Modelling of the flux in the brain lymphatic vessels using the Barenblatt-Pattle solution

Abstract

We have used a novel approach to describe pulse flux in the brain lymphatic vessel applying a mathematical analogy to the Barenblatt-Pattle solution of the non-linear diffusion equation that describes gas spreading in porous medium. Such simple mathematical model simulates adequately pulse motion leading to the initial increase of the transversal vessel deformation with following slow lateral distribution. Such approach allows to explain the high velocity motion of the compounds in the brain lymnhatic system.