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:我们展示了一个详细的视网膜生理模型,其中包括光转换、神经电联和眼球几何学的生物化学和电生理学,其中包括光转换、神经电联和眼球几何学。模型是一个基于双面方程式数学框架的局部偏振-椭圆方程系统,我们已普遍地将其分为多个细胞类型。我们以非单式的有限差异和跨步的方式在空间中分解,并使用一种定制的适应性时间步骤,采用落后的分化公式和不精确的牛顿方法。一项改进研究确认了我们数字方法的准确性和效率。使用模型进行的数字模拟与实验结果相比,如对光感光振动和光感缓冲钙等。其他数字模拟表明光受体隔热点与内部段(但不包括外部段)的相位裂裂痕、钙浓度之间的相互作用。这种模型和模拟的应用包括:对视像化成像实验的分析、电视像设计、视像修复术设计、以及视像性视像性视像性静脉图的透图研究。</s>