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.

翻译：我们提出了一种详细的视网膜生理模型，该模型涵盖了光转导的生物化学与电生理学、神经元电耦合以及眼球的球形几何结构。该模型是基于双域方程数学框架的抛物-椭圆形偏微分方程组，我们将其推广以考虑多种细胞类型。我们在空间上采用非均匀有限差分进行离散化，在时间上通过自定义自适应时间步进器推进，该步进器结合了后向微分公式和修正牛顿法。一项细化研究证实了我们数值方法的准确性和效率。利用该模型进行的数值模拟与实验结果吻合良好，例如光刺激的脱敏作用和感光细胞中的钙缓冲效应。其他数值模拟还揭示了感光细胞间隙连接与内段（而非外段）钙浓度之间的相互作用。该模型与模拟的应用包括：视网膜钙成像实验分析、视网膜电图设计、视觉假体设计以及视网膜内依突触耦合的研究。