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TECHNICAL PAPERS

An Active Membrane Model for Peristaltic Pumping: Part I—Periodic Activation Waves in an Infinite Tube

[+] Author and Article Information
E. O. Carew

Department of Biomedical Engineering, The Cleveland Clinic, 9500 Euclid Ave., Cleveland, OH 44195

T. J. Pedley

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, United Kingdom

J Biomech Eng 119(1), 66-76 (Feb 01, 1997) (11 pages) doi:10.1115/1.2796066 History: Received October 10, 1995; Revised April 18, 1996; Online October 30, 2007

Abstract

A model for the coupled problem of wall deformation and fluid flow, based on thin-shell and lubrication theories, and driven by a propagating wave of smooth muscle activation, is proposed for peristaltic pumping in the ureter. The model makes use of the available experimental data on the mechanical properties of smooth muscle and accounts for the soft material between the muscle layer and the vessel lumen. The main input is the activation wave of muscular contraction. Equations for the time-dependent problem in tubes of arbitrary length are derived and applied to the particular case of periodic activation waves in an infinite tube. Mathematical (small amplitude) and numerical analyses of this case are presented. Predictions on phase-lag in wall constriction with respect to peak activation wave, lumen occlusion due to thickening lumen material with contracting smooth muscle, and the general bolus shape are in qualitative agreement with observation. Some modifications to the mechanical, elastic, and hydrodynamic properties of the ureter that will make peristalsis less efficient, due for example to disease, are identified. In particular, the flow rate-pressure rise relationship is linear for weak to moderate activation waves, but as the lumen is squeezed shut, it is seen to be nonlinear in a way that increases pumping efficiency. In every case a ureter whose lumen can theoretically be squeezed shut is the one for which pumping is most efficient.

Copyright © 1997 by The American Society of Mechanical Engineers
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