# The determination of coronary artery wave speed using information theory

AbstractA method is described for estimating the wave speed of a coronary artery from simultaneous measurements of pressure and velocity. It involves finding the wave speed that minimises the distance between the probability density functions of the measured pressure and velocity and the probability density functions of the pressure and velocity obtained from the separation of the waves into their forward and backward components using the assumed wave speed.

# Introduction

The local wave speed in an artery is an important physical parameter. It depends upon the distensibility of the artery and hence is a parameter of direct clinical interest. It is also involved in the characteristic impedance of the artery and hence plays an important role in the impedance analysis of the arterial system. From the water hammer equations we know that the product of the density $$\rho$$ (which we assume to be constant) and the local wave speed $$c$$ is the constant of proportionality between the change in pressure, $$dP$$, and the change in velocity, $$dU$$, across a wave front $dP_\pm = \pm \rho c dU_\pm$ where the subscript $$\pm$$ refers to forward and backward traveling waves.

In wave intensity analysis, knowledge of the local wave speed is required to separate the measured $$dP$$ and $$dU$$ into their forward and backward components $dP_\pm = (dP \pm \rho c dU)/2$ $dU_\pm = \pm (dP \pm \rho c dU)/2 \rho c$ The net wave intensity does not depend upon the wave speed $dI = dP dU$ but the forward and backward wave intensities require knowledge of the wave speed $dI_\pm = dP_\pm dU_\pm = \pm (dP \pm \rho c dU)^2/4\rho c$

This separation of pressure, velocity and wave intensity into their forward and backward components has proven useful in the aorta, the pulmonary artery and other large systemic arteries [refs]. In the coronary arteries, moreover, it is proving essential for the analysis of the complex influences introduced by the compression of the intra-myocardial blood vessels during systole. Unfortunately, these additional mechanical complexities make it much more difficult to estimate the local wave speed in the coronary arteries.