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Multiscale modeling via split-step methods in neural firing
(English)In: Mathematical and Computer Modelling of Dynamical Systems, ISSN 1387-3954, E-ISSN 1744-5051Article in journal (Refereed) Accepted
Abstract [en]

Neuronal models based on the Hodgkin-Huxley equation form a  fundamental framework in the field of computational  neuroscience. While the neuronal state is often modeled  deterministically, experimental recordings show stochastic  fluctuations, presumably driven by molecular noise from the  underlying microphysical conditions. In turn, the firing of  individual neurons gives rise to an electric field in extracellular  space, also thought to affect the firing pattern of nearby neurons.  We develop a multiscale model which combines a stochastic ion  channel gating process taking place on the neuronal membrane,  together with the propagation of an action potential along the  neuronal structure. We also devise a numerical method relying on a  split-step strategy which effectively couples these two processes  and we experimentally test the feasibility of this approach. We  finally also explain how the approach can be extended with Maxwell's  equations to allow the potential to be propagated in extracellular  space.

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Biophysics Computational Mathematics
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URN: urn:nbn:se:uu:diva-332008OAI: oai:DiVA.org:uu-332008DiVA: diva2:1151107
Available from: 2017-10-22 Created: 2017-10-22 Last updated: 2017-10-22
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Bauer, PavolMikulovic, Sanja
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