A comparison of two mathematical models of the cerebrospinal fluid dynamics

TL;DR

This paper compares two mathematical models of cerebrospinal fluid dynamics through numerical simulations and real data validation, analyzing their accuracy and stability in representing brain fluid processes.

Contribution

It provides a detailed comparison and validation of two cerebrospinal fluid models, including mathematical analysis and stability conditions, with real-world data.

Findings

Models accurately simulate cerebrospinal flow and reabsorption.

Mathematical analysis identifies conditions preventing solution blow-up.

Numerical results align well with physiological data.

Abstract

In this paper we provide the numerical simulations of two cerebrospinal fluid dynamics models by comparing our results with the real data available in literature. The models describe different processes in the cerebrospinal fluid dynamics: the cerebrospinal flow in the ventricles of the brain and the reabsorption of the fluid. In the appendix we show in detail the mathematical analysis of both models and we identify the set of initial conditions for which the solutions of the systems of equations do not exhibit blow up. We investigate step by step the accuracy of these theoretical outcomes with respect to the real cerebrospinal physiology and dynamics.