Modelling gastrointestinal bioelectric activity

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.

Three-dimensional multi-field modelling of gastric arrhythmias and their effects on antral contractions

The contraction activation of smooth muscle in the stomach wall (SW) is coordinated by slow electrical waves. The interstitial cells of Cajal (ICC), specialised pacemaker cells, initiate and propagate these slow waves. By establishing an electrically coupled network, each ICC adjusts its intrinsic pacing frequency to a single dominant frequency, to be a key aspect in modelling the electrophysiology of gastric tissue. In terms of modelling, additional fields associated with electrical activation, such as voltage-dependent calcium influx and the resulting deformation, have hardly been considered so far. Here we present a three-dimensional model of the electro-chemomechanical activation of gastric smooth muscle contractions. To reduce computational costs, an adaptive multi-scale discretisation strategy for the temporal resolution of the electric field is used. The model incorporates a biophysically based model of gastric ICC pacemaker activity that aims to simulate stable entrainment and physiological conduction velocities of the electrical slow waves. Together with the simulation of concomitant gastric contractions and the inclusion of a mechanical feedback mechanism, the model is used to study dysrhythmias of gastric slow waves induced by abnormal stretching of the antral SW. The model is able to predict the formation of stretch-induced gastric arrhythmias, such as the emergence of an ectopic pacemaker in the gastric antrum. The results show that the ectopic event is accompanied by smooth muscle contraction and, although it disrupts the normal propagation pattern of gastric slow electrical waves, it can also catalyse the process of handling indigestible materials that might otherwise injure the gastric SW.

Effects of peristaltic amplitude and frequency on gastric emptying and mixing: a simulation study

The amplitude and frequency of peristaltic contractions are two major parameters for assessing gastric motility. However, it is not fully understood how these parameters affect the important functions of the stomach, such as gastric mixing and emptying. This study aimed to quantify the effects of peristaltic amplitude and frequency on gastric mixing and emptying using computational fluid dynamics simulation of gastric flow with an anatomically realistic model of the stomach. Our results suggest that both the increase and decrease in peristaltic amplitude have a significant impact on mixing strength and emptying rate. For example, when the peristaltic amplitude was 1.2 times higher than normal, the emptying rate was 2.7 times faster, whereas when the amplitude was half, the emptying rate was 4.2 times slower. Moreover, the emptying rate increased more than proportionally with the peristaltic frequency. The nearest contraction wave to the pylorus and the subsequent waves promoted gastric emptying. These results suggest the importance of maintaining parameters within normal ranges to achieve healthy gastric function.

Pacemaking function of two simplified cell models

Simplified nonlinear models of biological cells are widely used in computational electrophysiology. The models reproduce qualitatively many of the characteristics of various organs, such as the heart, brain, and intestine. In contrast to complex cellular ion-channel models, the simplified models usually contain a small number of variables and parameters, which facilitates nonlinear analysis and reduces computational load. In this paper, we consider pacemaking variants of the Aliev-Panfilov and Corrado two-variable excitable cell models. We conducted a numerical simulation study of these models and investigated the main nonlinear dynamic features of both isolated cells and 1D coupled pacemaker-excitable systems. Simulations of the 2D sinoatrial node and 3D intestine tissue as application examples of combined pacemaker-excitable systems demonstrated results similar to obtained previously. The uniform formulation for the conventional excitable cell models and proposed pacemaker models allows a convenient and easy implementation for the construction of personalized physiological models, inverse tissue modeling, and development of real-time simulation systems for various organs that contain both pacemaker and excitable cells.

A fully resolved multiphysics model of gastric peristalsis and bolus emptying in the upper gastrointestinal tract

Over the past few decades, in silico modeling of organ systems has significantly furthered our understanding of their physiology and biomechanical function. In spite of the relative importance of the digestive system in normal functioning of the human body, there is a scarcity of high-fidelity models for the upper gastrointestinal tract including the esophagus and the stomach. In this work, we present a detailed numerical model of the upper gastrointestinal tract that not only accounts for the fiber architecture of the muscle walls, but also the multiphasic components they help transport during normal digestive function. Construction details for 3D models of representative stomach geometry are presented along with a simple strategy for assigning circular and longitudinal muscle fiber orientations for each layer. We developed a fully resolved model of the stomach to simulate gastric peristalsis by systematically activating muscle fibers embedded in the stomach. Following this, for the first time, we simulate gravity-driven bolus emptying into the stomach due to density differences between ingested contents and fluid contents of the stomach. Finally, we present a case of retrograde flow of fluid from the stomach into the esophagus, resembling the phenomenon of acid reflux. This detailed computational model of the upper gastrointestinal tract provides a foundation for future models to investigate the biomechanics of acid reflux and probe various strategies for gastric bypass surgeries to address the growing problem of obesity.

In-Silico Prediction of Oral Drug Bioavailability: A multi-boluses approach

This work focuses on a new mathematical model able to describe in a simple manner the intestinal physiology, in order to better study drug absorption and bioavailability. The aim of our model is to overcome the limitations of physiological pharmacokinetics models of the literature, introducing a different modelling approach. The core of the new proposed model is a Discrete-Continuous Approach (DCA): a sequence of boluses travels in the investigated portion of the intestine, in counter-current with blood that flows in continuous mode. No empirical equations are implemented in this model. Simulation results show an excellent correlation between the predicted and experimental concentration profile used to validate our model. Our new approach provides a simple tool, with a good reliability, to analyze a very complex phenomenon, using only few parameters.

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.

Continuum Based Bioelectrical Simulations using Structurally Realistic Gastrointestinal Pacemaker Cell Networks

Cellular and tissue level bioelectrical activity was simulated over structurally realistic 3D interstitial cell of Cajal (ICC) networks reconstructed from confocal images of a wild type (WT) mouse model with a normal ICC distribution and a Spry4 knockout (KO) mouse model with a mild ICC hyperplasia. First, the ICC pixels within the confocal images were segmented. Then, the segmented images were visually inspected and the 3D surface mesh of the ICC tissue network was created from the 90 slices spanning the myenteric plexus ICC network. After two additional concentric meshes (representing the non-ICC and tissue bath regions) surrounding the ICC region were added, a 3D tetrahedral volume mesh containing the three regions was reconstructed. The electrical propagation through the tissue network was simulated using the bidomain continuum model. The results showed that the ICC network of the WT mouse had a smaller volume than the KO mouse (0.008 vs 0.012 mm³). The simulated bioelectrical activity for both mice showed an isotropic propagation from the initial activation region. Mean velocities of 4.2±1.5 and 4.1±1.3 mm/s were reported for the WT and KO mice, respectively. The velocity in the x-direction was higher than the y-direction for the WT mouse with a percent difference of 14.8%. On the other hand, the velocity in the y-direction was higher for the KO mouse with a percent difference of 9.5%. For both cases, there was no propagation in the z-direction as all the solution points along the same z-depth were simultaneously activated.

Modelling Flow and Mixing in the Proximal Small Intestine

The small intestine is the primary site of enzymatic digestion and nutrient absorption in humans. Intestinal contractions facilitate digesta mixing, transport and contact with the absorptive surfaces. These motility patterns are regulated by an underlying electrical activity, termed slow waves. In this study, we use computational fluid dynamics simulation of flow and mixing of intestinal contents in the human duodenum with anatomically realistic geometry and contraction patterns. Parameters including the amplitude of contraction (10-50% reduction of radius) and the rheology of the digesta (Newtonian vs Non-Newtonian power law fluid) were altered in-order to study their effects on mixing. Interesting flow features such as stagnation points and reversed flow were observed with digesta. Increases in the amplitude of contraction lead to increased propulsion of digesta along the intestine and increased mixing.

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.

Quantification of gastric emptying caused by impaired coordination of pyloric closure with antral contraction: a simulation study

Proper coordination of gastric motor functions is required for healthy gastric emptying. However, pyloric function may be impaired by functional disorders or surgical procedures. Here, we show how coordination between pyloric closure and antral contraction affects the emptying of liquid contents. We numerically simulated fluid dynamics using an anatomically realistic gastrointestinal geometry. Peristaltic contractions in the proximal stomach resulted in gastric emptying at a rate of 3-8 ml min-1. When the pylorus was unable to close, the emptying rate increased to 10-30 ml min-1, and instantaneous retrograde flow from the duodenum to the antrum occurred during antral relaxation. Rapid emptying occurred if the pylorus began to open during the terminal antral contraction, and the emptying rate was negative if the pylorus only opened during the antral relaxation phase. Our results showed that impaired coordination between antral contraction and pyloric closure can result in delayed gastric emptying, rapid gastric emptying and bile reflux.

Consistency of cutaneous electrical activity of the human colon with respect to serosal slow waves: A simulation study

The serosal slow waves in the human colon are complex, since their amplitude and frequency vary over time. Therefore, this study employed a simulation to investigate the consistency between serosal slow waves and cutaneous electrical activity by evaluating whether changes of the cutaneous waveform features due to anatomical and physiological parameters are detectable in the cutaneous electrical activity. The simulation results indicated that (a) changes in the dipole moment involve detectable changes in the amplitude of the cutaneous electrical activity; (b) changes in the annular band velocity induce modifications in the cutaneous signal frequency; and (c) changes in the anatomical factors affect both the amplitude and the frequency of the cutaneous signal. Therefore, we observed that there is consistency between serosal slow waves and cutaneous electrical activity. On these bases, we think that modifications in the cutaneous electrical activity observed in our study could represent the marker of specific physiological motor activity of the colon, and such information can improve the recording of the experimental measurements of the cutaneous electrical activity of the colon in humans.

Problems with extracellular recording of electrical activity in gastrointestinal muscle

Motility patterns of the gastrointestinal tract are important for efficient processing of nutrients and waste. Peristalsis and segmentation are based on rhythmic electrical slow waves that generate the phasic contractions fundamental to gastrointestinal motility. Slow waves are generated and propagated actively by interstitial cells of Cajal (ICC), and these events conduct to smooth muscle cells to elicit excitation-contraction coupling. Extracellular electrical recording has been utilized to characterize slow-wave generation and propagation and abnormalities that might be responsible for gastrointestinal motility disorders. Electrode array recording and digital processing are being used to generate data for models of electrical propagation in normal and pathophysiological conditions. Here, we discuss techniques of extracellular recording as applied to gastrointestinal organs and how mechanical artefacts might contaminate these recordings and confound their interpretation. Without rigorous controls for movement, current interpretations of extracellular recordings might ascribe inaccurate behaviours and electrical anomalies to ICC networks and gastrointestinal muscles, bringing into question the findings and validity of models of gastrointestinal electrophysiology developed from these recordings.

Relationship between gastric motility and liquid mixing in the stomach

The relationship between gastric motility and the mixing of liquid food in the stomach was investigated with a numerical analysis. Three parameters of gastric motility were considered: the propagation velocity, frequency, and terminal acceleration of peristaltic contractions. We simulated gastric flow with an anatomically realistic geometric model of the stomach, considering free surface flow and moving boundaries. When a peristaltic contraction approaches the pylorus, retropulsive flow is generated in the antrum. Flow separation then occurs behind the contraction. The extent of flow separation depends on the Reynolds number (Re), which quantifies the inertial forces due to the peristaltic contractions relative to the viscous forces of the gastric contents; no separation is observed at low Re, while an increase in reattachment length is observed at high Re. While mixing efficiency is nearly constant for low Re, it increases with Re for high Re because of flow separation. Hence, the effect of the propagation velocity, frequency, or terminal acceleration of peristaltic contractions on mixing efficiency increases with Re.

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.

Gastric electrical stimulation for obesity

Obesity is a growing health problem worldwide with a major impact on health and healthcare expenditures. Medical therapy in the form of diet and pharmacotherapy has limited effect on weight. Standard bariatric surgery is effective but is associated with morbidity and mortality, creating an unmet need for alternative therapies. One such therapy, the application of electrical stimulation to the stomach, has been studied extensively for the last two decades. Though pulse parameters differ between the various techniques used, the rationale behind this assumes that application of electrical current can interfere with gastric motor function or modulate afferent signaling to the brain or both. Initial studies led by industry failed to show an effect on body weight. However, more recently, there has been a renewed interest in this therapeutic modality with a number of concepts being evaluated in large human trials. If successful, this minimally invasive and low-risk intervention would be an important addition to the existing menu of therapies for obesity.

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.

Experimental evidence and mathematical modeling of thermal effects on human colonic smooth muscle contractility

It has been shown, in animal models, that gastrointestinal tract (GIT) motility is influenced by temperature; nevertheless, the basic mechanism governing thermal GIT smooth muscle responses has not been fully investigated. Studies based on physiologically tuned mathematical models have predicted that thermal inhomogeneity may induce an electrochemical destabilization of peristaltic activity. In the present study, the effect of thermal cooling on human colonic muscle strip (HCMS) contractility was studied. HCMSs were obtained from disease-free margins of resected segments for cancer. After removal of the mucosa and serosa layers, strips were mounted in separate chambers. After 30 min, spontaneous contractions developed, which were measured using force displacement transducers. Temperature was changed every hour (37, 34, and 31°C). The effect of cooling was analyzed on mean contractile activity, oscillation amplitude, frequency, and contraction to ACh (10(-5) M). At 37°C, HCMSs developed a stable phasic contraction (~0.02 Hz) with a significant ACh-elicited mean contractile response (31% and 22% compared with baseline in the circular and longitudinal axis, respectively). At a lower bath temperature, higher mean contractile amplitude was observed, and it increased in the presence of ACh (78% and 43% higher than the basal tone in the circular and longitudinal axis, respectively, at 31°C). A simplified thermochemomechanical model was tuned on experimental data characterizing the stress state coupling the intracellular Ca(2+) concentration to tissue temperature. In conclusion, acute thermal cooling affects colonic muscular function. Further studies are needed to establish the exact mechanisms involved to better understand clinical consequences of hypothermia on intestinal contractile activity.

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.

Antral recirculation in the stomach during gastric mixing

We investigate flow in the stomach during gastric mixing using a numerical simulation with an anatomically realistic geometry and free-surface flow modeling. Because of momentum differences between greater and lesser curvatures during peristaltic contractions, time-averaged recirculation is generated in the antrum, with retropulsive flow away from the pylorus and compensation flow along the greater curvature toward the pylorus. Gastric content in the distal stomach is continuously transported to the distal antrum by the forward flow of antral recirculation, and it is then mixed by the backward retropulsive flow. Hence, the content inside the antral recirculation is well mixed independently of initial location, whereas the content outside the recirculation is poorly mixed. Free-surface modeling enables us to analyze the effects of posture on gastric mixing. In the upright, prone, and right lateral positions, most of the antrum is filled with content, and the content is well mixed by antral recirculation. In contrast, in the supine and left lateral positions, most of the content is located outside antral recirculation, which results in poor mixing. The curved, twisted shape of the stomach substantially supports gastric mixing in fluid mechanical terms.

Gastric electrical stimulation for the treatment of obesity: from entrainment to bezoars-a functional review

GROWING WORLDWIDE OBESITY EPIDEMIC HAS PROMPTED THE DEVELOPMENT OF TWO MAIN TREATMENT STREAMS: (a) conservative approaches and (b) invasive techniques. However, only invasive surgical methods have delivered significant and sustainable benefits. Therefore, contemporary research exploration has focused on the development of minimally invasive gastric manipulation methods featuring a safe but reliable and long-term sustainable weight loss effect similar to the one delivered by bariatric surgeries. This antiobesity approach is based on placing external devices in the stomach ranging from electrodes for gastric electrical stimulation to temporary intraluminal bezoars for gastric volume displacement for a predetermined amount of time. The present paper examines the evolution of these techniques from invasively implantable units to completely noninvasive patient-controllable implements, from a functional, rather than from the traditional, parametric point of view. Comparative discussion over the available pilot and clinical studies related to gastric electrical stimulation outlines the promises and the fallacies of this concept as a reliable alternative anti-obesity strategy.

Modelling tissue electrophysiology with multiple cell types: applications of the extended bidomain framework

The bidomain framework has been extensively used to model tissue electrophysiology in a variety of applications. One limitation of the bidomain model is that it describes the activity of only one cell type interacting with the extracellular space. If more than one cell type contributes to the tissue electrophysiology, then the bidomain model is not sufficient. Recently, evidence has suggested that this is the case for at least two important applications: cardiac and gastrointestinal tissue electrophysiology. In the heart, fibroblasts ubiquitously interact with myocytes and are believed to play an important role in the organ electrophysiology. Along the GI tract, interstitial cells of Cajal (ICC) generate electrical waves that are passed on to surrounding smooth muscle cells (SMC), which are interconnected with the ICC and with each other. Because of the contribution of more than one cell type to the overall organ electrophysiology, investigators in different fields have independently proposed similar extensions of the bidomain model to incorporate multiple cell types and tested it on simplified geometries. In this paper, we provide a general derivation of such an extended bidomain framework applicable to any tissue and provide a generic and efficient implementation applicable to any geometry. Proof-of-concept results of tissue electrophysiology on realistic 3D organ geometries using the extended bidomain framework are presented for the heart and the stomach.

A multiscale model of the electrophysiological basis of the human electrogastrogram

The motility of the stomach is coordinated by an electrical activity termed "slow waves", and slow-wave dysrhythmias contribute to motility disorders. One major method for clinically evaluating gastric dysrhythmias has been electrogastrography (EGG); however, the clinical utility of EGG is limited partly due to the uncertainty regarding its electrophysiological basis. In this study, a multiscale model of gastric slow waves was generated from a biophysically based continuum description of cellular electrical events, coupled with a subject-specific human stomach model and high-resolution electrical mapping data. The model was then applied using a forward-modeling approach, within an anatomical torso model, to define how slow wave activity summates to generate the EGG potentials. The simulated EGG potentials were shown to be spatially varying in amplitude (0.27-0.33 mV) and duration (9.2-15.3 s), and the sources of this variance were quantified with respect to the activation timings of the underlying slow wave activity. This model constitutes an improved theory of the electrophysiological basis of the EGG, and offers a framework for optimizing the placement of EGG electrodes, and for interpreting the EGG changes occurring in disease states.

Gastrointestinal system

The functions of the gastrointestinal (GI) tract include digestion, absorption, excretion, and protection. In this review, we focus on the electrical activity of the stomach and small intestine, which underlies the motility of these organs, and where the most detailed systems descriptions and computational models have been based to date. Much of this discussion is also applicable to the rest of the GI tract. This review covers four major spatial scales: cell, tissue, organ, and torso, and discusses the methods of investigation and the challenges associated with each. We begin by describing the origin of the electrical activity in the interstitial cells of Cajal, and its spread to smooth muscle cells. The spread of electrical activity through the stomach and small intestine is then described, followed by the resultant electrical and magnetic activity that may be recorded on the body surface. A number of common and highly symptomatic GI conditions involve abnormal electrical and/or motor activity, which are often termed functional disorders. In the last section of this review we address approaches being used to characterize and diagnose abnormalities in the electrical activity and how these might be applied in the clinical setting. The understanding of electrophysiology and motility of the GI system remains a challenging field, and the review discusses how biophysically based mathematical models can help to bridge gaps in our current knowledge, through integration of otherwise separate concepts.

A model of slow wave propagation and entrainment along the stomach

Interstitial cells of Cajal (ICC) isolated from different regions of the stomach generate spontaneous electrical slow wave activity at different frequencies, with cells from the proximal stomach pacing faster than their distal counterparts. However, in vivo there exists a uniform pacing frequency; slow waves propagate aborally from the proximal stomach and subsequently entrain distal tissues. Significant resting membrane potential (RMP) gradients also exist within the stomach whereby membrane polarization generally increases from the fundus to the antrum. Both of these factors play a major role in the macroscopic electrical behavior of the stomach and as such, any tissue or organ level model of gastric electrophysiology should ensure that these phenomena are properly described. This study details a dual-cable model of gastric electrical activity that incorporates biophysically detailed single-cell models of the two predominant cell types, the ICC and smooth muscle cells. Mechanisms for the entrainment of the intrinsic pacing frequency gradient and for the establishment of the RMP gradient are presented. The resulting construct is able to reproduce experimentally recorded slow wave activity and provides a platform on which our understanding of gastric electrical activity can advance.

Characterization of gastric electrical activity using magnetic field measurements: a simulation study

Gastric disorders are often associated with abnormal propagation of gastric electrical activity (GEA). The identification of clinically relevant parameters of GEA using noninvasive measures would therefore be highly beneficial for clinical diagnosis. While magnetogastrograms (MGG) are known to provide a noninvasive representation of GEA, standard methods for their analysis are limited. It has previously been shown in simplistic conditions that the surface current density (SCD) calculated from multichannel MGG measurements provides an estimate of the gastric source location and propagation velocity. We examine the accuracy of this technique using more realistic source models and an anatomically realistic volume conductor model. The results showed that the SCD method was able to resolve the GEA parameters more reliably when the dipole source was located within 100 mm of the sensor. Therefore, the theoretical accuracy of SCD method would be relatively diminished for patients with a larger body habitus, and particularly in those patients with significant truncal obesity. However, many patients with gastric motility disorders are relatively thin due to food intolerance, meaning that the majority of the population of gastric motility patients could benefit from the methods developed here. Large errors resulted when the source was located deep within the body due to the distorting effects of the secondary sources on the magnetic fields. Larger errors also resulted when the dipole was oriented normal to the sensor plane. This was believed to be due to the relatively small contribution of the dipole source when compared to the field produced by the volume conductor. The use of three orthogonal magnetic field components rather than just one component to calculate the SCD yielded marginally more accurate results when using a realistic dipole source. However, this slight increase in accuracy may not warrant the use of more complex vector channels in future superconducting quantum interference device designs. When multiple slow waves were present in the stomach, the SCD map contained only one maximum point corresponding to the more dominant source located in the distal stomach. Parameters corresponding to the slow wave in the proximal stomach were obtained once the dominant slow terminated at the antrum. Additional validation studies are warranted to address the utility of the SCD method to resolve parameters related to gastric slow waves in a clinical setting.

A tissue framework for simulating the effects of gastric electrical stimulation and in vivo validation

Gastric pacing is used to modulate normal or abnormal gastric slow-wave activity for therapeutic purposes. New protocols are required that are optimized for motility outcomes and energy efficiency. A computational tissue model was developed, incorporating smooth muscle and interstitial cell of Cajal layers, to enable predictive simulations of slow-wave entrainment efficacy under different pacing frequencies. Concurrent experimental validation was performed via high-resolution entrainment mapping in a porcine model (bipolar pacing protocol: 2 mA amplitude; 400 ms pulsewidth; 17-s period; midcorpus). Entrained gastric slow-wave activity was found to be anisotropic (circular direction: 8.51 mm x s(-1); longitudinal: 4.58 mm x s(-1)), and the simulation velocities were specified accordingly. Simulated and experimental slow-wave activities demonstrated satisfactory agreement, showing similar propagation patterns and frequencies (3.5-3.6 cycles per minute), and comparable zones of entrainment (ZOEs; 64 cm(2)). The area of ZOE achieved was found to depend on the phase interactions between the native and entrained activities. This model allows the predictions of phase interactions between native and entrained activities, and will be useful for determining optimal frequencies for gastric pacing, including multichannel pacing studies. The model provides a framework for the development of more sophisticated predictive gastric pacing simulations in future.

Subject-specific, multiscale simulation of electrophysiology: a software pipeline for image-based models and application examples

Many simulation studies in biomedicine are based on a similar sequence of processing steps, starting from images and running through geometric model generation, assignment of tissue properties, numerical simulation and visualization of the results--a process known as image-based geometric modelling and simulation. We present an overview of software systems for implementing such a sequence both within highly integrated problem-solving environments and in the form of loosely integrated pipelines. Loose integration in this case indicates that individual programs function largely independently but communicate through files of a common format and support simple scripting, so as to automate multiple executions wherever possible. We then describe three specific applications of such pipelines to translational biomedical research in electrophysiology.

Hyperelastic Model of Anisotropic Fiber Reinforcements within Intestinal Walls for Applications in Medical Robotics

The development of an anatomically realistic model of intestinal tissue is essential for the progress of several clinical applications of medical robotics. A hyperelastic theory of the layered structure of the intestine is proposed in this paper to reproduce its purely elastic passive response from the structural organization of its main constituents. The hyperelastic strain energy function is decoupled into an isotropic term, describing the ground biological matrix, and an anisotropic term, describing the single contributions of the directional fiber-reinforcements. The response of the muscular coat layer has been modeled as a stiffening effect due to two longitudinal and circular muscular reinforcements. The contribution of the submucosa has been described from a uniform distribution of fibrillar collagen in a cross-ply arrangement. An experimental procedure has been proposed in order to characterize the passive response of porcine intestinal samples from planar uniaxial traction and shear tests. The experimental data have been non-linearly fitted in the least square sense with the results of the theoretical predictions. The mechanical parameters have been fitted with high accuracy (Rmin =0.9329, RMSEmax =0.01167), demonstrating the ability of the model to reproduce the mechanical coupling due to the presence of multiple directional reinforcements. The fundamental mechanical role of collagen morphology in the passive biomechanical behavior of intestinal wall is demonstrated. These results may drive a better understanding of the key factors in growth and remodeling of healthy and diseased tissue, together with numerous applications in robotic endoscopy, minimally invasive surgery, and biomedical research.

Surface current density mapping for identification of gastric slow wave propagation

The magnetogastrogram (MGG) records clinically relevant parameters of the electrical slow wave of the stomach noninvasively. Besides slow wave frequency, gastric slow wave propagation velocity is a potentially useful clinical indicator of the state of health of gastric tissue, but it is a difficult parameter to determine from noninvasive bioelectric or biomagnetic measurements. We present a method for computing the surface current density from multichannel MGG recordings that allows computation of the propagation velocity of the gastric slow wave. A moving dipole source model with hypothetical as well as realistic biomagnetometer parameters demonstrates that while a relatively sparse array of magnetometer sensors is sufficient to compute a single average propagation velocity, more detailed information about spatial variations in propagation velocity requires higher density magnetometer arrays. Finally, the method is validated with simultaneous MGG and serosal electromyography measurements in a porcine subject.

Gastrointestinal tract modelling in health and disease

The gastrointestinal (GI) tract is the system of organs within multi-cellular animals that takes in food, digests it to extract energy and nutrients, and expels the remaining waste. The various patterns of GI tract function are generated by the integrated behaviour of multiple tissues and cell types. A thorough study of the GI tract requires understanding of the interactions between cells, tissues and gastrointestinal organs in health and disease. This depends on knowledge, not only of numerous cellular ionic current mechanisms and signal transduction pathways, but also of large scale GI tissue structures and the special distribution of the nervous network. A unique way of coping with this explosion in complexity is mathematical and computational modelling; providing a computational framework for the multilevel modelling and simulation of the human gastrointestinal anatomy and physiology. The aim of this review is to describe the current status of biomechanical modelling work of the GI tract in humans and animals, which can be further used to integrate the physiological, anatomical and medical knowledge of the GI system. Such modelling will aid research and ensure that medical professionals benefit, through the provision of relevant and precise information about the patient’s condition and GI remodelling in animal disease models. It will also improve the accuracy and efficiency of medical procedures, which could result in reduced cost for diagnosis and treatment.

Biomechanical functional and sensory modelling of the gastrointestinal tract

The aim of this review is to describe the biomechanical, functional and sensory modelling work that can be used to integrate the physiological, anatomical and medical knowledge of the gastrointestinal (GI) system. The computational modelling in the GI tract was designed, implemented and evaluated using a series of information and communication technologies-based tools. These tools modelled the morphometry, biomechanics, functions and sensory aspects of the human GI tract. The research presented in this review is based on the virtual physiological human concept that pursues a holistic approach to representation of the human body. Such computational modelling combines imaging data, GI physiology, the gut-brain axis, geometrical and biomechanical reconstruction, and computer graphics for mechanical, electronic and pain analysis. The developed modelling will aid research and ensure that medical professionals benefit through the provision of relevant and precise information about a patient's condition. It will also improve the accuracy and efficiency of the medical procedures that could result in reduced cost for diagnosis and treatment.

Quantitative cellular description of gastric slow wave activity

Interstitial cells of Cajal (ICC) are responsible for the spontaneous and omnipresent electrical activity in the stomach. A quantitative description of the intracellular processes whose coordinated activity is believed to generate electrical slow waves has been developed and is presented here. In line with recent experimental evidence, the model describes how the interplay between the mitochondria and the endoplasmic reticulum in cycling intracellular Ca(2+) provides the primary regulatory signal for the initiation of the slow wave. The major ion channels that have been identified as influencing slow wave activity have been modeled according to data obtained from isolated ICC. The model has been validated by comparing the simulated profile of the slow waves with experimental recordings and shows good correspondence in terms of frequency, amplitude, and shape in both control and pharmacologically altered conditions.

Anatomically realistic torso model for studying the relative decay of gastric electrical and magnetic fields

Non-invasive assessment of the gastro-intestinal system has not obtained widespread clinical acceptance despite the fact that the first electrogastrograms were recorded almost a century ago. One technique that is gaining acceptance for non-invasively assessing the gastrointestinal system is the recording of cutaneous electrogastrograms. It has been proposed that measurement of the gastric magnetic field (magnetogastrogram) may produce more reliable signals in the form of a vector field and also allows the signals to be obtained with non-contact sensors. In this study, an anatomically realistic torso model of the gastrointestinal system is used to investigate the relative decay of electrical and magnetic fields resulting from gastric electrical activity. Typically the electrical fields are measured on the skin surface while the magnetic fields are recorded at locations close to, but not in contact with the skin surface. This is the first study which has used a temporal and multiple dipole source model to simulate resultant electrical and magnetic fields.

Comparison and analysis of inter-subject variability of simulated magnetic activity generated from gastric electrical activity

Electrogastrograms (EGGs) produced from gastric electrical activity (GEA) are used as a non-invasive method to aid in the assessment of a subject's gastric condition. It has been documented that recordings of the magnetic activity generated from GEA are more reliable. Typically, with magnetic measurements of GEA, only activity perpendicular to the body is recorded. Also, external anatomical landmarks are used to position the magnetic recording devices, SQUIDs, (Superconducting Quantum Interference Devices) over the stomach with no allowance made for body habitus. In the work presented here, GEA and its corresponding magnetic activity are simulated. Using these data, we investigate the effects of using a standard SQUID location as well as a customized SQUID position and the contribution the magnetic component perpendicular to the body makes to the magnetic field. We also explore the effects of the stomach wall thickness on the resultant magnetic fields. The simulated results show that the thicker the wall, the larger the magnitude of the magnetic field holding the same signal patterns. We conclude that most of the magnetic activity arising from GEA occurs in a plane parallel to the anterior body. We also conclude that using a standard SQUID position can be suboptimal.

A quantitative model of gastric smooth muscle cellular activation

A physiologically realistic quantitative description of the electrical behavior of a gastric smooth muscle (SM) cell is presented. The model describes the response of a SM cell when activated by an electrical stimulus coming from the network of interstitial cells of Cajal (ICC) and is mediated by the activation of different ion channels species in the plasma membrane. The conductances (predominantly Ca2+ and K+) that are believed to substantially contribute to the membrane potential fluctuations during slow wave activity have been included in the model. A phenomenological description of intracellular Ca2+ dynamics has also been included because of its primary importance in regulating a number of cellular processes. In terms of shape, duration, and amplitude, the resulting simulated smooth muscle depolarizations (SMDs) are in good agreement with experimentally recordings from mammalian gastric SM in control and altered conditions. This model has also been designed to be suitable for incorporation into large scale multicellular simulations.

Anatomically realistic multiscale models of normal and abnormal gastrointestinal electrical activity

One of the major aims of the International Union of Physiological Sciences (IUPS) Physiome Project is to develop multiscale mathematical and computer models that can be used to help understand human health. We present here a small facet of this broad plan that applies to the gastrointestinal system. Specifically, we present an anatomically and physiologically based modelling framework that is capable of simulating normal and pathological electrical activity within the stomach and small intestine. The continuum models used within this framework have been created using anatomical information derived from common medical imaging modalities and data from the Visible Human Project. These models explicitly incorporate the various smooth muscle layers and networks of interstitial cells of Cajal (ICC) that are known to exist within the walls of the stomach and small bowel. Electrical activity within individual ICCs and smooth muscle cells is simulated using a previously published simplified representation of the cell level electrical activity. This simulated cell level activity is incorporated into a bidomain representation of the tissue, allowing electrical activity of the entire stomach or intestine to be simulated in the anatomically derived models. This electrical modelling framework successfully replicates many of the qualitative features of the slow wave activity within the stomach and intestine and has also been used to investigate activity associated with functional uncoupling of the stomach.

Dynamics of intestinal propulsion

A biomechanical model and mathematical formulation of the problem of propulsion of a solid non-deformable pellet by an isolated segment of the gut are presented. The organ is modeled as a soft orthotropic cylindrical biological shell. Its wall is reinforced by transversely isotropic muscle fibers of orthogonal type of weaving embedded in a connective tissue stroma. The mechanical properties of the wall are assumed to be nonlinear, deformations are finite. The longitudinal smooth muscle syncitium possesses anisotropic and the circular muscle syncytium has anisotropic electrical properties. Their electromechanical activity is under control of a pacemaker, which is represented by interstitial cells of Cajal. The model describes the dynamics of the generation and propagation of mechanical waves of contraction-relaxation along the surface of the bioshell and propulsion of the pellet. The governing system of equations was solved numerically. The combined finite-difference and finite-element method was used. The results demonstrate that pendular movements alone provide an aboral transit, without mixing though, of the bolus. Non-propagating segmental contractions show small amplitude librations of the pellet without its visible propulsion. Only the coordinated activity of both smooth muscle layers in a form of the peristaltic reflex provides physiologically significant simultaneous propulsion and mixing of the intraluminal content (pellet).

Three-dimensional finite element modelling of muscle forces during mastication

This paper presents a three-dimensional finite element model of human mastication. Specifically, an anatomically realistic model of the masseter muscles and associated bones is used to investigate the dynamics of chewing. A motion capture system is used to track the jaw motion of a subject chewing standard foods. The three-dimensional nonlinear deformation of the masseter muscles are calculated via the finite element method, using the jaw motion data as boundary conditions. Motion-driven muscle activation patterns and a transversely isotropic material law, defined in a muscle-fibre coordinate system, are used in the calculations. Time-force relationships are presented and analysed with respect to different tasks during mastication, e.g. opening, closing, and biting, and are also compared to a more traditional one-dimensional model. The results strongly suggest that, due to the complex arrangement of muscle force directions, modelling skeletal muscles as conventional one-dimensional lines of action might introduce a significant source of error.

Solving the cardiac bidomain equations for discontinuous conductivities

Fast simulations of cardiac electrical phenomena demand fast matrix solvers for both the elliptic and parabolic parts of the bidomain equations. It is well known that fast matrix solvers for the elliptic part must address multiple physical scales in order to show robust behavior. Recent research on finding the proper solution method for the bidomain equations has addressed this issue whereby multigrid preconditioned conjugate gradients has been used as a solver. In this paper, a more robust multigrid method, called Black Box Multigrid, is presented as an alternative to conventional geometric multigrid, and the effect of discontinuities on solver performance for the elliptic and parabolic part is investigated. Test problems with discontinuities arising from inserted plunge electrodes and naturally occurring myocardial discontinuities are considered. For these problems, we explore the advantages to using a more advanced multigrid method like Black Box Multigrid over conventional geometric multigrid. Results will indicate that for certain discontinuous bidomain problems Black Box Multigrid provides 60% faster simulations than using conventional geometric multigrid. Also, for the problems examined, it will be shown that a direct usage of conventional multigrid leads to faster simulations than an indirect usage of conventional multigrid as a preconditioner unless there are sharp discontinuities.

An integrative software package for gastrointestinal biomagnetic data acquisition and analysis using SQUID magnetometers

The study of bioelectric and biomagnetic activity in the human gastrointestinal (GI) tract is of great interest in clinical research due to the proven possibility to detect pathological conditions thereof from electric and magnetic field recordings. The magnetogastrogram (MGG) and magnetoenterogram (MENG) can be recorded using superconducting quantum interference device (SQUID) magnetometers, which are the most sensitive magnetic flux-to-voltage converters currently available. To address the urgent need for powerful acquisition and analysis software tools faced by many researchers and clinicians in this important area of investigation, an integrative and modular computer program was developed for the acquisition, processing and analysis of GI SQUID signals. In addition to a robust hardware implementation for efficient data acquisition, a number of signal processing and analysis modules were developed to serve in a variety of both clinical procedures and scientific investigations. Implemented software features include data processing and visualization, waterfall plots of signal frequency spectra as well as spatial maps of GI signal frequencies. Moreover, a software tool providing powerful 3D visualizations of GI signals was created using realistic models of the human torso and internal organs.

Computational simulations of the human magneto- and electroenterogram

Many functional pathologies of the small intestine are difficult to diagnose clinically without an invasive surgical intervention. Often such conditions are associated with a disruption of the normal electrical activity occurring within the musculature of the small intestine. The far field electrical signals on the torso surface arising from the electrical activity within the small intestine cannot be reliably measured. However, it has been shown that abnormal electrical activity in the small intestine can be distinguished by recording the magnetic fields of intestinal origin immediately outside the torso surface. We have developed an anatomically-based computational model to simulate slow wave propagation in the small intestine, the resulting cutaneous electrical field and the magnetic field outside the torso. Using both a one-dimensional and a three-dimensional model of the duodenum we investigate the degree of detail that is required to realistically simulate this far field activity. Our results indicate that some of the qualitative behavior in the far field activity can be replicated using a one-dimensional model, although there are clear situations where the greater level modeling detail is required.

Three-dimensional surface model analysis in the gastrointestinal tract

The biomechanical changes during functional loading and unloading of the human gastrointestinal (GI) tract are not fully understood. GI function is usually studied by introducing probes in the GI lumen. Computer modeling offers a promising alternative approach in this regard, with the additional ability to predict regional stresses and strains in inaccessible locations. The tension and stress distributions in the GI tract are related to distensibility (tension-strain relationship) and smooth muscle tone. More knowledge on the tension and stress on the GI tract are needed to improve diagnosis of patients with gastrointestinal disorders. A modeling framework that can be used to integrate the physiological, anatomical and medical knowledge of the GI system has recently been developed. The 3-D anatomical model was constructed from digital images using ultrasonography, computer tomography (CT) or magnetic resonance imaging (MRI). Different mathematical algorithms were developed for surface analysis based on thin-walled structure and the finite element method was applied for the mucosa-folded three layered esophageal model analysis. The tools may be useful for studying the geometry and biomechanical properties of these organs in health and disease. These studies will serve to test the structure-function hypothesis of geometrically complex organs.