Numerical Simulation of Motility Patterns of the Small Bowel. 1. Formulation of a Mathematical Model

A Quantitative Model of Gastric Smooth Muscle Cellular Activation

“…Existing electrophysiological descriptions of the gastric musculature 12,40 rely upon equations that attempt to describe the behavior of a single cell but are not based on the underlying biological processes that cause the observed fluctuations in cell membrane potential. Moreover, our knowledge of the different nature and functionality of SM cells and ICC is relatively recent and consequently a number of previously published works do not incorporate this distinction (e.g., Mifthakov et al 33 ). Similarly, Skinner et al 46 developed a generic model of SM electrophysiology that is now inconsistent with current experimental data.…”

A Simple Nonlinear Model of Electrical Activity in the Intestine

“…3) in comparison to the experimentally measured ones. To simulate the shape of excitations with better precision, advanced ionic models of smooth muscle, such as presented in Miftakhov & Abdusheva (1996), Miftakhov et al (1999) and Vigmond & Bardakjian (1998), would be required. An obstacle for the application of ionic models is the large number of equations involved, which makes it di$cult to simulate on available computers distributed systems with hundreds or thousands cells linked together.…”

Numerical Simulation of Motility Patterns of the Small Bowel. II. Comparative Pharmacological Validation of a Mathematical Model

“…The de"ciency of direct experimental evidence and the enormous complexity of interactions among individual elements in the system demand the use of computational techniques to explore e$ciently and quantitatively the intricate regulatory mechanisms involved and thus to resolve questions of the function of the gut under both normal and pathological conditions. Our approach uses a previous strategy for designing a model of a locus of the small bowel with speci"c inputs and outputs (Miftakhov et al, 1999) to reproduce and to predict accurately the outcomes of pharmacological experiments. The variables and processes chosen in the simulation imply constructive assumptions, which are proposed and/or experimentally proven.…”

“…To be consistent with Part I of the study, we preserve the meanings of parameters and constants adopted in the formulation of the model (Miftakhov et al, 1999), which must be consulted in order to understand fully the simulations described here. Note that a diligent applied mathematician will not "nd here a rigorous analysis of the complex nonlinear system.…”

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A model of a locus of the small bowel, described earlier by the authors (Miftakhov et al, 1999) was validated in a comparison of the results of numerical simulations of pharmacological compounds to their e!ects in biological studies. The actions of the following four classes of drugs were simulated, those: (i) acting on the sarcoplasmic reticulum, (ii) altering the permeability of L-and T-type Ca> channels on the smooth muscle membrane, (iii) motilides, and (iv) benzodiazepines.

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