A reaction-diffusion model for relapsing-remitting multiple sclerosis with a treatment term

TL;DR

This paper develops a reaction-diffusion mathematical model for multiple sclerosis, incorporating immune cell dynamics, myelin degradation, and therapy effects, to understand lesion formation and treatment impacts.

Contribution

It introduces a novel reaction-diffusion model with a treatment term for multiple sclerosis, analyzing pattern formation and therapy effects.

Findings

Spatial patterns resembling brain lesions are predicted by the model.

The model shows oscillating patterns that mimic early-stage MS lesions.

Therapy influences the formation and dynamics of these patterns.

Abstract

We present a mathematical study for the development of multiple sclerosis based on a reaction-diffusion system. The model describes interactions among different populations of human cells, motion of immune cells stimulated by cytokines, consumption of myelin sheath due to anomalously activated lymphocytes and its restoration by oligodendrocytes. Successively, we introduce a therapy term representing injection of low-dose IL-2 interleukine. A natural step is then to study the system, investigating the formation of spatial patterns by means of a Turing instability analysis of the problem. In particular, we get spatial patterns oscillating in time that may reproduce brain lesions characteristic of the early stage of the pathology, in both non-treatment and treatment scenarios.