用紧致差分格式求解缆索方程--被动体胞枝晶
Solving the Cable Equation Using a Compact Difference Scheme -- Passive Soma Dendrite
摘要：
树突是大脑中神经元细胞体的延伸，其具有从电和化学区室化到同步检测的多种功能。树突在不同的细胞类型中各不相同，但它们共有的一个共同特征是分支结构。电缆方程是描述枝晶中电压演变的偏微分方程。这个方程的解通常是用有限差分法求得的。谱方法也被用来以更好的精度求解该方程。在这里，我们报告的解决方案，电缆方程使用一个紧凑的有限差分格式，使频谱般的分辨率，可以更容易地使用电缆方程的修改，如非线性，分支和其他形态变换。广泛用于湍流和波传播的研究，这是第一次被用于研究大脑中的传导。在这里，我们讨论它的使用在一个被动的，体细胞树突结构。随着模型复杂性的增加，该方案与中心差分方案相比具有更高的分辨率。
英文摘要：
Dendrites are extensions to the neuronal cell body in the brain which are posited in several functions ranging from electrical and chemical compartmentalization to coincident detection. Dendrites vary across cell types but one common feature they share is a branched structure. The cable equation is a partial differential equation that describes the evolution of voltage in the dendrite. A solution to this equation is normally found using finite difference schemes. Spectral methods have also been used to solve this equation with better accuracy. Here we report the solution to the cable equation using a compact finite difference scheme which gives spectral like resolution and can be more easily used with modifications to the cable equation like nonlinearity, branching and other morphological transforms. Widely used in the study of turbulent flow and wave propagation, this is the first time it is being used to study conduction in the brain. Here we discuss its usage in a passive, soma dendrite construct. The superior resolving power of this scheme compared to the central difference scheme becomes apparent with increasing complexity of the model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
