A Multiscale Tridomain Model for Simulating Bioelectric Gastric Pacing

Abstract

Goal Gastric motility disorders have been associated with abnormal slow wave electrical activity (‘gastric dysrhythmias’). Gastric pacing is a potential therapy for gastric dysrhythmias, however, new pacing protocols are required that can effectively modulate motility patterns, while being power efficient. This study presents a novel comprehensive 3D multi-scale modeling framework of the human stomach, including anisotropic conduction, capable of evaluating pacing strategies. Methods A high resolution anatomically realistic mesh was generated from CT images taken from a human stomach. Principal conduction axes were calculated and embedded within this model based on a modified Laplace-Dirichlet rule based algorithm. A continuum based tridomain formulation was implemented and evaluated for performance, and used to model the slow wave propagation, which takes into account the two main cell types present in gastric musculature. Model parameters were found by matching predicted normal slow-wave activity to experimental observation and data. These simulation parameters were applied while modeling an external pacing event to entrain slow wave patterns. Results The proposed formulation was found to be 2 times more efficient than a previous formulation for a normal slow wave simulation. Convergence analysis showed that a mesh resolution of ≈ 0.4 –0.5mm is required for an accurate solution process. Conclusion The effect of different pacing frequencies on entrainment demonstrated that the pacing protocols are limited by the frequency of the native propagation and the refractory period of the cellular activity. Significance The model is expected to become an important tool in studying pacing protocols for both efficiency and effectiveness.

A comparison of solver performance for complex gastric electrophysiology models

“…The conservation of current in and between these three domains following previous studies [5], [6] can be expressed as: $${\chi }^{false(ICCfalse)}true({\xi }^{false(ICCfalse)}\frac{\partial V_m^{false(ICCfalse)}}{\partial t}+I_{ion}^{false(ICCfalse)}true(u^{false(ICCfalse)},{\varphi }_i^{false(ICCfalse)},{\varphi }_{e}true)true)-\nabla \cdot true({\sigma }_i^{false(ICCfalse)}\nabla true(V_m^{false(ICCfalse)}+{\varphi }_{e}true)true)+{\chi }^{false(ICCfalse)}{I}_{stim}^{false(ICCfalse)}-{\chi }^{gap}{I}_{gap}=0$$ $${\chi }^{false(SMCfalse)}true({\xi }^{false(SMCfalse)}\frac{\partial V_m^{false(SMCfalse)}}{\partial t}+I_{ion}^{false(SMCfalse)}true(u^{false(SMCfalse)},{\varphi }_i^{false(SMCfalse)},{\varphi }_{e}true)true)-\nabla \cdot true({\sigma }_i^{false(SMCfalse)}\nabla true(V_m^{false(SMCfalse)}+{\varphi }_{e}true)true)+{\chi }^{false(SMCfalse)}{I}_{stim}^{false(SMCfalse)}+{\chi }^{gap}{I}_{gap}=0$$ $$-\nabla \cdot true({\sigma }_i^{false(ICCfalse)}\nabla V_m^{false(ICCfalse)}$$…”

“…A semi-implicit finite-element discretisation of this coupled continuum model formulation generates a large, highly sparse system of linear equations in the form of Ax = b [6] to be solved for each discrete time-step. x forms the vector of unknowns $V_m^{false(ICCfalse)},V_m^{false(SMCfalse)}$ and ϕ e .…”

“…Recently, a continuum modeling framework was proposed capable of incorporating two intracellular domains (communicating through gap junctions) and an extracellular space [5]. The framework was further refined and was utilized for simulating gastric electrophysiology and effects of pacing [6]. …”

“…There have been extensive studies developing and defining efficient solvers for solving the linear system arising from the bidomain equations [7]–[9]. However, the efficiency of solvers for the system of equations arising from equations arising in gastric electrophysiology context have not been studied [5], [6]. For bidomain problems, preconditioned conjugate gradient solvers with preconditioners ranging from symmetric successive over relaxation to incomplete LU factorization, block Jacobi and multigrid techniques [7] have been proven to be successful.…”

“…Gastric electrophysiology simulations with varying electrical anisotropy and extracellular stimuli in anatomically realistic stomach models were considered [6]. Specifically, we have compared Jacobi, block Jacobi and the BoomerAMG algebraic multigrid method [11] and implemented these in the Chaste [12] modeling framework.…”