Modelling the effect of gap junctions on tissue-level cardiac electrophysiology

When modelling tissue-level cardiac electrophysiology, continuum approximations to the discrete cell-level equations are used to maintain computational tractability. One of the most commonly used models is represented by the bidomain equations, the derivation of which relies on a homogenisation technique to construct a suitable approximation to the discrete model. This derivation does not explicitly account for the presence of gap junctions connecting one cell to another. It has been seen experimentally [Rohr, Cardiovasc. Res. 2004] that these gap junctions have a marked effect on the propagation of the action potential, specifically as the upstroke of the wave passes through the gap junction. In this paper we explicitly include gap junctions in a both a 2D discrete model of cardiac electrophysiology, and the corresponding continuum model, on a simplified cell geometry. Using these models we compare the results of simulations using both continuum and discrete systems. We see that the form of the action potential as it passes through gap junctions cannot be replicated using a continuum model, and that the underlying propagation speed of the action potential ceases to match up between models when gap junctions are introduced. In addition, the results of the discrete simulations match the characteristics of those shown in Rohr 2004. From this, we suggest that a hybrid model -- a discrete system following the upstroke of the action potential, and a continuum system elsewhere -- may give a more accurate description of cardiac electrophysiology.Comment: In Proceedings HSB 2012, arXiv:1208.315

Electrokinetic Lattice Boltzmann solver coupled to Molecular Dynamics: application to polymer translocation

We develop a theoretical and computational approach to deal with systems that involve a disparate range of spatio-temporal scales, such as those comprised of colloidal particles or polymers moving in a fluidic molecular environment. Our approach is based on a multiscale modeling that combines the slow dynamics of the large particles with the fast dynamics of the solvent into a unique framework. The former is numerically solved via Molecular Dynamics and the latter via a multi-component Lattice Boltzmann. The two techniques are coupled together to allow for a seamless exchange of information between the descriptions. Being based on a kinetic multi-component description of the fluid species, the scheme is flexible in modeling charge flow within complex geometries and ranging from large to vanishing salt concentration. The details of the scheme are presented and the method is applied to the problem of translocation of a charged polymer through a nanopores. In the end, we discuss the advantages and complexities of the approach

Astrocytic Ion Dynamics: Implications for Potassium Buffering and Liquid Flow

We review modeling of astrocyte ion dynamics with a specific focus on the implications of so-called spatial potassium buffering, where excess potassium in the extracellular space (ECS) is transported away to prevent pathological neural spiking. The recently introduced Kirchoff-Nernst-Planck (KNP) scheme for modeling ion dynamics in astrocytes (and brain tissue in general) is outlined and used to study such spatial buffering. We next describe how the ion dynamics of astrocytes may regulate microscopic liquid flow by osmotic effects and how such microscopic flow can be linked to whole-brain macroscopic flow. We thus include the key elements in a putative multiscale theory with astrocytes linking neural activity on a microscopic scale to macroscopic fluid flow.Comment: 27 pages, 7 figure