A continuum model of electrical stimulation of multi-compartmental retinal ganglion cells

A multi-scale simulation of retinal physiology

We present a detailed physiological model of the (human) retina that includes the biochemistry and electrophysiology of phototransduction, neuronal electrical coupling, and the spherical geometry of the eye. The model is a parabolic-elliptic system of partial differential equations based on the mathematical framework of the bi-domain equations, which we have generalized to account for multiple cell-types. We discretize in space with non-uniform finite differences and step through time with a custom adaptive time-stepper that employs a backward differentiation formula and an inexact Newton method. A refinement study confirms the accuracy and efficiency of our numerical method. Numerical simulations using the model compare favorably with experimental findings, such as desensitization to light stimuli and calcium buffering in photoreceptors. Other numerical simulations suggest an interplay between photoreceptor gap junctions and inner segment, but not outer segment, calcium concentration. Applications of this model and simulation include analysis of retinal calcium imaging experiments, the design of electroretinograms, the design of visual prosthetics, and studies of ephaptic coupling within the retina.

Optimizing Stimulation Strategies for Retinal Electrical Stimulation: a Modelling Study

In this research, a continuum multi-compartmental model of retinal electrical stimulation was utilized to find the best strategy for activating retinal ganglion cells (RGCs). Two types of return electrodes configuration placed suprachoroidally were used: monopolar and hexapolar. The current was delivered either simultaneously or sequentially with two kinds of waveforms: biphasic symmetric charge-balanced cathodic and anodic first pulses. Our results revealed there is no significant difference in current threshold between single monopolar and hexapolar stimulation regardless of the applied current stimulus waveform. Moreover, sequential stimulation for both monopolar or hexapolar was more effective in reducing current threshold than simultaneous stimulation when biphasic cathodic first pulses were used. Concurrent monopolar stimulation was significant in reducing the current threshold compared to single monopolar whereas concurrent hexapolar did not alter the current threshold. Overall, concurrent monopolar stimulation was efficacious in reducing current threshold regardless of the stimulus waveforms and sequential stimulation was more useful only with biphasic cathodic first pulses.

A Multi-Domain Continuum Model of Electrical Stimulation of Healthy and Degenerate Retina

A continuum multi-domain model of electrical stimulation of the retina is presented and validated against retinal ganglion cell (RGC) excitation thresholds reported in a recently published in vitro experimental study. We applied our model to investigate the response of the RGC layer to electrical stimulation during mid-to-late stage retinal degeneration for both epiretinal and suprachoroidal configurations. Interestingly, our model predicted that suprachoroidal stimulation of the degenerate retina required increased current thresholds, mainly because of the presence of the glial scar layer. In contrast, epiretinal stimulation thresholds were almost similar for both healthy and degenerate models. The latter finding implies that there is no influence of the glial scar layer on epiretinal stimulation current thresholds.

A Multiphysics Biventricular Cardiac Model: Simulations With a Left-Ventricular Assist Device

Computational models have become essential in predicting medical device efficacy prior to clinical studies. To investigate the performance of a left-ventricular assist device (LVAD), a fully-coupled cardiac fluid-electromechanics finite element model was developed, incorporating electrical activation, passive and active myocardial mechanics, as well as blood hemodynamics solved simultaneously in an idealized biventricular geometry. Electrical activation was initiated using a simplified Purkinje network with one-way coupling to the surrounding myocardium. Phenomenological action potential and excitation-contraction equations were adapted to trigger myocardial contraction. Action potential propagation was formulated within a material frame to emulate gap junction-controlled propagation, such that the activation sequence was independent of myocardial deformation. Passive cardiac mechanics were governed by a transverse isotropic hyperelastic constitutive formulation. Blood velocity and pressure were determined by the incompressible Navier-Stokes formulations with a closed-loop Windkessel circuit governing the circulatory load. To investigate heart-LVAD interaction, we reduced the left ventricular (LV) contraction stress to mimic a failing heart, and inserted a LVAD cannula at the LV apex with continuous flow governing the outflow rate. A proportional controller was implemented to determine the pump motor voltage whilst maintaining pump motor speed. Following LVAD insertion, the model revealed a change in the LV pressure-volume loop shape from rectangular to triangular. At higher pump speeds, aortic ejection ceased and the LV decompressed to smaller end diastolic volumes. After multiple cycles, the LV cavity gradually collapsed along with a drop in pump motor current. The model was therefore able to predict ventricular collapse, indicating its utility for future development of control algorithms and pre-clinical testing of LVADs to avoid LV collapse in recipients.