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Am J Physiol Heart Circ Physiol 280: H1472-H1479, 2001;
0363-6135/01 $5.00
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Vol. 280, Issue 4, H1472-H1479, April 2001

Infinite number of solutions to the hemodynamic inverse problem

Christopher M. Quick1, William L. Young2, and Abraham Noordergraaf3

1 Center for Cerebrovascular Research, 2 Departments of Anesthesia, Neurosurgery, and Neurology, University of California, San Francisco, California 94110; and 3 Cardiovascular Studies Unit, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6392

Investigators have had much success solving the "hemodynamic forward problem," i.e., predicting pressure and flow at the entrance of an arterial system given knowledge of specific arterial properties and arterial system topology. Recently, the focus has turned to solving the "hemodynamic inverse problem," i.e., inferring mechanical properties of an arterial system from measured input pressure and flow. Conventional methods to solve the inverse problem rely on fitting to data simple models with parameters that represent specific mechanical properties. Controversies have arisen, because different models ascribe pressure and flow to different properties. However, an inherent assumption common to all model-based methods is the existence of a unique set of mechanical properties that yield a particular pressure and flow. The present work illustrates that there are, in fact, an infinite number of solutions to the hemodynamic inverse problem. Thus a measured pressure-flow pair can result from an infinite number of different arterial systems. Except for a few critical properties, conventional approaches to solve the inverse problem for specific arterial properties are futile.

modeling; input impedance; effective length; apparent compliance; windkessel


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