Weakly nonlinear analysis of a reaction-diffusion model for demyelinating lesions in Multiple Sclerosis

TL;DR

This paper investigates how reaction-diffusion models can explain the formation of demyelinating lesions in Multiple Sclerosis through stability analysis and numerical simulations.

Contribution

It introduces a reaction-diffusion model based on kinetic theory and performs a weakly nonlinear analysis to explore pattern formation in MS lesions.

Findings

Key parameters influence pattern types and stability.

Numerical simulations confirm analytical predictions.

Distinct spatial structures emerge under different conditions.

Abstract

Multiple Sclerosis is a chronic autoimmune disorder characterized by the degradation of the myelin sheath in the central nervous system, leading to neurological impairments. In this work, we analyze a reaction-diffusion model derived from kinetic theory to study the formation of demyelinating lesions. We perform a Turing instability analysis and a weakly nonlinear analysis to investigate different spatial patterns that may emerge. Our study examines how key parameters, including the squeezing probability of immune cells and the chemotactic response, impact pattern formation. Numerical simulations confirm the analytical results, revealing the emergence of distinct spatial structures.