In silico coronary wave intensity analysis: application of an integrated one-dimensional and poromechanical model of cardiac perfusion

Abstract

Coronary wave intensity analysis (cWIA) is a diagnostic technique based on invasive measurement of coronary pressure and velocity waveforms. The theory of WIA allows the forward- and backward-propagating coronary waves to be separated and attributed to their origin and timing, thus serving as a sensitive and specific cardiac functional indicator. In recent years, an increasing number of clinical studies have begun to establish associations between changes in specific waves and various diseases of myocardium and perfusion. These studies are, however, currently confined to a trial-and-error approach and are subject to technological limitations which may confound accurate interpretations. In this work, we have developed a biophysically based cardiac perfusion model which incorporates full ventricular–aortic–coronary coupling. This was achieved by integrating our previous work on one-dimensional modelling of vascular flow and poroelastic perfusion within an active myocardial mechanics framework. Extensive parameterisation was performed, yielding a close agreement with physiological levels of global coronary and myocardial function as well as experimentally observed cumulative wave intensity magnitudes. Results indicate a strong dependence of the backward suction wave on QRS duration and vascular resistance, the forward pushing wave on the rate of myocyte tension development, and the late forward pushing wave on the aortic valve dynamics. These findings are not only consistent with experimental observations, but offer a greater specificity to the wave-originating mechanisms, thus demonstrating the value of the integrated model as a tool for clinical investigation.

Impact of coronary bifurcation morphology on wave propagation

“…The mathematical background of the 1D blood flow formulation has been extensively described in the literature (14, 36, 37, 58, 59). Importantly, the forward and backward wave reflection coefficients at a bifurcation derive from the following system of conservation equations (mass and momentum) in three variables: cross-sectional area, pressure, and velocity ( A , p, v ): $\frac{\partial A}{\partial t}+\frac{\partial \left(Av\right)}{\partial x}=0$ $\frac{\partial v}{\partial t}+\alpha v\frac{\partial v}{\partial x}+\frac{1}{\rho }\frac{\partial p}{\partial x}=-\kappa v.$…”

“…Therefore, in the following, we examine several common hypotheses employed in the literature. Two simpler assumptions are to impose a constant uniform PWS (37) (which implies decreasing β* distally) or uniform material property (implying an increase in the PWS distally) (42) throughout the network. A third common approach (43, 69) relies on an empirical relationship described by Olufsen (45), based on measurements from mostly the systemic circulation: $\frac{Eh}{r_0}=k_1{e}^{k_2{r}_0}+k_3$…”

Major influence of a ‘smoke and mirrors’ effect caused by wave reflection on early diastolic coronary arterial wave intensity

“…More detailed microvascular models, such as the poromechanical model described by Lee et al . (), may be useful for further investigating some of the issues raised in this paper.…”

“…Lee et al . () investigated the sensitivity of the major coronary waves to several key parameters in their model and found a dependence of BDW dia on myocardial relaxation rate and degree of dysynchrony, consistent with the distal suction mechanism; however, a possible contribution of wave reflection was not explored.…”

“…; Lee et al . ; Raphael et al . ), a key conclusion of this study is that, mechanistically, both upstream and downstream processes can have a significant effect on the magnitude of both forward and backward waves (directly and via wave reflection).…”