视网膜生理的多尺度模拟
A Multi-Scale Simulation of Retinal Physiology
摘要：
我们提出了一个详细的生理模型的视网膜，包括生物化学和电生理学的光转导，神经元电耦合，和球形几何的眼睛。该模型是一个抛物椭圆偏微分方程组的基础上的数学框架的双域方程，我们已经推广到多种细胞类型。我们在空间中离散与非均匀有限差分和一个自定义的自适应时间步进，采用向后微分公式和不精确的牛顿法通过时间的步骤。精化研究证实了我们的数值方法的准确性和效率。使用该模型的数值模拟比较有利的实验结果，如脱敏光刺激和钙缓冲光感受器。其他数值模拟表明，感光细胞间隙连接和内段，但不是外段，钙浓度之间的相互作用。该模型和仿真的应用包括视网膜钙成像实验的分析，视网膜电图的设计，视觉假体的设计，以及视网膜内的ephaptic耦合的研究。
英文摘要：
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.
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