On the electrical intestine turbulence induced by temperature changes

Biomechanical constitutive modeling of the gastrointestinal tissues: a systematic review

The gastrointestinal (GI) tract is a continuous channel through the body that consists of the esophagus, the stomach, the small intestine, the large intestine, and the rectum. Its primary functions are to move the intake of food for digestion before storing and ultimately expulsion of feces. The mechanical behavior of GI tissues thus plays a crucial role for GI function in health and disease. The mechanical properties are characterized by a biomechanical constitutive model, which is a mathematical representation of the relation between load and deformation in a tissue. Hence, validated biomechanical constitutive models are essential to characterize and simulate the mechanical behavior of the GI tract. Here, a systematic review of these constitutive models is provided. This review is limited to studies where a model of the strain energy function is proposed to characterize the stress-strain relation of a GI tissue. Several needs are identified for more advanced modeling including: 1) Microstructural models that provide actual structure-function relations; 2) Validation of coupled electro-mechanical models accounting for active muscle contractions; 3) Human data to develop and validate models. The findings from this review provide guidelines for using existing constitutive models as well as perspective and directions for future studies.

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.

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

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

Relationships between serum electrolyte concentrations and ileus: A joint clinical and mathematical modeling study

Aim

Prolonged postoperative ileus (PPOI) occurs in around 15% of patients after major abdominal surgery, posing a significant clinical and economic burden. Significant fluid and electrolyte changes may occur peri‐operatively, potentially contributing to PPOI; however, this association has not been clearly elucidated. A joint clinical‐theoretical study was undertaken to evaluate peri‐operative electrolyte concentration trends, their association with ileus, and predicted impact on bioelectrical slow waves in interstitial cells of Cajal (ICC) and smooth muscle cells (SMC).

Methods

Data were prospectively collected from 327 patients undergoing elective colorectal surgery. Analyses were performed to determine associations between peri‐operative electrolyte concentrations and prolonged ileus. Biophysically based ICC and SMC mathematical models were adapted to evaluate the theoretical impacts of extracellular electrolyte concentrations on cellular function.

Results

Postoperative day (POD) 1 calcium and POD 3 chloride, sodium were lower in the PPOI group (p < 0.05), and POD3 potassium was higher in the PPOI group (p < 0.05). Deficits beyond the reference range in PPOI patients were most notable for sodium (Day 3: 29.5% ileus vs. 18.5% no ileus, p = 0.04). Models demonstrated an 8.6% reduction in slow‐wave frequency following the measured reduction in extracellular NaCl on POD5, with associated changes in cellular slow‐wave morphology and amplitude.

Conclusion

Low serum sodium and chloride concentrations are associated with PPOI. Electrolyte abnormalities are unlikely to be a primary mechanism of ileus, but their pronounced effects on cellular electrophysiology predicted by modeling suggest these abnormalities may adversely impact motility recovery. Resolution and correction of electrolyte abnormalities in ileus may be clinically relevant.

Characteristics of Intestinal Myoelectrical and Motor Activities in Diet-Induced Obese Rats: Obesity and Motility

BACKGROUND

Gastrointestinal motility has been reported to be altered in obesity. However, it is unknown whether intestinal myoelectrical activity (IMA) is also changed in obesity.

AIMS

The aim of this study was to characterize intestinal myoelectrical and motility activities in the fasting state, during feeding, and postprandial state after various test meals in diet-induced obese (DIO) rats in comparison with regular rats.

METHODS

IMA was recorded in the fasting, feeding, and postprandial states in DIO and regular rats. Regular laboratory chow, high-fat solid food, and high-fat liquid food were used to test IMA responses to different meals.

RESULTS

(1) The intestinal slow waves in the DIO rats were not different from those in normal rats in the fasting or postprandial state. Neither intestinal transit nor the number of intestinal contractions per minute was altered in DIO rats although gastric emptying was accelerated. (2) Both DIO rats and normal rats showed altered IMA during the first minute of feeding (cephalic stimulation). (3) The intestinal slow waves in both DIO rats and regular rats were impaired slightly but significantly after intake of a high-fat meal.

CONCLUSIONS

Our study demonstrates that intestinal myoelectrical activity is not altered in DIO rats and its postprandial responses to various meals are not altered either. High-fat meals induce intestinal dysrhythmia but do not have a chronic impact on intestinal slow waves in DIO rats.

Modeling and simulation of hypothermia effects on cardiac electrical dynamics

Previous experimental evidence has shown the effect of temperature on the action potential duration (APD). It has also been demonstrated that regional cooling of the heart can prolong the APD and promote the termination of ventricular tachycardia. The aim of this study is to demonstrate the effect of hypothermia in suppressing cardiac arrhythmias using numerical modeling. For this purpose, we developed a mathematical model that couples Pennes’ bioheat equation and the bidomain model to simulate the effect of heat on the cardiac action potential. The simplification of the proposed heat–bidomain model to the heat–monodomain model is provided. A suitable numerical scheme for this coupling, based on a time adaptive mesh finite element method, is also presented. First, we performed two-dimensional numerical simulations to study the effect of heat on a regular electrophysiological wave, with the comparison of the calculated and experimental values of Q₁₀. Then, we demonstrated the effect of global hypothermia in suppressing single and multiple spiral waves.

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.

Nonlinear diffusion and thermo-electric coupling in a two-variable model of cardiac action potential

This work reports the results of the theoretical investigation of nonlinear dynamics and spiral wave breakup in a generalized two-variable model of cardiac action potential accounting for thermo-electric coupling and diffusion nonlinearities. As customary in excitable media, the common Q₁₀ and Moore factors are used to describe thermo-electric feedback in a 10° range. Motivated by the porous nature of the cardiac tissue, in this study we also propose a nonlinear Fickian flux formulated by Taylor expanding the voltage dependent diffusion coefficient up to quadratic terms. A fine tuning of the diffusive parameters is performed a priori to match the conduction velocity of the equivalent cable model. The resulting combined effects are then studied by numerically simulating different stimulation protocols on a one-dimensional cable. Model features are compared in terms of action potential morphology, restitution curves, frequency spectra, and spatio-temporal phase differences. Two-dimensional long-run simulations are finally performed to characterize spiral breakup during sustained fibrillation at different thermal states. Temperature and nonlinear diffusion effects are found to impact the repolarization phase of the action potential wave with non-monotone patterns and to increase the propensity of arrhythmogenesis.

Experimental characterization of the biaxial mechanical properties of porcine gastric tissue

Health problems related to the stomach are among the most important sources of morbidity in industrialized countries. There is evidence that mechanics may play an important role in various such pathologies. However, so far experimental data characterizing the mechanical properties of gastric tissue remain scarce, which significantly limits our understanding of the mechanics of the stomach. To help close this gap, we performed biaxial mechanical tests of porcine gastric tissue patches. Our experiments reveal a considerable anisotropy and different mechanical properties in the three major regions of the stomach (fundus, corpus, antrum). Moreover, they demonstrate that the mechanical properties of the gastric wall and the physiological function of the different regions of the stomach are closely related. This finding suggests that further examination of the mechanics of the gastric wall may indeed be a promising avenue of research towards a better understanding of the organic causes of frequent health problems related to the stomach.

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.

Electrophysiological Mechanisms of Gastrointestinal Arrhythmogenesis: Lessons from the Heart

Disruptions in the orderly activation and recovery of electrical excitation traveling through the heart and the gastrointestinal (GI) tract can lead to arrhythmogenesis. For example, cardiac arrhythmias predispose to thromboembolic events resulting in cerebrovascular accidents and myocardial infarction, and to sudden cardiac death. By contrast, arrhythmias in the GI tract are usually not life-threatening and much less well characterized. However, they have been implicated in the pathogenesis of a number of GI motility disorders, including gastroparesis, dyspepsia, irritable bowel syndrome, mesenteric ischaemia, Hirschsprung disease, slow transit constipation, all of which are associated with significant morbidity. Both cardiac and gastrointestinal arrhythmias can broadly be divided into non-reentrant and reentrant activity. The aim of this paper is to compare and contrast the mechanisms underlying arrhythmogenesis in both systems to provide insight into the pathogenesis of GI motility disorders and potential molecular targets for future therapy.

Spatial Noise in Coupling Strength and Natural Frequency within a Pacemaker Network; Consequences for Development of Intestinal Motor Patterns According to a Weakly Coupled Phase Oscillator Model

Pacemaker activities generated by networks of interstitial cells of Cajal (ICC), in conjunction with the enteric nervous system, orchestrate most motor patterns in the gastrointestinal tract. It was our objective to understand the role of network features of ICC associated with the myenteric plexus (ICC-MP) in the shaping of motor patterns of the small intestine. To that end, a model of weakly coupled oscillators (oscillators influence each other's phase but not amplitude) was created with most parameters derived from experimental data. The ICC network is a uniform two dimensional network coupled by gap junctions. All ICC generate pacemaker (slow wave) activity with a frequency gradient in mice from 50/min at the proximal end of the intestine to 40/min at the distal end. Key features of motor patterns, directly related to the underlying pacemaker activity, are frequency steps and dislocations. These were accurately mimicked by reduction of coupling strength at a point in the chain of oscillators. When coupling strength was expressed as a product of gap junction density and conductance, and gap junction density was varied randomly along the chain (i.e., spatial noise) with a long-tailed distribution, plateau steps occurred at pointsof low density. As gap junction conductance was decreased, the number of plateaus increased, mimicking the effect of the gap junction inhibitor carbenoxolone. When spatial noise was added to the natural interval gradient, as gap junction conductance decreased, the number of plateaus increased as before but in addition the phase waves frequently changed direction of apparent propagation, again mimicking the effect of carbenoxolone. In summary, key features of the motor patterns that are governed by pacemaker activity may be a direct consequence of biological noise, specifically spatial noise in gap junction coupling and pacemaker frequency.

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.

Inhomogeneities in the propagation of the slow wave in the stomach

The propagation of the slow wave in the stomach and its role in inducing sweeping peristaltic contractions toward the pylorus, essential for a proper digestion and emptying, have been studied for many years. Irregularities in the timing or in the pattern of propagation of the slow wave have been known to induce various gastric malfunctions and, recently, several types of gastric dysrhythmias have been described which could lead to gastric contraction abnormalities. In this study, Du et al. have analyzed the disturbances caused by a simple transmural incision in a human stomach, performed to obtain a biopsy of the muscle, on the propagation pattern of the slow wave. In addition, they show that such an incision may by itself also induce new types of gastric dysrhythmias. These results are important in demonstrating that the function of the stomach can easily be disturbed by such procedures. This mini-review describes several ways in which inhomogeneities in propagation may affect the conduction pattern of the slow wave, including the genesis of several dysrhythmias, and what is currently known about their impact on gastric contraction and digestion.

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.

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.

Mechanistic insights into hypothermic ventricular fibrillation: the role of temperature and tissue size

AIMS

Hypothermia is well known to be pro-arrhythmic, yet it has beneficial effects as a resuscitation therapy and valuable during intracardiac surgeries. Therefore, we aim to study the mechanisms that induce fibrillation during hypothermia. A better understanding of the complex spatiotemporal dynamics of heart tissue as a function of temperature will be useful in managing the benefits and risks of hypothermia.

METHODS AND RESULTS

We perform two-dimensional numerical simulations by using a minimal model of cardiac action potential propagation fine-tuned on experimental measurements. The model includes thermal factors acting on the ionic currents and the gating variables to correctly reproduce experimentally recorded restitution curves at different temperatures. Simulations are implemented using WebGL, which allows long simulations to be performed as they run close to real time. We describe (i) why fibrillation is easier to induce at low temperatures, (ii) that there is a minimum size required for fibrillation that depends on temperature, (iii) why the frequency of fibrillation decreases with decreasing temperature, and (iv) that regional cooling may be an anti-arrhythmic therapy for small tissue sizes however it may be pro-arrhythmic for large tissue sizes.

CONCLUSION

Using a mathematical cardiac cell model, we are able to reproduce experimental observations, quantitative experimental results, and discuss possible mechanisms and implications of electrophysiological changes during hypothermia.

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.

Arrhythmias in the gut

In recent years, it has become possible to record, from a large number of extracellular electrodes, the electrical activities of smooth muscle organs. These recordings, after proper processing and analysis, may reveal origin and propagation of normal and abnormal electrical activities in these organs. Several publications have appeared in the past 5 years describing origin and propagation of slow waves in the stomach of experimental animals and in humans. Furthermore, publications are now starting to appear that describe pathophysiological patterns of propagation and these studies provide us with novel concepts regarding potential mechanisms of arrhythmias in the gut, crucial information if we are ever going to successfully treat patients suffering from such arrhythmias. In this issue of Neurogastroenterology & Motility, Angeli et al. have mapped the slow wave propagation in the porcine small intestine and discovered two types of reentry; functional reentry and circumferential reentry. Next to the descriptions of arrhythmias in the stomach, the fact that reentrant arrhythmias may also occur in the small intestine further extends this new emerging field of gastrointestinal (GI) arrhythmias. In this viewpoint, the relevance of these arrhythmias is further discussed and a few ideas for future research in this field, not necessarily constrained to the GI system, proposed.

Role of temperature on nonlinear cardiac dynamics

Thermal effects affecting spatiotemporal behavior of cardiac tissue are discussed by relating temperature variations to proarrhythmic dynamics in the heart. By introducing a thermoelectric coupling in a minimal model of cardiac tissue, we are able to reproduce experimentally measured dynamics obtained simultaneously from epicardial and endocardial canine right ventricles at different temperatures. A quantitative description of emergent proarrhythmic properties of restitution, conduction velocity, and alternans regimes as a function of temperature is presented. Complex discordant alternans patterns that enhance tissue dispersion consisting of one wave front and three wave backs are described in both simulations and experiments. Possible implications for model generalization are finally discussed.

A stochastic mathematical model to study the autoimmune progression towards type 1 diabetes

BACKGROUND

The integrity of the interactions and the 3D architecture among beta cell populations in pancreatic islets is critical for proper biosynthesis, storage and release of insulin. The aim of this study was to evaluate the effect on electrophysiological signalling of beta cells that is produced by progressive lymphocytic islet cell infiltration (insulitis), by modelling the disruption of pancreatic islet anatomy as a consequence of insulitis and altered glucose concentrations.

METHODS

On the basis of histopathological images of murine islets from non-obese diabetic mice, we simulated the electrophysiological dynamics of a 3D cluster of mouse beta cells via a stochastic model. Progressive damage was modelled at different glucose concentrations, representing the different glycaemic states in the autoimmune progression towards type 1 diabetes.

RESULTS

At 31% of dead beta cells (normoglycaemia) and 69% (hyperglycaemia), the system appeared to be biologically robust to maintain regular Ca(2+) ion oscillations guaranteeing an effective insulin release. Simulations at 84%, 94% and 98% grades (severe hyperglycemia) showed that intracellular calcium oscillations were absent. In such conditions, insulin pulsatility is not expected to occur.

CONCLUSIONS

Our results suggest that the islet tissue is biophysically robust enough to compensate for high rates of beta cell loss. These predictions can be experimentally tested in vitro by quantifying space and time electrophysiological dynamics of animal islets kept at different glucose gradients. The model indicates the necessity of maintaining glycaemia within the physiological range as soon as possible after diabetes onset to avoid a dramatic interruption of Ca(2+) pulsatility and the consequent drop of insulin release.

Functional reentry and circus movement arrhythmias in the small intestine of normal and diabetic rats

In a few recent studies, the presence of arrhythmias based on reentry and circus movement of the slow wave have been shown to occur in normal and diseased stomachs. To date, however, reentry has not been demonstrated before in any other part of the gastrointestinal system. No animals had to be killed for this study. Use was made of materials obtained during the course of another study in which 11 rats were treated with streptozotocin and housed with age-matched controls. After 3 and 7 mo, segments of duodenum, jejunum, and ileum were isolated and positioned in a tissue bath. Slow wave propagation was recorded with 121 extracellular electrodes. After the experiment, the propagation of the slow waves was reconstructed. In 10 of a total of 66 intestinal segments (15%), a circus movement of the slow wave was detected. These reentries were seen in control (n = 2) as well as in 3-mo (n = 2) and 7-mo (n = 6) diabetic rats. Local conduction velocities and beat-to-beat intervals during the reentries were measured (0.42 ± 0.15 and 3.03 ± 0.67 cm/s, respectively) leading to a wavelength of 1.3 ± 0.5 cm and a circuit diameter of 4.1 ± 1.5 mm. This is the first demonstration of a reentrant arrhythmia in the small intestine of control and diabetic rats. Calculations of the size of the circuits indicate that they are small enough to fit inside the intestinal wall. Extrapolation based on measured velocities and rates indicate that reentrant arrhythmias are also possible in the distal small intestine of larger animals including humans.