Multiscale Modelling of Ion Transport Dynamics in Nervous Tissue: An Asymptotic Homogenisation Approach

Alejandro Roque Piedra (University of Glasgow, UK)

Tuesday 21st May 12:20-13:00 Lecture Theatre 116


This research focuses on the overall modelling of ion transport dynamics across cell membranes in nervous tissue. The first section focuses on the homogenised characterisation of nervous tissue, assuming a constant ionic concentration. The starting model is derived from Maxwell’s equations and key aspects of the Poisson-Nerst-Plank (PNP) model. An asymptotic homogenisation approach is employed to account for the multiscale behaviour of nervous tissue. This leads to the identification of a local problem, which is associated with the influence of the microstructure on the membrane potential through effective coefficients. Then, this problem is solved numerically along with the homogenised problem. Benchmark problems are solved for uniaxially oriented axon bundles, representative structures of white matter and peripheral nerves. Furthermore, the propagation of membrane potential is compared for different geometries in the microstructure, mimicking physical changes in white matter due to neurological disorders.

Due to the importance of ionic concentration for studying some neurological diseases, the role of ions is included in a second section to account for the chemical effects on nervous tissue. A model is developed on the limit of electroneutrality, implying that the derived equations are valid in the interior of the extracellular and intracellular spaces and relatively far from the cell membrane. The introduction of ion evolution into the model requires the consideration of two different time scales, associated with ion diffusion and variations of membrane potential. This added complexity results in a new homogenised model where the influence of ionic current and ion diffusion is coupled in the local problem.

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