Multiple Sclerosis (MS) is a chronic autoimmune disease affecting approximately 1.8 million people worldwide and demands improved tools for diagnosis and disease understanding. This talk presents two complementary computational models addressing distinct challenges in MS research and care. The first focuses on medical imaging and builds upon an MS lesion segmentation dataset \cite{1}. To...
In multiple sclerosis patients, immune cells attack myelinated nerve axons, creating demyelinated regions called lesions. MRI observations show that individual lesions can grow or shrink over time. These lesion dynamics provide important insights into disease progression, as well as the efficacy of treatment. We develop a moving boundary model to represent lesion boundaries as sharp interfaces...
In this talk, I review a class of mathematical models for the early stages of Multiple Sclerosis (MS). A central immunological question concerns the trigger of the immune cascade initiating MS pathology. We compare two scenarios: one based on local microglia activation, recruitment of systemic immune responses, and oligodendrocyte apoptosis \cite{ BBGLPS16,GLRSS24,KhonCal,LBBGPS17}; the other...
We present the derivation of a class of reaction-diffusion models for Multiple Sclerosis starting from kinetic equations for the distribution functions of the cell populations involved in the biological processes underlying the evolution of the disease. The kinetic setting for the cell distributions is outlined, detailing interaction operators that account for conservative and non-conservative...
The mathematical modelling of MS so far has focussed on a few aspects of the disease, but an overall modelling framework is missing. Here we propose a paradigm for the mathematical modelling of MS. Based on biological principles we propose six consecutive modelling levels. We develop models on Level 1,2, and 3, and test if these models can describe known effects related to MS. We first show...
We develop and analyze a nonlinear mathematical model for autoimmune-mediated demyelination in multiple sclerosis that captures interactions between healthy myelin, autoreactive immune cells, regulatory immune cells, and neuronal functional capacity. Immune activation is driven by myelin damage through a saturating response function, while regulatory cells suppress pathogenic activity and...
Multiple sclerosis (MS) is a chronic autoimmune disease affecting almost 3 million people worldwide and causing substantial physical and cognitive disability. In MS, dysregulated immune responses target myelin—the protective coating of neurons—leading to neurodegeneration and progressive neurological impairment. There is currently no cure for MS, and existing treatments are only partially...
