An Extended Bidomain Framework Incorporating Multiple Cell Types

Abstract

The muscular layers within the walls of the gastrointestinal tract contain two distinct cell types, the interstitial cells of Cajal and smooth muscle cells, which together produce rhythmic depolarizations known as slow waves. The bidomain model of tissue-level electrical activity consists of single intracellular and extracellular domains separated by an intervening membrane at all points in space and is therefore unable to adequately describe the presence of two distinct cell types in its conventional form. Here, an extension to the bidomain framework is presented whereby multiple interconnected cell types can be incorporated. Although the derivation is focused on the interactions of the interstitial cells of Cajal and smooth muscle cells, the conceptual framework can be more generally applied. Simulations demonstrating the feasibility of the proposed model are also presented.

A Multiscale Tridomain Model for Simulating Bioelectric Gastric Pacing

“…Domain 1 corresponds to the ICC; domain 2 the SMC; and the third domain the extracellular space. The conservation of current in these three domains can be expressed as [18]: $${\chi }^{false(1false)}\left({\xi }^{false(1false)}\frac{\partial V_m^{false(1false)}}{\partial t}+I_{\mathit{ion}}^{false(1false)}false(u^{false(1false)},{\varphi }_i^{false(1false)},{\varphi }_{e}false)\right)-\nabla ·false({{\sigma }_i}^{false(1false)}\nabla V_m^{false(1false)}+{\varphi }_{e}false)+I_{\mathit{stim}}^{false(1false)}+{\chi }^{\mathit{gap}}{I}_{\mathit{gap}}=0$$ $${\chi }^{false(2false)}\left({\xi }^{false(2false)}\frac{\partial V_m^{false(2false)}}{\partial t}+I_{\mathit{ion}}^{false(2false)}false(u^{false(2false)},{\varphi }_i^{false(2false)},{\varphi }_{e}false)\right)-\nabla ·false({{\sigma }_i}^{false(2false)}\nabla V_m^{false(2false)}+{\varphi }_{e}false)+I_{\mathit{stim}}^{false(2false)}-{\chi }^{\mathit{gap}}{I}_{\mathit{gap}}=0$$ $$-\nabla ·\left({{\sigma }_i}^{false(1false)}\nabla V_m^{false(1false)}\right)-\nabla ·\left({{\sigma }_i}^{false(2false)}\nabla V_m^{false(2false)}\right)-\nabla ·false({\sigma }_i^{false(1false)}+{\sigma }_i^{false(2false)}+{\sigma }_{e}false)\nabla {\varphi }_e$$…”

“…In the full scale stomach simulation of normal slow wave activity, the tridomain formulation was used with parameters as shown in Table I, motivated from a previous study [18]. The conductivity parameters reflect the effect of multiple ICC layers and the resulting impact on the conduction velocity.…”

“…An alternative to the single cell type and extracellular space bidomain formulation that accounts for the multiple cell types present in the stomach has been recently proposed by Buist and colleagues [18], [19]. However, this “extended-bidomain” formulation results in non-symmetric systems of equations, limiting the choice of efficient and stable linear solvers.…”

A Preliminary Model of Gastrointestinal Electromechanical Coupling

“…Slow wave entrainment at higher spatial scales has been simulated using the bidomain equations in several studies [6], [12]. A system of two equations (3 and 4) constitute the basic bidomain model.…”

A comparison of solver performance for complex gastric electrophysiology models

“…Networks of specialized cells called interstitial Cells of Cajal (ICC) generate and propagate these slow waves, and they are conducted to the surrounding smooth muscle cells (SMC) which in turn drives the muscle contraction [1]–[3]. The bidomain reaction-diffusion equations, commonly used in cardiac modeling do not capture the effects of intermingled ICC and SMC cells coupled through gap junctions [4], [5]. Recently, a continuum modeling framework was proposed capable of incorporating two intracellular domains (communicating through gap junctions) and an extracellular space [5].…”