Electromechanical computational model of the human stomach

TL;DR

This paper develops a comprehensive organ-scale model of human gastric electromechanics by integrating a nonlinear 7-parameter rotation-free shell with a constrained mixture material framework and a two-cell-type electrophysiology model. Spatial heterogeneity is implemented through harmonic-field-based parameter maps for fiber directions, excitability, and diffusion, enabling realistic slow-wave entrainment and region-specific contractions. The authors demonstrate robust numerical convergence and compare element formulations, concluding that the shell offers an effective balance between accuracy and efficiency for large, curved gastric geometries. Fully coupled simulations on a realistic stomach geometry reproduce physiologically plausible slow-wave dynamics, conduction-velocity gradients, and large peristaltic deformations, with open-source 4C implementation paving the way for personalized, clinically relevant in silico studies. Limitations include the absence of fluid-structure interaction and mechanosensitive feedback, suggesting avenues for future work toward more complete and clinically translatable gastric motility models.

Abstract

The stomach plays a central role in digestion through coordinated muscle contractions, known as gastric peristalsis, driven by slow-wave electrophysiology. Understanding this process is critical for treating motility disorders such as gastroparesis, dyspepsia, and gastroesophageal reflux disease. Computer simulations can be a valuable tool to deepen our understanding of these disorders and help to develop new therapies. However, existing approaches often neglect spatial heterogeneity, fail to capture large anisotropic deformations, or rely on computationally expensive three-dimensional formulations. We present here a computational framework of human gastric electromechanics, that combines a nonlinear, rotation-free shell formulation with a constrained mixture material model. The formulation incorporates active-strain, constituent-specific prestress, and spatially non-uniform parameter fields. Numerical examples demonstrate that the framework can reproduce characteristic features of gastric motility, including slow-wave entrainment, conduction velocity gradients, and large peristaltic contractions with physiologically realistic amplitudes. The proposed framework enables robust electromechanical simulations of the whole stomach at the organ scale. It thus provides a promising basis for future in silico studies of both physiological function and pathological motility disorders.

Figures (19)

• Figure 1: Anatomy and microstructure of the stomach. Left: Schematic of the stomach showing key anatomical regions. Right: Cross-sectional view of the gastric wall highlighting its layered structure and the orientation of the circular and longitudinal smooth muscle fibers. This organization informs the fiber architecture in the electromechanical model.
• Figure 2: We define a fictitious reference configuration $\Omega_\textup{R}$ whose geometry is identical to the one acquired through medical imaging, but where we assume that the whole material is free of stress. The shape of the initial configuration $\Omega_0$ is identical to the one of $\Omega_\textup{R}$, so that $\boldsymbol{F}(0) = \boldsymbol{I}$. However, in $\Omega_0$, the body is subjected to physiological loading, which introduces some prestress and thus elastic deformation through $\boldsymbol{F}_\textup{e}^i(0)$. The constant $\boldsymbol{F}_\textup{gr}^i$ generally represent some inelastic deformation from growth and remodeling before time $t=0$. In subsequent, deformed configurations, the deformation gradient additionally comprises an active part $\boldsymbol{F}_\textup{a}^i(0)$, representing muscle contraction. At each point, the material is a mixture of collagen fibers and in longitudinal ($i=\textup{l}$) and circumferential ($i=\textup{c}$) directions, as well as the ground matrix ($i=\textup{gm}$).
• Figure 3: Flowchart of the iterative prestress algorithm for computing for the ground matrix the tensor $\boldsymbol{F}_\textup{gr}^\textup{gm}$ that characterizes the inelastic deformation through tissue formation prior to time $t = 0$ and thus determines the elastic prestress in the loaded configuration at $t = 0$. This tensor is adopted iteratively such that the deformation between reference and initial configuration becomes smaller and smaller until it vanishes within a certain tolerance $\epsilon$.
• Figure 4: Definition of stomach-specific harmonic fields, computed fiber directions, and spatially heterogeneous parameters. (a–c) Harmonic scalar fields computed via Laplace-Dirichlet problems, used to construct stomach-specific coordinate axes: (a) $\phi_\textup{ep}$ from the lower esophageal sphincter ($\Gamma_\textup{eso}$) to the pyloric sphincter ($\Gamma_\textup{pyl}$), (b) $\phi_\textup{fp}$ from the fundus apex ($\Gamma_\textup{fundus}$) to $\Gamma_\textup{pyl}$, and (c) $\phi_\textup{gl}$ from the greater ($\Gamma_\textup{greater}$) to the lesser curvature ($\Gamma_\textup{lesser}$). (d–f) Surface vector fields representing fiber directions and the surface normal direction: (d) longitudinal $\boldsymbol{f}_\textup{R}^\textup{l}$, (e) circumferential $\boldsymbol{f}_\textup{R}^\textup{c}$, and (f) outward normal direction $\boldsymbol{n}$. (g-i) Spatial distributions of key parameters: (g) the excitability parameter $a^\textup{icc}$, (f) the weighting factor $\chi^\textup{icc}$, and (i) the diffusion coefficient $\sigma^\textup{icc}$. These parameter fields are mapped based on the anatomical coordinate system defined by the harmonic fields.
• Figure 5: Control variables used for spatial parameter modulation visualized from two perspectives. (a) The normalized longitudinal coordinate $\xi_l$, defined piecewise in \ref{['eq:control_variable_long']}, distinguishes the proximal and distal regions of the stomach and allows longitudinal variation of model parameters. (b) The normalized circumferential coordinate $\xi_c$ follows the longitudinal field $\phi_\textup{gl}$ and allows circumferential parameter modulation. These coordinates provide a structured framework to spatially vary parameters such as excitability along anatomically meaningful axes.