Resolving the hemodynamic inverse problem

Abstract

The "hemodynamic inverse problem" is the determination of arterial system properties from pressures and flows measured at the entrance of an arterial system. Conventionally, investigators fit reduced arterial system models to data, and the resulting model parameters represent putative arterial properties. However, no unique solution to the inverse problem exists-an infinite number of arterial system topologies result in the same input impedance (Zin) and, therefore, the same pressure and flow. Nevertheless, there are exceptions to this theoretical limitation; total peripheral resistance (Rtot), total arterial compliance (Ctot), and characteristic impedance (ZO) can be uniquely determined from input pressure and flow. Zin is determined completely by Ctot and Rtot at low frequencies, Zo at high frequencies, and arterial topology and reflection effects at intermediate frequencies. We present a novel method to determine the relative contribution of Zo, Ctot, Rtot and arterial topology/reflection to Zin without assuming a particular reduced model. This method is tested with a large-scale distributed model of the arterial system, and is applied to illustrative cases of measured pressure and flow. This work, thus, lays the theoretical foundation for determining the arterial properties responsible for increased pulse pressure with age and various arterial system pathologies.