Mathematical description of concentric demyelination in the human brain: Self-organization models, from Liesegang rings to chemotaxis

Abstract

Baló’s concentric sclerosis (BCS) is an atypical variant of multiple sclerosis (MS) characterized by remarkable concentric demyelination patterns in the white matter of the brain and in the spinal chord. In Khonsari and Calvez (2006), we introduced a very simple model based on cellular self-organization, which reproduced quite accurately the quantitative and qualitative aspects of this disease. The present paper provides more details on the mathematical framework underlying our precedent work. We first review the basics of the chemotaxis aggregation principle and the modeling of the Liesegang rings (LR) phenomenon. We then present our local macrophages recruitment model, which derives from the reconsideration of the classical analogy between LR and BCS. This new model provides several non-obvious insights, such as the link between the level of aggressivity of the disease and the emergence of patterns.