Prediction of coronary blood flow with a numerical model based on collapsible tube dynamics

Abstract

We present a theoretical, hydrodynamic model of the vascular system feeding the left ventricle from which the inflow and outflow waveforms can be predicted given the waveforms of aortic and left ventricular pressure. The main feature of the model is that the central portion of the tubes representing intramyocardial vessels is subjected to an external pressure equal to left ventricular pressure, and they therefore collapse (and empty) when that pressure exceeds the internal pressure. The model is a one-dimensional model, so that the propagation of the collapse waves into the vessels can be properly described; this process takes a finite time, and volume change is not in phase with transmural pressure change. Parameters of the model are assessed from independent physiological data. The predicted inflow waveform is compared with experimental data, and the model is shown to reproduce all the main features, in particular the second minimum of flow rate in late systole as well as the first minimum in early systole. The corresponding lumped-parameter model, which cannot take account of wave propagation, is shown not to agree with experiments and in particular to predict unphysiological spikes in the inflow waveform.