Lumped Parameter Modeling of Valveless Pumping in Closed Elastic Tubes

 

A recent paper by J.T. Ottesen: "Valveless Pumping in a Fluid-Filled Closed Elastic Tube-System: One-Dimensional Theory with Experimental Validation," J. Math. Biol., 46, 309-332 (2003), describes an experiment in which one soft and one stiff elastic tube are connected together to form a fluid-filled torus.  Upon periodic compression of one region near one of the junctions, a time-averaged flow is established within the torus, even in the absence of any valves that could restrict the flow in one direction. The paper provides a model of this phenomenon based upon a one-dimensional analog of the Navier-Stokes equations. Our goal, during the workshop, will be to construct a simpler, zero-dimensional (i.e., lumped parameter) model for this system, using concepts from electrical circuits theory (e.g., resistances, compliances, intertances, etc.; possibly nonlinear) that have been applied to blood flow modeling.  Applications include understanding the pumping function of the fetus heart prior to development of heart valves, as well as valveless circulatory systems of certain organisms, and possible improvements to cardiopulmonary resuscitation method (CPR).