Speakers
Description
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 that can advance or recede. Existing moving boundary extensions of reaction–diffusion equations, such as the Fisher–KPP equation, typically use a Stefan-like condition in which boundary motion is determined by the flux of cells. Instead, we model the boundary velocity as a function of local cell density, allowing us to represent biological processes where cells degrade or deposit material to move a boundary without being consumed. We observe a variety of behaviours depending on the parameterisation of the boundary velocity function, including regimes supporting multiple invading and receding travelling waves, unstable travelling waves, and receding solutions with population blow-up.
