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

Computational models of autonomic regulation in gastric motility: Progress, challenges, and future directions

The stomach is extensively innervated by the vagus nerve and the enteric nervous system. The mechanisms through which this innervation affects gastric motility are being unraveled, motivating the first concerted steps towards the incorporation autonomic regulation into computational models of gastric motility. Computational modeling has been valuable in advancing clinical treatment of other organs, such as the heart. However, to date, computational models of gastric motility have made simplifying assumptions about the link between gastric electrophysiology and motility. Advances in experimental neuroscience mean that these assumptions can be reviewed, and detailed models of autonomic regulation can be incorporated into computational models. This review covers these advances, as well as a vision for the utility of computational models of gastric motility. Diseases of the nervous system, such as Parkinson’s disease, can originate from the brain-gut axis and result in pathological gastric motility. Computational models are a valuable tool for understanding the mechanisms of disease and how treatment may affect gastric motility. This review also covers recent advances in experimental neuroscience that are fundamental to the development of physiology-driven computational models. A vision for the future of computational modeling of gastric motility is proposed and modeling approaches employed for existing mathematical models of autonomic regulation of other gastrointestinal organs and other organ systems are discussed.

Organisation of the musculature of the rat stomach

The strengths, directions and coupling of the movements of the stomach depend on the organisation of its musculature. Although the rat has been used as a model species to study gastric function, there is no detailed, quantitative study of the arrangement of the gastric muscles in rat. Here we provide a descriptive and quantitative account, and compare it with human gastric anatomy. The rat stomach has three components of the muscularis externa, a longitudinal coat, a circular coat and an internal oblique (sling) muscle in the region of the gastro-oesophageal junction. These layers are similar to human. Unlike human, the rat stomach is also equipped with paired muscular oesophago-pyloric ligaments that lie external to the longitudinal muscle. There is a prominent muscularis mucosae throughout the stomach and strands of smooth muscle occur in the mucosa, between the glands of the corpus and antrum. The striated muscle of the oesophageal wall reaches to the stomach, unlike the human, in which the wall of the distal oesophagus is smooth muscle. Thus, the continuity of gastric and oesophageal smooth muscle bundles, that occurs in human, does not occur in rat. Circular muscle bundles extend around the circumference of the stomach, in the fundus forming a cap of parallel muscle bundles. This arrangement favours co-ordinated circumferential contractions. Small bands of muscle make connections between the circular muscle bundles. This is consistent with a slower conduction of excitation orthogonal to the circular muscle bundles, across the corpus towards the distal antrum. The oblique muscle merged and became continuous with the circular muscle close to the gastro-oesophageal junction at the base of the fundus, and in the corpus, lateral to the lesser curvature. Quantitation of muscle thickness revealed gradients of thickness of both the longitudinal and circular muscle. This anatomical study provides essential data for interpreting gastric movements.

The gastric conduction system in health and disease: a translational review

Gastric peristalsis is critically dependent on an underlying electrical conduction system. Recent years have witnessed substantial progress in clarifying the operations of this system, including its pacemaking units, its cellular architecture, and slow-wave propagation patterns. Advanced techniques have been developed for assessing its functions at high spatiotemporal resolutions. This review synthesizes and evaluates this progress, with a focus on human and translational physiology. A current conception of the initiation and conduction of slow-wave activity in the human stomach is provided first, followed by a detailed discussion of its organization at the cellular and tissue level. Particular emphasis is then given to how gastric electrical disorders may contribute to disease states. Gastric dysfunction continues to grow in their prevalence and impact, and while gastric dysrhythmia is established as a clear and pervasive feature in several major gastric disorders, its role in explaining pathophysiology and informing therapy is still emerging. New insights from high-resolution gastric mapping are evaluated, together with historical data from electrogastrography, and the physiological relevance of emerging biomarkers from body surface mapping such as retrograde propagating slow waves. Knowledge gaps requiring further physiological research are highlighted.

Electrophysiological modeling of the effect of potassium channel blockers on the distribution of stimulation wave in the human gastric wall cells

The purpose of this study is to model the electrophysiological behavior of excitable membrane and wavefront propagation in the Stomach Wall in physiological and pharmacological states. The propagation of this wave is based on cellular electrophysiological activity and ionic channel properties. In this study, we arranged the stomach wall cells together using the Gap Junctions approach. Slow wave is generated by gastric pacemaker cells. This wave propagates via the interaction of cells with each other throughout the stomach wall. Potassium currents are one of the main factors in regulating the pattern of wavefront propagation. To investigate the effect of limiting the exchange of potassium currents from cell membranes, 10%, 50%, 90%, and complete blockade were applied on both non-inactivating potassium current (I_Kni) and fast-inactivating potassium current (I_Kfi). The results show that I_Kniion channel blockage has a considerable effect on the plateau phase in the propagation of the excitation wave. The maximum value of the action potential in the plateau phase in the excitation wave with complete obstruction from -40.92 mV in the physiological state reached -18.97 mV, which is about 54% higher than the physiological state. Also, compared to the physiological state, complete blockage of the I_Kfi causes a 15% increase in the slow-wave spike phase (from -36.72 mV to -31.36 mV). Using this model, the effect of ions in different phases of slow-wave can be investigated. In addition, by blocking ion channels, functional disorders and smooth muscle contraction can be improved.

Strategies to Refine Gastric Stimulation and Pacing Protocols: Experimental and Modeling Approaches

Gastric pacing and stimulation strategies were first proposed in the 1960s to treat motility disorders. However, there has been relatively limited clinical translation of these techniques. Experimental investigations have been critical in advancing our understanding of the control mechanisms that innervate gut function. In this review, we will discuss the use of pacing to modulate the rhythmic slow wave conduction patterns generated by interstitial cells of Cajal in the gastric musculature. In addition, the use of gastric high-frequency stimulation methods that target nerves in the stomach to either inhibit or enhance stomach function will be discussed. Pacing and stimulation protocols to modulate gastric activity, effective parameters and limitations in the existing studies are summarized. Mathematical models are useful to understand complex and dynamic systems. A review of existing mathematical models and techniques that aim to help refine pacing and stimulation protocols are provided. Finally, some future directions and challenges that should be investigated are discussed.

Transmural recordings of gastrointestinal electrical activity using a spatially-dense microelectrode array

Objective. High-resolution serosal recordings provide detailed information about the bioelectrical conduction patterns in the gastrointestinal (GI) tract. However, equivalent knowledge about the electrical activity through the GI tract wall remains largely unknown. This study aims to capture and quantify the bioelectrical activity across the wall of the GI tract.Approach. A needle-based microelectrode array was used to measure the bioelectrical activity across the GI wallin vivo. Quantitative and qualitative evaluations of transmural slow wave characteristics were carried out in comparison to the serosal slow wave features, through which the period, amplitude, and SNR metrics were quantified and statistically compared.Main results. Identical periods of 4.7 ± 0.3 s with amplitudes of 0.17 ± 0.04 mV versus 0.31 ± 0.1 mV and signal to noise ratios of 5.5 ± 1.3 dB versus 14.4 ± 1.1 dB were observed for transmural and serosal layers, respectively. Four different slow wave morphologies were observed across the transmural layers of the GI wall. Similar amplitudes were observed for all morphology types, and Type 1 and Type 2 were of the highest prevalence, dominating the outer and inner layers. Type 2 was exclusive to the middle layer while Type 4 was primarily observed in the middle layer as well.Significance. This study demonstrates the validity of new methodologies for measuring transmural slow wave activation in the GI wall and can now be applied to investigate the source and origin of GI dysrhythmias leading to dysmotility, and to validate novel therapeutics for GI health and disease.

Body surface mapping of the stomach: New directions for clinically evaluating gastric electrical activity

BACKGROUND

Gastric motility disorders, which include both functional and organic etiologies, are highly prevalent. However, there remains a critical lack of objective biomarkers to guide efficient diagnostics and personalized therapies. Bioelectrical activity plays a fundamental role in coordinating gastric function and has been investigated as a contributing mechanism to gastric dysmotility and sensory dysfunction for a century. However, conventional electrogastrography (EGG) has not achieved common clinical adoption due to its perceived limited diagnostic capability and inability to impact clinical care. The last decade has seen the emergence of novel high-resolution methods for invasively mapping human gastric electrical activity in health and disease, providing important new insights into gastric physiology. The limitations of EGG have also now become clearer, including the finding that slow-wave frequency alone is not a reliable discriminator of gastric dysrhythmia, shifting focus instead toward altered spatial patterns. Recently, advances in bioinstrumentation, signal processing, and computational modeling have aligned to allow non-invasive body surface mapping of the stomach to detect spatiotemporal gastric dysrhythmias. The clinical relevance of this emerging strategy to improve diagnostics now awaits determination.

PURPOSE

This review evaluates these recent advances in clinical gastric electrophysiology, together with promising emerging data suggesting that novel gastric electrical signatures recorded at the body surface (termed "body surface mapping") may correlate with symptoms. Further technological progress and validation data are now awaited to determine whether these advances will deliver on the promise of clinical gastric electrophysiology diagnostics.

The influence of interstitial cells of Cajal loss and aging on slow wave conduction velocity in the human stomach

Loss of interstitial cells of Cajal (ICC) has been associated with gastric dysfunction and is also observed during normal aging at ~13% reduction per decade. The impact of ICC loss on gastric slow wave conduction velocity is currently undefined. This study correlated human gastric slow wave velocity with ICC loss and aging. High-resolution gastric slow wave mapping data were screened from a database of 42 patients with severe gastric dysfunction (n = 20) and controls (n = 22). Correlations were performed between corpus slow wave conduction parameters (frequency, velocity, and amplitude) and corpus ICC counts in patients, and with age in controls. Physiological parameters were further integrated into computational models of gastric mixing. Patients: ICC count demonstrated a negative correlation with slow wave velocity in the corpus (i.e., higher velocities with reduced ICC; r2  = .55; p = .03). ICC count did not correlate with extracellular slow wave amplitude (p = .12) or frequency (p = .84). Aging: Age was positively correlated with slow wave velocity in the corpus (range: 25-74 years; r2  = .32; p = .02). Age did not correlate with extracellular slow wave amplitude (p = .40) or frequency (p = .34). Computational simulations demonstrated that the gastric emptying rate would increase at higher slow wave velocities. ICC loss and aging are associated with a higher slow wave velocity. The reason for these relationships is unexplained and merit further investigation. Increased slow wave velocity may modulate gastric emptying higher, although in gastroparesis other pathological factors must dominate to prevent emptying.

Polygonally Meshed Dipole Model Simulation of the Electrical Field Produced by the Stomach and Intestines

Cutaneous electrogastrography (EGG) is used in clinical and physiological fields to noninvasively measure the electrical activity of the stomach and intestines. Dipole models that mathematically express the electrical field characteristics generated by the stomach and intestines have been developed to investigate the relationship between the electrical control activity (ECA) (slow waves) shown in EGG and the internal gastric electrical activity. However, these models require a mathematical description of the movement of an annular band of dipoles, which limits the shape that can be modeled. In this study, we propose a novel polygonally meshed dipole model to conveniently reproduce ECA based on the movement of the annular band in complex shapes, such as the shape of the stomach and intestines, constructed in three-dimensional (3D) space. We show that the proposed model can reproduce ECA simulation results similar to those obtained using conventional models. Moreover, we show that the proposed model can reproduce the ECA produced by a complex geometrical shape, such as the shape of the intestines. The study results indicate that ECA simulations can be conducted based on structures that more closely resemble real organs than those used in conventional dipole models, with which, because of their intrinsic construction, it would be difficult to include realistic complex shapes, using the mathematical description of the movement of an annular band of dipoles. Our findings provide a powerful new approach for computer simulations based on the electric dipole model.

Current applications of mathematical models of the interstitial cells of Cajal in the gastrointestinal tract

The interstitial cells of Cajal (ICC) form interconnected networks throughout the gastrointestinal (GI) tract. ICC act as the pacemaker cells that initiate the rhythmic bioelectrical slow waves and intermediary between the GI musculature and nerves, both of which are critical to GI motility. Disruptions to the number of ICC and the integrity of ICC networks have been identified as a key pathophysiological mechanism in a number of clinically challenging GI disorders. The current analyses of ICC generally rely on either functional recordings taken directly from excised tissue or morphological analysis based on images of labeled ICC, where the structural-functional relationship is investigated in an associative manner rather than mechanistically. On the other hand, computational physiology has played a significant role in facilitating our understanding of a number of physiological systems in both health and disease, and investigations in the GI field are beginning to incorporate several mathematical models of the ICC. The main aim of this review is to present the major modeling advances in GI electrophysiology, in order to introduce a multi-scale framework for mathematically quantifying the functional consequences of ICC degradation at both cellular and tissue scales. The outcomes will inform future investigators utilizing modeling techniques in their studies. This article is categorized under: Metabolic Diseases > Computational Models.

On a coupled electro-chemomechanical model of gastric smooth muscle contraction

The stomach is a central organ in the gastrointestinal tract that performs a variety of functions, in which the spatio-temporal organisation of active smooth muscle contraction in the stomach wall (SW) is highly regulated. In the present study, a three-dimensional model of the gastric smooth muscle contraction is presented, including the mechanical contribution of the mucosal and muscular layer of the SW. Layer-specific and direction-dependent model parameters for the active and passive stress-stretch characteristics of the SW were determined experimentally using porcine smooth muscle strips. The electrical activation of the smooth muscle cells (SMC) due to the pacemaker activity of the interstitial cells of Cajal (ICC) is modelled by using FitzHugh-Nagumo-type equations, which simulate the typical ICC and SMC slow wave behaviour. The calcium dynamic in the SMC depends on the SMC membrane potential via a gaussian function, while the chemo-mechanical coupling in the SMC is modelled via an extended Hai-Murphy model. This cascade is coupled with an additional mechano-electrical feedback-mechanism, taking into account the mechanical response of the ICC and SMC due to stretch of the SW. In this way the relaxation responses of the fundus to accommodate incoming food, as well as the typical peristaltic contraction waves in the antrum for mixing and transport of the chyme, have been well replicated in simulations performed at the whole organ level. STATEMENT OF SIGNIFICANCE: In this article, a novel three-dimensional electro-chemomechanical model of the gastric smooth muscle contraction is presented. The propagating waves of electrical membrane potential in the network ofinterstitial cells of Cajal (ICC) and smooth muscle cells (SMC) lead to a global pattern of change in the calciumdynamics inside the SMC. Taking additionally into account the mechanical response of the ICC and SMC due to stretch of the stomach wall, also referred to as mechanical feedback-mechanism, the result is a complex spatio-temporal regulation of the active contraction and relaxation of the gastric smooth muscle tissue. Being a firstapproach, in future view such a three-dimensional model can give an insight into the complexload transferring system of the stomach wall, as well as into the electro-chemomechanicalcoupling process underlying smooth muscle contraction in health and disease.

Multi-scale models of lung fibrosis

The architectural complexity of the lung is crucial to its ability to function as an organ of gas exchange; the branching tree structure of the airways transforms the tracheal cross-section of only a few square centimeters to a blood-gas barrier with a surface area of tens of square meters and a thickness on the order of a micron or less. Connective tissue comprised largely of collagen and elastic fibers provides structural integrity for this intricate and delicate system. Homeostatic maintenance of this connective tissue, via a balance between catabolic and anabolic enzyme-driven processes, is crucial to life. Accordingly, when homeostasis is disrupted by the excessive production of connective tissue, lung function deteriorates rapidly with grave consequences leading to chronic lung conditions such as pulmonary fibrosis. Understanding how pulmonary fibrosis develops and alters the link between lung structure and function is crucial for diagnosis, prognosis, and therapy. Further information gained could help elaborate how the healing process breaks down leading to chronic disease. Our understanding of fibrotic disease is greatly aided by the intersection of wet lab studies and mathematical and computational modeling. In the present review we will discuss how multi-scale modeling has facilitated our understanding of pulmonary fibrotic disease as well as identified opportunities that remain open and have produced techniques that can be incorporated into this field by borrowing approaches from multi-scale models of fibrosis beyond the lung.

Understanding the Potential for Dissolution Simulation to Explore the Effects of Medium Viscosity on Particulate Dissolution

Viscosity, influenced by medium composition, will affect the hydrodynamics of a dissolution system. Dissolution simulation methods are valuable tools to explore mechanistic dissolution effects, with an understanding of limitations of any simulation method essential to its appropriate use. The aims of this paper were a) to explore, using dissolution simulation, the effects of slightly viscous media on particulate dissolution and b) to illustrate approaches to, and limitations of, the dissolution simulations. A lumped parameter fluid dynamics dissolution simulation model (SIMDISSO™) was used to simulate particulate (20 and 200 μm diameter) dissolution in media with viscosity at 37 °C of water (0.7 mPa.s), milk (1.4 mPa.s) and a nutrient drink (12.3 mPa.s). Effects of flow rate, modality (constant vs pulsing), viscosity and gravitational and particle motion/sedimentation effects on simulated dissolution were explored, in the flow through and paddle apparatuses as appropriate. Shadowgraph imaging (SGI) was used to visualise particle suspension behaviour. Flow rate, hydrodynamic viscous effects and disabling particle motion and gravitational effects affected simulated dissolution of larger particles. SGI imaging revealed retention of particles in suspension in 1.4 mPa.s medium, which sedimented in water. The effect of diffusion adjusted for viscosity was significant for both particle sizes. The limitations of this 1D simulation approach would be greater for larger particles in low velocity regions of the paddle apparatus. Even slightly viscous media can affect dissolution of larger particles with dissolution simulation affording insight into the mechanisms involved, provided the assumptions and limitations of the simulation approach are clarified and understood.

Methods for High-Resolution Electrical Mapping in the Gastrointestinal Tract

Over the last two decades, high-resolution (HR) mapping has emerged as a powerful technique to study normal and abnormal bioelectrical events in the gastrointestinal (GI) tract. This technique, adapted from cardiology, involves the use of dense arrays of electrodes to track bioelectrical sequences in fine spatiotemporal detail. HR mapping has now been applied in many significant GI experimental studies informing and clarifying both normal physiology and arrhythmic behaviors in disease states. This review provides a comprehensive and critical analysis of current methodologies for HR electrical mapping in the GI tract, including extracellular measurement principles, electrode design and mapping devices, signal processing and visualization techniques, and translational research strategies. The scope of the review encompasses the broad application of GI HR methods from in vitro tissue studies to in vivo experimental studies, including in humans. Controversies and future directions for GI mapping methodologies are addressed, including emerging opportunities to better inform diagnostics and care in patients with functional gut disorders of diverse etiologies.

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.

Relationships between gastric slow wave frequency, velocity, and extracellular amplitude studied by a joint experimental-theoretical approach

BACKGROUND

Gastric slow wave dysrhythmias are accompanied by deviations in frequency, velocity, and extracellular amplitude, but the inherent association between these parameters in normal activity still requires clarification. This study quantified these associations using a joint experimental-theoretical approach.

METHODS

Gastric pacing was conducted in pigs with simultaneous high-resolution slow wave mapping (32-256 electrodes; 4-7.6 mm spacing). Relationships between period, velocity, and amplitude were quantified and correlated for each wavefront. Human data from two existing mapping control cohorts were analyzed to extract and correlate these same parameters. A validated biophysically based ICC model was also applied in silico to quantify velocity-period relationships during entrainment simulations and velocity-amplitude relationships from membrane potential equations.

KEY RESULTS

Porcine pacing studies identified positive correlations for velocity-period (0.13 mm s^-1 per 1 s, r² =.63, P<.001) and amplitude-velocity (74 μV per 1 mm s^-1 , r² =.21, P=.002). In humans, positive correlations were also quantified for velocity-period (corpus: 0.11 mm s^-1 per 1 s, r² =.16, P<.001; antrum: 0.23 mm s^-1 per 1 s, r² =.55; P<.001), and amplitude-velocity (94 μV per 1 mm s^-1 , r² =.56; P<.001). Entrainment simulations matched the experimental velocity-period relationships and demonstrated dependence on the slow wave recovery phase. Simulated membrane potential relationships were close to these experimental results (100 μV per 1 mm s^-1 ).

CONCLUSIONS AND INFERENCES

These data quantify the relationships between slow wave frequency, velocity, and extracellular amplitude. The results from both human and porcine studies were in keeping with biophysical models, demonstrating concordance with ICC biophysics. These relationships are important in the regulation of gastric motility and will help to guide interpretations of dysrhythmias.

High-resolution mapping of gastric slow-wave recovery profiles: biophysical model, methodology, and demonstration of applications

Slow waves play a central role in coordinating gastric motor activity. High-resolution mapping of extracellular potentials from the stomach provides spatiotemporal detail on normal and dysrhythmic slow-wave patterns. All mapping studies to date have focused exclusively on tissue activation; however, the recovery phase contains vital information on repolarization heterogeneity, the excitable gap, and refractory tail interactions but has not been investigated. Here, we report a method to identify the recovery phase in slow-wave mapping data. We first developed a mathematical model of unipolar extracellular potentials that result from slow-wave propagation. These simulations showed that tissue repolarization in such a signal is defined by the steepest upstroke beyond the activation phase (activation was defined by accepted convention as the steepest downstroke). Next, we mapped slow-wave propagation in anesthetized pigs by recording unipolar extracellular potentials from a high-resolution array of electrodes on the serosal surface. Following the simulation result, a wavelet transform technique was applied to detect repolarization in each signal by finding the maximum positive slope beyond activation. Activation-recovery (ARi) and recovery-activation (RAi) intervals were then computed. We hypothesized that these measurements of recovery profile would differ for slow waves recorded during normal and spatially dysrhythmic propagation. We found that the ARi of normal activity was greater than dysrhythmic activity (5.1 ± 0.8 vs. 3.8 ± 0.7 s; P < 0.05), whereas RAi was lower (9.7 ± 1.3 vs. 12.2 ± 2.5 s; P < 0.05). During normal propagation, RAi and ARi were linearly related with negative unit slope indicating entrainment of the entire mapped region. This relationship was weakened during dysrhythmia (slope: -0.96 ± 0.2 vs -0.71 ± 0.3; P < 0.05).NEW & NOTEWORTHY The theoretical basis of the extracellular gastric slow-wave recovery phase was defined using mathematical modeling. A novel technique utilizing the wavelet transform was developed and validated to detect the extracellular slow-wave recovery phase. In dysrhythmic wavefronts, the activation-to-recovery interval (ARi) was shorter and recovery-to-activation interval (RAi) was longer compared with normal wavefronts. During normal activation, RAi vs. ARi had a slope of -1, whereas the weakening of the slope indicated a dysrhythmic propagation.

Functional physiology of the human terminal antrum defined by high-resolution electrical mapping and computational modeling

High-resolution (HR) mapping has been used to study gastric slow-wave activation; however, the specific characteristics of antral electrophysiology remain poorly defined. This study applied HR mapping and computational modeling to define functional human antral physiology. HR mapping was performed in 10 subjects using flexible electrode arrays (128-192 electrodes; 16-24 cm²) arranged from the pylorus to mid-corpus. Anatomical registration was by photographs and anatomical landmarks. Slow-wave parameters were computed, and resultant data were incorporated into a computational fluid dynamics (CFD) model of gastric flow to calculate impact on gastric mixing. In all subjects, extracellular mapping demonstrated normal aboral slow-wave propagation and a region of increased amplitude and velocity in the prepyloric antrum. On average, the high-velocity region commenced 28 mm proximal to the pylorus, and activation ceased 6 mm from the pylorus. Within this region, velocity increased 0.2 mm/s per mm of tissue, from the mean 3.3 ± 0.1 mm/s to 7.5 ± 0.6 mm/s (P < 0.001), and extracellular amplitude increased from 1.5 ± 0.1 mV to 2.5 ± 0.1 mV (P < 0.001). CFD modeling using representative parameters quantified a marked increase in antral recirculation, resulting in an enhanced gastric mixing, due to the accelerating terminal antral contraction. The extent of gastric mixing increased almost linearly with the maximal velocity of the contraction. In conclusion, the human terminal antral contraction is controlled by a short region of rapid high-amplitude slow-wave activity. Distal antral wave acceleration plays a major role in antral flow and mixing, increasing particle strain and trituration.

The virtual esophagus: investigating esophageal functions in silico

Esophageal and gastroesophageal junction (GEJ) diseases are highly prevalent worldwide and are a significant socioeconomic burden. Recently, applications of multiscale mathematical models of the upper gastrointestinal tract have gained attention. These in silico investigations can contribute to the development of a virtual esophagus modeling framework as part of the larger GIome and Physiome initiatives. There are also other modeling investigations that have potential screening and treatment applications. These models incorporate detailed anatomical models of the esophagus and GEJ, tissue biomechanical properties and bolus transport, sensory properties, and, potentially, bioelectrical models of the neural and myogenic pathways of esophageal and GEJ functions. A next step is to improve the integration between the different components of the virtual esophagus, encoding standards, and simulation environments to perform more realistic simulations of normal and pathophysiological functions. Ultimately, the models will be validated and will provide predictive evaluations of the effects of novel endoscopic, surgical, and pharmaceutical treatment options and will facilitate the clinical translation of these treatments.

The Esophagiome: concept, status, and future perspectives

The term "Esophagiome" is meant to imply a holistic, multiscale treatment of esophageal function from cellular and muscle physiology to the mechanical responses that transport and mix fluid contents. The development and application of multiscale mathematical models of esophageal function are central to the Esophagiome concept. These model elements underlie the development of a "virtual esophagus" modeling framework to characterize and analyze function and disease by quantitatively contrasting normal and pathophysiological function. Functional models incorporate anatomical details with sensory-motor properties and functional responses, especially related to biomechanical functions, such as bolus transport and gastrointestinal fluid mixing. This brief review provides insight into Esophagiome research. Future advanced models can provide predictive evaluations of the therapeutic consequences of surgical and endoscopic treatments and will aim to facilitate clinical diagnostics and treatment.

A Theoretical Analysis of Electrogastrography (EGG) Signatures Associated With Gastric Dysrhythmias

Routine screening and accurate diagnosis of chronic gastrointestinal motility disorders represent a significant problem in current clinical practice. The electrogastrography (EGG) provides a noninvasive option for assessing gastric slow waves, as a means of diagnosing gastric dysrhythmias, but its uptake in motility practice has been limited partly due to an incomplete sensitivity and specificity. This paper presents the development of a human whole-organ gastric model to enable virtual (in silico) testing of gastric electrophysiological dispersion in order to improve the diagnostic accuracy of EGG. The model was developed to simulate normal gastric slow wave conduction as well as three types of dysrhythmias identified in recent high-resolution gastric mapping studies: conduction block, re-entry, and ectopic pacemaking. The stomach simulations were then applied in a torso model to identify predicted EGG signatures of normal and dysrhythmic slow wave profiles. The resulting EGG data were compared using percentage differences and correlation coefficients. Virtual EGG channels that demonstrated a percentage difference over 100% and a correlation coefficient less than ±0.2 (threshold relaxed to ±0.5 for the ectopic pacemaker case) were further investigated for their specific distinguishing features. In particular, anatomical locations from the epigastric region and specific channel configurations were identified that could be used to clinically diagnose the three classes of human gastric dysrhythmia. These locations and channels predicted by simulations present a promising methodology for improving the clinical reliability and applications of EGG.

Original Research: Combined model of bladder detrusor smooth muscle and interstitial cells

Although patients with lower urinary tract symptoms constitute a large and still growing population, understanding of bladder detrusor muscle physiology remains limited. Understanding the interactions between the detrusor smooth muscle cells and other bladder cell types (e.g. interstitial cells, IC) that may significantly contribute to coordinating and modulating detrusor contractions represents a considerable challenge. Computer modeling could help to elucidate some properties that are difficult to address experimentally; therefore, we developed in silico models of detrusor smooth muscle cell and interstitial cells, coupled through gap junctions. The models include all of the major ion conductances and transporters described in smooth muscle cell and interstitial cells in the literature. The model of normal detrusor muscle (smooth muscle cell and interstitial cells coupled through gap junctions) completely reproduced the experimental results obtained with detrusor strips in the presence of several pharmacological interventions (ryanodine, caffeine, nimodipine), whereas the model of smooth muscle cell alone (without interstitial cells) failed to reproduce the experimental results. Next, a model of overactive bladder, a highly prevalent clinical condition in both men and women with increasing incidence at older ages, was produced by modifying several processes as reported previously: a reduction of Ca(2+)-release through ryanodine receptors and a reduction of Ca(2+)-dependent K(+)-conductance with augmented gap junctional coupling. This model was also able to reproduce the pharmacological modulation of overactive bladder. In conclusion, a model of bladder detrusor muscle was developed that reproduced experimental results obtained in both normal and overactive bladder preparations. The results indicate that the non-smooth muscle cells of the detrusor (interstitial cells) contribute significantly to the contractile behavior of bladder detrusor muscle and should not be neglected. The model suggests that reduced Ca(2+)-release through ryanodine receptors and Ca(2+)-dependent K(+)-conductance together with augmented gap junctional coupling might play a major role in overactive bladder pathogenesis.

A Multiphase Flow in the Antroduodenal Portion of the Gastrointestinal Tract: A Mathematical Model

A group of authors has developed a multilevel mathematical model that focuses on functional disorders in a human body associated with various chemical, physical, social, and other factors. At this point, the researchers have come up with structure, basic definitions and concepts of a mathematical model at the "macrolevel" that allow describing processes in a human body as a whole. Currently we are working at the "mesolevel" of organs and systems. Due to complexity of the tasks, this paper deals with only one meso-fragment of a digestive system model. It describes some aspects related to modeling multiphase flow in the antroduodenal portion of the gastrointestinal tract. Biochemical reactions, dissolution of food particles, and motor, secretory, and absorbing functions of the tract are taken into consideration. The paper outlines some results concerning influence of secretory function disorders on food dissolution rate and tract contents acidity. The effect which food density has on inflow of food masses from a stomach to a bowel is analyzed. We assume that the future development of the model will include digestive enzymes and related reactions of lipolysis, proteolysis, and carbohydrates breakdown.

The virtual intestine: in silico modeling of small intestinal electrophysiology and motility and the applications

The intestine comprises a long hollow muscular tube organized in anatomically and functionally discrete compartments, which digest and absorb nutrients and water from ingested food. The intestine also plays key roles in the elimination of waste and protection from infection. Critical to all of these functions is the intricate, highly coordinated motion of the intestinal tract, known as motility, which is coregulated by hormonal, neural, electrophysiological and other factors. The Virtual Intestine encapsulates a series of mathematical models of intestinal function in health and disease, with a current focus on motility, and particularly electrophysiology. The Virtual Intestine is being cohesively established across multiple physiological scales, from sub/cellular functions to whole organ levels, facilitating quantitative evaluations that present an integrative in silico framework. The models are also now finding broad physiological applications, including in evaluating hypotheses of slow wave pacemaker mechanisms, smooth muscle electrophysiology, structure-function relationships, and electromechanical coupling. Clinical applications are also beginning to follow, including in the pathophysiology of motility disorders, diagnosing intestinal ischemia, and visualizing colonic dysfunction. These advances illustrate the emerging potential of the Virtual Intestine to effectively address multiscale research challenges in interdisciplinary gastrointestinal sciences.

The impact of surgical excisions on human gastric slow wave conduction, defined by high-resolution electrical mapping and in silico modeling

BACKGROUND

Gastric contractions are coordinated by slow waves, generated by interstitial cells of Cajal (ICC). Gastric surgery affects slow wave conduction, potentially contributing to postoperative gastric dysfunction. However, the impact of gastric cuts on slow waves has not been comprehensively evaluated. This study aimed to define consequences of surgical excisions on gastric slow waves by applying high-resolution (HR) electrical mapping and in silico modeling.

METHODS

Patients undergoing gastric stimulator implantation (n = 10) underwent full-thickness stapled excisions (25 × 15 mm, distal corpus) for histological evaluation, enabling HR mapping (256 electrodes; 36 cm(2) ) over and adjacent to excisions. A biophysically based in silico model of bidirectionally coupled ICC networks was developed and applied to investigate the underlying conduction mechanisms and importance of excision orientation.

KEY RESULTS

Normal gastric slow waves propagated aborally (3.0 ± 0.2 cpm). Excisions induced complete conduction block and wavelets that rotated around blocks, then propagated rapidly circumferentially distal to the blocks (8.5 ± 1.2 vs normal 3.6 ± 0.4 mm/s; p < 0.01). This 'conduction anisotropy' homeostatically restored antegrade propagating gastric wavefronts distal to excisions. Excisions were associated with complex dysrhythmias in five patients: retrograde propagation (3/10), ectopics (3/10), functional blocks (2/10), and collisions (1/10). Simulations demonstrated conduction anisotropy emerged from bidirectional coupling within ICC layers and showed transverse incision length and orientation correlated with the degree of conduction distortion.

CONCLUSIONS & INFERENCES

Orienting incisions in the longitudinal gastric axis causes least disruption to electrical conduction and motility. However, if transverse incisions are made, a homeostatic mechanism of gastric conduction anisotropy compensates by restoring aborally propagating wavefronts. Complex dysrhythmias accompanying excisions could modify postoperative recovery in susceptible patients.

Gastrointestinal Safety Pharmacology in Drug Discovery and Development

Although the basic structure of the gastrointestinal tract (GIT) is similar across species, there are significant differences in the anatomy, physiology, and biochemistry between humans and laboratory animals, which should be taken into account when conducting a gastrointestinal (GI) assessment. Historically, the percentage of cases of drug attrition associated with GI-related adverse effects is small; however, this incidence has increased over the last few years. Drug-related GI effects are very diverse, usually functional in nature, and not limited to a single pharmacological class. The most common GI signs are nausea and vomiting, diarrhea, constipation, and gastric ulceration. Despite being generally not life-threatening, they can greatly affect patient compliance and quality of life. There is therefore a real need for improved and/or more extensive GI screening of candidate drugs in preclinical development, which may help to better predict clinical effects. Models to identify drug effects on GI function cover GI motility, nausea and emesis liability, secretory function (mainly gastric secretion), and absorption aspects. Both in vitro and in vivo assessments are described in this chapter. Drug-induced effects on GI function can be assessed in stand-alone safety pharmacology studies or as endpoints integrated into toxicology studies. In silico approaches are also being developed, such as the gut-on-a-chip model, but await further optimization and validation before routine use in drug development. GI injuries are still in their infancy with regard to biomarkers, probably due to their greater diversity. Nevertheless, several potential blood, stool, and breath biomarkers have been investigated. However, additional validation studies are necessary to assess the relevance of these biomarkers and their predictive value for GI injuries.

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 [Formula: see text] 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.

Slow wave conduction patterns in the stomach: from Waller's foundations to current challenges

This review provides an overview of our understanding of motility and slow wave propagation in the stomach. It begins by reviewing seminal studies conducted by Walter Cannon and Augustus Waller on in vivo motility and slow wave patterns. Then our current understanding of slow wave patterns in common laboratory animals and humans is presented. The implications of slow wave arrhythmic patterns that have been recorded in animals and patients suffering from gastroparesis are discussed. Finally, current challenges in experimental methods and techniques, slow wave modulation and the use of mathematical models are discussed.

A theoretical analysis of the electrogastrogram (EGG)

In this study, a boundary element model was developed to investigate the relationship between the gastric electrical activity, also known as slow waves, and the electrogastrogram (EGG). A dipole was calculated to represent the equivalent net activity of gastric slow waves. The dipole was then placed in an anatomically-realistic torso model to simulate EGG. The torso model was constructed from a laser-scanned geometry of an adult male torso phantom with 190 electrode sites equally distributed around the torso so that simulated EGG could be directly compared between the physical model and the mathematical model. The results were analyzed using the Fast Fourier Transforms (FFT), spatial distribution of EGG potential and a resultant EGG based on a 3-lead configuration. The FFT results showed both the dipole and EGG contained identical dominant frequency component of 3 cycles per minute (cpm), with this result matching known physiological phenomenon. The -3 dB point of the EGG was 110 mm from the region directly above the dipole source. Finally, the results indicated that electrode coupling could theoretically be used in a similar fashion to ECG coupling to gain greater understanding of how EGG correlate to gastric slow waves.

A theoretical study of the initiation, maintenance and termination of gastric slow wave re-entry

Gastric slow wave dysrhythmias are associated with motility disorders. Periods of tachygastria associated with slow wave re-entry were recently recognized as one important dysrhythmia mechanism, but factors promoting and sustaining gastric re-entry are currently unknown. This study reports two experimental forms of gastric re-entry and presents a series of multi-scale models that define criteria for slow wave re-entry initiation, maintenance and termination. High-resolution electrical mapping was conducted in porcine and canine models and two spatiotemporal patterns of re-entrant activities were captured: single-loop rotor and double-loop figure-of-eight. Two separate multi-scale mathematical models were developed to reproduce the velocity and entrainment frequency of these experimental recordings. A single-pulse stimulus was used to invoke a rotor re-entry in the porcine model and a figure-of-eight re-entry in the canine model. In both cases, the simulated re-entrant activities were found to be perpetuated by tachygastria that was accompanied by a reduction in the propagation velocity in the re-entrant pathways. The simulated re-entrant activities were terminated by a single-pulse stimulus targeted at the tip of re-entrant wave, after which normal antegrade propagation was restored by the underlying intrinsic frequency gradient.

MAIN FINDINGS

(i) the stability of re-entry is regulated by stimulus timing, intrinsic frequency gradient and conductivity; (ii) tachygastria due to re-entry increases the frequency gradient while showing decreased propagation velocity; (iii) re-entry may be effectively terminated by a targeted stimulus at the core, allowing the intrinsic slow wave conduction system to re-establish itself.

Automated classification and identification of slow wave propagation patterns in gastric dysrhythmia

The advent of high-resolution (HR) electrical mapping of slow wave activity has significantly improved the understanding of gastric slow wave activity in normal and dysrhythmic states. One of the current limitations of this technique is it generates a vast amount of data, making manual analysis a tedious task for research and clinical development. In this study we present new automated methods to classify, identify, and locate patterns of interest in gastric slow wave propagation. The classification method uses a similarity metric to classify slow wave propagations, while the identification algorithm uses the divergence and mean curvature of the slow wave propagation to identify and regionalize patterns of interest. The methods were applied to synthetic and experimental datasets and were also compared to manual analysis. The methods classified and identified patterns of slow wave propagation in less than 1 s, compared to manual analysis which took up to 40 min. The automated methods achieved 96% accuracy in classifying AT maps, and 95% accuracy in identifying the propagation pattern with a mean spatial error of 1.5 mm in comparison to manual methods. These new methods will facilitate the efficient translation of gastrointestinal HR mapping techniques to clinical practice.

Mapping and modeling gastrointestinal bioelectricity: from engineering bench to bedside

A key discovery in gastrointestinal motility has been the central role played by interstitial cells of Cajal (ICC) in generating electrical slow waves that coordinate contractions. Multielectrode mapping and multiscale modeling are two emerging interdisciplinary strategies now showing translational promise to investigate ICC function, electrophysiology, and contractions in the human gut.