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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.

Computational modeling has been used routinely in the pre-clinical development of medical devices such as coronary artery stents. The ability to simulate and predict physiological and structural parameters such as flow disturbance, wall shear-stress, and mechanical strain patterns is beneficial to stent manufacturers. These methods are now emerging as useful clinical tools, used by physicians in the assessment and management of patients. Computational models, which can predict the physiological response to intervention, offer clinicians the ability to evaluate a number of different treatment strategies in silico prior to treating the patient in the cardiac catheter laboratory. For the first time clinicians can perform a patient-specific assessment prior to making treatment decisions. This could be advantageous in patients with complex disease patterns where the optimal treatment strategy is not clear. This article reviews the key advances and the potential barriers to clinical adoption and translation of these virtual treatment planning models.

Background: Measuring the extent to which renal artery stenosis (RAS) alters renal haemodynamics may permit precision medicine by physiologically guided revascularization. This currently requires invasive intra-arterial pressure measurement with associated risks and is rarely performed. The present proof-of-concept study investigates an in silico approach that uses computational fluid dynamic (CFD) modeling to non-invasively estimate renal artery haemodynamics from routine anatomical computed tomography (CT) imaging of RAS.Methods: We evaluated 10 patients with RAS by CT angiography. Intra-arterial renal haemodynamics were invasively measured by a transducing catheter under resting and hyperaemic conditions, calculating the translesional ratio of distal to proximal pressure (Pd/Pa). The diagnostic and quantitative accuracy of the CFD-derived virtual Pd/Pa ratio (vPd/Pa) was evaluated against the invasively measured Pd/Pa ratio (mPd/Pa).Results: Hyperaemic haemodynamics was infeasible and CT angiography in 4 patients had insufficient image resolution. Resting flow data is thus reported for 7 stenosed arteries from 6 patients (one patient had bilateral RAS). The comparison showed a mean difference of 0.015 (95% confidence intervals of ± 0.08), mean absolute error of 0.064, and a Pearson correlation coefficient of 0.6, with diagnostic accuracy for a physiologically significant Pd/Pa of ≤ 0.9 at 86%.Conclusion: We describe the first in silico estimation of renal artery haemodynamics from CT angiography in patients with RAS, showing it is feasible and diagnostically accurate. This provides a methodological framework for larger prospective studies to ultimately develop non-invasive precision medicine approaches for studies and interventions of RAS and resistant hypertension.