Refining Our Understanding of the Flow Through Coronary Artery Branches; Revisiting Murray’s Law in Human Epicardial Coronary Arteries

Abstract

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.

Validation of a novel numerical model to predict regionalized blood flow in the coronary arteries

“…In this retrospective study, we have validated a regionalized porous wall boundary method for simulating side branch Q and compared the results with those from the original homogeneous method. 15 The main aim of this work was to regionalize the side branch and main branch flow. This was achieved with no major difference in overall side branch flow compared with the homogeneous method.…”

“…Previously, one direct in-vitro validation of virtuQ outlet Q results has been performed, reporting a bias of +2.08 ± 3.45 mL/min 13 and our previous validation of inlet Q CFD using the homogeneous porous wall boundary method reported zero bias between CIT results with 95% limits of agreement of ±168 mL/min. 15 More data are available for the latest, monorail Rayflow catheter design. An in-vitro trial of Q CIT reported a bias of −6.5 ± 15.5 mL/min 12 and one animal study reported a bias of +5 ± 8 mL/min from Q measured in 12 pigs (mean Q 37 mL/min).…”

“…A derivation analysis of Murray’s exponent, based upon the same raw clinical dataset as this study, has already been published. 15 …”

“…Full exclusion criteria have previously been published. 15 In brief, cases were excluded if transferred clinical data were unsuitable for computational processing or major arterial side branches were present within 3.0 cm of the Rayflow™ infusion port. The latter criterion was used because side branches close to the infusion port can draw a significant portion of saline infusate and therefore affect Q CIT and Rmicro CIT results.…”

“… 22–24 The magnitude of side branch flow (i.e. flow across the porous wall) was dependent upon the value used for this proportionality constant (which was optimized in a previous study 15 ) and the method used to distribute side branch losses (homogeneous vs. regional, see below). The aim of this study was to compare accuracy of the homogeneous and regional techniques against the invasively derived measures.…”