Multiscale Modelling of Multiple Sclerosis Initiation and Progression

Abstract Multiple Sclerosis (MS) is an autoimmune disease that affects the central nervous system. It can lead to inflammation, neurodegeneration, and physical or cognitive disability. Currently, no cure for MS exists, but medications are available to slow its progression. To date, mathematical modelling of MS has focussed on a few aspects of the disease, but an overall modelling framework is missing. In this paper, we propose a multiscale paradigm for the mathematical modelling of MS. Based on the underlying biological scale, we propose six consecutive modelling levels and develop the first three model levels in this work using systems of ordinary differential equations. We test if these models can describe known effects related to MS disease risk, with particular focus on estrogen, vitamin D, Epstein-Barr virus (EBV) and HLA-DR mutations. We first show that periodic disease outbreaks are possible in this framework through interactions by antigen-presenting cells, regulatory cells and memory B cells. We show that the presence of Epstein-Barr virus infections can initiate the disease, low and high levels of estrogen and vitamin D deficiency can alleviate it, mutations in the HLA-DR gene can promote MS. We can identify a stable steady state of our model as the widely discussed MS prodrome, and we find that memory B-cells play a dominant role in the disease progression. We hope that this framework may serve as a reference for the development and comparative evaluation of future mathematical and computational models of MS. Graphical Abstract Highlights We present a modelling paradigm for MS using systems of ordinary differential equations Based on biological principles, we propose six consecutive modelling levels and develop the first three model levels here. We investigate the link between risk factors, such as HLA-DR mutations, Epstein-Barr virus infection, estrogen levels, and vitamin D deficiency, to MS expression.