Refining our understanding of the flow through coronary artery branches; revisiting Murray’s law in human epicardial coronary arteries

Background: Quantification of coronary blood flow is used to evaluate coronary artery disease, but our understanding of flow through branched systems is poor. Murray’s law defines coronary morphometric scaling, the relationship between flow (Q) and vessel diameter (D) and is the basis for minimum lumen area targets when intervening on bifurcation lesions. Murray’s original law (Q α DP) dictates that the exponent (P) is 3.0, whilst constant blood velocity throughout the system would suggest an exponent of 2.0. In human coronary arteries, the value of Murray’s exponent remains unknown.

Aim: To establish the exponent in Murray’s power law relationship that best reproduces coronary blood flows (Q) and microvascular resistances (Rmicro) in a bifurcating coronary tree.

Methods and Results: We screened 48 cases, and were able to evaluate inlet Q and Rmicro in 27 branched coronary arteries, taken from 20 patients, using a novel computational fluid dynamics (CFD) model which reconstructs 3D coronary anatomy from angiography and uses pressure-wire measurements to compute Q and Rmicro distribution in the main- and side-branches. Outputs were validated against invasive measurements using a Rayflow™ catheter. A Murray’s power law exponent of 2.15 produced the strongest correlation and closest agreement with inlet Q (zero bias, r = 0.47, p = 0.006) and an exponent of 2.38 produced the strongest correlation and closest agreement with Rmicro (zero bias, r = 0.66, p = 0.0001).

Conclusions: The optimal power law exponents for Q and Rmicro were not 3.0, as dictated by Murray’s Law, but 2.15 and 2.38 respectively. These data will be useful in assessing patient-specific coronary physiology and tailoring revascularisation decisions.