Journal
BULLETIN OF MATHEMATICAL BIOLOGY
Volume 73, Issue 11, Pages 2773-2790Publisher
SPRINGER
DOI: 10.1007/s11538-011-9647-3
Keywords
Cortical spreading depression; Ion transport; Porous media; Partial differential equations; Finite difference solutions
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Funding
- Shanghai Leading Academic Discipline Project [B112]
- MITACS
- NSERC
- NSF
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1022848] Funding Source: National Science Foundation
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Cortical spreading depression (CSD) waves can occur in the cortices of various brain structures and are associated with the spread of depression of the electroencephalogram signal. In this paper, we present a continuum neuronal model for the instigation and spreading of CSD. Our model assumes that the brain-cell microenvironment can be treated as a porous medium consisting of extra- and intracellular compartments. The main mechanisms in our model for the transport of ions into and out of neurons are cross-membrane ionic currents and (active) pumps, coupled with diffusion in the extracellular space. To demonstrate the applicability of our model, we have carried out extensive numerical simulations under different initial conditions and inclusion of various mechanisms. Our results show that CSD waves can be instigated by injecting cross-membrane ionic currents or by applying KCl in the extracellular space. Furthermore, the estimated speeds of CSD waves are within the experimentally observed range. Effects of specific ion channels, background ion concentrations, extracellular volume fractions, and cell swelling on the propagation speed of CSD are also investigated.
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