Quantitative cellular description of gastric slow wave activity

A novel compartmental approach for modeling stomach motility and gastric emptying

The stomach, a central organ in the Gastrointestinal (GI) tract, regulates the processing of ingested food through gastric motility and emptying. Understanding the stomach function is crucial for treating gastric disorders. Experimental studies in this field often face difficulties due to limitations and invasiveness of available techniques and ethical concerns. To counter this, researchers resort to computational and numerical methods. However, existing computational studies often isolate one aspect of the stomach function while neglecting the rest and employ computationally expensive methods. This paper proposes a novel cost-efficient multi-compartmental model, offering a comprehensive insight into gastric function at an organ level, thus presenting a promising alternative. The proposed approach divides the spatial geometry of the stomach into four compartments: Proximal/Middle/Terminal antrum and Pyloric sphincter. Each compartment is characterized by a set of ordinary differential equations (ODEs) with respect to time to characterize the stomach function. Electrophysiology is represented by simplified equations reflecting the "slow wave behavior" of Interstitial Cells of Cajal (ICC) and Smooth Muscle Cells (SMC) in the stomach wall. An electro-mechanical coupling model translates SMC "slow waves" into smooth muscle contractions. Muscle contractions induce peristalsis, affecting gastric fluid flow velocity and subsequent emptying when the pyloric sphincter is open. Contraction of the pyloric sphincter initiates a retrograde flow jet at the terminal antrum, modeled by a circular liquid jet flow equation. The results from the proposed model for a healthy human stomach were compared with experimental and computational studies on electrophysiology, muscle tissue mechanics, and fluid behavior during gastric emptying. These findings revealed that each "ICC" slow wave corresponded to a muscle contraction due to electro-mechanical coupling behavior. The rate of gastric emptying and mixing efficiency decreased with increasing viscosity of gastric liquid but remained relatively unchanged with gastric liquid density variations. Utilizing different ODE solvers in MATLAB, the model was solved, with ode15s demonstrating the fastest computation time, simulating 180 s of real-time stomach response in just 2.7 s. This multi-compartmental model signifies a promising advancement in understanding gastric function, providing a cost-effective and comprehensive approach to study complex interactions within the stomach and test innovative therapies like neuromodulation for treating gastric disorders.

In Silico Electrophysiological Investigation of Transient Receptor Potential Melastatin-4 Ion Channel Biophysics to Study Detrusor Overactivity

Enhanced electrical activity in detrusor smooth muscle (DSM) cells is a key factor in detrusor overactivity which causes overactive bladder pathological disorders. Transient receptor potential melastatin-4 (TRPM4) channels, which are calcium-activated cation channels, play a role in regulating DSM electrical activities. These channels likely contribute to depolarizing the DSM cell membrane, leading to bladder overactivity. Our research focuses on understanding TRPM4 channel function in the DSM cells of mice, using computational modeling. We aimed to create a detailed computational model of the TRPM4 channel based on existing electrophysiological data. We employed a modified Hodgkin-Huxley model with an incorporated TRP-like current to simulate action potential firing in response to current and synaptic stimulus inputs. Validation against experimental data showed close agreement with our simulations. Our model is the first to analyze the TRPM4 channel's role in DSM electrical activity, potentially revealing insights into bladder overactivity. In conclusion, TRPM4 channels are pivotal in regulating human DSM function, and TRPM4 channel inhibitors could be promising targets for treating overactive bladder.

Biophysical Mechanisms of Vaginal Smooth Muscle Contraction: The Role of the Membrane Potential and Ion Channels

The vagina is an essential component of the female reproductive system and is responsible for providing female sexual satisfaction. Vaginal smooth muscle contraction plays a crucial role in various physiological processes, including sexual arousal, childbirth, and urinary continence. In pathophysiological conditions, such as pelvic floor disorders, aberrations in vaginal smooth muscle function can lead to urinary incontinence and pelvic organ prolapse. A set of cellular and sub-cellular physiological mechanisms regulates the contractile properties of the vaginal smooth muscle cells. Calcium influx is a crucial determinant of smooth muscle contraction, facilitated through voltage-dependent calcium channels and calcium release from intracellular stores. Comprehensive reviews on smooth muscle biophysics are relatively scarce within the scientific literature, likely due to the complexity and specialized nature of the topic. The objective of this review is to provide a comprehensive description of alterations in the cellular physiology of vaginal smooth muscle contraction. The benefit associated with this particular approach is that conducting a comprehensive examination of the cellular mechanisms underlying contractile activation will enable the creation of more targeted therapeutic agents to control vaginal contraction disorders.

Neural regulation of slow waves and phasic contractions in the distal stomach: a mathematical model

Objective.Neural regulation of gastric motility occurs partly through the regulation of gastric bioelectrical slow waves (SWs) and phasic contractions. The interaction of the tissues and organs involved in this regulatory process is complex. We sought to infer the relative importance of cellular mechanisms in inhibitory neural regulation of the stomach by enteric neurons and the interaction of inhibitory and excitatory electrical field stimulation.Approach.A novel mathematical model of gastric motility regulation by enteric neurons was developed and scenarios were simulated to determine the mechanisms through which enteric neural influence is exerted. This model was coupled to revised and extended electrophysiological models of gastric SWs and smooth muscle cells (SMCs).Main results.The mathematical model predicted that regulation of contractile apparatus sensitivity to intracellular calcium in the SMC was the major inhibition mechanism of active tension development, and that the effect on SW amplitude depended on the inhibition of non-specific cation currents more than the inhibition of calcium-activated chloride current (kiNSCC= 0.77 vs kiAno1= 0.33). The model predicted that the interaction between inhibitory and excitatory neural regulation, when applied with simultaneous and equal intensity, resulted in an inhibition of contraction amplitude almost equivalent to that of inhibitory stimulation (79% vs 77% decrease), while the effect on frequency was overall excitatory, though less than excitatory stimulation alone (66% vs 47% increase).Significance.The mathematical model predicts the effects of inhibitory and excitatory enteric neural stimulation on gastric motility function, as well as the effects when inhibitory and excitatory enteric neural stimulation interact. Incorporation of the model into organ-level simulations will provide insights regarding pathological mechanisms that underpin gastric functional disorders, and allow forin silicotesting of the effects of clinical neuromodulation protocols for the treatment of these disorders.

Steady-state approximations for Hodgkin-Huxley cell models: Reduction of order for uterine smooth muscle cell model

Multi-scale mathematical bioelectrical models of organs such as the uterus, stomach or heart present challenges both for accuracy and computational tractability. These multi-scale models are typically founded on models of biological cells derived from the classic Hodkgin-Huxley (HH) formalism. Ion channel behaviour is tracked with dynamical variables representing activation or inactivation of currents that relax to steady-state dependencies on cellular membrane voltage. Timescales for relaxation may be orders of magnitude faster than companion ion channel variables or phenomena of physiological interest for the entire cell (such as bursting sequences of action potentials) or the entire organ (such as electromechanical coordination). Exploiting these time scales with steady-state approximations for relatively fast-acting systems is a well-known but often overlooked approach as evidenced by recent published models. We thus investigate feasibility of an extensive reduction of order for an HH-type cell model with steady-state approximations to the full dynamical activation and inactivation ion channel variables. Our effort utilises a published comprehensive uterine smooth muscle cell model that encompasses 19 ordinary differential equations and 105 formulations overall. The numerous ion channel submodels in the published model exhibit relaxation times ranging from order 10-1 to 105 milliseconds. Substitution of the faster dynamic variables with steady-state formulations demonstrates both an accurate reproduction of the full model and substantial improvements in time-to-solve, for test cases performed. Our demonstration here of an effective and relatively straightforward reduction method underlines the particular importance of considering time scales for model simplification before embarking on large-scale computations or parameter sweeps. As a preliminary complement to more intensive reduction of order methods such as parameter sensitivity and bifurcation analysis, this approach can rapidly and accurately improve computational tractability for challenging multi-scale organ modelling efforts.

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.

Engaging biological oscillators through second messenger pathways permits emergence of a robust gastric slow-wave during peristalsis

Peristalsis, the coordinated contraction—relaxation of the muscles of the stomach is important for normal gastric motility and is impaired in motility disorders. Coordinated electrical depolarizations that originate and propagate within a network of interconnected layers of interstitial cells of Cajal (ICC) and smooth muscle (SM) cells of the stomach wall as a slow-wave, underly peristalsis. Normally, the gastric slow-wave oscillates with a single period and uniform rostrocaudal lag, exhibiting network entrainment. Understanding of the integrative role of neurotransmission and intercellular coupling in the propagation of an entrained gastric slow-wave, important for understanding motility disorders, however, remains incomplete. Using a computational framework constituted of a novel gastric motility network (GMN) model we address the hypothesis that engaging biological oscillators (i.e., ICCs) by constitutive gap junction coupling mechanisms and enteric neural innervation activated signals can confer a robust entrained gastric slow-wave. We demonstrate that while a decreasing enteric neural innervation gradient that modulates the intracellular IP₃ concentration in the ICCs can guide the aboral slow-wave propagation essential for peristalsis, engaging ICCs by recruiting the exchange of second messengers (inositol trisphosphate (IP₃) and Ca²⁺) ensures a robust entrained longitudinal slow-wave, even in the presence of biological variability in electrical coupling strengths. Our GMN with the distinct intercellular coupling in conjunction with the intracellular feedback pathways and a rostrocaudal enteric neural innervation gradient allows gastric slow waves to oscillate with a moderate range of frequencies and to propagate with a broad range of velocities, thus preventing decoupling observed in motility disorders. Overall, the findings provide a mechanistic explanation for the emergence of decoupled slow waves associated with motility impairments of the stomach, offer directions for future experiments and theoretical work, and can potentially aid in the design of new interventional pharmacological and neuromodulation device treatments for addressing gastric motility disorders.

The coordinated contraction and relaxation of the muscles of the stomach, known as peristalsis is important for normal gastric motility and primarily governed by electrical depolarizations that originate and propagate within a network of interconnected layers of interstitial cells of Cajal (ICCs) and smooth muscle cells of the stomach wall as a slow-wave. Under normal conditions, a gastric slow-wave oscillates with a single period and uniform rostrocaudal lag, exhibiting network entrainment. However, the understanding of intrinsic and extrinsic mechanisms that ensure propagation of a robust entrained slow-wave remains incomplete. Here, using a computational framework, we show that in conjunction with an enteric neural innervation gradient along the rostrocaudal ICC chain, and intercellular electrical coupling, the intercellular exchange of inositol trisphosphate between ICCs prevents decoupling by extending the longitudinal entrainment range along the stomach wall, even when variability in intercellular coupling exists. The findings from our study indicate ways that ensure the rostrocaudal spread of a robust gastric slow-wave and provide a mechanistic explanation for the emergence of decoupled slow waves associated with motility impairments of the stomach.

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.

A novel approach for model-based design of gastric pacemakers

Understanding the slow wave propagation patterns of Interstitial Cells of Cajal (ICC) is essential when designing Gastric Electrical Stimulators (GESs) to treat motility disorders. A GES with the ability to both sense and pace, working in closed-loop with the ICC, will enable efficient modulation of Gastrointestinal (GI) dysrhythmias. However, existing GESs targeted at modulating GI dysrhythmias operate in an open-loop and hence their clinical efficacy is uncertain. This paper proposes a novel model-based approach for designing GESs that operate in closed-loop with the GI tract. GES is modelled using Hybrid Input Output Automata (HIOA), a well-known formal model, which is suitable for designing safety-critical systems. A two-dimensional ICC network working in real-time with the GES is developed using the same compositional HIOA framework. The ICC network model is used to simulate normal and diseased action potential propagation patterns akin to those observed during GI dysrhythmias. The efficacy of the proposed GES is then validated by integrating it in closed-loop with the ICC network. Results show that the proposed GES is able to sense the propagation patterns and modulate the dysrhythmic patterns of bradygastria back to its normal state automatically. The proposed design of the GES is flexible enough to treat a variety of diseased dysrhythmic patterns using closed-loop operation.

Four Ways to Fit an Ion Channel Model

Mathematical models of ionic currents are used to study the electrophysiology of the heart, brain, gut, and several other organs. Increasingly, these models are being used predictively in the clinic, for example, to predict the risks and results of genetic mutations, pharmacological treatments, or surgical procedures. These safety-critical applications depend on accurate characterization of the underlying ionic currents. Four different methods can be found in the literature to fit voltage-sensitive ion channel models to whole-cell current measurements: method 1, fitting model equations directly to time-constant, steady-state, and I-V summary curves; method 2, fitting by comparing simulated versions of these summary curves to their experimental counterparts; method 3, fitting to the current traces themselves from a range of protocols; and method 4, fitting to a single current trace from a short and rapidly fluctuating voltage-clamp protocol. We compare these methods using a set of experiments in which hERG1a current was measured in nine Chinese hamster ovary cells. In each cell, the same sequence of fitting protocols was applied, as well as an independent validation protocol. We show that methods 3 and 4 provide the best predictions on the independent validation set and that short, rapidly fluctuating protocols like that used in method 4 can replace much longer conventional protocols without loss of predictive ability. Although data for method 2 are most readily available from the literature, we find it performs poorly compared to methods 3 and 4 both in accuracy of predictions and computational efficiency. Our results demonstrate how novel experimental and computational approaches can improve the quality of model predictions in safety-critical applications.

A Formal Approach for Scalable Simulation of Gastric ICC Electrophysiology

OBJECTIVE

Efficient and accurate organ models are crucial for closed-loop validation of implantable medical devices. This paper investigates bio-electric slow wave modeling of the stomach, so that gastric electrical stimulator (GES) can be validated and verified prior to implantation. In particular, we consider high-fidelity, scalable, and efficient modeling of the pacemaker, Interstitial cells of Cajal (ICC), based on the formal hybrid input output automata (HIOA) framework.

METHODS

Our work is founded in formal methods, a collection of mathematically sound techniques originating in computer science for the design and validation of safety-critical systems. We modeled each ICC cell using an HIOA. We also introduce an HIOA path model to capture the electrical propagation delay between cells in a network. The resultant network of ICC cells can simulate normal and diseased action potential propagation patterns, making it useful for device validation.

RESULTS

The simulated slow wave of a single ICC cell had high correlation ( ≈ 0.9) with the corresponding biophysical models.

CONCLUSIONS

The proposed model is able to simulate the slow wave activity of a network of ICC cells with high-fidelity for device validation.

SIGNIFICANCE

The proposed HIOA model is significantly more efficient than the corresponding biophysical models, scales to larger networks of ICC cells, and is capable of simulating varying propagation patterns. This has the potential to enable verification and validation of implantable GESs in closed-loop with gastrointestinal models in the future.

Computational motility models of neurogastroenterology and neuromodulation

The success of neuromodulation therapies, particularly in the brain, spinal cord, and peripheral nerves, has been greatly aided by computational, biophysical models. However, treating gastrointestinal disorders with electrical stimulation has been much less explored, partly because the mode of action of such treatments is unclear, and selection of stimulation parameters is often empirical. Progress in gut neuromodulation is limited by the comparative lack of biophysical models capable of simulating neuromodulation of gastrointestinal function. Here, we review the recently developed biophysical models of electrically-active cells in the gastrointestinal system that contribute to motility. Biophysical models are replacing phenomenologically-defined models due to advancements in electrophysiological characterization of key players in the gut: enteric neurons, smooth muscle fibers, and interstitial cells of Cajal. In this review, we explore existing biophysically-defined cellular and network models that contribute to gastrointestinal motility. We focus on recent models that are laying the groundwork for modeling electrical stimulation of the gastrointestinal system. Developing models of gut neuromodulation will improve our mechanistic understanding of these treatments, leading to better parameterization, selectivity, and efficacy of neuromodulation to treat gastrointestinal disorders. Such models may have direct clinical translation to current neuromodulation therapies, such as sacral nerve stimulation.

A biophysically constrained computational model of the action potential of mouse urinary bladder smooth muscle

Urinary incontinence is associated with enhanced spontaneous phasic contractions of the detrusor smooth muscle (DSM). Although a complete understanding of the etiology of these spontaneous contractions is not yet established, it is suggested that the spontaneously evoked action potentials (sAPs) in DSM cells initiate and modulate the contractions. In order to further our understanding of the ionic mechanisms underlying sAP generation, we present here a biophysically detailed computational model of a single DSM cell. First, we constructed mathematical models for nine ion channels found in DSM cells based on published experimental data: two voltage gated Ca2+ ion channels, an hyperpolarization-activated ion channel, two voltage-gated K+ ion channels, three Ca2+-activated K+ ion channels and a non-specific background leak ion channel. The ion channels' kinetics were characterized in terms of maximal conductances and differential equations based on voltage or calcium-dependent activation and inactivation. All ion channel models were validated by comparing the simulated currents and current-voltage relations with those reported in experimental work. Incorporating these channels, our DSM model is capable of reproducing experimentally recorded spike-type sAPs of varying configurations, ranging from sAPs displaying after-hyperpolarizations to sAPs displaying after-depolarizations. The contributions of the principal ion channels to spike generation and configuration were also investigated as a means of mimicking the effects of selected pharmacological agents on DSM cell excitability. Additionally, the features of propagation of an AP along a length of electrically continuous smooth muscle tissue were investigated. To date, a biophysically detailed computational model does not exist for DSM cells. Our model, constrained heavily by physiological data, provides a powerful tool to investigate the ionic mechanisms underlying the genesis of DSM electrical activity, which can further shed light on certain aspects of urinary bladder function and dysfunction.

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

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

Progress in Mathematical Modeling of Gastrointestinal Slow Wave Abnormalities

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

A mechanistic model of a PDGFRα(+) cell

A novel platelet-derived growth factor receptor alpha-positive cell (PDGFRα(+)) has recently been identified as part of the purinergic inhibitory neural control mechanism in the gastrointestinal (GI) tract. The mechanism through which PDGFRα(+) cells mediate GI muscle relaxation has been found to be associated with the purine receptors P2Y1 and apamin-sensitive SK3 channels that are highly expressed in these cells. This study aims to develop a mechanistic model elucidating a proposed mechanism through which PDGFRα(+) cells contribute to purinergic inhibitory neuromuscular transmission. In accordance with recent experimental findings, the model describes how the binding of neurotransmitters, released from enteric neurons, triggers the release of Ca(2+) from the endoplasmic reticulum in the PDGFRα(+) cells, and how this subsequently leads to large amplitude transient outward currents, which in turn hyperpolarize the cell. The model has been validated against experimental recordings and good agreement was found under normal and pharmacologically-altered conditions. This model demonstrates the feasibility of the proposed mechanism and provides a basis for understanding the mechanism underlying purinergic control of colonic motility.

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.

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.

A simplified biophysical cell model for gastric slow wave entrainment simulation

Gastric electrical activity, also termed slow wave activity, is generated by a class of pacemaker cells called the interstitial cells of Cajal (ICC), which are organized with decreasing intrinsic frequencies along the stomach. In the healthy stomach, slow waves of different intrinsic frequencies converge to a single frequency with a constant phase-lag, in a process called entrainment. The main aim of this study was to develop a simplified biophysical ICC model that is capable of modeling the self-excitatory behavior and standard morphology of gastric slow waves. Entrainment of gastric slow waves was simulated in a one-dimensional (1D) model, with a linear gradient of intrinsic slow wave frequencies. In a coupled 1D model, the simulated slow waves were entrained to a single frequency; whereas in an uncoupled 1D model, the simulated slow waves occurred at different frequencies, resulting in loss of entrainment. The new cell model presents an option for future large multi-scale simulations of gastric slow waves in intact ICC network and diseased conditions where the loss of entrainment may lead to slow wave dysrhythmias and diminished gastric motility.

Cellular automaton model for simulating tissue-specific intestinal electrophysiological activity

Depletion of interstitial cell of Cajal (ICC) networks is known to occur in various gastrointestinal (GI) motility disorders. Although techniques for quantifying the structure of ICC networks are available, the ICC network structure-function relationships are yet to be well elucidated. Existing methods of relating ICC structure to function are computationally expensive, and it is difficult to up-scale them to larger multiscale simulations. A new cellular automaton model for simulating tissue-specific slow wave propagation was developed, and in preliminary studies the automaton model was applied on jejunal ICC network structures from wild-type and 5-HT2B receptor knockout (ICC depleted) mice. Two metrics were also developed to quantify the simulated propagation patterns: 1) ICC and 2) non-ICC activation lag metrics. These metrics measured the average delay in time taken for the slow wave to propagate across the ICC and non-ICC domain throughout the entire network compared to the theoretical fastest propagation, respectively. Slow wave propagation was successfully simulated across the ICC networks with greatly reduced computational time compared to previous methods, and the propagation pattern metrics quantitatively revealed an impaired propagation during ICC depletion. In conclusion, the developed slow wave propagation model and propagation pattern metrics offer a computationally efficient framework for relating ICC structure to function. These tools can now be further applied to define ICC structure-function relationships across various spatial and temporal scales.

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.

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

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

Normal and abnormal electrical propagation in the small intestine

As in other muscular organs, small intestinal motility is determined to a large degree by the electrical activities that occur in the smooth muscle layers of the small intestine. In recent decades, the interstitial cells of Cajal, located in the myenteric plexus, have been shown to be responsible for the generation and propagation of the electrical impulse: the slow wave. It was also known that the slow waves as such do not cause contraction, but that the action potentials ('spikes') that are generated by the slow waves are responsible for the contractions. Recording from large number of extracellular electrodes simultaneously is one method to determine origin and pattern of propagation of these electrical signals. This review reports the characteristics of slow wave propagation through the intestinal tube, the occurrence of propagation blocks along its length, which explains the well-known decrease in frequency, and the specific propagation pattern of the spikes that follow the slow waves. But the value of high-resolution mapping is highest in discovering and analysing mechanisms of arrhythmias in the gut. Most recently, circus movements (also called 're-entries') have been described in the small intestine in several species. Moreover, several types of re-entries have now been described, some similar to what may occur in the heart, such as functional re-entries, but others more unique to the small intestine, such as circumferential re-entry. These findings seem to suggest the possibilities of hitherto unknown pathologies that may be present in the small intestine.

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.

Modeling of stochastic behavior of pacemaker potential in interstitial cells of Cajal

It is widely accepted that interstitial cells of Cajal (ICCs) generate pacemaker potentials to propagate slow waves along the whole gastrointestinal tract. Previously, we constructed a biophysically based model of ICCs in mouse small intestine to explain the pacemaker mechanism. Our previous model, however, could not explain non-uniformity of pacemaker potentials and random occurrence of unitary potentials, thus we updated our model. The inositol 1,4,5-trisphosphate (IP3)-mediated Ca(2+) mobilization is a key event to drive the cycle of pacemaker activity and was updated to reproduce its stochastic behavior. The stochasticity was embodied by simulating random opening and closing of individual IP3-mediated Ca(2+) channel. The updated model reproduces the stochastic features of pacemaker potentials in ICCs. Reproduced pacemaker potentials are not uniform in duration and interval. The resting and peak potentials are -75.5 ± 1.1 mV and -0.8 ± 0.5 mV, respectively (n = 55). Frequency of pacemaker potential is 14.3 ± 0.4 min(-1) (n = 10). Width at half-maximal amplitude of pacemaker potential is 902 ± 6 ms (n = 55). There are random events of unitary potential-like depolarization. Finally, we compared our updated model with a recently published model to speculate which ion channel is the best candidate to drive pacemaker depolarization. In conclusion, our updated mathematical model could now reproduce stochastic features of pacemaker activity in ICCs.

Mitochondrial calcium handling within the interstitial cells of Cajal

The interstitial cells of Cajal (ICC) drive rhythmic pacemaking contractions in the gastrointestinal system. The ICC generate pacemaking signals by membrane depolarizations associated with the release of intracellular calcium (Ca(2+)) in the endoplasmic reticulum (ER) through inositol-trisphosphate (IP3) receptors (IP3R) and uptake by mitochondria (MT). This Ca(2+) dynamic is hypothesized to generate pacemaking signals by calibrating ER Ca(2+) store depletions and membrane depolarization with ER store-operated Ca(2+) entry mechanisms. Using a biophysically based spatio-temporal model of integrated Ca(2+) transport in the ICC, we determined the feasibility of ER depletion timescale correspondence with experimentally observed pacemaking frequencies while considering the impact of IP3R Ca(2+) release and MT uptake on bulk cytosolic Ca(2+) levels because persistent elevations of free intracellular Ca(2+) are toxic to the cell. MT densities and distributions are varied in the model geometry to observe MT influence on free cytosolic Ca(2+) and the resulting frequencies of ER Ca(2+) store depletions, as well as the sarco-endoplasmic reticulum Ca(2+) ATP-ase (SERCA) and IP3 agonist concentrations. Our simulations show that high MT densities observed in the ICC are more relevant to ER establishing Ca(2+) depletion frequencies than protection of the cytosol from elevated free Ca(2+), whereas the SERCA pump is more relevant to containing cytosolic Ca(2+) elevations. Our results further suggest that the level of IP3 agonist stimulating ER Ca(2+) release, subsequent MT uptake, and eventual activation of ER store-operated Ca(2+) entry may determine frequencies of rhythmic pacemaking exhibited by the ICC across species and tissue types.

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

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

Computational modeling of anoctamin 1 calcium-activated chloride channels as pacemaker channels in interstitial cells of Cajal

Interstitial cells of Cajal (ICC) act as pacemaker cells in the gastrointestinal tract by generating electrical slow waves to regulate rhythmic smooth muscle contractions. Intrinsic Ca(2+) oscillations in ICC appear to produce the slow waves by activating pacemaker currents, currently thought to be carried by the Ca(2+)-activated Cl(-) channel anoctamin 1 (Ano1). In this article we present a novel model of small intestinal ICC pacemaker activity that incorporates store-operated Ca(2+) entry and a new model of Ano1 current. A series of simulations were carried out with the ICC model to investigate current controversies about the reversal potential of the Ano1 Cl(-) current in ICC and to predict the characteristics of the other ion channels that are necessary to generate slow waves. The model results show that Ano1 is a plausible pacemaker channel when coupled to a store-operated Ca(2+) channel but suggest that small cyclical depolarizations may still occur in ICC in Ano1 knockout mice. The results predict that voltage-dependent Ca(2+) current is likely to be negligible during the slow wave plateau phase. The model shows that the Cl(-) equilibrium potential is an important modulator of slow wave morphology, highlighting the need for a better understanding of Cl(-) dynamics in ICC.

Reconstruction of normal and abnormal gastric electrical sources using a potential based inverse method

The use of cutaneous recordings to non-invasively characterize gastric slow waves has had limited clinical acceptance, primarily due to the uncertainty in relating the recorded signal to the underlying gastric slow waves. In this study we aim to distinguish and quantitatively reconstruct different slow wave patterns using an inverse algorithm. Slow wave patterns corresponding to normal, retrograde and uncoupled activity at different frequencies were imposed on a stomach surface model. Gaussian noise (10% peak-to-peak) was added to cutaneous potentials and the Greensite-Tikhonov inverse method was used to reconstruct the potentials on the stomach. The effectiveness of the number or location of electrodes on the accuracy of the inverse solutions was investigated using four different electrode configurations. Results showed the reconstructed solutions were able to reliably distinguish the different slow wave patterns and waves with lower frequency were better correlated to the known solution than those with higher. The use of up to 228 electrodes improved the accuracy of the inverse solutions. However, the use of 120 electrodes concentrated around the stomach was able to achieve similar results. The most efficient electrode configuration for our model involved 120 electrodes with an inter-electrode distance of 32 mm.

A biophysically based finite-state machine model for analyzing gastric experimental entrainment and pacing recordings

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

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.

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

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

A quantitative model of human jejunal smooth muscle cell electrophysiology

Recently, a number of ion channel mutations have been identified in the smooth muscle cells of the human jejunum. Although these are potentially significant in understanding diseases that are currently of unknown etiology, no suitable computational cell model exists to evaluate the effects of such mutations. Here, therefore, a biophysically based single cell model of human jejunal smooth muscle electrophysiology is presented. The resulting cellular description is able to reproduce experimentally recorded slow wave activity and produces realistic responses to a number of perturbations, providing a solid platform on which the causes of intestinal myopathies can be investigated.

Quantification of gastrointestinal sodium channelopathy

Na(v)1.5 sodium channels, encoded by SCN5A, have been identified in human gastrointestinal interstitial cells of Cajal (ICC) and smooth muscle cells (SMC). A recent study found a novel, rare missense R76C mutation of the sodium channel interacting protein telethonin in a patient with primary intestinal pseudo-obstruction. The presence of a mutation in a patient with a motility disorder, however, does not automatically imply a cause-effect relationship between the two. Patch clamp experiments on HEK-293 cells previously established that the R76C mutation altered Na(v)1.5 channel function. Here the process through which these data were quantified to create stationary Markov state models of wild-type and R76C channel function is described. The resulting channel descriptions were included in whole cell ICC and SMC computational models and simulations were performed to assess the cellular effects of the R76C mutation. The simulated ICC slow wave was decreased in duration and the resting membrane potential in the SMC was depolarized. Thus, the R76C mutation was sufficient to alter ICC and SMC cell electrophysiology. However, the cause-effect relationship between R76C and intestinal pseudo-obstruction remains an open question.

A preliminary model of gastrointestinal electromechanical coupling

Gastrointestinal (GI) motility is coordinated by several cooperating mechanisms, including electrical slow wave activity, the enteric nervous system (ENS), and other factors. Slow waves generated in interstitial cells of Cajal (ICC) depolarize smooth muscle cells (SMC), generating basic GI contractions. This unique electrical coupling presents an added layer of complexity to GI electromechanical models, and a current barrier to further progress is the lack of a framework for ICC-SMC-contraction coupling. In this study, an initial framework for the electromechanical coupling was developed in a 2-D model. At each solution step, the slow wave propagation was solved first and [Ca(2+)](i) in the SMC model was related to a Ca(2+)-tension-extension relationship to simulate active contraction. With identification of more GI-specific constitutive laws and material parameters, the ICC-SMC-contraction approach may underpin future GI electromechanical models of health and disease states.

A stochastic multi-scale model of electrical function in normal and depleted ICC networks

Multi-scale modeling has become a productive strategy for quantifying interstitial cells of Cajal (ICC) network structure-function relationships, but the lack of large-scale ICC network imaging data currently limits modeling progress. The single normal equation simulation (SNESIM) algorithm was utilized to generate realistic virtual images of small real wild-type (WT) and 5-HT(2B)-receptor knockout (Htr2b(-/-)) mice ICC networks. Two metrics were developed to validate the performance of the algorithm: 1) network density, which is the proportion of ICC in the tissue; and 2) connectivity, which reflects the degree of connectivity of the ICC network. Following validation, the SNESIM algorithm was modified to allow variation in the degree of ICC network depletion. ICC networks from a range of depletion severities were generated, and the electrical activity over these networks was simulated. The virtual ICC networks generated by the original SNESIM algorithm were similar to that of their real counterparts. The electrical activity simulations showed that the maximum current density magnitude increased as the network density increased. In conclusion, the SNESIM algorithm is an effective tool for generating realistic virtual ICC networks. The modified SNESIM algorithm can be used with simulation techniques to quantify the physiological consequences of ICC network depletion at various physical scales.

Biophysically based modeling of the interstitial cells of cajal: current status and future perspectives

Gastrointestinal motility research is progressing rapidly, leading to significant advances in the last 15 years in understanding the cellular mechanisms underlying motility, following the discovery of the central role played by the interstitial cells of Cajal (ICC). As experimental knowledge of ICC physiology has expanded, biophysically based modeling has become a valuable tool for integrating experimental data, for testing hypotheses on ICC pacemaker mechanisms, and for applications in in silico studies including in multiscale models. This review is focused on the cellular electrophysiology of ICC. Recent evidence from both experimental and modeling domains have called aspects of the existing pacemaker theories into question. Therefore, current experimental knowledge of ICC pacemaker mechanisms is examined in depth, and current theories of ICC pacemaking are evaluated and further developed. Existing biophysically based ICC models and their physiological foundations are then critiqued in light of the recent advances in experimental knowledge, and opportunities to improve these models are identified. The review concludes by examining several potential clinical applications of biophysically based ICC modeling from the subcellular through to the organ level, including ion channelopathies and ICC network degradation.

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.

Multiscale modeling of gastrointestinal electrophysiology and experimental validation

Normal gastrointestinal (GI) motility results from the coordinated interplay of multiple cooperating mechanisms, both intrinsic and extrinsic to the GI tract. A fundamental component of this activity is an omnipresent electrical activity termed slow waves, which is generated and propagated by the interstitial cells of Cajal (ICCs). The role of ICC loss and network degradation in GI motility disorders is a significant area of ongoing research. This review examines recent progress in the multiscale modeling framework for effectively integrating a vast range of experimental data in GI electrophysiology, and outlines the prospect of how modeling can provide new insights into GI function in health and disease. The review begins with an overview of the GI tract and its electrophysiology, and then focuses on recent work on modeling GI electrical activity, spanning from cell to body biophysical scales. Mathematical cell models of the ICCs and smooth muscle cell are presented. The continuum framework of monodomain and bidomain models for tissue and organ models are then considered, and the forward techniques used to model the resultant body surface potential and magnetic field are discussed. The review then outlines recent progress in experimental support and validation of modeling, and concludes with a discussion on potential future research directions in this field.

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 computational approach to understanding gastrointestinal motility in health and disease

Gastrointestinal (GI) motility disorders are not well understood, resulting in patient management that typically controls symptoms. Patients suffer from reduced quality of life and incur large costs from chronic GI disorders. It is imperative to elucidate underlying mechanisms causing GI motility disorders that, in turn, can facilitate development of treatment such as drug therapeutics. To this end, we seek to use multi-scale computational models to better understand GI motility in health and disease. An initial computational framework was established to study genetic perturbation in causing a phenotypical change at the GI tissue level. Computer models describing a couple of genetic perturbations were developed and examined in the multi-scale framework. Preliminary findings suggest alterations to phenotype that may adversely affect GI motility. However, much work remains, given the tissue complexity and uncertainties in our knowledge of the GI organs. A future direction will be to incorporate multi-scale mechanical models in the current framework.

An extended bidomain framework incorporating multiple cell types

The muscular layers within the walls of the gastrointestinal tract contain two distinct cell types, the interstitial cells of Cajal and smooth muscle cells, which together produce rhythmic depolarizations known as slow waves. The bidomain model of tissue-level electrical activity consists of single intracellular and extracellular domains separated by an intervening membrane at all points in space and is therefore unable to adequately describe the presence of two distinct cell types in its conventional form. Here, an extension to the bidomain framework is presented whereby multiple interconnected cell types can be incorporated. Although the derivation is focused on the interactions of the interstitial cells of Cajal and smooth muscle cells, the conceptual framework can be more generally applied. Simulations demonstrating the feasibility of the proposed model are also presented.

Spatio-temporal calcium dynamics in pacemaking units of the interstitial cells of Cajal

The interstitial cells of Cajal (ICC) are responsible for producing pacemaking signals that stimulate rhythmic contractions in the gastro-intestinal system. The pacemaking signals are generated by membrane depolarizations, which are in turn linked to the integrated transport of calcium between the endoplasmic reticulum (ER), through inositol-trisphosphate receptor (IP(3)R) release, and mitochondria, through the uniporter. A non-specific cation channel (NSCC) is associated with the membrane depolarizations, and is inhibited by intracellular calcium. One theory proposes that the integrated calcium transport occurs within specific regions of the ICC called "pacemaker units," and results in localized calcium concentration reductions within these units, which in turn activate the NSCC and depolarize the membrane. We have constructed a model of the spatio-temporal calcium dynamics within an ICC pacemaker unit to determine under what conditions the local calcium concentrations may reduce below baseline. We obtain reductions of calcium concentrations below baseline but only under certain conditions. Without strong and persistent stimulation of the IP(3)R, reductions of calcium below baseline occur only with a non-physiological, time-dependent uniporter. Alternatively, sufficient IP(3)R release leads to reductions of calcium below baseline, due to depletion of the ER calcium store over the time scale of seconds, although these reductions require strong mitochondrial and ER calcium uptake.

Tissue-specific mathematical models of slow wave entrainment in wild-type and 5-HT(2B) knockout mice with altered interstitial cells of Cajal networks

Gastrointestinal slow waves are generated within networks of interstitial cells of Cajal (ICCs). In the intact tissue, slow waves are entrained to neighboring ICCs with higher intrinsic frequencies, leading to active propagation of slow waves. Degradation of ICC networks in humans is associated with motility disorders; however, the pathophysiological mechanisms of this relationship are uncertain. A recently developed biophysically based mathematical model of ICC was adopted and updated to simulate entrainment of slow waves. Simulated slow wave propagation was successfully entrained in a one-dimensional model, which contained a gradient of intrinsic frequencies. Slow wave propagation was then simulated in tissue models which contained a realistic two-dimensional microstructure of the myenteric ICC networks translated from wild-type (WT) and 5-HT(2B) knockout (degraded) mouse jejunum. The results showed that the peak current density in the WT model was 0.49 muA mm(-2) higher than the 5-HT(2B) knockout model, and the intracellular Ca(2+) density after 400 ms was 0.26 mM mm(-2) higher in the WT model. In conclusion, tissue-specific models of slow waves are presented, and simulations quantitatively demonstrated physiological differences between WT and 5-HT(2B) knockout models. This study provides a framework for evaluating how ICC network degradation may impair slow wave propagation and ultimately motility and transit.