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Taylor DJ, Saxton H, Halliday I, Newman T, Hose DR, Kassab GS, Gunn JP, Morris PD. Systematic review and meta-analysis of Murray's law in the coronary arterial circulation. Am J Physiol Heart Circ Physiol 2024; 327:H182-H190. [PMID: 38787386 DOI: 10.1152/ajpheart.00142.2024] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 03/06/2024] [Revised: 05/01/2024] [Accepted: 05/20/2024] [Indexed: 05/25/2024]
Abstract
Murray's law has been viewed as a fundamental law of physiology. Relating blood flow ([Formula: see text]) to vessel diameter (D) ([Formula: see text]·∝·D3), 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 March 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 4,772 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% confidence interval: 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.
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Affiliation(s)
- Daniel J Taylor
- Division of Clinical Medicine, School of Medicine and Population Health, University of Sheffield, Sheffield, United Kingdom
- Insigneo Institute for In Silico Medicine, University of Sheffield, Sheffield, United Kingdom
- NIHR Sheffield Biomedical Research Centre, Sheffield Teaching Hospitals NHS Foundation Trust, Sheffield, United Kingdom
| | - Harry Saxton
- Materials and Engineering Research Institute, Sheffield Hallam University, Sheffield, United Kingdom
| | - Ian Halliday
- Division of Clinical Medicine, School of Medicine and Population Health, University of Sheffield, Sheffield, United Kingdom
- Insigneo Institute for In Silico Medicine, University of Sheffield, Sheffield, United Kingdom
| | - Tom Newman
- Division of Clinical Medicine, School of Medicine and Population Health, University of Sheffield, Sheffield, United Kingdom
- Insigneo Institute for In Silico Medicine, University of Sheffield, Sheffield, United Kingdom
- Department of Cardiology, Sheffield Teaching Hospitals NHS Foundation Trust, Sheffield, United Kingdom
- NIHR Sheffield Biomedical Research Centre, Sheffield Teaching Hospitals NHS Foundation Trust, Sheffield, United Kingdom
| | - D R Hose
- Division of Clinical Medicine, School of Medicine and Population Health, University of Sheffield, Sheffield, United Kingdom
- Insigneo Institute for In Silico Medicine, University of Sheffield, Sheffield, United Kingdom
| | - Ghassan S Kassab
- California Medical Innovations Institute, San Diego, California, United States
| | - Julian P Gunn
- Division of Clinical Medicine, School of Medicine and Population Health, University of Sheffield, Sheffield, United Kingdom
- Insigneo Institute for In Silico Medicine, University of Sheffield, Sheffield, United Kingdom
- Department of Cardiology, Sheffield Teaching Hospitals NHS Foundation Trust, Sheffield, United Kingdom
- NIHR Sheffield Biomedical Research Centre, Sheffield Teaching Hospitals NHS Foundation Trust, Sheffield, United Kingdom
| | - Paul D Morris
- Division of Clinical Medicine, School of Medicine and Population Health, University of Sheffield, Sheffield, United Kingdom
- Insigneo Institute for In Silico Medicine, University of Sheffield, Sheffield, United Kingdom
- Department of Cardiology, Sheffield Teaching Hospitals NHS Foundation Trust, Sheffield, United Kingdom
- NIHR Sheffield Biomedical Research Centre, Sheffield Teaching Hospitals NHS Foundation Trust, Sheffield, United Kingdom
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Schwarz JCV, van Lier MGJTB, van den Wijngaard JPHM, Siebes M, VanBavel E. Topologic and Hemodynamic Characteristics of the Human Coronary Arterial Circulation. Front Physiol 2020; 10:1611. [PMID: 32038291 PMCID: PMC6989553 DOI: 10.3389/fphys.2019.01611] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2019] [Accepted: 12/23/2019] [Indexed: 11/26/2022] Open
Abstract
Background Many processes contributing to the functional and structural regulation of the coronary circulation have been identified. A proper understanding of the complex interplay of these processes requires a quantitative systems approach that includes the complexity of the coronary network. The purpose of this study was to provide a detailed quantification of the branching characteristics and local hemodynamics of the human coronary circulation. Methods The coronary arteries of a human heart were filled post-mortem with fluorescent replica material. The frozen heart was alternately cut and block-face imaged using a high-resolution imaging cryomicrotome. From the resulting 3D reconstruction of the left coronary circulation, topological (node and loop characteristics), topographic (diameters and length of segments), and geometric (position) properties were analyzed, along with predictions of local hemodynamics (pressure and flow). Results The reconstructed left coronary tree consisted of 202,184 segments with diameters ranging from 30 μm to 4 mm. Most segments were between 100 μm and 1 mm long. The median segment length was similar for diameters ranging between 75 and 200 μm. 91% of the nodes were bifurcations. These bifurcations were more symmetric and less variable in smaller vessels. Most of the pressure drop occurred in vessels between 200 μm and 1 mm in diameter. Downstream conductance variability affected neither local pressure nor median local flow and added limited extra variation of local flow. The left coronary circulation perfused 358 cm3 of myocardium. Median perfused volume at a truncation level of 100 to 200 μm was 20 mm3 with a median perfusion of 5.6 ml/min/g and a high local heterogeneity. Conclusion This study provides the branching characteristics and hemodynamic analysis of the left coronary arterial circulation of a human heart. The resulting model can be deployed for further hemodynamic studies at the whole organ and local level.
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Affiliation(s)
- Janina C V Schwarz
- Department of Biomedical Engineering and Physics, Amsterdam UMC, University of Amsterdam, Amsterdam, Netherlands
| | - Monique G J T B van Lier
- Department of Biomedical Engineering and Physics, Amsterdam UMC, University of Amsterdam, Amsterdam, Netherlands
| | | | - Maria Siebes
- Department of Biomedical Engineering and Physics, Amsterdam UMC, University of Amsterdam, Amsterdam, Netherlands
| | - Ed VanBavel
- Department of Biomedical Engineering and Physics, Amsterdam UMC, University of Amsterdam, Amsterdam, Netherlands
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Colebank MJ, Paun LM, Qureshi MU, Chesler N, Husmeier D, Olufsen MS, Fix LE. Influence of image segmentation on one-dimensional fluid dynamics predictions in the mouse pulmonary arteries. J R Soc Interface 2019; 16:20190284. [PMID: 31575347 DOI: 10.1098/rsif.2019.0284] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
Computational fluid dynamics (CFD) models are emerging tools for assisting in diagnostic assessment of cardiovascular disease. Recent advances in image segmentation have made subject-specific modelling of the cardiovascular system a feasible task, which is particularly important in the case of pulmonary hypertension, requiring a combination of invasive and non-invasive procedures for diagnosis. Uncertainty in image segmentation propagates to CFD model predictions, making the quantification of segmentation-induced uncertainty crucial for subject-specific models. This study quantifies the variability of one-dimensional CFD predictions by propagating the uncertainty of network geometry and connectivity to blood pressure and flow predictions. We analyse multiple segmentations of a single, excised mouse lung using different pre-segmentation parameters. A custom algorithm extracts vessel length, vessel radii and network connectivity for each segmented pulmonary network. Probability density functions are computed for vessel radius and length and then sampled to propagate uncertainties to haemodynamic predictions in a fixed network. In addition, we compute the uncertainty of model predictions to changes in network size and connectivity. Results show that variation in network connectivity is a larger contributor to haemodynamic uncertainty than vessel radius and length.
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Affiliation(s)
| | - L Mihaela Paun
- Mathematics and Statistics, University of Glasgow, Glasgow G12 8SQ, UK
| | - M Umar Qureshi
- Mathematics, NC State University, Raleigh, NC 27695, USA
| | - Naomi Chesler
- Biomedical Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA
| | - Dirk Husmeier
- Mathematics and Statistics, University of Glasgow, Glasgow G12 8SQ, UK
| | | | - Laura Ellwein Fix
- Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23220, USA
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Evaluation of fractional flow reserve in patients with stable angina: can CT compete with angiography? Eur Radiol 2019; 29:3669-3677. [DOI: 10.1007/s00330-019-06023-z] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2018] [Revised: 12/20/2018] [Accepted: 01/18/2019] [Indexed: 10/27/2022]
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Mynard JP, Penny DJ, Smolich JJ. Major influence of a 'smoke and mirrors' effect caused by wave reflection on early diastolic coronary arterial wave intensity. J Physiol 2018; 596:993-1017. [PMID: 29318640 DOI: 10.1113/jp274710] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2017] [Accepted: 01/02/2018] [Indexed: 01/25/2023] Open
Abstract
KEY POINTS Coronary wave intensity analysis (WIA) is an emerging technique for assessing upstream and downstream influences on myocardial perfusion. It is thought that a dominant backward decompression wave (BDWdia ) is generated by a distal suction effect, while early-diastolic forward decompression (FDWdia ) and compression (FCWdia ) waves originate in the aorta. We show that wave reflection also makes a substantial contribution to FDWdia , FCWdia and BDWdia , as quantified by a novel method. In 18 sheep, wave reflection accounted for ∼70% of BDWdia , whereas distal suction dominated in a computer model representing a hypertensive human. Non-linear addition/subtraction of mechanistically distinct waves (e.g. wave reflection and distal suction) obfuscates the true contribution of upstream and downstream forces on measured waves (the 'smoke and mirrors' effect). The mechanisms underlying coronary WIA are more complex than previously thought and the impact of wave reflection should be considered when interpreting clinical and experimental data. ABSTRACT Coronary arterial wave intensity analysis (WIA) is thought to provide clear insight into upstream and downstream forces on coronary flow, with a large early-diastolic surge in coronary flow accompanied by a prominent backward decompression wave (BDWdia ), as well as a forward decompression wave (FDWdia ) and forward compression wave (FCWdia ). The BDWdia is believed to arise from distal suction due to release of extravascular compression by relaxing myocardium, while FDWdia and FCWdia are thought to be transmitted from the aorta into the coronary arteries. Based on an established multi-scale computational model and high-fidelity measurements from the proximal circumflex artery (Cx) of 18 anaesthetized sheep, we present evidence that wave reflection has a major impact on each of these three waves, with a non-linear addition/subtraction of reflected waves obscuring the true influence of upstream and downstream forces through concealment and exaggeration, i.e. a 'smoke and mirrors' effect. We also describe methods, requiring additional measurement of aortic WIA, for unravelling the separate influences of wave reflection versus active upstream/downstream forces on coronary waves. Distal wave reflection accounted for ∼70% of the BDWdia in sheep, but had a lesser influence (∼25%) in the computer model representing a hypertensive human. Negative reflection of the BDWdia at the coronary-aortic junction attenuated the Cx FDWdia (by ∼40% in sheep) and augmented Cx FCWdia (∼5-fold), relative to the corresponding aortic waves. We conclude that wave reflection has a major influence on early-diastolic WIA, and thus needs to be considered when interpreting coronary WIA profiles.
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Affiliation(s)
- Jonathan P Mynard
- Heart Research, Clinical Sciences, Murdoch Children's Research Institute, Parkville, VIC 3052, Australia.,Department of Paediatrics, University of Melbourne, Parkville, VIC 3052, Australia.,Department of Cardiology, Royal Children's Hospital, Parkville, VIC 3052, Australia
| | - Daniel J Penny
- Heart Research, Clinical Sciences, Murdoch Children's Research Institute, Parkville, VIC 3052, Australia.,Department of Paediatrics, University of Melbourne, Parkville, VIC 3052, Australia.,Department of Cardiology, Royal Children's Hospital, Parkville, VIC 3052, Australia.,Institute of Reproduction and Development, Monash University, Clayton, VIC, Australia
| | - Joseph J Smolich
- Heart Research, Clinical Sciences, Murdoch Children's Research Institute, Parkville, VIC 3052, Australia.,Department of Paediatrics, University of Melbourne, Parkville, VIC 3052, Australia.,Institute of Reproduction and Development, Monash University, Clayton, VIC, Australia
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