  We present a detailed physiological model of the 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.
