A fundamental physics-based derivation of intraspecific scaling laws of vascular trees has not been previously realized. Here, we provide such a theoretical derivation for the volume–diameter and flow–length scaling laws of intraspecific vascular trees. In conjunction with the minimum energy hypothesis, this formulation also results in diameter–length, flow–diameter and flow–volume scaling laws. The intraspecific scaling predicts the volume–diameter power relation with a theoretical exponent of 3, which is validated by the experimental measurements for the three major coronary arterial trees in swine (where a least-squares fit of these measurements has exponents of 2.96, 3 and 2.98 for the left anterior descending artery, left circumflex artery and right coronary artery trees, respectively). This scaling law as well as others agrees very well with the measured morphometric data of vascular trees in various other organs and species. This study is fundamental to the understanding of morphological and haemodynamic features in a biological vascular tree and has implications for vascular disease.

Aims: Conventional fractional flow reserve (FFR) is measured invasively using a coronary guidewire equipped with a pressure sensor. A non-invasive derived FFR would eliminate risk of coronary injury, minimize technical limitations, and potentially increase adoption. We aimed to evaluate the diagnostic performance of a computational pressure-flow dynamics derived FFR (caFFR), applied to coronary angiography, compared to invasive FFR.Methods and results: The FLASH FFR study was a prospective, multicentre, single-arm study conducted at six centres in China. Eligible patients had native coronary artery target lesions with visually estimated diameter stenosis of 30–90% and diagnosis of stable or unstable angina pectoris. Using computational pressure-fluid dynamics, in conjunction with thrombolysis in myocardial infarction (TIMI) frame count, applied to coronary angiography, caFFR was measured online in real-time and compared blind to conventional invasive FFR by an independent core laboratory. The primary endpoint was the agreement between caFFR and FFR, with a pre-specified performance goal of 84%. Between June and December 2018, matched caFFR and FFR measurements were performed in 328 coronary arteries. Total operational time for caFFR was 4.54 ± 1.48 min. caFFR was highly correlated to FFR (R = 0.89, P = 0.76) with a mean bias of −0.002 ± 0.049 (95% limits of agreement −0.098 to 0.093). The diagnostic performance of caFFR vs. FFR was diagnostic accuracy 95.7%, sensitivity 90.4%, specificity 98.6%, positive predictive value 97.2%, negative predictive value 95.0%, and area under the receiver operating characteristic curve of 0.979.Conclusions: Using wire-based FFR as the reference, caFFR has high accuracy, sensitivity, and specificity. caFFR could eliminate the need of a pressure wire, technical error and potentially increase adoption of physiological assessment of coronary artery stenosis severity.Clinical Trial Registration: URL: http://www.chictr.org.cn Unique Identifier: ChiCTR1800019522.

A coronary angiography-derived index of microvascular resistance (caIMR) is proposed for physiological assessment of microvasular diseases in coronary circulation. The aim of the study is to assess diagnostic performance of caIMR, using wire-derived index of microvascular resistance (IMR) as the reference standard. IMR was demonstrated in 56 patients (57 vessels) with stable/unstable angina pectoris and no obstructive coronary arteries in three centers using the Certus pressure wire. Based on the aortic pressure wave and coronary angiograms from two projections, the caIMR was computed and assessed in blinded fashion against the IMR at an independent core laboratory. Diagnostic accuracy, sensitivity, specificity, positive predictive value and negative predictive value of the caIMR with a cutoff value of 25 were 84.2% (95% CI: 72.1% to 92.5%), 86.1% (95% CI: 70.5% to 95.3%), 81.0% (95% CI: 58.1% to 94.6%), 88.6% (95% CI: 76.1% to 95.0%), and 77.3% (95% CI: 59.5% to 88.7%) against the IMR with a cutoff value of 25. The receiver-operating curve had area under the curve of 0.919 and the correlation coefficient equaled to 0.746 between caIMR and wire-derived IMR. Hence, caIMR could eliminate the need of a pressure wire, reduce technical error, and potentially increase adoption of physiological assessment of microvascular diseases in patients with ischemic heart disease.

The branching pattern of epicardial coronary arteries is clearly three-dimensional, with correspondingly complex flow patterns. The objective of the present study was to perform a detailed hemodynamic analysis using a three-dimensional finite element method in a left anterior descending (LAD) epicardial arterial tree, including main trunk and primary branches, based on computed tomography scans. The inlet LAD flow velocity was measured in an anesthetized pig, and the outlet pressure boundary condition was estimated based on scaling laws. The spatial and temporal wall shear stress (WSS), gradient of WSS (WSSG), and oscillatory shear index (OSI) were calculated and used to identify regions of flow disturbances in the vicinity of primary bifurcations. We found that low WSS and high OSI coincide with disturbed flows (stagnated, secondary, and reversed flows) opposite to the flow divider and lateral to the junction orifice of the main trunk and primary branches. High time-averaged WSSG occurs in regions of bifurcations, with the flow divider having maximum values. Low WSS and high OSI were found to be related through a power law relationship. Furthermore, zones of low time-averaged WSS and high OSI amplified for larger diameter ratio and high inlet flow rate. Hence, different focal atherosclerotic-prone regions may be explained by different physical mechanism associated with certain critical levels of low WSS, high OSI, and high WSSG, which are strongly affected by the diameter ratio. The implications of the flow patterns for atherogenesis are enumerated.