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

Eugene B. Postnikov; Anastasia I. Lavrova

doi:10.1117/12.2588423

4 May 2021 Computational realization of non-linear diffusion generalizing Barenblatt-Pattle's approach on the case of flows' simulations in elastic microvessels

Eugene B. Postnikov, Anastasia I. Lavrova

Author Affiliations +

Proceedings Volume 11847, Saratov Fall Meeting 2020: Computations and Data Analysis: from Molecular Processes to Brain Functions; 1184706 (2021) https://doi.org/10.1117/12.2588423
Event: Saratov Fall Meeting 2020, 2020, Saratov, Russian Federation

Abstract

The discovery of meningeal 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.

Citation Download Citation

Eugene B. Postnikov and Anastasia I. Lavrova "Computational realization of non-linear diffusion generalizing Barenblatt-Pattle's approach on the case of flows' simulations in elastic microvessels", Proc. SPIE 11847, Saratov Fall Meeting 2020: Computations and Data Analysis: from Molecular Processes to Brain Functions, 1184706 (4 May 2021); https://doi.org/10.1117/12.2588423

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