Infinite number of solutions to the hemodynamic inverse problem

Investigators have had much success solving the "hemodynamic forward proble m," i. e., predicting pressure and flow at the entrance of an arterial syst em given knowledge of specific arterial properties and arterial system topo logy. Recently, the focus has turned to solving the "hemodynamic inverse pr oblem," i. e., inferring mechanical properties of an arterial system from m easured input pressure and flow. Conventional methods to solve the inverse problem rely on fitting to data simple models with parameters that represen t specific mechanical properties. Controversies have arisen, because differ ent models ascribe pressure and flow to different properties. However, an i nherent assumption common to all model- based methods is the existence of a unique set of mechanical properties that yield a particular pressure and f low. The present work illustrates that there are, in fact, an infinite numb er of solutions to the hemodynamic inverse problem. Thus a measured pressur e-flow pair can result from an infinite number of different arterial system s. Except for a few critical properties, conventional approaches to solve t he inverse problem for specific arterial properties are futile.