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Mathematical modeling of spreading cortical depression: spiral and reverberating waves
Mathematical models of spreading depression are considered in the form of reaction-diffusion systems in two space dimensions. The systems are solved numerically. In the two component model with potassium and calcium ion concentrations, we demonstrate travelling solitary waves and the collision of waves resulting in a large wavefront. With special geometries and timing and location of stimuli we have succeeded in finding reverberating waves and spiral waves which parallel those found experimentally. The six-component model, which contains additionally sodium, chloride, glutamate and GABA, is also investigated in 2 space dimensions, including an experimentally based exchange pump for sodium and potassium. Solutions are obtained without (amplitude 29mM external K$^+$ and with action potentials (amplitude 44 mM external K$^+$). When action potentials are included a somewhat higher pump strength is required to ensure the return to resting state.
Mathematical modeling of spreading cortical depression : spiral and reverberating waves
In: Collective dynamics : topics on competition and cooperation in the biosciences ; a selection of papers in the proceedings of the BIOCOMP2007 International Conference ; Vietri sul Mare (Italy), 24-28 september 2007 Melville, New York : American Institute of Physics, 2008. - pp. 46-64 (AIP conference proceedings ; 1028)