Mathematical Modeling of Cortical Spreading Depression (SD) and Related Phenomena

This workshop will bring together mathematical and computational scientists with experimental researchers studying cortical spreading depression (SD) and related phenomena. SD is a disorder of the central nervous system in which a population of brain cells experience complete depolarization, as associated with a massive redistribution of ion concentrations across the cell membrane. This disturbance spreads at speeds of 2 to 7mm per minute, which is several orders of magnitude slower than the more familiar action potential. Understanding SD is important for several reasons. First, SD is widely accepted to be the physiological substrate of migraine aura and is thus closely linked to migraine headaches. SD or SD-like phenomena also play a significant role in traumatic brain injury, cerebral ischemia, and stroke, all of which are clinically important neurological conditions. Second, an understanding of SD should provide important insights into the homeostatic control of the brain ionic environment and therefore into the workings of the central nervous system. Since its discovery by Leao 70 years ago, SD has been a subject of continuous experimental and theoretical study. However, despite sustained efforts, many fundamental questions remain.

Among the topics to be discussed at the workshop are the relationship of SD to other pathological phenomena, including epilepsy. It is becoming increasingly clear that epilepsy and SD form a pathological continuum, and several attempts have been made in the modeling literature to unify different disease states. This is, however, a potentially difficult theoretical and computational task, given the very fast time scales for seizures spiking and the very slow time scales over which changes in ion concentrations characteristic of SD take place. It should also be pointed out that spatial models of epilepsy and of SD are quite different; epilepsy models often employ neuronal network models reflecting the belief in the importance of network topology, whereas SD models view the nervous system as a homogenized continuum. Other topics to be discussed at the workshop include the biophysical basis of SD and the significance of 2D or 3D spatial patterns in SD, as well as electrophysiological control of SD and related phenomena.