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Am J Physiol Heart Circ Physiol (January 30, 2003). doi:10.1152/ajpheart.00762.2002
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Submitted on August 30, 2002
Accepted on January 20, 2003

Flow and Pressure Distributions in Vascular Networks Consisting of Distensible Vessels

Gary S. Krenz1* and Christopher A. Dawson2

1 Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, WI, USA; Research Service, Zablocki Veterans Affairs Medical Center, Milwaukee, WI, USA
2 Department of Physiology, Medical College of Wisconsin, Milwaukee, WI, USA; Research Service, Zablocki Veterans Affairs Medical Center, Milwaukee, WI, USA; Department of Biomedical Engineering, Marquette University, Milwaukee, WI, USA

* To whom correspondence should be addressed. E-mail: gary.krenz{at}marquette.edu.

We examine the influence of vessel distensibility on the fraction of the total network flow passing through each vessel of a model vascular network. An exact computational methodology is developed yielding an analytical proof that, for a class of structurally heterogeneous asymmetrical vascular networks, if all the individual vessels share a common distensibility relationship, when the total network flow is changed, each vessel will continue to receive the same fraction of the total network flow. This constant flow partitioning occurs despite a redistribution of pressures, which may result in a decrease in the diameter of one and an increase in diameter of the other of two vessels having a common diameter at a common pressure. This theoretical observation taken along with published experimental observations on pulmonary vessel distensibilities suggests that vessel diameter independent distensibility in the pulmonary vasculature may be an evolutionary adaptation for preserving the spatial distribution of pulmonary blood flow in the face of large variations in cardiac output.




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