Shameer Sathar

Toward the virtual stomach: progress in multiscale modeling of gastric electrophysiology and motility.

Experimental progress in investigating normal and disordered gastric motility is increasingly being complimented by sophisticated multiscale modeling studies. Mathematical modeling has become a valuable tool in this effort, as there is an ever‐increasing need to gain an integrative and quantitative understanding of how physiological mechanisms achieve coordinated functions across multiple biophysical scales. These interdisciplinary efforts have been particularly notable in the area of gastric electrophysiology, where they are beginning to yield a comprehensive and integrated in silico organ modeling framework, or ‘virtual stomach’. At the cellular level, a number of biophysically based mathematical cell models have been developed, and these are now being applied in areas including investigations of gastric electrical pacemaker mechanisms, smooth muscle electrophysiology, and electromechanical coupling. At the tissue level, micro‐structural models are being creatively developed and employed to investigate clinically significant questions, such as the functional effects of ICC degradation on gastrointestinal (GI) electrical activation. At the organ level, high‐resolution electrical mapping and modeling studies are combined to provide improved insights into normal and dysrhythmic gastric electrical activation. These efforts are also enabling detailed forward and inverse modeling studies at the ‘whole body’ level, with implications for diagnostic techniques for gastric dysrhythmias. These recent advances, together with several others highlighted in this review, collectively demonstrate a powerful trend toward applying mathematical models to effectively investigate structure–function relationships and overcome multiscale challenges in basic and clinical GI research. WIREs Syst Biol Med 2013, 5:481–493. doi: 10.1002/wsbm.1218

Multi-channel wireless mapping of gastrointestinal serosal slow wave propagation.

High‐resolution (HR) extracellular mapping allows accurate profiling of normal and dysrhythmic slow wave patterns. A current limitation is that cables traverse the abdominal wall or a natural orifice, risking discomfort, dislodgement or infection. Wireless approaches offer advantages, but a multi‐channel system is required, capable of recording slow waves and mapping propagation with high fidelity.

A Biophysically Based Finite-State Machine Model for Analyzing Gastric Experimental Entrainment and Pacing Recordings

Gastrointestinal motility is coordinated by slow waves (SWs) generated by the interstitial cells of Cajal (ICC). Experimental studies have shown that SWs spontaneously activate at different intrinsic frequencies in isolated tissue, whereas in intact tissues they are entrained to a single frequency. Gastric pacing has been used in an attempt to improve motility in disorders such as gastroparesis by modulating entrainment, but the optimal methods of pacing are currently unknown. Computational models can aid in the interpretation of complex in vivo recordings and help to determine optimal pacing strategies. However, previous computational models of SW entrainment are limited to the intrinsic pacing frequency as the primary determinant of the conduction velocity, and are not able to accurately represent the effects of external stimuli and electrical anisotropies. In this paper, we present a novel computationally efficient method for modeling SW propagation through the ICC network while accounting for conductivity parameters and fiber orientations. The method successfully reproduced experimental recordings of entrainment following gastric transection and the effects of gastric pacing on SW activity. It provides a reliable new tool for investigating gastric electrophysiology in normal and diseased states, and to guide and focus future experimental studies.

High-resolution electrical mapping of porcine gastric slow-wave propagation from the mucosal surface

Gastric motility is coordinated by bioelectrical slow waves, and gastric dysrhythmias are reported in motility disorders. High‐resolution (HR) mapping has advanced the accurate assessment of gastric dysrhythmias, offering promise as a diagnostic technique. However, HR mapping has been restricted to invasive surgical serosal access. This study investigates the feasibility of HR mapping from the gastric mucosal surface.

Acute Slow Wave Responses to High-Frequency Gastric Electrical Stimulation in Patients With Gastroparesis Defined by High-Resolution Mapping.

High‐frequency gastric electrical stimulation (GES) has emerged as a therapy for gastroparesis, but the mechanism(s) of action remain unclear. There is a need to refine stimulation protocols for clinical benefit, but a lack of accurate techniques for assessing mechanisms in clinical trials, such as slow wave modulation, has hindered progress. We thereby aimed to assess acute slow wave responses to GES in gastroparesis patients using high‐resolution (HR) (multi‐electrode) mapping, across a range of stimulation doses achievable by the Enterra stimulation device (Medtronic Inc., MN, USA).

Developmental changes in postnatal murine intestinal interstitial cell of Cajal network structure and function.

The mammalian gastrointestinal (GI) tract undergoes rapid development during early postnatal life in order to transition from a milk to solid diet. Interstitial cells of Cajal (ICC) are the pacemaker cells that coordinate smooth muscle contractility within the GI tract, and hence we hypothesized that ICC networks undergo significant developmental changes during this early postnatal period. Numerical metrics for quantifying ICC network structural properties were applied on confocal ICC network imaging data obtained from the murine small intestine at various postnatal ages spanning birth to weaning. These imaging data were also coupled to a biophysically-based computational model to simulate pacemaker activity in the networks, to quantify how changes in structure may alter function. The results showed a pruning-like mechanism which occurs during postnatal development, and the temporal course of this phenomenon was defined. There was an initial ICC process overgrowth to optimize network efficiency and increase functional output volume. This was followed by a selective retaining and strengthening of processes, while others were discarded to further elevate functional output volume. Subsequently, new ICC processes were formed and the network was adjusted to its adult morphology. These postnatal ICC network developmental events may be critical in facilitating mature digestive function.

Progress in Mathematical Modeling of Gastrointestinal Slow Wave Abnormalities

Gastrointestinal (GI) motility is regulated in part by electrophysiological events called slow waves, which are generated by the interstitial cells of Cajal (ICC). Slow waves propagate by a process of “entrainment,” which occurs over a decreasing gradient of intrinsic frequencies in the antegrade direction across much of the GI tract. Abnormal initiation and conduction of slow waves have been demonstrated in, and linked to, a number of GI motility disorders. A range of mathematical models have been developed to study abnormal slow waves and applied to propose novel methods for non-invasive detection and therapy. This review provides a general outline of GI slow wave abnormalities and their recent classification using multi-electrode (high-resolution) mapping methods, with a particular emphasis on the spatial patterns of these abnormal activities. The recently-developed mathematical models are introduced in order of their biophysical scale from cellular to whole-organ levels. The modeling techniques, main findings from the simulations, and potential future directions arising from notable studies are discussed.

A Stochastic Algorithm for Generating Realistic Virtual Interstitial Cell of Cajal Networks

Interstitial cells of Cajal (ICC) play a central role in coordinating normal gastrointestinal (GI) motility. Depletion of ICC numbers and network integrity contributes to major functional GI motility disorders. However, the mechanisms relating ICC structure to GI function and dysfunction remains unclear, partly because there is a lack of large-scale ICC network imaging data across a spectrum of depletion levels to guide models. Experimental imaging of these large-scale networks remains challenging because of technical constraints, and hence, we propose the generation of realistic virtual ICC networks in silico using the single normal equation simulation (SNESIM) algorithm. ICC network imaging data obtained from wild-type (normal) and 5-HT2B serotonin receptor knockout (depleted ICC) mice were used to inform the algorithm, and the virtual networks generated were assessed using ICC network structural metrics and biophysically-based computational modeling. When the virtual networks were compared to the original networks, there was less than 10% error for four out of five structural metrics and all four functional measures. The SNESIM algorithm was then modified to enable the generation of ICC networks across a spectrum of depletion levels, and as a proof-of-concept, virtual networks were successfully generated with a range of structural and functional properties. The SNESIM and modified SNESIM algorithms, therefore, offer an alternative strategy for obtaining the large-scale ICC network imaging data across a spectrum of depletion levels. These models can be applied to accurately inform the physiological consequences of ICC depletion.

A Multiscale Tridomain Model for Simulating Bioelectric Gastric Pacing

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 3-D multiscale 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 two times more efficient than a previous formulation for a normal slow-wave simulation. Convergence analysis showed that a mesh resolution of ≈0.4-0.5 mm 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.

Tissue specific simulations of interstitial cells of cajal networks using unstructured meshes

Gastrointestinal motility is facilitated by specialized pacemaker cells called Interstitial Cells of Cajal (ICC). ICC play a critical role in coordinating normal motility and its degradation in the gastrointestinal tract is associated with many functional motility disorders. Nonetheless, the degree of degradation and associated clinical impact remains unclear. Continuum modeling frameworks offers a virtual mean to simulate the electrical activity, and analyze the ICC activity in both normal and diseased states. Confocal images of the ICC networks were obtained from the intestine of normal mice. In this study, a new approach is presented where meshes of ICC networks were generated using a Delaunay triangulation and used to solve finite-element based reaction-diffusion equations describing gastrointestinal electrophysiology. The electrical activity was simulated on the ICC network and solutions were compared to those of a regular mesh based on individual pixel locations. The simulation results showed the proposed approach to be approximately 80% more efficient than a pixel-based mesh. The difference in activation time for the entire network between the different methods was observed to be around 4% (about 20 ms). The proposed approach will enable efficient examination of the ICC slow wave activity in larger networks and for longer temporal duration that has been previously impossible. This will provide valuable insights relating ICC degradation to gastrointestinal motility disorders.