High performance computational simulations of gastrointestinal electrical activity

Abstract

Gastric motility, essential for physical propulsion and digestion of food, is coordinated by an underlying electrical activity called slow waves (SWs). SWs are initiated and propagated by specialised cells called interstitial cells of Cajal (ICC) supplying the smooth muscle cells (SMC) with the necessary stimulus for muscle contractions. Gastric dysrhythmias, and hence the role of ICC and SMC, have been linked to the pathophysiology of several functional motility disorders of the gastrointestinal (GI) tract. External delivery of current impulses, for example gastric pacing (high energy low frequency current pulses), is able to modulate the electrical propagation for therapeutic purposes. Multiscale mathematical GI models have been developed to simulate the gastric electrophysiology, spanning from single-cell to full-scale whole organ model. However, realistic stomach models capable of studying gastric pacing with predictive capability have yet to be developed. The main reasons are: the (i) incapability of the underlying cell model in modelling the effects of external current inputs; (ii) conduction velocity of the propagation being primarily dependent on the intrinsic frequency of the cell model; and (iii) large computational requirements in solving spatially and temporally larger gastric electrophysiology simulations. The reaction-diffusion equations coupled with biophysically detailed cell description are solved on large anatomically realistic models, and over a temporal scale ranging up to minutes/hours/days. In this thesis, an efficient cell-model was developed capable of simulating gastric pacing and its effects on normal activity. A new method was presented for modelling SW propagation with a biophysically based reaction term, which was then applied to experimental studies for investigating entrainment, and the effects of gastric pacing on entrainment. Subsequently, an existing open source high performance computing (HPC) library called CHASTE was adapted and developed as a framework for GI electrophysiology simulations. The utility of the newly developed cell model was explored in analysing the structure-function relationship of ICC network from different stages of postnatal development in murine intestine, using ICC imaging data, to quantify how changes in structure may alter ICC network function. An efficient triangulation of ICC network imaging data was developed. This reduced the computational load by reducing the number of degrees of freedom to less than 80% of a previous implementation. Furthermore, an efficient tridomain continuum model was developed that accounted for the two different cell types as seen in gastric musculature, overcoming the single cell type limitations of using a bidomain continuum equations in modelling the GI electrophysiology. The proposed model was found to be 2 times more efficient than a previous formulation. New techniques were developed to employ the tridomain continuum framework for simulating gastric pacing on a anatomically realistic human stomach model. A detailed convergence analysis showed that a mesh resolution of ∼0.4-0.5 mm was required for an accurate solution process. A comprehensive 3D multi-scale modelling framework of human stomach with synthetic fibres was developed for diverse applications including efficiently evaluating pacing strategies. Synthetic muscle fibre directions were calculated and embedded within this model, based on a modified Laplace-Dirichlet Rule based algorithm. It was discovered that the pacing protocols were limited by the frequency of the native propagation and the refractory period of the underlying cellular activity. Finally, the computational performance of different preconditioners for tridomain model was analysed. The block-Jacobi preconditioned conjugate-gradient solver was found to be the most efficient for the simulations in terms of the time-spent (anisotropic problem with extracellular stimulus mean solve time for each time-step: block-Jacobi 0.4 s; Jacobi 1.6 s; and boomerAMG 5.8 s), whereas an algebraic multigrid-based boomerAMG preconditioned conjugate-gradient solver was found to be most efficient in terms of solver iteration count (anisotropic problem with extracellular stimulus mean solver iteration count: block-Jacobi 74; Jacobi 581; and boomerAMG 46). The thesis concludes with a discussion on the results and possible future research directions in the field. In total, this thesis developed an efficient HPC-enabled computational environment for investigating gastric electrophysiology. The methods and framework presented in this thesis will advance the GI modelling studies in conjunction with clinical experiments, specifically to improve the pacing strategies/protocols of existing pacing devices, and also other diverse studies to improve the diagnosis and treatment of patients with functional and GI motility disorders.