Computational realization of non-linear diffusion generalizing Barenblatt-Pattle's approach on the case of flows' simulations in elastic microvessels

摘要

The discovery of meningcal lymphatic vessels [Louveau et al, 2015] is one of the most impressive breakthroughs of neurophysiology of last years, and the problem of its functioning is a hot topic far from the complete resolution. In addition, first video recordings in vivo, which allows revealing spatio-temporal dynamics potentially possible, are made available only recently [Castranova et al., 2020]. This talk comprises two main issues in this respect, both of which address the practical sides of computational biophysics and data analysis: ⅰ) the computational analysis of the mentioned video records by means of MATLAB's tools for video and image processing as well as a presentation of its quantitative results; ⅱ) the methodology of numerical simulations of the proposed nonlinear partial differential equation that generalizes the Barenblatt-Pattle's solution for moving fronts spread in porous media on the case of distributed sources and channels with a finite width associated with lymphatic micro-vessels.