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XIX conference

Propagation characteristics of self-sustained peristaltic waves. Analytical calculation

Dudchenko O., Guria G.1

Moscow Institute of Physics and Technology, Institutskiy per. 9, Dolgoprudnyy, 141700, Russia, (499) 761-13-71, dudcha@blood.ru

1National Research Center for Hematology, Novyy Zykovskiy proezd 4, Moscow, 125167, Russia, (495) 614-99-48, guria@blood.ru

1 pp. (accepted)

Peristaltic pumping is a process of directional transport in a hollow tubular organ, which occurs in response to rhythmic contractions of the organ’s muscular walls. Peristalsis is generally accepted to be the mechanism behind bolus propulsion through the esophagus, the movement of chime in the gastro-intestinal tract and the functioning of the ureter and the lymphatic system. Directional transport in these systems usually requires that the lumen distortion resulting from rhythmic contractility takes the form a traveling deformation wave [1].

The velocity of the wave is one of the key characteristics of the process of peristaltic pumping. It has long been attractive as a diagnostic tool in peristaltic motility research [2]. So far, however, no relationships have been established that would allow one to easily interpret the speed of the peristaltic wave in terms of the parameters which characterize the transporting system, i.e. the viscosity of the transported fluid, the rigidity of the vessel wall, the degree to which the contractile machinery is activated etc.

We aim to address this deficiency by introducing a rather simple mathematical model of peristaltic pumping. The model relies on a phenomenological representation of the electrical activity behind peristaltic contractions: it is simulated by a series of excitable elements [3]. Traveling wave solutions are found for the model equations and their stability is analyzed. Existence conditions for traveling wave solutions are established. Explicit analytical formulas for propagation velocity are derived for several biologically relevant limiting cases. Physiological and clinical significance of the results is discussed.

The authors thank Prof. A.I. Vorob'ev for his valuable comments on the medical aspects of the problem. We acknowledge financial support from the Schlumberger Foundation (Faculty for the Future program) and the International Science and Technology Center (grant #3744).

References

1. Human physiology / eds. Schmidt R., Thews G. – Springer-Verlag, 1989. 797 pages.

2. Dooley C.P., Schlossmacher B., Valenzuela J.E. Effects of alterations in bolus viscosity on esophageal peristalsis in humans // Am. J. Physiol. Vol. 254, no1, 1988. Pp. G8-11.

3. Vasil'ev V.A., Romanovskiy U.M., Yakhno V.G. Avtovolnovye protsessy (Autowave Processes). - Moscow: Nauka, 1987. 240 pages.



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