一般几何的分数电缆方程，一个具有散射和反常扩散的轴突模型
Fractional cable equation for general geometry, a model of axons with swellings and anomalous diffusion
摘要：
不同的实验研究已经报道了脑组织中的异常扩散，并且值得注意的是，这种异常扩散通过分数导数表示。轴突对于理解神经退行性疾病如多发性硬化症、阿尔茨海默病和帕金森病是很重要的。事实上，轴突中蛋白质和细胞器的异常积累是这些疾病的标志性特征。由于这种异常，轴突中的扩散可以变得异常。在这种情况下，轴突中的电压传播受到影响。不同神经退行性疾病的另一个标志性特征是沿着轴突的离散的轴突。为了模拟具有反常扩散和散射的轴突中的电压传播，本文提出了一个适用于一般几何的分数阶电缆方程。这个广义方程取决于分数参数和几何量，例如电缆的曲率和扭转。对于具有恒定半径的电缆，我们表明，当分数效应增加时，电压降低。在有膨胀的电缆中，我们发现当分数效应或膨胀半径增加时，电压降低。当粒子数和分数效应增加时，也得到类似的行为。此外，我们还发现当半径膨胀（或表面层数目）和分数效应同时增加时，电压显著降低。
英文摘要：
Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as multiple sclerosis, Alzheimer's disease and Parkinson's disease. Indeed, abnormal accumulation of proteins and organelles in axons is a hallmark feature of these diseases. The diffusion in the axons can become to anomalous as a result from this abnormality. In this case the voltage propagation in axons is affected. Another hallmark feature of different neurodegenerative diseases is given by discrete swellings along the axon. In order to model the voltage propagation in axons with anomalous diffusion and swellings, in this paper we propose a fractional cable equation for general geometry. This generalized equation depends on fractional parameters and geometric quantities such as the curvature and torsion of the cable. For a cable with a constant radius we show that the voltage decreases when the fractional effect increases. In cables with swellings we find that when the fractional effect or the swelling radius increase, the voltage decreases. A similar behavior is obtained when the number of swellings and the fractional effect increase. Moreover, we find that when the radius swelling (or the number of swellings) and the fractional effect increase at the same time, the voltage dramatically decreases.
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。
