Numerical simulation of motility patterns of the small bowel. II. Comparative pharmacological validation of a mathematical model

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.

Simulations of Myenteric Neuron Dynamics in Response to Mechanical Stretch

Background

Intestinal sensitivity to mechanical stimuli has been studied intensively in visceral pain studies. The ability to sense different stimuli in the gut and translate these to physiological outcomes relies on the mechanosensory and transductive capacity of intrinsic intestinal nerves. However, the nature of the mechanosensitive channels and principal mechanical stimulus for mechanosensitive receptors are unknown. To be able to characterize intestinal mechanoelectrical transduction, that is, the molecular basis of mechanosensation, comprehensive mathematical models to predict responses of the sensory neurons to controlled mechanical stimuli are needed. This study aims to develop a biophysically based mathematical model of the myenteric neuron with the parameters constrained by learning from existing experimental data. Findings. The conductance-based single-compartment model was selected. The parameters in the model were optimized by using a combination of hand tuning and automated estimation. Using the optimized parameters, the model successfully predicted the electrophysiological features of the myenteric neurons with and without mechanical stimulation.

Conclusions

The model provides a method to predict features and levels of detail of the underlying physiological system in generating myenteric neuron responses. The model could be used as building blocks in future large-scale network simulations of intrinsic primary afferent neurons and their network.

NUMERICAL SIMULATION OF THE ROLE OF CO-TRANSMISSION BY ACETYLCHOLINE AND SEROTONIN ON MOTILITY OF THE GUT

Electrophysiological mechanisms of co-transmission by serotonin (5-HT) and acetylcholine (ACh), co-expression of their receptor types, i.e., 5-HT type 3 and 4, nicotinic cholinerginc (nACh) and muscarinic cholinergic (μACh), and effects of selective and non-selective 5-HT3 and 5-HT4 receptor agonists/antagonists, on electromechanical activity of the gut were studied numerically. Two series of numerical experiments were performed. First, the dynamics of the generation and propagation of electrical signals interconnected with the primary sensory (AH) neurons, motor (S) neurons and smooth muscle cells were studied in a one-dimensional model. Simulations showed that stimulation of the 5-HT3 receptors reduced the threshold of activation of the mechanoreceptors by 17.6%. Conjoint excitation of the 5-HT3 and 5-HT4 receptors by endogenous serotonin converted the regular firing pattern of electrical discharges of the AH and S neurons to a beating mode. Activation confined to 5-HT3 receptors, located on the somas of the adjacent AH and S type neurons, could not sustain normal signal transduction between them. It required ACh as a co-transmitter and co-activation of the nACh receptors. Application of selective 5-HT3 receptor antagonists inhibited dose-dependently the production of action potentials at the level of mechanoreceptors and the soma of the primary sensory neuron and increased the threshold activation of the mechanoreceptors. Normal mechanical contractile activity depended on co-stimulation of the 5-HT4 and μACh receptors on the membrane of smooth muscle cells. In the second series of simulations, which involved a spatio-temporal model of the functional unit, effects of co-transmission by ACh and 5-HT on the electromechanical response in a segment of the gut were analyzed. Results indicated that propagation of the wave of excitation between the AH and S neurons within the myenteric nervous plexus in the presence of 5-HT3 receptor antagonists was supported by co-release of ACh. Co-stimulation of 5-HT3, nACh and μACh receptors impaired propulsive activity of the gut. The bolus showed uncoordinated movements. In an ACh-free environment Lotronex (GlaxoSmithKline), a 5-HT3 receptor antagonist, significantly increased the transit time of the pellet along the gut. In the presence of ACh, Lotronex produced intensive tonic-type contractions in the longitudinal and circular smooth muscle layers and eliminated propulsive activity. The 5HT4 receptor agonist, Zelnorm (Novartis), preserved the reciprocal electromechanical relationships between the longitudinal and circular smooth muscle layers. The drug changed the normal propulsive pattern of activity to an expulsive (non-mixing) type. Treatment of the gut with selective 5HT4 receptor antagonists increased the transit time by disrupting the migrating myoelectrical complex. Cisapride (Janssen), a mixed 5HT3 and 5HT4 receptor agonist, increased excitability of the AH and S neurons and the frequency of slow waves. Longitudinal and circular smooth muscle syncytia responded with the generation of long-lasting tonic contractions, resulting in a "squeezing" type of pellet movement. Comparison of the theoretical results obtained on one-dimensional and spatio-temporal models to in vivo and in vitro experimental data indicated satisfactory qualitative, and where available, quantitative agreement.

Neurochemical bases of visceral nociception: mathematical model

A mathematical model of visceral perception was constructed, comprising primary sensory, motor, intestinofugal and principal neurons, interstitial cells of Cajal and smooth muscle elements that are arranged in a functional circuit through chemical synapses. The mathematical description of constructive elements was based on detailed morphological, anatomical, electrophysiological and neuropharmacological characteristics of cells and chemical processes of electrochemical coupling. Emphasis was given to signal transduction mechanisms that involved multiple neurotransmitters and receptor polymodality. The role of co-transmission by acetylcholine (ACh), serotonin (5-HT), noradrenalin (NA), N-methyl-d-aspartate (NMDA) and alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) and their corresponding receptors-muscarinic and nicotinic type ACh receptors, beta-adrenoceptors, 5-HT(3/4) type serotonergic receptors, NMDA and AMPA receptors in pathogenesis of nociception was studied numerically. Results of computer simulations reproduced patterns of electrical activity of neurons and mechanical responses of the smooth muscle similar to those observed in in vivo and in vitro experiments when ACh, 5-HT, NA, NMDA and AMPA were acting either alone or co-jointly. The results provide neurochemical bases for explanation of pathophysiological mechanisms of visceral nociception, which cannot be elucidated by existing experimental methods. Care should be taken though when extrapolating the numerical results onto the actual system because of limiting assumptions of the model.

Intestinal propulsion of a solid non-deformable bolus

A mathematical model of a segment of the gut with an enclosed pellet is constructed. The gut is represented as a thin deformable soft biological shell with the pellet modeled as a non-deformable solid. Mechanical properties of the gut wall were represented as longitudinal and circular smooth muscle layers embedded in stroma that satisfies the general type of nonlinear orthotropy. Deformations of the wall are finite. Bolus propulsion is numerically simulated by generation and propagation of an electromechanical wave along the syncytia. Pharmacological manipulation is applied to model 5-HT type 3 antagonist (Lotronex, GlaxoSmithKline) and 5-HT type 4 agonist (Zelnorm, Novartis, AB) drugs on the dynamics of bolus progression. The results lead to new quantitative insights into the complex spatio-temporal patterns of gastrointestinal transit. It is demonstrated that the reciprocal relationship in contraction of the longitudinal and circular smooth muscle syncytia is necessary to provide the "mixing" type of movements during the preparatory phase of propulsion. Strong simultaneous contractions of the both smooth muscle layers are required to expel the "mixed" pellet from the segment. The model is implemented as an interactive software system, Gut Discovery(www.aincompany.com), and accurately predicts the effects of drugs on gut motility.