Model of the coronary circulation based on pressure dependence of coronary resistance and compliance

Abstract

The effect of pressure-dependent changes in vascular volume, resistance and capacitance in the coronary micro-circulation, has been studied by a distributed mathematical model of the coronary micro-vasculature in the left ventricular wall. The model does not include regulation of coronary blood flow and is evaluated only for the fully dilated coronary vasculature. The left ventricular wall was thought to consist of eight parallel layers, each of them with an arteriolar, capillary and venular compartment. The resistance of each vessel was thought to depend on the inverse of squared volume, according to Poiseuille's Law for tubes with constant length. Tissue pressure has been assumed to be equal to left ventricular cavity pressure at the endocardium and to decrease linearly to atmospheric level at the epicardium. The pressure-volume relation of the vessel compartments were assumed to be sigmoidal. There is a rest volume at transmural pressure zero and delta V/delta P decreases with increasing transmural pressure. Simulation of experimental protocols described by other authors yielded results which were similar to the experimental outcomes, illustrated by: (1) a parallel shift to the flow axis of the pressure-flow curves due to cardiac arrest (2) steady-state endo/epi ratio of flow as a function of heart rate. It is concluded that interpretation of transients in coronary flow and/or pressure by models containing fixed resistance and capacitance may seriously underestimate intramyocardial capacitative effects and characteristic time constants for pressure-induced resistance changes.

Scalability and in vivo validation of a multiscale numerical model of the left coronary circulation

“…5D, data shown only for arterial side). The reduction in microvascular volume caused by high-systolic p im increased resistance as in Bruinsma et al (11) and was responsible for 40 Ϯ 8 and 42 Ϯ 8% of total effective resistance in adults and newborns, respectively.…”

“…The 0D model of the coronary microvasculature ( Fig. 2) was based on the models of Bruinsma et al (11) and Spaan et al (65). Whereas in those studies a single instance of the model was used to represent the entire left coronary arterial system, in the current study numerous 0D instances each represented a small region of myocardium.…”

“…The compliances C 1 and C2 were 0.013 and 0.254 ml·mmHg Ϫ1 ·100 g Ϫ1 , respectively, while V0,1 and V0,2 were 2.5 and 8.0 ml/100 g (62,65), with a subendocardial-to-subepicardial ratio of 1.14 for both parameters (11,74). In preliminary simulations, we found that accounting for the volume-dependence of compliance using the method described by Bruinsma et al (11) had a negligible effect on coronary flow waveforms (as in Ref .…”

“…Given the findings of Algranati et al (2) that the combination of CEP and SIP are best able to account for current experimental data, in the present study we assume ␣ ϭ 1. As in previous modeling studies (4,11), CEP for the LV free wall was assumed to vary linearly from cavity pressure at the endocardium to pericardial pressure (here assumed to be atmospheric pressure) at the epicardium. Hence, for the three transmural layers, average CEP in the subendocardium, midwall, and subepicardium was therefore 5/6, 1/2, and 1/6 of p LV, respectively.…”

Mechanical blood-tissue interaction in contracting muscles

“…According to the vascular waterfall mechanism, blood flow decreases with increasing tissue pressure, because venous blood pressure increases to tissue pressure due to collapse of the distal venous blood vessels. Mathematical models of blood perfusion that account for this behaviour by non-linear vessel compliance have been developed (Arts and Reneman, 1985, Spaan, 1985, Bruinsma et al, 1988. Intramuscular pressure, determined from experiments or estimated with simple models, is prescribed in these models.…”