Pre-processing and Simulation in NEURON
In this study, we obtained cell morphology and connectivity data from the open-source RPC1 database. We
used a Python script to download the morphology of the selected cell in .swc file format and the direct (onehop) connections it makes with neighboring cells in a .txt file format. The .swc file was then processed using
a MATLAB script to ensure that there is no more than a single root, to bridge any broken edges and missing
annotations, and to define the compartment type (soma, axon, or dendrite). The processed .swc files, along
with the synaptic connectivity data, were then used to create the model simulated in the NEURON software.
The membrane potential response to a photocurrent (current clamp) stimulation at single compartment
resolution is solved in NEURON for each cell type. We used a compartmentalization system, following the
principles of the cable theory, to model the cells and their biophysical properties [158]. Each compartment
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was defined as a tapered cylinder, connected to neighboring compartments with an intracellular resistor,
and assigned passive or active membrane currents represented by an equivalent electrical circuit. The
synapses between cells were defined by type and weight. The synaptic weight indicates the post-synaptic
density area covered in the connection between two cells and directly impacts its strength. Both the
synapse type and the weight values were determined from the connectome annotations.
5.3.1.3 Pre-processing and Simulation in NEURON
The stimulation protocol used in this analysis is based on the method developed in previous work to capture the natural light response of the cone pathway [156]. This method was validated using patch clamp
recordings of photoreceptor photocurrents [159, 160, 161, 162] and the corresponding change in photoreceptor [163, 164] and bipolar cell membrane potentials [165, 166, 167]. Photoreceptors are represented as
point sources with a static output waveform at their inner segment, as modeling the natural phototransduction process in their outer segment is challenging. The natural light stimulation is delivered using a
current clamp on the photoreceptors, modeled as a static waveform. This waveform is a mathematical
function that captures the shape of the current generated at the inner segment as a result of natural phototransduction at the outer segment. To validate the cell responses to a saturating flash of light, a realistic
synaptic convergence pattern was used. The amplitude of the saturated rod photocurrent was set to 30 pA,
and the amplitude of the saturated cone photocurrent was set to 20 pA (Fig. 5.2) [156]. Carrying over this
stimulation protocol to the network presented here is achieved by evaluating the light-evoked responses
of the RodBCs, ConeBCs, Aii GACs and RGCs [164, 165, 168, 169] and matching their EPSPs during stimulation as closely as possible, while complying with the rod-RodBC and cone-ConeBC convergence pattern
as described in the literature [170, 171].
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5.3.2 Cell Biophysical Models
Cells in the model are multi-compartmental and each compartment is defined by cell type-specific membrane properties. Voltage-gated ionic channels are represented by conductance-based kinetic models derived from patch clamp recordings of individual cells. The references that describe membrane properties
of degenerated cells were limited at the time of this report and the biophysical parameters used here reflect
those of healthy cells. Recent studies on photoreceptors and bipolar cells at early-stage RP have shown
a clear decline in electroretinogram (ERG) amplitudes of photoreceptors and bipolar cells to light stimulation [172, 173]. However, ERG lacks the accuracy of patch clamp recordings when translating it to
a computational model that represents the cell’s membrane response; therefore, we did not incorporate
these findings to our current modeling approach.
5.3.2.1 Rod Photoreceptor
The signal pathway originating from rod photoreceptors is referred to as the “rod pathway”. There are
differing observations on how many rod inputs each rod bipolar cell has in the healthy rabbit, with one
study claiming that up to thirty rods deliver input to a single RodBC [170], another study showing roughly
fifty rods fall within the dendritic field of a RodBC where each rod may be contacting more than one
RodBC on average [174], and others suggesting this number may be close to one hundred on average
[175, 176]. We used the number of 30 in our previous computational study for evaluating the differences
in membrane depolarization of healthy and degenerate RodBCs [177], the circuitry of which was largely
based on mouse [178, 179]. Because the model parameters such as the compartment diameter and ionic
channel conductances were tuned at that time to match the patch clamp data of rabbit, we chose to use the
same convergence pattern and biophysical parameters here to keep consistent with the optimized model.
However, additional simulations for different number of rods inputs per RodBC were generated to better
understand how the number of rod inputs may impact the RGC output, which will be discussed in the
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results section. Because the rod photoreceptor is the first cell type to undergo cell stress and subsequent
apoptosis as part of the RP process [140], a diminished rod count was observed in the pathoconnectome
data. It was found that the outer nuclear layer thickness was reduced by about 50% in the selected region
of the degenerate retina [149]. Based on this observation, and inconclusive identification of some photoreceptor inputs detailed below, it is inferred that the rod signal strength may have been weakened by up to
50%. We note that this approach may not perfectly reflect the actual mapping of the rod-RodBC connections in the RPC1 volume because while the number of remaining rods may be halved, this number almost
certainly contains rods that are degenerating. The annotated RodBCs appear to retract their dendrites from
the degenerating rods and make new aberrant connections with cones even prior to complete rod death,
dramatically decreasing the number of confirmed rod connections. Further, an indeterminate class was
detailed during the annotations, which may be a degenerating rod or a cone neurite sprout [149]. Overall,
connecting 15 rods on average to each RodBC can be statistically viable at this stage of the degeneration
and allows for more thorough evaluation of the impact of novel RodBC connections in the inner plexiform
layer. Improvements on precision can easily be made as the annotations evolve over time. A MATLAB
script was used to randomize the spread of photoreceptors and form synapses across the bipolar cell dendritic terminals . Our rod model is a modified version of the one previously used in a similar ON-type
retinal network [153]. We used a transient light stimulation protocol to define the generated photocurrent, as described in our preceding work [156, 177], which is the most common technique in the referenced
patch clamp studies. The model attempts to recreate the currents measured from rod photoreceptors stimulated with a 10-millisecond flash at 500 nm wavelength [180, 181]. Six membrane currents were used to
model the change in membrane potential at the inner segment due to the photocurrent input: hyperpolarization activated current (Ih), non-inactivating potassium current (IKx), delayed rectifying potassium
current (IKv), calcium current (ICa), calcium-dependent chloride current (ICl(Ca)
) and calcium-dependent
potassium current (IK(Ca)
). This led to the membrane hyperpolarization of the photoreceptor membrane
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upon photocurrent activation (Fig. 5.2). The hyperpolarized membrane reduces the release rate of glutamate neurotransmitters into the rod-RodBC synaptic cleft and initiates the depolarization of the RodBCs.
The compartment dimension is an important factor when tuning the cell’s membrane potential response
to match experimental recordings. As the photoreceptors are treated as point sources in the model, there
is flexibility from a modeling perspective in adjusting the compartment size to achieve a response that
matches experimental observation. Thus, the rod compartment is set to be 1 µ m in radius and 1 µm in
length to achieve the target membrane potential response.
5.3.2.2 Cone Photoreceptor
In most mammalian retinas, cone photoreceptors are less abundant compared to rods but play a crucial
role in both mesopic (dim-light) and photopic (daylight) vision. The cones are modeled similarly to rods,
with some differences in the photocurrent waveform, membrane currents, and compartment dimension.
Cones have a faster photocurrent decay rate, repolarizing in 0.5 seconds after a flash input, compared to
the 7 seconds of rods. The amplitude of the photocurrent in cones is also smaller, reaching saturation at
20 pA compared to 30 pA of rods [159, 180, 181]. Most of the membrane currents present in rods are also
found in cones, except for IKv [152]. Additionally, the conductance and reversal potential values for these
channels are different, resulting in a weaker hyperpolarization response in cones (Fig. 5.2). Like rods, the
compartment dimension of the cones was tuned to reach the target membrane potential response from
the patch clamp recordings [156]. In this case, the compartment size for cones was set to be 2.25 µm in
radius and 2 µm in length. As the cone synapses with ConeBCs were not annotated in the dataset at this
time, we referred to the literature to estimate the average number of cone inputs per bipolar cell [178,
182]. Based on these estimates, 10 cones were connected to each cone bipolar cell in the network, which
would be a high-end estimation for the ConeBCs but is regionally appropriate as the RPC1 volume is from
a peri-streak region containing a high density of cones. These studies also note that each cone pedicle can
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feed light signals into different cone bipolar cells via over 100 different post-synaptic points; however, due
to the complexity of setting up this kind of mosaic, we chose to feed single cone inputs to a single bipolar
cell, resulting in 60 cones being equally distributed among 6 bipolar cells. The same approach when adding
artificial rods was repeated and the locations of the synapses were randomly selected using a MATLAB
script.
Figure 5.2: Changes in photoreceptor membrane potentials following the generated photocurrent due to a
flash of light input. Cells begin at rest (dark-adapted) and the input is applied at the 2-second mark. The
photocurrent amplitude scale is shifted to rest on 0 for convenience (in the actual simulation, the “dark
current” during absence of stimulation is accounted for and the resting potential of the photoreceptors
reflect it).
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5.3.2.3 Rod Bipolar Cell
The biophysics of RodBCs are modeled using a conductance-based model with the following ionic currents [151, 153, 183]: voltage-dependent potassium current (IKv), calcium-dependent potassium current
(IK(Ca)
), calcium current (ICa), hyperpolarization-activated current (Ih), and transient outward current
(IA). These ionic currents are implemented using modified Hodgkin–Huxley equations, and the parameters for the kinetics were tuned to reproduce experimental electrophysiological recordings of rat RodBCs
[184, 185, 186] and the voltage clamp recordings presented in [187]. In a healthy retina, RodBCs receive
direct input exclusively from rod photoreceptors. However, during the early stages of degeneration, it has
been observed that RodBCs extend their neurites to the terminals of cone photoreceptors as the connections with rod photoreceptors degrade [188, 189]. It is discovered that the aberrant synapses formed by
cones with RodBCs resemble the natural synapses cones form with hyperpolarizing OFF-ConeBCs [29].
We took this into consideration when modeling the aberrant cone inputs to RodBCs, which will be discussed in detail in the next section. Our network has a total of 15 RodBCs that formed aberrant cone
synapses and/or aberrant gap junctions as a result of degeneration [149].
5.3.2.4 ON-Cone Bipolar Cell
ConeBCs, which form the principal visual pathway with direct synaptic connections to the RGCs, receive
their inputs from cone photoreceptors. There are two major types of ConeBCs, known as depolarizing (ONtype) or hyperpolarizing (OFF-type), with multiple sub-types that have been identified in rat [190], mouse
[191, 192, 193], and human [194] and have at least in part been associated with rabbit classes [195]. While
we can differentiate RodBCs and ConeBCs as well as subtypes of the ConeBCs in the pathoconnectome
data, incomplete annotation prevents comprehensive labeling and precise class assignment. Therefore, we
have adopted a general model for the depolarizing ConeBC, which is non-spiking and has the biophysical
properties as outlined in [153]. While spiking bipolar cells with a sodium current have been reported in
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ground squirrel [196], we do not consider it for the generalized ConeBC model in this study. This model
shares the same membrane channels as RodBCs, but without IA (Table 5.2). Hyperpolarizing OFF-ConeBCs
have not been included in the network as the modeling of the OFF-pathway, including OFF-type ganglion
cells, is not yet complete as of this report.
5.3.2.5 Aii Amacrine Cell
The Aii GACs are a critical subtype of amacrine cells in the rod pathway, responsible for transmitting rod
signals to RGCs through electrical synapses with the ConeBCs. Current-clamp data in the literature suggests that the membrane potential response of Aii GACs has two components. A transient response with
a large amplitude and short time constant occurs immediately after stimulation, followed by a sustained
depolarization with reduced amplitude, which coincides with the depolarization duration of the ConeBCs
that is shared through the bidirectional gap junctions mediating the electrical synapse [164, 168, 197, 198,
199]. The Aii GACs express Hodgkin and Huxley sodium (IHHNa) and potassium (IHHK) channels, calcium channel (ICa) and A-type potassium channel (IKa) [153, 154]. The passive membrane parameters
were modified to align with the curve-fitted, electrically coupled Aii GAC model [200]. Additionally, there
is another amacrine cell type in RPC1 that exhibits signs of rewiring during early degeneration, which is
a subset of the GABAergic amacrine cells that forms aberrant processes extending to the outer plexiform
layer [201]. However, due to limited published models and patch-clamp data for this cell type, it is not
included as part of the network at this time.
5.3.2.6 ON-Retinal Ganglion Cell
RGCs are one of the most extensively studied cell types in the retina. They are responsible for collecting
the entire visual signal and relaying the information to the visual cortex through the optic nerve. For our
network, we extracted a single RGC that gathers the electrical signal originating from the photoreceptors
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and processed through the rest of the network, as shown in Fig. 5.1(b), illustrating the signal flow pattern.
The RGC responds to light stimulation by firing a train of action potentials, and the firing rate depends
on the amplitude of the photocurrent [202]. The kinetics of the RGC membrane potential are based on a
model [203] that has been previously used to investigate targeted electrical stimulation of RGC subtypes
[204]. It’s important to note that this model does not account for the spontaneous firing observed in RGCs
in the absence of stimulation [205], and thus, the membrane potential remains at rest until light input is
applied.
Table 5.2: Voltage-Gated Ionic Channel Distribution for Retinal Cells
Biophysical Properties of Cells in the ON Pathway
Cell Type Ionic Channels Reference Model
Rod Photoreceptor Ih,IKx,IKv,ICa,ICl(Ca)
,IK(Ca)
[153, 183]
Cone Photoreceptor Ih,IKv,ICa,ICl(Ca)
,IK(Ca)
[152, 156]
Rod Bipolar Ih,IKv,ICa,IA,IK(Ca)
,Ileak [151, 153]
Cone Bipolar Ih,IKv,ICa,IA,IK(Ca)
,Ileak [153, 156]
Aii Amacrine IHHNa,IHHK,ICa,IKa [153, 154, 200]
Retinal Ganglion Ih,IKv,ICa,IK(Ca)
,Ileak [203]
5.3.3 Synaptic Models
The network only includes the ON pathway (Fig. 5.1), which has metabotropic and ionotropic ribbon
synapses and electrical synapses mediated by gap junctions (GJs). The ribbon synapses were modeled
as either graded, which occur at the post-synaptic terminals of bipolar cells with the photoreceptors and
post-synaptic terminals of RGCs [206], or as exponential synapses that define the fast, transient potential
change of Aii GACs [207]. GJs, which are accepted as the anatomical basis of electrical synapses between
neurons and are bidirectional by their nature in vertebrates [208], were used in our model to establish
electrical coupling.
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5.3.3.1 Rod Photoreceptor - Rod Bipolar Cell
We use the same ribbon synapse model presented in Publio’s work [183], which is a simplified version of
Mulloney’s graded synapse model [209] with its parameters adapted from Sikora’s ribbon synapse model
[206]. It is a glutamatergic synapse that is dependent on the rate of glutamate release by the photoreceptors
and leads to a graded voltage response on the bipolar cells. A photoreceptor becomes hyperpolarized after
light stimulation and reduces its rate of glutamate release into the synaptic cleft. This reduction leads to
an increase of the membrane potential of depolarizing bipolar cells or decrease of the membrane potential
in hyperpolarizing bipolar cells. We made minor modifications to the reference model [206] to reach the
target EPSP amplitude on the bipolar cells. The voltage threshold of the synapse was reduced and the
channel conductances were increased to comply with the literature recordings that were used to validate
our models [156].
5.3.3.2 Cone Photoreceptor – ON Cone Bipolar Cell
Similar to the rod photoreceptor synapse, cone synapse is driven by glutamate release and modeled in the
same manner, as a graded response. The same synaptic model for rod-RodBC was used and the synaptic
strength (weight) was tuned to get a realistic EPSP on the ConeBCs that matches well with experimental
recordings [156]. Thus, the weight of the cone-ConeBCs synapse is set to be about three times greater
than that of the rod-RodBCs synapse in our model.
5.3.3.3 Cone Photoreceptor – Rod Photoreceptor
While some of the published network models have considered the electrical coupling between rods and
cones [153, 210], we did not include it here because the imaged volume does not extend beyond the outer
nuclear layer and a synaptic mapping as with other cell types is not available for this connectome. Furthermore, because the photoreceptors were randomly distributed along the bipolar cell terminals in our model,
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the density of the rod-cone coupling could not be reliably included as described in the literature [211]. Experimental evidence suggests that the connexin 36 protein is dominantly expressed in these connections
and the coupling is bidirectionally symmetric [212, 213]. The implications of not having electrically coupled photoreceptors on the results are addressed in the discussion section.
5.3.3.4 ON Cone Bipolar Cell – Aii Amacrine Cell
The Aii GACs cells are both postsynaptic to the ribbon synapses from RodBCs and electrically coupled
to ConeBCs via GJs. This is confirmed in the connectomics data from humans and all mammalian model
organisms that have this cell type to date. Gap junctions form a direct electrical coupling between cells and
their blockage was observed to reduce the time constant of the membrane potential [214, 215], suggesting
a linear resistive relationship for the equivalent circuit model of the synapse. Thus, the gap junction is
represented by a resistor in our model, with a conductance of 200 pS as used in preceding modeling work
[153, 216]. Some of the studies on rat suggest that this value could be higher, at an average of 700 pS [217,
218]. More recent evidence shows that the gap junction conductance between Aii GACs and ConeBCs
may be closer to 400 pS [219]. While the value of 200 pS was used here across all the gap junctions in our
core simulations to keep consistent with previous models, the effect of using higher conductance values is
covered in the results section.
5.3.3.5 Aii Amacrine Cell – Aii Amacrine Cell
The Aii GACs in the network are electrically coupled via gap junctions. This coupling may improve the
signal-to-noise ratio within the rod pathway by amplifying smaller correlated rod signals while reducing
the uncorrelated noise [213]. The extent of Aii GAC coupling has been shown to vary greatly depending
on its state of light adaptation, ranging from 20 cells in the dark-adapted to over 300 cells in the lightadapted rabbit retina [198]. Tight coupling between a small number of cells ensures reception of single
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photon-activated rod signals by filtering the noise from inactive areas during scotopic conditions, drastically increasing the sensitivity [214, 220]. However, it was also observed that the Aii GACs uncouple
following intense background illumination, possibly reflecting increased activation of D1 receptors [198].
We note that the model presented here has only 8 coupled Aii GACs, which may be best suited for simulating either dark-adapted or high intensity levels. A computational model with a wider receptive field
containing hundreds of Aii GACs could be a more realistic approximation of the mesopic vision regime.
5.3.3.6 ON Cone Bipolar Cell – Ganglion Cell
In our network model, the ConeBCs are coupled to the rod pathway via the Aii GACs. The ConeBC is the
only cell type that is pre-synaptic to the RGC in this network and determines its firing rate. The synapse
is graded with first order kinetics, similar to that of the photoreceptor-bipolar cell described in section
5.3.3.1, with adjusted equilibrium potential and conductance values to match the light-evoked response of
RGC as outlined in [203]. One limitation we had at the time of this work was missing annotations between
these two cell types. Therefore, we adapted a similar approach to how rod and cone photoreceptors were
integrated into the network and created artificial synapses by leveraging the annotations from a previous
study on a healthy connectome dataset for rabbit [157]. We averaged both the number of synapses and the
synaptic weights formed between the RGC and ConeBC in that dataset and patched it into our synaptic
mapping. This approach leans on the assumption that the topology within the ganglion cell layer has been
minimally affected at the early stages of degeneration.
5.3.3.7 Rod Bipolar Cell – Aii Amacrine Cell
The synaptic pattern in a healthy retina suggests a unidirectional signal flow from RodBCs to Aii GACs
through excitatory ribbon synapses [157]. The previous connectome study of the wild type rabbit has
shown that the Aii GACs’ arboreal dendrites were always postsynaptic to RodBCs and never presynaptic
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[221]. The synaptic connection between them is modeled as ionotropic glutamate receptors (iGluR) with a
fast depolarization and a slower repolarization rate upon excitation, as indicated by light response recordings of the Aii GACs [154, 164, 168, 197, 198]. NEURON’s exponential synapse function "ExpSyn" was used
to form the RodBC to Aii GAC connections representing iGluR. The connections between RodBCs and Aii
GACs during early-stage degeneration undergo rewiring and form aberrant GJs that are not observed in
the wild type rabbit [149]. In the absence of molecular and physiological characterization, this aberrant
gap junction is modeled in the same way as the gap junction between the Aii GACs and ON ConeBCs,
which is a passive resistive element with a conductance of 0.2 nS.
5.3.3.8 Cone Photoreceptor – Rod Bipolar Cell
Another instance of rewiring in RPC1 occurs between cone photoreceptors and RodBCs. While it is known
that rod photoreceptors can occasionally be presynaptic to OFF-ConeBCs in the healthy retina, cone photoreceptors that are presynaptic to RodBCs are rare [179]. A study in mice has shown that cone photoreceptor pedicles may come into contact with RodBC dendrites [222], but further investigation is needed
to determine if this is a common occurrence in the mammalian retina. Therefore, the aberrant synapses
between cone photoreceptors and RodBCs observed in RPC1 are considered unique to degeneration [39].
Evidence suggests that the postsynaptic terminals of these aberrant connections are similar to those observed between cones and OFF-ConeBCs [139, 223], indicating that the newly formed cone synapses during early-stage degeneration will hyperpolarize the RodBCs in response to light increments, whereas rods
would normally have a depolarizing contribution. The class switching of RodBCs’ glutamate receptors
into those of OFF-type cells was shown in both mouse and human [139], as well as in the rabbit RP model
which is used in this work [223]. Therefore, we adapted an ionotropic glutamate model for these new
synapses.
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1-Hop Connections Non-Aberrant (Baseline) New Synapses
Synapses due to Rewiring
Rods - RodBCs 225 (Rg) 0
Cones - ConeBCs 60 (Rg) 0
Cones - RodBCs 0 21 (−Rg)
RodBCs - Aii GACs 191 (Re) 44 (G)
Aii GACs - Aii GACs 67 (G) 0
Aii GACs - ConeBCs 34 (G) 0
ConeBCs - RGC 28 (Rg) 0
Table 5.3: Synaptic distribution in the network model between neighboring cells. (Rg): metabotropic
graded ribbon, (−Rg): ionotropic graded ribbon, (Re): excitatory exponential ribbon, (G): gap junction.
Individual values for each biophysical parameter such as membrane channel conductances and synaptic thresholds are provided in an open access GitHub repository. The RPC1 model files with the complete
parameters can be accessed and simulated using the instructions in the following link:
https://github.com/ankaraliegos/ConnectomeModeling/tree/master
5.4 Simulation Results
5.4.1 Baseline
First, we simulate the baseline natural light response of each cell type in the retina network, serving as a
"ground truth" before adding degeneration features of early-stage RP, extracted from the RPC1 dataset. The
differences in synaptic connections between baseline and degenerate networks are summarized in Table
5.3. The response of the RodBCs, ConeBCs, Aii GACs and the RGC was evaluated during the depolarization phase after light stimulation (Fig. 5.3(a)). Both types of ON bipolar cells had sustained depolarizing
responses due to the graded ribbon synapses with photoreceptors. Consequently, the RGC fired action
potentials during the depolarization phase of ConeBCs but not during the sustained depolarization phase
of RodBCs after the ConeBCs repolarized. The Aii GACs showed transient and sustained components in
their EPSP. The initial transient spike was triggered by the rod input, and it did not develop when the
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rod photocurrent was set to 0 pA. This finding is consistent with experimental recordings of RodBC-Aii
GAC ribbon synapses, which show that a sustained inwards calcium current elicits a transient spike in the
Aii GACs EPSP before settling to a steady-state depolarization level [224]. Furthermore, our results show
that the steady-state sustained depolarization of Aii GACs lasted as long as ConeBCs were depolarized, in
agreement with the model description from Section 5.3.2.5 and patch clamp recordings of Aii GACs stimulated with the same protocol. The peak firing rate of the RGC simulated at full cone saturation (20 pA)
was 190 Hz, which falls within the ranges reported in patch-clamp studies of light-evoked responses in
RGCs that were up to 200 Hz [225] and 300 Hz [226]. The membrane properties of the RGC model closely
followed the impulse response as presented in [227] and the alpha subtype of cat RGC [203], which was
shown to sustain a firing rate around 150-200 Hz. We considered the spiking frequency of the RGC as the
"visual output" and compared it between the baseline and degenerate network, suggesting that changes in
RGC firing rate could serve as a measure of the impact of early-stage RP on retinal function in the model.
5.4.2 Early-Stage Degeneration
Two types of rewiring were considered in the early-stage degeneration model: aberrant cone synapses
with RodBCs and aberrant GJs between RodBCs and Aii GACs. The aberrant cone synapses are presumed
similar to those that are found between cones and OFF-ConeBCs, in the form of iGluR [29] . The effect
of the aberrant cones on the RodBCs is thus modeled to hyperpolarize its membrane potential during the
light input, which is considered as a "signal corruption" in the rod pathway, since RodBCs are only present
as the depolarizing type in the healthy retina [167, 170]. The aberrant GJs between RodBCs and Aii GACs
are based on the documented connections in RPC1, where 44 were identified across the 15 RodBCs that
were used for this network [149]. Like the cone-RodBCs synapses, these GJs are exclusive to RPC1 and
a result of the rewiring that takes place during degeneration. By incorporating these aberrant synapses
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Figure 5.3: Changes in membrane potentials of the main cell types following a saturating flash of light input
shown in Fig. 3 at the 2-second mark. Left column: cell responses in the baseline network. Right column:
cell responses in the degenerated network with aberrant cones and GJs added. Notable differences are:
(a) Increased RodBC resting potentials, (b) suppressed transient component of the Aii GAC as well as an
increased difference between resting and steady-state voltages, (c) suppressed initial peak of the ConeBC
and (d) rhythmic firing at the RGC after stimulation is turned off. Some of the overlapping RodBCs were
not plotted for visualization
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into the network model, the effects of early-stage degeneration unique to RPC1 can be simulated and their
impact on each cell’s EPSP can be compared to the baseline.
5.4.2.1 Photopic Conditions
A "bright" stimulation level that saturates the cones (20 pA amplitude) is initially assumed to capture the
photocurrent profile of cones during photopic or daylight vision. Right column of Fig. 5.3 shows the
differences in individual cell EPSPs when the aberrant connections are added under the same stimulation
parameters as Fig. 5.2(a). The addition of aberrant cone synapses results in a depolarizing shift in the
resting potential of RodBCs. This is a consequence of the aberrant cones affecting the photoreceptor dark
current [228] during the absence of stimulation, which in turn affects the resting potential of RodBCs.
Additionally, during the period when the cones generate a photocurrent, a hyperpolarizing effect can be
observed in the first 500 ms of the RodBC EPSP, again due to the aberrant cone synapses (Fig. 5.3(a)). The
Aii GACs show a suppressed initial transient peak in the degenerated case, due to the smaller ∆V of the
RodBC EPSP caused by the depolarized resting potential. The resting potential of the Aii GACs is also
affected from degeneration, leading to a more depolarized steady state (Fig.5.3(b)). This is a consequence
of the aberrant GJs between RodBCs and Aii GACs, which result in an electrical coupling that does not
occur in the baseline network. The depolarization of Aii GACs’ steady-state potential is reflected on the
ConeBCs EPSP, which in turn becomes slightly more depolarized compared to the baseline (Fig.5.3(c)). All
these changes in the EPSPs of RodBCs, Aii GACs, and ConeBCs culminate in an increased firing rate of
the RGC and sustained rhythmic firing even after the stimulation is turned off (Fig. 5.3(d)).
5.4.2.2 Mesopic Conditions
The effects of aberrant cone synapses and GJs on the RGC output were investigated under different background brightness levels, ranging from 2 pA to 20 pA cone photocurrent amplitude. We broadly define
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Figure 5.4: (a) Comparison of RGC firing rate at varying degrees of degeneration. The firing rate saturates
with increasing cone input strength. (b) Percentage difference in the RGC firing rate compared to the baseline (x = 0). Ten percent saturation corresponds to 2 pA of cone photocurrent amplitude. The contribution
from gap junction degeneration to the RGC firing rate is independent from cone input strength and the
relative contribution is less pronounced at stronger light levels.
this as mesopic conditions, which relates to vision under intermediate levels of illumination. Rods are
assumed to be in saturation at all stages; thus, the contribution from the rod pathway will be comparatively stronger when the cone photocurrent is weaker. The simulation results showed that even under
low-light conditions, before cones reach saturation amplitude, the resting membrane potential of RodBCs
was higher when aberrant cone inputs were added, indicating that the aberrant cone synapses could affect
the RodBC EPSP at all levels of illumination. When considering only the aberrant cone input , the firing
rate of the RGC did not change significantly compared to the baseline (Fig. 5.4(a)). This did not change as
the cone input strength increased, with the absolute difference in the firing rate of only 2 Hz at 10% cone
saturation and no difference beyond (Fig. 5.4(b)).
On the other hand, when the aberrant GJs were isolated, the firing rate of the RGC increased compared
to the baseline network at a steady absolute difference (Fig. 5.4(a)). Because this type of rewiring is primarily connected to the rod pathway, its effect is most noticeable during low cone saturation levels (Fig. 5.4(b)).
The difference in the firing rate begins at 23% during 10% cone saturation and decreases to 4% during 100%
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Figure 5.5: EPSPs in the baseline (top) and gap junction degenerated (bottom) networks while the cone
photocurrent is zero. Aii GACs in the healthy network generate a strong transient that repolarizes to
resting state from rod-only input. This is reflected as a high-frequency burst on the ganglion cell for the
duration of the transient. The degenerated case leads to a suppressed transient on the Aii GACs and a
more depolarized steady state after the transient. This causes oscillatory firing at the RGC.
saturation. It is noted that the absolute difference in firing rate was near constant at all saturation levels,
indicating an oscillatory activity resulting from the aberrant connections. The difference in the firing rate
did not change significantly when cone degeneration was added to the gap junction degeneration, with
only minor fluctuations at various saturation levels. The percentage difference in the firing rates across
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three different cases demonstrated that the increased RGC firing rate was primarily driven by the aberrant
GJs and the contribution from aberrant cone synapses is minimal (Fig. 5.4(b)).
5.4.2.3 Scotopic Conditions
The simulation results under dark (scotopic) conditions, where the cone photocurrent was set to zero,
revealed interesting findings. Because the initial symptoms of RP include loss of low-light vision due to
degenerating rods, analysis of this regime could provide insight towards changes in the network’s signaling
at the disease onset. A rod-only input at varying levels of photocurrent saturation (7.5-30 pA) was applied
to the degenerated network and oscillatory activity was observed at the RGC only when the aberrant GJs
were included. This accounted for the increased firing of the RGC observed previously (Fig 5.4). In contrast,
the same oscillatory activity was not observed when the GJs between RodBCs and Aii GACs were removed
(Fig. 5.5). In the baseline simulation, a short burst of RGC action potentials was observed, temporally
corresponding to the large transient on the Aii GACs and ConeBCs from t = 2 to t = 2.05 seconds. However,
in the degenerated network with aberrant GJs, an oscillatory firing pattern was observed that persisted
after the transient. The RGC oscillations occurred at a rate of 8 to 12 Hz, observed when the photocurrent
amplitude was increased from 7.5 pA to 30 pA, respectively. Steady-state membrane potentials of the Aii
GACs increased by up to 5.5 mV and ConeBCs increased by up to 0.5 mV. These changes in signaling were
attributed to the aberrant GJs, as the cone photocurrent was set to zero and contribution from the aberrant
cone synapses was absent. A difference between pre-transient and post-transient steady-state membrane
potentials among the six Aii GACs was observed, reaching up to 2.4 mV. Similarly, ConeBCs’ resting
membrane potentials increased after the transient phase, up to 0.9 mV (Fig. 5.5). The overall increase in
the steady-state membrane potential of these cells was the likely cause of the aberrant oscillations at the
RGC. In comparison, the pre-and post-transient potentials of Aii GACs and ConeBCs were the same in the
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baseline case. These findings provide insights into changes in the network’s signaling during the disease
onset of RP, specifically under scotopic conditions where rod degeneration is prominent.
5.4.3 Model Parameter Sweep and Impact on the Output
5.4.3.1 Number of Rod Inputs per RodBC
In Section 5.3.2.1, we discussed varying reports regarding the number of rod inputs received by each RodBC
in the healthy retina. Initially, we established this count at 30 based on referenced modeling studies;
however, additional evidence suggests the possibility of it reaching as high as 100 in rabbit [176]. We
noted that the ONL thickness had reduced by 50 percent in the RPC1 and the degenerating rods that are
still alive may have already lost their synapses with the RodBCs. Consequently, accurately estimating
the intact connections within the imaged volume became challenging. To address this uncertainty, we
performed simulations, sweeping through 5 to 100 rod inputs per RodBC in the degenerate retina model
using the maximum photocurrent amplitude of 30 pA, and subsequently plotted the RGC output (Fig. 5.6).
The RGC output was evaluated in two regimes: the peri-stimulation regime between t = 2 s and t = 2.5 s,
and the post-stimulation regime between t = 3 s and t = 4 s. The peri-stimulation RGC firing rate did not
vary with increasing rod inputs per RodBC, remaining at 190 Hz as the cone signal drove the output in
this regime. In contrast, we observed a logarithmic pattern in the RGC firing rate in the post-stimulation
regime while the cone input was off, indicative of the effect of rod convergence with an increasing number
of rod inputs. A cut-off for characterizing the post-stimulation activity was found, where the oscillatory
activity after t = 3 s started to dampen and disappear before t = 4 s. The cut-off was determined to be 7
rods per RodBC in this model for a sustained aberrant rhythmic firing of the RGC post-stimulation. The
increase in the rhythmic firing is attributed to the elevated steady-state membrane potential of the Aii
GACs and the resulting depolarization of the ConeBCs.
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Figure 5.6: Left: The RGC membrane potential in the degenerate retina plotted when (a) 7 rods were
connected to each RodBC, (b) 30 rods were connected to each RodBC and (c) 100 rods were connected to
each RodBC. A sustained post-stimulation firing was observed for 30 and 100 rods per RodBC whereas
dampening was observed before t = 4 s when 7 or less rods per RodBC were connected. The duration
of the oscillations depend on that of the rod photocurrent. Right: The peri-stimulation (saturated cone
photocurrent) RGC firing rate remained at 190 Hz whereas the post-stimulation RGC firing rate (between
t = 3 s and t = 4 s) followed a logarithmic relationship with respect to the number of rods per RodBC. The
cut-off for characterizing the rhythmic firing is set to be 7 rods per RodBC due to the dampening where
its rate was assumed zero for less. The minimum firing rate characterized as aberrant rhythmic was 6 Hz
and a saturation towards 20 Hz was observed as the rod number increased.
5.4.3.2 Gap Junction Blockage and Conductance
Similar to the rod input strength, the GJs are important components of the degenerate retina model and it
is of interest to isolate their contribution to the RGC output. These occur at three instances in our model:
between Aii GACs, between Aii GACs and ConeBCs and between RodBCs and Aii GACs (degenerate).
Previously, we simulated the effect of the aberrant cone and aberrant GJ rewiring individually and observed
that the aberrant GJs led to an elevated firing rate of the RGC (Fig. 5.4). In section 5.4.2.2, we observed
that the elevated firing rate of the RGC persisted in the absence of cone photocurrent, suggesting that the
rhythmic firing was originating in the rod pathway. We simulated the contribution of all three types of
GJs to the RGC output by blocking (setting conductance to 0) them one at a time, as well as using a greater
conductance value as discussed in section 5.3.3.4. The results showed that the rhythmic RGC firing occurs
when RBC-Aii GAC GJs are active. Blocking the Aii GAC-Aii GAC GJs did not affect the rhythmic firing
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Figure 5.7: The effect of blocking the gap junctions between different cell types on the RGC output. (a)
Aii GAC and RGC responses do not change significantly when the Aii GAC-Aii GAC GJs are blocked
compared to the simulations of Fig 5.3(b). (b) Blocking Aii-ConeBC GJs severs the connection to the rod
pathway and eliminates the rhythmic firing of the RGC after t = 3 s. The Aii GACs lose their sustained
depolarization response from ConeBC coupling. This also brings the resting EPSPs of the Aii GACs near
the same resting potential compared to (a), except Aii GAC 69, which does not have GJs with other Aii
GACs. This suggests that the GJs between Aii GACs help regulate their resting EPSPs. (c) Blocking the
RodBC-Aii GACs eliminates the rhythmic firing of the RGC while coupled to the rod pathway through
the Aii-ConeBC GJs. The resting EPSPs of the Aii GACs are compact like in (b), while significantly more
hyperpolarized at rest. Combined results suggest that the aberrant RodBC-Aii GAC GJs are the source of
the aberrant oscillations at the RGC in this model.
but led to a higher peak of the Aii GAC transient and a large spread of resting potentials between cells (Fig.
5.7(a)). Blocking the Aii-CBC GJs cut off the entire connection between these cells and the rhythmic firing
did not occur. However, this also led to a strong depolarization of the Aii GAC cells (Fig. 5.7(b)). When the
aberrant RodBC-Aii GAC GJs were blocked, the rhythmic firing ceased, even though the rod pathway was
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still coupled to the RGC output. Blocking them led to a strong hyperpolarization of the Aii GAC resting
EPSP and the difference between rest and steady-state potentials became zero (Fig. 5.7(c)). These results
agree with the observation that the aberrant GJs between the RodBC and Aii GACs are a potential cause
for the oscillatory activity observed in the degenerate retina. How the electrical coupling between each cell
type affects the RGC output is quantified in Table 5.4. Increasing the conductance of Aii GAC-ConeBC GJs
from 0.2 nS to 0.7 nS led to an increase in the post-stimulation RGC firing rate of about 2 Hz. The blockage
of different GJ groups also affected the RGC firing rate during the light stimulation. The maximum rate
was 190 Hz while all GJs were active and blocking either Aii GAC-ConeBC or Aii GAC-RodBC GJs led to
a decreased rate of 2 Hz and 6 Hz, respectively.
Gap Junctions Peri-Stimulation Post-Stimulation Post-Stimulation
GJ conductance 0.2 nS GJ conductance 0.7 nS
All GJs Active 190 Hz 12 Hz 14 Hz
Aii-Aii GJs Blocked 190 Hz 12 Hz 14 Hz
Aii-CBC GJs Blocked 188 Hz 0 0
RBC-Aii GJs Blocked 184 Hz 0 0
Table 5.4: The impact of blocking different gap junction groups and increasing the conductance on the
RGC firing rate peri-stimulation (cone photocurrent active, 2 s < t < 2.5 s) and post-stimulation (cone
photocurrent zero, t > 2.5 s).
5.5 Discussion
1) Rewiring Affects RGCs Response During Low-Light Conditions
An important aspect in understanding retinal disease mechanisms and optimizing the therapeutic approaches based on electric stimulation is to have an accurate computational network model with predictive capabilities. Towards this goal, we constructed a retinal network model that successfully captured
the natural light response within the ON-pathway and used it as “ground truth” to assess the effects of
early-stage degeneration in the signaling patterns of retinal cells. We used connectome data of early-stage
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degeneration to make precise modifications to the synapses by adding the aberrant synapses one at a time,
simulating the effects of cone-RodBCs ribbon synapses and RodBCs-Aii GACs gap junctions on the output
of the RGC. The results showed that aberrant cone-RodBCs synapses did not lead to a significant change in
firing rate of the RGCs, while aberrant RodBCs-Aii GACs gap junctions increased the RGC firing rate when
simulated separately. When both aberrant synapses were included, the overall change in the firing rate
was very close to the gap junction-only case, suggesting that the contribution from aberrant gap junctions
between RodBCs and Aii GACs is the dominant rewiring feature affecting RGC output. The simulations
showed that the ionotropic connections between cones and RodBCs had minimal impact on the firing rate
of the RGC. This was consistent across different cone saturation levels (Fig. 5.4(b)), suggesting that this
conflation of the ON-pathway with OFF-type signals may not significantly affect visual coding during scotopic (dark) and mesopic (dim) conditions. Conversely, the contribution from gap junction degeneration
to the RGC output was proportionally more substantial during low cone saturation levels, corresponding
to dim background conditions. The loss of night vision is among the early symptoms of RP [229, 230]. Our
simulations show that both scotopic and mesopic vision may be affected during early stages of the disease,
at a low cone photocurrent saturation, where the changes in RGC output represent a greater ratio of the
expected natural activity. Presently, the evidence from pathoconnectomics suggests that RodBCs make
pathological GJs with Aii GACs prior to photoreceptor cell loss and Aii GACs alter their synaptic contacts
early in the photoreceptor degeneration phase [231]. If rewiring precedes rod death, it may be possible
to detect disease onset through the changes in RGC activity before symptoms of diminished night vision,
as suggested by Fig. 5.6. This feature is especially relevant for early intervention therapeutics that aim to
preserve the rod photoreceptors as long as possible [232].
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2) Network Depolarization via Aberrant RodBC - Aii GAC Gap Junctions Drives the Rhythmic
Firing of the RGC
Hyperactivity and rhythmic activity of RGCs in the photoreceptor-degenerated retina have been reported in previous studies that show gap junctions play a critical role, summarized in the reviews of aberrant activity in the retina by Zeck [233] and by Trenholm [234]. Previous modeling efforts based on the
known coupling motifs of healthy retina (homocellular Aii-Aii gap junctions and heterocellular ConeBCAii gap junctions) largely lean on intrinsic cellular mechanisms and gap junctions at the Aii GAC – ConeBC
level to explain the rhythmic firing at the RGC [234, 235]. Notably, one study in the rd1 mouse has shown
that a rhythmic activity of up to 9 Hz was triggered by a 2-3 mV increase in the median Aii GAC membrane
potential following removal of ConeBC-Aii coupling [235]. Indeed, a similar conclusion is supported by
our model, where an 8-14 Hz oscillation develops after a 2.4 mV increase in resting potential. Blocking only
the Aii-Aii gap junctions did not impact the rhythmic firing rate whereas blocking the ConeBC-Aii gap
junctions eliminated it (Table 5.4). However, a previously unrecognized gap junction motif in degenerating
retina – the aberrant/novel RodBC-Aii GAC gap junctions [149] – may in fact induce these oscillations by
changing the basal resting potential of Aii GAC cells. Critically, the simulations show that blockage of
RodBC-Aii GAC gap junctions, while maintaining the Aii GAC – ConeBC gap junctions, both prevented
the depolarization of the Aii GAC membrane at steady state and eliminated the rhythmic firing at the RGC
(Fig. 5.7). Furthermore, the rhythmic firing rate observed in the simulations (4-15 Hz) agrees well with the
whole-cell recordings of Aii GACs and RGCs of degenerated retina in the literature [236, 237, 238, 239, 240,
241]. We observe that the depolarization of RodBCs, which normally leads to a transient EPSP on Aii GACs,
instead results in a post-transient potential in the presence of aberrant RodBC-Aii GAC gap junctions, as
long as the rod photocurrent is active. This elevated potential level is transmitted to ConeBCs via their
normal gap junctions with Aii GACs, resulting in an oscillatory firing pattern at the RGC. Together, our
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multi-layered analysis supports the hypothesis that the aberrant connections between Aii GACs and RodBCs, coupled with the elevated steady-state cell membrane potentials during rod activation, are the cause
of the rhythmic firing in the degenerate retina. Our conclusions about the source of aberrant activity agree
with a similar computational study that evaluates later stages of retinal degeneration [242]. Their simulations show that depolarization of the ON-pathway and the Aii GACs lead to a patterned rhythmic activity,
mediated by progressive reduction in the cone photoreceptor count. The authors acknowledge that the
contribution of the rod pathway may be underestimated in their model, and that rod-driven oscillations
might occur in earlier stages where partial loss of rods depolarize the Aii GACs to an intermediate state.
This is indeed what we have observed in this study, where We reach the same conclusion on the rhythmic
activity, albeit the depolarization was mediated by the new aberrant RodBC- Aii GAC gap junction motif.
3) Aberrant Activity Scales with the Intensity of Rod Signal and Gap Junction Conductance
Our computational model was designed to address uncertainties inherent in the connectome data.
Given the classification of numerous photoreceptor synapses as indeterminate and our focus on the degeneration of the rod pathway, we conducted a series of simulations by varying the number of rod inputs.
These simulations yielded valuable insights into the threshold conditions and saturation levels essential
for observing aberrant rhythmic firing in the RGC. Our findings indicated that a minimum rod density of
approximately 7 rods per RodBC was necessary to generate aberrant rhythmic firing. Approaching the
highest observed convergence number for rabbit (100 rods per RodBC) resulted in the saturation of the
rhythmic firing rate, reaching 18-20 Hz. This shows us that the convergence of the rod pathway plays a
critical role in modeling a realistic network. The coupling and receptive areas of RodBCs and Aii GACs
exhibit substantial variation based on light intensity levels and eye size. A recent study highlighted these
variations, revealing a higher convergence of more numerous rods and RodBCs to a single downstream
Aii GAC in macaques compared to mice [220]. This increased convergence led to a receptive area twofold
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greater, maintaining necessary resolution within the same visual angle. Moreover, the same study underscored the impact of light adaptation on the coupling between Aii GACs, modulating a balance between
resolution and sensitivity. We further delved into the influence of gap junction conductance, as our simulations identified RodBC-Aii GAC gap junctions as the source of aberrant firing. Modulating gap junction
conductance had a modest effect on aberrant firing rates, up to 2 Hz (Table 5.4). However, the implications
of variable gap junction coupling between different cell types may become more significant in larger network models with more cells and synapses. Physiologically, a higher gap junction conductance has been
suggested to reduce signal noise between adjacent cells, and a coupled network of Aii GACs can amplify
to small but correlated rod signals [216, 243]. Lastly, we were unable to evaluate the effect of rod-cone
coupling in this study due to the limitations described in section 5.3.3.3. However, other studies provide
insights into the role of these gap junctions, indicating that they act as a smoothing function that can
attenuate noise fluctuations and enhance contrast sensitivity at low spatial frequencies, potentially at the
cost of visual acuity due to the lateral averaging [244]. Both rod and cone signals were detected in each
other, suggesting that the cone photocurrent may not completely reach zero post-stimulation [245]. Had
we included rod-cone gap junctions in our model, the RGC might have exhibited stronger post-stimulation
activity, resulting in a faster firing rate. However, the relatively small scale of our model and the absence
of horizontal cells limit the true impact of photoreceptor coupling on visual coding within the network.
4) Model Limitations and Future Steps
Finally, we acknowledge several limitations in our computational modeling approach and outline the
future steps for its development. One major challenge is modeling the biophysics of degeneration, as the
experimental evidence of how cell responses may vary from their healthy state is limited. Because of this,
the biophysical models used in this study are based on available data from healthy cells obtained through
patch clamp experiments. Incorporating biophysical parameters based on patch clamp recordings from
an early-stage degenerated retina could improve the accuracy of the model for predicting changes in the
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signaling pattern. Another challenge in building a realistic network with consistency is the availability
of models of different cell types from the same species and stimulation protocol. Patch clamp studies
typically focus on individual cells, and recordings of an entire network’s response to the same stimulation
parameters is not readily available. Our study utilizes patch clamp recordings from various aquatic species
to characterize the photocurrent generated in cone photoreceptors, while the membrane potential changes
in cone bipolar cells are modeled based on data from both rabbit and mouse. Thus, the model here is based
on the cellular responses of multiple species, and would benefit from data obtained from the same species
and stimulation protocol for all cell types. The network model presented in this study represents the ON
pathway, and the inclusion of the OFF pathway is equally important in understanding the changes in
signaling caused by degeneration. Our continued efforts focus on including OFF-ConeBCs and OFF-RGCs
in the network model, which will allow the assessment of its response while the photocurrent input is
zero. Furthermore, aberrant synapses were also observed between cell types that control the OFF pathway
(horizontal, GABAergic-amacrine, and OFF-cone bipolar) in RPC1 [149]. Most recently, a new gap junction
motif that occured between Aii GAC and OFF-ConeBC in the RPC1 database was reported [231] and may
have implications towards the response of OFF-RGC as well as the ON-RGC as reported here. The next
steps of the connectomics-simulation study will focus on incorporating these missing cell types together
with the ON-type to assess all aspects of early-stage RP on the network’s output.
The predictive capability of such a computational model will be invaluable towards the development of
therapeutic approaches using electric stimulation. We utilized the AM-NEURON computational platform
in the past, where the neuronal models were integrated with three dimensional bulk tissue models to visualize the induced extracellular potentials and respective cell responses during neurostimulation of retina
and hippocampus [38, 39, 148, 204]. This analysis was used to optimize the waveform patterns for targeted
functions, providing an input/output relationship in electrical stimulation. For instance, transcorneal electrical stimulation, a non-invasive therapeutic method for preserving photoreceptor integrity and slowing
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down disease progression [246, 247], can benefit from rigorously validated predictive computational models to compute the current density generated in the retina and predict the network’s response to it. This
can guide the development of optimized stimulators for maximum efficiency without the need for trials
on live subjects.
5.6 Conclusion
In this work, we proposed a two-stage computational modeling framework to investigate the effects of
retinal degeneration on the signaling patterns of retinal neurons in its early stages. First, we captured
the natural photopic response of the ON-pathway in the baseline retina by combining a validated lightflash stimulation protocol for rods and cones with light-evoked response models of rod and cone bipolar
cells, Aii amacrine cells, and retinal ganglion cells. Second, we utilized pathoconnectomics data to develop
morphologically and topologically precise model of the degenerate retina. Simulation results suggested
that the rewiring in a degenerate network may alter the retina’s visual output as measured at the RGC.
Specifically, aberrant gap junctions in the rod pathway increased the RGC firing rate by depolarizing the
membrane of the coupled cells at rest. A low-frequency oscillatory pattern of 8-14 Hz was observed in
the degenerate network, which is consistent with the Aii GACs and RGC recordings from rd1 and rd10
mice. This suggests that the characteristic hyperactivity of the degenerate retina may largely be due to
the new gap junction motif discovered in our dataset, occuring between the RodBCs and Aii GACs in
the rod pathway. Although the interpretation of how the RGC firing rate can be mapped to different
aspects of vision such as resolution, edge-detection, or color perception is ambiguous, simulations such
as the one presented here can serve as predictive tools for changes in retina’s signaling patterns during
the early stages of degeneration. Early detection of these changes before photoreceptor loss may provide
an improved window of successful intervention and potentially facilitate the development of targeted
therapeutic approaches to correct the aberrant activity and slow down disease progression.
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Chapter 6
An External Circuit Technique for Improving Neurostimulation
Tolerance In Vivo
Chapter 6
E. Iseri, M. Machnoor, T. D. Nguyen, C.e Sideris, K. K. Gokoffski, and G. Lazzi. Improving Stimulation
Tolerance for Implantable Neurostimulators Through Enhanced Capacitive Conduction. IEEE Transactions
in Biomedical Circuits and Systems (Under review, 2024)
6.1 Abstract
Significant interest exists in optimizing electric field (EF) applications in the clinical arena for therapeutics
such to directing regeneration of nerves or eliciting membrane response in the target cells. While larger
voltage gradients in a bipolar stimulation setup were shown to be more effective at neuroregeneration,
neuroprotective effects and neuronal activation, stimulation amplitudes are limited by the subject’s tolerance and safety boundaries of charge injection. Any strategy that can increase the rate of charge delivery
per phase, and remain within safety and tolerance limits, could boost the efficacy of neuromodulation techniques using electrical stimulation. We modeled and simulated two external circuit prototypes to explore
how a neurostimulator can be optimized for maximum current injection by targeting the capacitive region
of the stimulation pulse. We then validated our modeling predictions in vivo by measuring from rats stimulated at the optic nerve. The external circuits connected in series to a two-electrode system effectively
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reduced the time constant of the current waveform, leading to a phase shift towards higher frequency in the
Bode analysis. This was confirmed in vivo as the animals tolerated up to 20% greater charge injection on
average in the first 200 µs of a rectangular pulse, where more capacitive than faradaic charge transfer takes
place, corresponding to the high-frequency regime in the Fourier domain. Enhancing voltage-controlled
neurostimulators using an external circuit design can be a promising approach to overcome previous limitations to translating EF application to the clinical arena. As electrotherapy techniques require a threshold
of EF amplitude for regeneration, any improvement in the tolerance of conscious subjects will contribute
to the effectiveness of these treatments.
6.2 Introduction
Application of electric field (EF) in the clinical setting has exhibited success across various domains of
neuromodulation such as treatment of neurological disorders, regeneration of nerve tissue damage and
neuronal activation. While EF-based techniques for neural stimulation are widespread, certain methodologies face limitations due to their high amplitude requisites for ensuring efficacy. Delivering adequate
charge to achieve the desired therapeutic effects becomes challenging, particularly when balancing longterm feasibility and the patient’s tolerance towards implanted devices. For example, there is growing
interest in advancing EF applications as a pioneering technology guiding axon regeneration within the
nervous system. A large body of research has revealed that nerve axons are electro-sensitive and grow
towards the more negative potential in the presence of an EF [248, 249, 250, 251]. Despite concerted efforts to mimic endogenous EFs and exploit cellular responses for directing skin wound healing, spinal
cord regeneration, and more recently, optic nerve regeneration [252, 253], proposed EF therapies have encountered hurdles in transitioning to clinical practice. One barrier impeding the clinical translation of EF
applications is the accumulation of excessive toxic charge from the stimulating system, potentially causing
discomfort to subjects and risking damage to electrodes. Specifically, previous studies were successful in
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eliciting cellular responses and regeneration by using direct current (DC) [254, 255]. However, the toxicity
arising from charge accumulation limits the voltage amplitudes that can be safely employed, consequently
curbing both efficacy and translatability [256]. Additionally, challenges associated with nervous system
stimulation stem from constraints on electrode size. The central nervous system has low space tolerance,
necessitating the use of small electrodes. While these enable precise targeting with minimal off-target
tissue activation, they exhibit higher impedance and charge density, leading to elevated levels of toxic
currents [257, 258, 259, 260]. One strategy to enhance the safety profile of an electrical stimulator is to employ alternating current (AC), which, being charge-balanced, offers a safer alternative to DC stimulation.
While some studies have demonstrated mild visual gain with AC stimulation of the optic nerve [261], these
strategies often result in non-specific stimulation. In fact, certain studies indicate that AC may even delay
healing of epithelial skin wounds [262]. Alternatively, the application of asymmetric, charged balanced
(ACB) biphasic waveforms presents a promising strategy for directing wound healing because they combine the benefits of DC and AC. These waveforms generate preferential voltage gradients in the direction
of desired growth, traditionally achieved using DCs, while maintaining the safety of charge-neutrality,
traditionally achieved using ACs. In this study, we employ an ACB waveform previously shown to effectively direct axonal growth towards the cathode [51] utilizing it as our test case for in vivo stimulation.
We propose an external circuit enhancement approach to maximize the total charge injected within safe
tolerance limits. This study proceeds by initially presenting an overview of electrical stimulation safety
from an equivalent circuit model perspective and discusses leveraging the charge delivery mechanism to
enhance tolerance. Subsequently, it describes the methodology used to evaluate design choices when considering a voltage-controlled stimulation protocol. Further, the proposed systems are modeled using both
frequency and time domain simulations, and their efficacy in neurostimulation is validated through in vivo
experiments.
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6.3 Methods
6.3.1 Approaches for Improving Stimulation Tolerance and Efficacy
Electrical stimulation therapy in conscious subjects involves a delicate balance between achieving the required stimulation amplitude for effective treatment and managing the potential discomfort it may cause.
This becomes especially challenging in animal experiments, where any perception of external stimuli, even
if not painful, can lead to shock and stress. Consequently, optimization of stimulation parameters to ensure tolerance is a fundamental aspect of in vivo studies. This optimization can be realized by tailoring
waveform parameters or employing external circuitry to control the rate of charge delivery into the stimulated tissue, which demands the electrical modeling of an implanted electrode system. In this context, we
explore two external circuit strategies for manipulating the equivalent parameters of the electrochemical
circuit model and discuss their applications in enhancing tolerance to electrical stimulation.
6.3.1.1 Electrode Equivalent Circuit Model
A two-electrode stimulator can be modeled as an equivalent circuit comprised of resistive and capacitive
elements that account for the electric properties of the electrolyte (tissue) and the electrochemical interface between the electrodes and the tissue. This widely used equivalent electrical circuit model, known as
the Randles circuit, includes an electrolyte resistance (Rs) in series with a shunt double-layer capacitance
(Cp) and a double-layer resistance (Rp) (Fig. 6.1) [263]. This model serves as the foundation for understanding the stimulator’s frequency response. The equivalent system impedance influences the charge
transfer dynamics at different time intervals. From a circuit perspective, current can either flow through
the capacitor, known as capacitive conduction, or through the resistor, known as faradaic conduction.
Stimulation safety depends on the form of charge transfer at the interface. Capacitive conduction, involving the charging/discharging of the capacitor and a redistribution of charged particles in the electrolyte
without electron transfer, is considered the safe stimulation region, whereas faradaic conduction, taking
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Figure 6.1: A neurostimulator setup typically demonstrates the characteristics of an RC circuit. (A) An example of the potential that develops across the electrodes and the resulting current flow when stimulating
with a voltage-controlled charge-balanced asymmetric biphasic pulse. The potential across the resistor R1
is equivalent to the input current of the system when divided by 1 kΩ. (B) The equivalent circuit model
of the stimulator. Tissue resistance Rs can be approximated through voltage divider calculation at t = 0,
when the reactance of the capacitor is zero. Next, double layer capacitance Rp can be approximated the
same way when the reactance becomes large approaching the low-frequency limit (roughly at t = 1 ms).
Double layer capacitance Cp can be approximated by first measuring the time constant τ of the current
waveform during discharge, shown in (A). The Thevenin equivalent resistance can then be calculated to
solve for Cp through τ = Rth × Cp.
place across the resistor, involves electron transfer and may potentially harm the tissue by altering its
chemical balance through redox reactions [264]. Any approach directed towards improving the stimulation safety and tolerance must then shift the charge transfer ratio towards the capacitive regime, which
is dominant at higher frequencies. A frequency shift can effectively be modeled as the change in the circuit time constant, a function of resistance and capacitance. A shift towards the high-frequency regime,
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where capacitive conduction is dominant, can be achieved by having a shorter time constant, which requires either the resistance or capacitance of the equivalent system to be reduced. Normally, the only way
to manipulate these parameters is to change the electrode’s surface area, which may not be feasible for
implanted devices with a size restriction. We propose an alternative approach to reduce the equivalent
time constant of the stimulator by using external circuits that can modulate the current flow and allow for
using higher amplitudes within tolerance.
6.3.1.2 Stimulation Waveform Design
Charge delivery from the electrode to the tissue can be controlled using two methods. A voltage-controlled
(VC) stimulation will set the electrode potential to the user-defined values and drive a current that is
proportional to the input impedance. Conversely, a current-controlled (CC) stimulation will adjust the
electrode potential to ensure the user-defined current value is delivered through the equivalent input
impedance. Because its impedance is highly capacitive, the following equations govern the dynamics of
electrode potential or current flow across the electrode interface:
Ic(t) = Cp
dV
dt (6.1)
Iv(t) = Vi
R
e
−t
τ (6.2)
τ = RthCth (6.3)
The CC input current (Ic) is a linear function of the change of capacitor voltage (V(t)) over time, which
must be positive to keep the current constant. The shunt capacitance is assumed to be ideal and constant
at a given frequency; however, electrochemical impedance spectroscopy analysis for Pt microelectrodes
suggests that Cp is non-ideal and its value changes with frequency [265]. VC input current (Iv) is an
exponential function of the initial capacitor voltage (Vi
) and the time constant (τ ) of the system, which is a
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product of the Thevenin equivalent series resistance (Rth) and equivalent capacitance (Cth). Iv will decay
exponentially when the voltage is kept constant, rate of which depends on τ . The mechanism of the current
flow at the interface must be considered when choosing the optimal stimulation method. The CC method
is commonly used for generating electrical fields across the target area or stimulating excitable tissue in
the form of pulsing [266]. The main advantage of delivering a current-controlled pulse is its immunity
to variations in the system’s impedance as long as the input amplitude remains within the compliance
voltage range of the stimulator [267]. The same consistency cannot be achieved with a VC stimulator as
any change or fluctuation in the input impedance will impact the input current. Moreover, due to the
capacitive nature of the electrode interface, the input current will be maximum at the pulse onset and
decay rapidly as the capacitor voltage saturates, as described in equation 6.2. Despite these limitations,
there are advantages to using a VC stimulation method from a safety and tolerance perspective. Notably,
it is easier to adhere to the safety limits for electrode polarization (water window) as the amplitudes are
user-defined and unrecoverable charge accumulation in the tissue is minimized thanks to the discharge of
the working electrode through shorting with the counter electrode during the interpulse interval [266].
Here, we investigate another possible advantage of VC over CC stimulation, offering greater rate of charge
injection during the high-frequency regime of the pulse. This approach leverages the charge flow dynamics
through the electrochemical interface and maximizes the capacitive conduction, thereby increasing the
tolerance threshold to stimulation. The following subsection describes how the ratio of capacitive-tofaradaic conduction can be increased with VC waveforms using external circuitry that effectively change
the τ of the system. The same approach cannot be applied towards the CC method due to its inherent
feedback mechanism for keeping a constant current and the focus of this study will be limited to the VC
method.
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6.3.1.3 Proposed Circuit Design for Improving Stimulation Tolerance
The goal of connecting an external circuit to an electrode stimulator is to change its equivalent resistive and capacitive parameters such that the time constant becomes smaller and the system effectively
operates closer to the capacitive, high-frequency regime. When considering a parallel RC circuit, the highfrequency regime corresponds to the time interval shortly after the pulse onset; the capacitor’s reactance
will increase over time, representing a decreasing frequency, while the shunt resistance remains constant.
The interval at which the capacitor reactance is less than the shunt resistance can be considered as the
high-frequency interval, where capacitive conduction is dominant. The circuits described here aim to
improve the stimulation tolerance at this operating point.
6.3.1.4 Active Circuit Design.
The first component of τ is Rth, which corresponds to the combination of tissue resistance and shunt resistance from the interface. Rth of the stimulator in Fig. 6.1(b) is approximated as Rs//Rp by a Thevenin
equivalent circuit. Reducing Rp is not possible without changing electrode properties and reducing Rs is
not feasible without altering the electrical properties of the target tissue. However, it is possible to introduce a "negative" resistance into this equivalent circuit by employing active circuit components capable
of adding energy into the system and reversing the electrode polarity while maintaining the current flow
direction. We have harnessed this concept to design a non-Foster circuit, serving as a negative impedance
converter, effectively reducing Rth of the stimulator. As per Foster’s reactance theorem, passive twoterminal devices must have a positive slope of susceptance with respect to frequency and any elements
that have a negative slope violate this property and are called non-Foster elements [268]. A “negative”
capacitor with an impedance of j/ωC, inductor with impedance -jωL, and resistor with resistance -R would
be referred to as non-Foster elements. Non-Foster components cannot be passive and require an active
circuit design. For instance, Linvill’s Negative Impedance Converter (NIC) circuit utilizes a cross-coupled
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Figure 6.2: Schematic of a typical NIC circuit. Conditions necessary to achieve a negative input impedance
are described. The simulations demonstrate that the NIC is equivalent to a series negative resistor, where
the input current between the standard system with Rs = 1 kΩ is the same as the NIC system with Rs
= 2 kΩ and Rload = 1 kΩ. The same resistance value Rf = 12 Ω was used for R1 and R2 to satisfy the
conditions of equation 6.6.
transistor to negate the RC network at the output [269]. Active circuits for generating non-Foster elements
work on the principle of inverting current through their load while maintaining the voltage drop across
it or vice versa, effectively negating the load impedance [268], as demonstrated in several NIC designs
[269, 270, 271]. Such circuits have been successfully applied to enhance the bandwidth [272, 273, 274],
improve signal to noise ratios [275], and improve the quality factor [276] in RF and antenna applications.
Our NIC design employs an operational amplifier (op-amp) as its active element, enabling the generation
of negative resistance. This provides additional degrees of freedom compared to linear passive impedance
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matching elements, as it can deliver power gain and negative impedance. The operating conditions of the
NIC design is summarized as follows:
I1 =
Va − Vout
R1
(6.4)
I2 =
Vout − Vb
R2
=
Va
R3
(6.5)
F or R1 = R2 , Va = −I1R3 (6.6)
The op-amp output voltage (Vout) must be solved to determine the equivalent circuit the NIC generates.
Because an op-amp drives a current from its output terminal, it keeps the voltage at both input nodes the
same (Va = Vb), preventing current flow into or out of either input terminal. Manipulating the equations
6.4, 6.5) and recognizing that I2 will also flow through R3, the circuit can be simplified as shown in (6).
When a positive voltage is applied at Va, the current will flow from the ground terminal to the voltage
input, effectively becoming a negative resistance. Simulations demonstrate that the op-amp can reverse
the polarity of the node V− while maintaining the current flow direction, effectively generating negative
resistance (Fig. 6.2(b)). The input current of a standard system with Rs = 1 kΩ was simulated to be the
same as the standard system having Rs = 2 kΩ in series to a NIC with Rload = 1 kΩ. This demonstrates
that the negative resistance generated is ideally equal to Rload. Although the active elements confer the
power gain and generate the negative impedance, they can also decrease the electrical stability of the
system [277, 278, 279]. The electrical instability stems from impedances within the system. Resistance
Rload can be tuned by keeping all the other impedances fixed to achieve a negative value. It is noted that
there is a threshold for Rload beyond which negative feedback converts to positive feedback, leading to
136
instability. Thus, a potential limitation to using NIC is its inherent electrical instability if Rload is too large.
The stability criteria to avoid positive feedback is as follows:
B+ =
V+
Vout
=
Rload
Rload + Rf
(6.7)
B− =
V−
Vout
=
Zchannel
Zchannel + Rf
(6.8)
B− > B+ , Rload < Zchannel = Rs (6.9)
6.3.1.5 Passive Circuit Design.
The second component of τ is Cth, which is equal to Cp of the standard system. Cth can be reduced by
adding a capacitor in series with the electrodes; however, a single capacitor can quickly impede current
flow due to its increasing impedance over time. To maintain a continuous current path across the shunt
resistance as the reactance grows, this circuit should adopt the form of a parallel RC configuration. Unlike
the NIC, the RC circuit design relies solely on passive elements, offering an advantage in terms of power
consumption. However, its element values are dependent on the specific interface impedance, which may
vary significantly between subjects and add complexity to their optimization. Moreover, the input voltage must be increased to have a gain over the standard system. This is usually not problem, unless the
waveform generator has already reached its compliance voltage limit. Since the RC circuit is not as easily
tunable in a feedback loop as the NIC’s variable load resistance can be, it is considered more of a theoretical
validation than a practical choice for this study.
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6.3.2 Electrodes, Waveform and Polarity
Platinum wire electrodes (250 µm diameter, Plastics1, Roanoke, VA) were chosen as both stimulating and
ground electrodes due to platinum’s established biocompatibility and low toxicity profile in stimulation
applications [280]. The wire electrodes, being insulated, had a 1 mm length at the tip scraped to expose
the metal, confining the charge transfer area. To ensure stable attachment, the optic nerve electrode was
bent in a hook shape. The amplitude and pulse width of cathodic and anodic phases were adjustable
based on the specific application; in this study, it was tailored to direct axonal migration in a crushed
optic nerve 3. This requires an ACB waveform with cathodic to anodic phase width ratio of 1:4, as it
was the most effective at directing axonal migration (Fig. 6.3) [281]. A monopolar type of connection
was employed because a bipolar connection is not compatible in series with an NIC circuit, necessitating
Rload grounding, upon which the voltage across Rs depends. A VC arbitrary waveform generator (DG822
2-Channel, RIGOL, Portland, OR, 97223) delivered the stimulation waveform. Potentials were recorded
using an oscilloscope (DSOX2014A 4-channel, Keysight, Santa Rosa, CA), which concurrently calculated
the arithmetic subtraction between channels to plot VR, used to determine Iin (Fig. 6.3). High-resolution
acquisition mode was enabled with 150 MHz 10:1 passive probes.
6.3.3 Circuit Simulations
Simulations using MATLAB’s Simulink tool were conducted with the equivalent circuits of each stimulator
system to depict the current waveform among three configurations. The frequency response of each system
was assessed through Bode plots. To simulate a biologically relevant system, the values for the parameters
Rp, Rs, Cp were approximated according to the preliminary experimental data collected from rats, as
outlined in Fig. 6.3. The rats were stimulated using a sufficiently long (∼ 2 ms) monophasic pulse to attain
the saturation level of the input current and a small amplitude (200 mV) to ensure safety (Fig. 6.4). The
values for the resistances and the capacitor were estimated using the method described in section 6.3.1.1
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Figure 6.3: The connection setup along a rat’s optic nerve. The stimulating electrode is hooked on the
nerve while the ground electrode is inserted in the optic chiasm. An ACB waveform with 1:4 phase width
ratio is delivered using a VC waveform generator. The input current is measured across a 1 kΩ series
resistor at the input terminal.
and Fig. 6.1. This equivalent circuit formed the foundation for the standard system, and the NIC and RC
components were introduced in series to manipulate its time constant (Fig. 6.5). The specific values utilized
in the simulations are provided in Table 6.1.
139
Figure 6.4: The equivalent circuit model of the micro-electrode neurostimulator, plotted for one of the rats
tested. The circuit elements are approximated using the measurement waveform and the method outlined
in Fig. 6.1. The values of the elements are setup dependent and must be computed for each subject.
6.4 Results
6.4.1 Circuit Simulations
The equivalent circuits of the standard, NIC and RC systems were simulated using a voltage source and the
input currents were plotted. A monophasic anodic pulse, set at an amplitude of 1 V and a pulse width of
400 µs, was utilized for both the standard and NIC circuits, while the RC circuit used an amplitude of 1.33
V. Notably, within the initial 100 µs of the pulse, both the NIC and RC circuits exhibited a higher current
amplitude compared to the standard circuit. However, all three circuits reached the same saturation level
beyond this time frame (Fig. 6.6). The behavior observed can be elucidated by considering a capacitor’s
voltage-current relationship and the circuit’s time constant, as detailed in section 6.3.1.1 and equations
6.2, 6.3). The NIC system shortens the time constant by reducing the equivalent series resistance Rth and
140
Figure 6.5: The schematics for the three configurations. These circuit models contain ideal elements and
are an approximation of the real system.
the RC achieves the same outcome by reducing the equivalent capacitance Cth. Since the NIC reduces
Rin, which equals to Rs at t = 0 and approaches Rs+Rp at the low-frequency limit when the capacitor
reactance becomes large (Fig. 6.1), Iin reaches its peak at the stimulation onset. As the reactance increases
over time, Rp becomes the dominant contributor to Rin and Iin approaches a saturation akin to both the
standard and the NIC systems. The RC circuit achieves a comparable performance by reducing τ through
C; however, since it only uses passive components, the source voltage must be increased to deliver greater
charge. A stimulation amplitude of 1.33 V yielded an Iin profile similar to that of the NIC system with
a 1 V amplitude and an Rload of 450 Ω, corresponding to a series resistance of -450 Ω, signifying a 33%
reduction of Rs. The frequency response analysis of the three circuits validates the mechanism facilitating
greater charge injection within the initial 100 µs. Bode plots demonstrate a closely aligned magnitude
141
System Circuit Parameters
Standard
Rs = 1.36 kΩ
Rp = 54.5 kΩ
Cp = 110 nF
Vin = 1 V
NIC
Rf = 12 kΩ
Rload = 450 kΩ
Vcc +/- = +10/-10 V
Vin = 1 V
RC
Rn = 10 kΩ
Cn = 470 nF
Vin = 1.33 V
Table 6.1: Parameters for the simulated systems shown in Fig. 6.5. Same components for the NIC and RC
systems were also used in the in vivo experiments.
response among the three circuits until approximately 5 kHz, beyond which the magnitudes of both the
NIC and RC circuits surpass that of the standard circuit (Fig. 6.7). The difference in magnitude levels after
50 kHz signifies the increased charge injection capabilities conferred by these circuits. Considering that
the conduction in the high-frequency regime is predominantly capacitive, it remains safe and tolerable
for the subject. As the magnitude response remains consistent for all three circuits below 5 kHz, where
faradaic conduction prevails, higher amplitudes can be safely stimulated with the assistance of the NIC
and RC circuits. The impact of these circuits can also be captured by manually changing the values of the
standard circuit’s elements. An NIC load of 450 Ω can be emulated by reducing Rs of the standard system
by the same amount and the RC response can be emulated by reducing Cp and increasing the stimulation
amplitude (Fig. 6.7). In both cases, a phase shift towards higher frequencies occurs, enabling enhanced
charge delivery within tolerable limits.
142
Figure 6.6: Time domain simulation of the input current between the three systems. Total charge is the
area below the curve. The normalized charge for the standard, NIC and RC systems were 1, 1.165 and 1.16
respectively.
6.4.2 In Vivo Testing
Once the electrodes were implanted and the animals could rest and recover for seven days, a tolerance
test was conducted using the three systems. An asymmetric biphasic waveform, ensuring charge balance,
was employed with a phase width ratio of 1:4 and an amplitude ratio of 4:1 (Fig. 6.3). The peak-to-peak
amplitude was gradually increased until observable signs of discomfort in the animals emerged. At the
onset of stimulation, various responses deviating from normal behavior were noted, such as eye squinting, scratching around the implant area, or backing away. An amplitude was deemed intolerable if these
aberrant behaviors persisted for more than a minute. The voltage across the series resistor (Rs) was then
recorded at this amplitude for all three circuits. The total injected charge was determined by calculating
143
Figure 6.7: A linear analysis of Vin/Iin shows the differences in the frequency response of the three systems. The magnitude response of both NIC and RC systems is greater in the high-frequency regime while
the same in the low-frequency as the standard system. The phase response confirms a shift towards the
more capacitive region, signifying the change in the time constant. Either domain can be emulated by
manipulating the standard system’s parameters, where reducing Rs yields the same response as the NIC
and reducing Cp yields the same response as RC. One discrepancy with the RC system is the necessity of
using an additional resistor, which leads to a smaller magnitude and greater phase response in the lowfrequency regime than reducing the Cp of the standard system.
the area under the recorded waveform and dividing by the resistance Rs. Both the NIC- and RC-enhanced
circuits had higher peak amplitudes than the standard circuit and were capable of delivering greater charge
during the first 200 µs of the 400 µs phase duration (Fig. 6.8), aligning with the simulations conducted (Fig.
6.6). On average, the NIC and RC systems delivered 20% and 19% more charge, respectively, compared to
the standard system before the animals demonstrated sensations (Table 6.2). Both the NIC and RC systems demonstrated a comparable enhancement in stimulation tolerance, and their recorded waveforms
concurred with the simulations, indicating a shared operational principle. Both systems reduced the time
constant of the current waveform while achieving higher amplitudes, facilitating greater charge injection
144
Figure 6.8: The input current waveform recorded across the series 1 kΩ resistor for rat #1 at the point
of discomfort (Table 6.2). (a) Both the NIC and RC enhancement techniques lead to greater tolerance
levels. (b) A gain of about 13% over the standard system was observed during the anodic phase in either
approach. This occurs during the initial 0.2 ms of the phase and later decays to the level of the standard
system, signifying that the enhanced tolerance corresponds to the high-frequency regime.
within tolerable limits. The enhancement in tolerance was facilitated by the higher current amplitude
corresponding to the high-frequency regime of the rectangular waveform, where capacitive conduction
dominates across the electrode-tissue interface. The node voltages across the resistor Rs demonstrate the
145
NIC operation (Fig. 6.9). Specifically, the voltage at node A reflects the current flow in a standard system, while node B signifies an ideal electrical ground when Rload is zero. A slight parasitic component
is evident at node B during the pulse due to the NIC circuit’s internal resistance not being precisely zero.
Upon setting Rload to 450 Ω and activating the NIC a polarity reversal occurred at both nodes, effectively
introducing a negative resistance and amplifying the current flow.
Figure 6.9: Principal of operation for the NIC system illustrated. When Rload = 0, the input current is the
same as the standard system, where node B is grounded. When Rload = 450 Ω, the NIC becomes active and
reverses the polarity of node while maintaining the current flow direction.
6.5 Discussion
Our findings demonstrate that enhancing charge delivery within safe limits for awake animals is achievable
by reducing the time constant of the stimulator. As the current waveform approaches asymptotic saturation approximately 200 µs into the phase transition, the increased charge gained from higher current
146
Figure 6.10: The simulation parameters are tuned to obtain a better fit of the experimental data (Fig. 6.8).
This is achieved when the interface capacitance Cp, which normally shouldn’t change, is increased. These
results suggest a possible shift in Cp in reality when an external circuit is connected. A greater interface
capacitance is desirable in terms of safety as it reduces the capacitor reactance, extending the interval of
capacitive conduction.
amplitudes was impactful in the high-frequency regime of the rectangular pulse. Increasing the current
amplitude during this regime where capacitive conduction is dominant may improve the stimulator’s efficacy without compromising safety or tolerance. Both the equivalent circuit estimation (Fig. 6.4) and the
in vivo data (Fig. 6.8) were conducted on the same animal (rat #1). Our simulation estimates regarding
the enhancement in charge delivery aligned with experimental data. The simulations predicted a gain of
approximately 16% for either circuit approach. In vivo trials using the same parameters for NIC and RC
systems recorded gains of 20% and 19% on average, respectively, corroborating the simulations. However,
a notable disparity between the simulations and animal recordings was identified in the non-ideal nature
of the electrode-tissue interface. While the simulations matched the measurements at frequency extremes,
the equivalent time constant varied over time, corresponding to frequencies where the strongest phase
response occurs. The decay of the measured input current waveform was faster at stimulation onset and
147
Total Charge Injected at Sensation (nC)
Rat # Standard NIC RC
1 77 87 86
2 61.2 72.8 N/A
3 37.3 46.1 N/A
4 30.2 N/A 37.5
5 58.6 70 62.5
6 49.6 61 60.8
7 29.1 35.3 37.8
Normalized
Average 1 1.20 1.19
Table 6.2: The total charge tolerated during the anodic phase by each animal between standard, NIC and
RC systems. The total charge is the area under the curve, calculated using trapezoidal integration of the
anodic phase from t = 0.1 ms to t = 0.5 ms (Fig. 6.8).
slower after the 0.5 millisecond mark compared to the simulation waveform (Fig. 6.4). The same phenomenon was observed in a comparable study that also used Pt electrodes with 0.05 mm2
surface area,
where they observed a changing time constant with respect to the measurement method and concluded
that the electrodes cannot be accurately modeled by an RC network with a fixed time constant [265]. Consequently, this discrepancy was reflected in the NIC and RC circuit measurements, where the decay profiles
(Fig. 6.8) were different than the simulated ones (Fig. 6.6). Surprisingly, the larger equivalent time constant
during the low-frequency regime of in vivo data yielded more favorable results than the simulated predictions. Both the NIC and RC systems’ input current waveforms saturated at the same level as the standard
system, contrary to the lower level suggested by simulations, resulting in a gain of 3-4%. Subsequent simulations shed light on potential changes occurring within the actual system. Manually reducing Cp in the
NIC simulation brought the current waveform closer to the real data (Fig. 6.10). Although Cp is typically
contingent upon interface properties and not subject to manipulation using an external circuit approach,
the in vivo data suggested otherwise. Ideal circuits components cannot perfectly simulate the measured
response of a micro-electrode stimulator, making it imperative to acknowledge this limitation when replicating the real response of such stimulators through circuit modeling. The practical application of the
148
external circuit technique presented in this study hinges upon two key factors: i) utilizing a VC stimulator
and ii) employing short phase widths. While a CC stimulator might be more favorable in cases where
the system’s input impedance is anticipated to fluctuate, a VC stimulator remains a viable option when
such variations aren’t a concern. The safety advantages associated with VC stimulation can be particularly advantageous, especially for small-surface microelectrodes. A VC stimulator has its leads grounded
during the interpulse interval, thereby dissipating residual charge via capacitive conduction, whereas a
CC stimulator maintains a high impedance that hinders the discharge [264]. The grounding property
of the VC stimulator prevents a steady-state voltage offset, which could otherwise indicate charge accumulation in tissues, particularly in scenarios involving smaller electrode areas. Short phase widths find
relevance across various branches of electrotherapeutics. For instance, in deep brain stimulation (DBS),
phase widths shorter than 100 µs are preferred. Clinical trials on patients with Parkinson’s disease have
shown comparable therapeutic efficacy between pulse lengths of 30 µs and 60 µs, the shorter pulse length
being more energy efficient [282]. The efficacy of DBS heavily relies on achieving the required stimulation
amplitude while minimizing potential damage caused by charge injection. A clinical study using thalamic
DBS concluded that a shorter pulse was more effective in reducing stimulation-induced ataxia compared to
longer pulse widths [283]. A VC stimulator, augmented by the proposed external circuit approach, can help
achieve the threshold amplitude for effective therapeutics while keeping the phase width short for safety
or tolerance. Given the variability of the equivalent system impedance among subjects, a feedback-based
design becomes imperative for the practical implementation of the proposed method. As depicted in Fig.
6.1, estimating the equivalent tissue and interface resistances from the input current waveform is crucial.
A system capable of monitoring these parameters’ changes and adjusting the waveform shape accordingly
is pivotal in maintaining consistency during stimulation. The NIC system, with its tunable Rload, facilitates this feedback mechanism. However, it’s important to note that the NIC system demands additional
power requirements due to the necessity for a high voltage range (+/- 10 V) for the operational amplifier.
149
This requirement might entail a separate DC power supply or a larger battery, potentially compromising
the stimulator’s compactness and portability. Ensuring stability criteria when utilizing an operational amplifier is crucial. Preventing positive feedback can be achieved by integrating a microcontroller into the
design, regulating the variable resistor based on the measured output. On the other hand, the RC system
introduces complexity by necessitating simultaneous tuning of all its parameters (Rn, Cn and Vin). This
complexity, involving the adjustment of both a variable resistor and a capacitor while accommodating the
input voltage, elevates the design’s susceptibility to errors. However, the lower complexity usually takes
precedence over equipment limitations, favoring the NIC design in most applications due to its tunability.
Overall, the NIC design stands as a preferable choice in various applications, despite potential equipment
limitations, owing to its tunability and lower complexity.
6.6 Conclusion
An external circuit design was proposed to improve tolerance to electrical stimulation for in vivo and
clinical studies. We evaluated two different approaches that can reduce the time constant of the current
waveform, thereby allowing for greater charge injection during the high-frequency regime of a rectangular
pulse. Both the series negative resistance generated using an NIC circuit and the series capacitance added
using an RC circuit led to a reduced system time constant. This reduction shifted the input current towards
a higher frequency regime and allowed for greater charge injection during the first 200 µs of the phase. The
outcome of this study is relevant for neurostimulators that use VC waveforms and stimulation protocols
that consider a fast charge injection, with phase widths less than 200 µs. Because electrotherapeutics such
as deep brain stimulation, axonal regeneration and promotion of neurotrophic factors typically require a
threshold amplitude, and these amplitudes may exceed tolerance limits of awake subjects, any improvement in the total charge injection capacity can be valuable for improving efficacy. This study demonstrated
that 20% greater charge on average can be applied using the external circuit enhancement.
150
Chapter 7
Summary and Future Steps
ch:conclusions
This dissertation delved into the neuromodulation of retinal neurons, providing a comprehensive exploration through both computational models and experimental techniques. The primary objective was to
understand how electrical stimulation can strategically influence neuronal behavior. The culmination of
both computational and experimental investigations in this dissertation yielded clinically applicable neuromodulation methodologies. Computational modeling played a crucial role in designing and optimizing
our stimulation protocols, allowing exploration of neural responses to electrical stimulation before animal
testing. Our findings highlighted the tissue-level responses to extracellular electrical stimulation and the
network-mediated reactions of degenerating retinal neurons. This work particularly focused on: i) the
stimulation of damaged axons of retinal ganglion cells, ii) the stimulation of photoreceptors in a degenerating retina, and iii) understanding signaling in the degenerate retina through computational modeling.
Additionally, the capacitive charge transfer characteristics of a microelectrode neural interface were investigated through equivalent circuit modeling, proposing a design to improve the ratio of capacitive to
faradaic current during a monophasic stimulation pulse.
Chapter 2 presented an effective waveform to direct axon growth, demonstrated in vivo on an optic
nerve crush model in Chapter 3. The novelty was in the utilization of asymmetric charge-balanced waveforms, which generated sufficient imbalance in the electric field direction to promote migration while
151
adhering to safety limits of charge injection. Chapter 4 explored alternative electrode designs to the conventional transcorneal electrical stimulator for targeting the retina to maximize the induced current density
near the photoreceptor layer. Computational results, validated by in vivo measurements, provided insight
into the requirements for electrode design of a neuroprotective stimulator yielding consistent outcomes in
animal studies. Chapter 5 introduced a computational model of the degenerate retina during early-stage
retinitis pigmentosa, utilizing precise cell morphology and topology annotated from TEM images. The
network model simulated the aberrant rhythmic activity observed in the rd1 and rd10 mice models, serving as a benchmark for predictive analyses on how signaling changes in the retina during the early stages
of the disease. The presented model’s predictive capability is an important step towards the development
of therapeutic approaches to correct aberrant signaling and slow down disease progression. Finally, Chapter 6 investigated the possibility of increasing the capacitive charge transfer ratio in a neural interface by
manipulating the effective time constant. A negative impedance converter connected in series with the
electrodes generated an equivalent negative resistance, reducing the system time constant while increasing
the maximum current amplitude in a voltage-controlled stimulator. A 20 % gain in the total charge injected
was achieved using this method, validated experimentally on rats using the same stimulation protocol as
presented in Chapter 3.
Despite longstanding efforts in developing electrical field (EF)-based therapeutics and neuroprosthetics for the visual system, the intricate variability and complex physiological mechanisms of different cell
types pose challenges in adopting generalized approaches. Consistent physiological outcomes are vital for
the clinical adoption of novel research ideas, requiring both application- and patient-specific stimulation
design. Tailored stimulation parameters are essential to elicit specific responses from diverse cell groups.
Moreover, the electrochemical mechanisms of charge transfer, characterized by significant non-linearity,
must be thoroughly understood when designing stimulators interfacing with neural tissue. A significant
152
challenge in the development of prosthetics for complex neuronal networks, such as the retina, lies in controlling responses within a tightly organized and functionally unique cell network. The signal traverses
multiple layers of cells and processing before reaching the visual cortex to form vision, contributing to the
difficulty in target-specific stimulation. Recognizing the unexplored potential in EF-based therapeutics,
our group has directed research efforts toward understanding the physiological mechanisms governing
the regeneration and preservation of retinal cell function through bioelectromagnetics and applied animal
studies. This dissertation presented application-specific bioelectromagnetic models and input-output relationships for stimulation amplitude vs. generated current densities at the target tissue through equivalent
circuit approximation.
While the models discussed here were successful in predicting the electric field distribution in tissue
and the resulting neuronal responses, there is potential for improvement, particularly in our understanding of the intracellular mechanisms that drive neuroregeneration and neuroprotection. Future work will
encompass experiments such as patch clamp measurements to isolate membrane currents and evaluate
their contribution toward directional regenerative processes. The development of predictive computational models for humans is the natural next step for our work, where an optimized electrode design that
can be translated into clinical trials is the ultimate goal.
153
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Abstract (if available)
Abstract
The human nervous system is vulnerable to irreversible damage which may result from physical trauma or degenerative disorders, culminating in the loss of neurological functions. Recovery from damage to the central nervous system (CNS) is challenging, given its inherent incapability for regeneration. Conversely, while the peripheral nervous system (PNS) can regenerate itself, severe damage may still result in permanent loss or distorted regeneration, leading to functional deficits. In such scenarios, external interventions are necessary to stimulate cellular responses to activate growth factors and overcome inhibitory cues to facilitate complete regeneration. The field of electrotherapy has evolved considerably, offering promising avenues for addressing neurological impairments. The application of externally induced electric fields has demonstrated remarkable potential across various domains, ranging from treating neuronal damage to replacing impaired neural function through prosthetics. These advancements stand as pivotal breakthroughs in unraveling the complexities of the human nervous system and the development of neural prostheses.
While electrical stimulation has found widespread application in stimulating tissues at easily accessible sites and yielding straightforward functional outcomes for some neural implants, challenges persist when attempting to target tissues with limited accessibility and evoke desired functional responses within complex neuronal networks. This dissertation introduces innovative approaches in neuroregeneration and neuroprotection using electrical stimulation, specifically tailored for the visual system—from the retina to the optic nerve. Distinct stimulation strategies involving electrode and waveform designs for each application are presented, supported by rigorous computational models and experimental validations. The three-dimensional Admittance Method (AM) computational platform developed for solving large scale bioelectromagnetic models is used in conjunction with the NEURON simulation environment for simulating responses of individual neurons to an induced extracellular electric field. Moreover, the study employs a connectome-based network model of the degenerating retina, leveraging the AM-NEURON simulation platform to decipher underlying signaling patterns during retinitis pigmentosa. The primary goal is to gain insights for optimizing therapeutic interventions during the early-stage of the disease. Lastly, this work explores an innovative external circuit design aimed at enhancing the tolerance to electrical stimulation. The proposed design optimizes the mechanism of charge injection, holding significant promise in improving the effectiveness and safety of stimulation protocols.
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Iseri, Ege
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Therapeutic electrical stimulation strategies for neuroregeneration and neuroprotection of retinal neurons
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Viterbi School of Engineering
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Doctor of Philosophy
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Biomedical Engineering
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2024-05
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transcorneal electrical stimulation