SCIENTIFIC PROGRAMS AND ACTIVITIES

Overview

In this workshop, we will bring together a group of researchers from the areas of mathematical modeling and experimentalists in neuroscience to address some of the fundamental issues related to neurovascular coupling and cortical spreading depression (CSD) and related neurological phenomenon. CSD is a slow propagating wave of pathological elevation of extracellular potassium. It is linked to migraine with aura, stroke, and possibly other neurological disorders. The main objective of the workshop is to discuss and incorporate recent advances in experimental studies into mathematical models that are capable of reproducing observed phenomenon and to make predictions that can be verified by further experimental studies.

Frederike Kneer
Nucleation, front and pulse propagation in reaction-diffusion models

To describe CSD by an effective model that also allows for analytical approximations, we study reaction-diffusion waves on curved two-dimensional surfaces and determine the influence of curvature upon the nucleation and propagation of spatially localized waves in an excitable medium modelled by the generic FHN model. We show, that the stability of propagating wave segments crucially depends on the curvature of the surface. Besides, to get deeper insight in biophysical processes involved in CSD, an ion-based Hodgkin-Huxley-type model is used. Focussing on propagation of CSD, we describe spatial coupling by the assupmtion of extracellular diffusing potassium. We find, that this bistable model provides coexisting wave fronts and backs propagating with different velocities. Introducing glial potassium uptake into the model, phasespace structure changes. The hence monostable model has propagating pulse solutions.

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