A systematic review and meta-analysis of Murray's Law in the coronary arterial circulation

Murray's law has been viewed as a fundamental law of physiology. Relating blood flow (Q) to vessel diameter (D) (Q µD3), it dictates minimum lumen area (MLA) targets for coronary bifurcation percutaneous coronary intervention (PCI). The cubic exponent (3.0) however, has long been disputed, with alternative theoretical derivations arguing this should be closer to 2.33 (7/3). The aim of this meta-analysis was to quantify the optimum flow-diameter exponent in human and mammalian coronary arteries. We conducted a systematic review and meta-analysis of all articles quantifying an optimum flow-diameter exponent for mammalian coronary arteries within the Cochrane library, PubMed Medline, Scopus, and Embase databases on 20/3/2023. A random-effects meta-analysis was used to determine a pooled flow-diameter exponent. Risk of bias was assessed with the National Institutes of Health (NIH) quality assessment tool, funnel plots and Egger regression. From a total of 4,524 articles, 18 were suitable for meta-analysis. Studies included data from 1,070 unique coronary trees, taken from 372 humans and 112 animals. The pooled flow diameter exponent across both epicardial and transmural arteries was 2.39 (95% CI 2.24 - 2.54, I2 = 99%). The pooled exponent of 2.39 showed very close agreement with the theoretical exponent of 2.33 (7/3) reported by Kassab and colleagues. This exponent may provide a more accurate description of coronary morphometric scaling in human and mammalian coronary arteries, as compared with Murray's original law. This has important implications for the assessment, diagnosis, and interventional treatment of coronary artery disease.