Multiscale modelling via split-step methods in neural firing. Issue 4 (4th July 2018)

• Record Type: Journal Article
• Authors: Bauer, Pavol; Engblom, Stefan; Mikulovic, Sanja; Senek, Aleksandar
• Is Part Of: Mathematical and computer modelling of dynamical systems. Volume 24:Issue 4(2018)
• Page Start: 426
• Page End: 445
• Publication Date: 2018-07-04
• Subjects: Computational neuroscience -- Hodgkin–Huxley equation -- stochastic simulation -- multiphysics coupling -- lie-trotter splitting; Engineering -- Mathematical models -- Periodicals; Computer simulation -- Periodicals; 515.39
• DOI: 10.1080/13873954.2018.1488740
• Languages: English
• ISSNs: 1387-3954

Abstract

ABSTRACT: Neuronal models based on the Hodgkin–Huxley equation form a fundamental framework in the field of computational neuroscience. While the neuronal state is often modelled 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.