Tuttle, Austin2019-08-202019-08-202019-05https://hdl.handle.net/11299/206356University of Minnesota Ph.D. dissertation. May 2019. Major: Mathematics. Advisor: Yoichiro Mori. 1 computer file (PDF); vii, 126 pages.Cortical Spreading Depression(CSD) is a pathological phenomenon in the central nervous system in which normal cellular function is disrupted by a prolonged depolarization due to massive ionic fluxes. This spreads at a rate of millimeters per minute and is connected to with several medical conditions: migraine aura, stroke, traumatic brain injury, etc. In this thesis we present a multi-phasic continuum electrodiffusion model of spreading depression. The main result of this work is the efficient numerical simulation of 2D and 3D versions of this model. We make use of these simulations by focusing on the introduction of NMDA receptors and their effects on previous findings. From there, we investigate spatial variance of CSD in two ways. First, the natural occurrence of spiral wave patterns in a homogeneous domain. Second, we introduce spatial dependence of parameters to investigate how the varied structure of the hippocampus can impact CSD.enCorticalDepressionModelNMDA ReceptorsSpreadingThesis or Dissertation