### A Simulation of the Electrical Activity of Retinal Tissue and Electroretinogram Design

Adam Stinchcombe

Department of Mathematics

University of Toronto

An electroretinogram (ERG) is a diagnostic test that measures the electrical activity of the neuronal cells of the retina. A light stimulus causes transmembrane currents in the photoreceptors (the rods and cones) and in the other retinal neurons via synaptic connections with the photorecpetors. These currents are detected by electrodes on the surface of the eye. We use an extended bidomain framework to model the whole-tissue electrical activity of the retina. Detailed ionic current models of the rods, cones, and bipolar cells, including the phototransduction pathway and the neuronal connectivity of the retina, are coupled to an elliptic PDE for the electrostatic potential inside the interior of the eye. To numerically integrate the stiff dynamics, we employ an adaptive time-stepping routine, a Newton iteration, and an efficient spatial discretization of the PDE. The simulation provides a physical basis for the a and b waves in ERG recordings used by ophthalmologists to diagnose disease. For ERG recordings indicative of disease, we solve an inverse problem to infer a biophysical basis of the retinal disease. We solve a numerical optimal control problem to design a light stimulus to produce an efficient, patient-specific, and adaptive diagnosis procedure.