MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Mathematical modeling of spreading cortical depression: spiral and reverberating waves

Henry Tuckwell


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.


Related publications

2008 Repository Open Access
Henry C. Tuckwell

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)