

Preprint 14/2008
Mathematical modeling of spreading cortical depression: spiral and reverberating waves
Henry Tuckwell
Contact the author: Please use for correspondence this email.
Submission date: 10. Feb. 2008
published 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 / L. M. Ricciardi
Melville, New York : American Institute of Physics, 2008. - P. 46 - 64
(AIP conference proceedings ; 1028)
DOI number (of the published article): 10.1063/1.2965101
Bibtex
Abstract:
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.