Speakers
Description
Multiple sclerosis is characterised by the formation of localised lesions in the white matter of the brain and spinal cord, resulting from immune-mediated damage to nervous tissue. Mathematical models that incorporate the chemotactic migration of immune cells provide a natural framework through which to investigate how such structures can emerge through self-organisation.
In this talk, I analyse a reaction-diffusion-chemotaxis model of multiple sclerosis. Building on previous work demonstrating the emergence of spatial patterns for biologically relevant parameter regimes, I focus on the mathematical mechanisms that govern pattern selection, stability and morphological transitions. In particular, I discuss the role of secondary instabilities, such as Eckhaus and zigzag instabilities. These are known as mechanisms of pattern selection and can account for the formation of defects frequently observed in real patterns. I also present a weakly nonlinear analysis of radially symmetric solutions to characterise the existence and stability of axisymmetric structures that resemble the concentric lesion patterns observed in Balo's sclerosis.
These results demonstrate how tools from pattern formation theory can shed light on the spatiotemporal evolution of immune-driven lesions and emphasise their wider applicability in analysing the emergence and stability of spatial structures within various modelling frameworks, including multiscale and phenotype-structured models.
