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

Single View Techniques for Modelling Coronary Pressures Losses. Comment on Tsigkas et al. Rapid and Precise Computation of Fractional Flow Reserve from Routine Two-Dimensional Coronary Angiograms Based on Fluid Mechanics: The Pilot FFR2D Study. J. Clin. Med. 2024, 13, 3831

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Association of Murray's law with atherosclerosis risk: Numerical validation of a general scaling law of arterial tree

Atherogenesis is prone in medium and large-sized vessels, such as the aorta and coronary arteries, where hemodynamic stress is critical. Low and oscillatory wall shear stress contributes significantly to endothelial dysfunction and inflammation. Murray's law minimizes energy expenditure in vascular networks and applies to small arteries. However, its assumptions fail to account for the pulsatile nature of blood flow in larger, atherosclerosis-prone arteries. This study aims to numerically validate a novel general scaling law that extends Murray's law to incorporate pulsatile flow effects and demonstrate its applications in vascular health and artificial graft design. The proposed scaling law establishes an optimal relationship between arterial bifurcation characteristics and pulsatile flow dynamics, applicable throughout the vascular system. This work examines the relationship between deviations from Murray's law and the development of atherosclerosis in both coronary arteries and abdominal aorta bifurcations, explaining observed deviations from Murray's law in these regions. A finite volume method is applied to evaluate flow patterns in coronary arteries and aortoiliac bifurcations, incorporating in vivo pulsatile inflow and average outlet pressure. The results indicate that the proposed scaling law enhances wall shear stress distribution compared to Murray's law, which is characterized by higher wall shear stress and reduced oscillatory shear index. These findings suggest that vessels adhering to this scaling law are less susceptible to atherosclerosis. Furthermore, the results are consistent with clinical morphometric data, underscoring the potential of the proposed scaling law to optimize vascular graft designs, promoting favorable hemodynamic patterns and minimizing the occlusion risk in clinical applications.

Main Coronary Flow Calculation With the Assistance of Physiological Side Branch Flow

OBJECTIVE

Fractional flow reserve (FFR) derived from coronary angiography, referred to as ICA-FFR, is a less-invasive alternative for invasive FFR measurement based on computational fluid dynamics. Blood flow into side branches influences the accuracy of ICA-FFR. However, properly compensating for side branch flow in ICA-FFR analysis is challenging. In this study, we proposed a physiological side branch flow model to comprehensively compensate side branch flow for ICA-FFR analysis with no need for reconstructing side branch geometry.

METHODOLOGY

the physiological side branch flow model employed a reduced-order model to calculate the pressure distribution in vessel segments. The main coronary artery (without side branches) was delineated and divided based on bifurcation nodes. The model compensates for flow to invisible side branches within each segment and flow to visible side branches at each bifurcation node. Lastly, ICA-FFR based on physiological side branch flow model (ICA-FFR) was calculated from a single angiographic view. Functional stenosis is defined by FFR 0.80.

RESULT

Our study involved 223 vessels from 172 patients. Using invasive FFR as a reference, the Pearson correlation coefficient of ICA-FFR was 0.93. ICA-FFR showed a high AUC (AUC = 0.96) and accuracy (91.9) in predicting functional stenosis.

CONCLUSION

The proposed model accurately compensates for flow to side branches without their geometry in ICA-FFR analysis. ICA-FFR analysis exhibits high feasibility and diagnostic performance in identifying functional stenosis.

Relative Residence Time Can Account for Half of the Anatomical Variation in Fatty Streak Prevalence Within the Right Coronary Artery

PURPOSE

The patchy anatomical distribution of atherosclerosis has been attributed to variation in haemodynamic wall shear stress (WSS). The consensus is that low WSS and a high Oscillatory Shear Index (OSI) trigger the disease. We found that atherosclerosis at aortic branch sites correlates threefold better with transverse WSS (transWSS), a metric which quantifies multidirectional near-wall flow. Coronary artery disease has greater clinical significance than aortic disease but computation of WSS metrics is complicated by the substantial vessel motion occurring during each cardiac cycle. Here we present the first comparison of the distribution of atherosclerosis with WSS metrics computed for moving coronary arteries.

METHODS

Maps of WSS metrics were computed using dynamic geometries reconstructed from angiograms of ten non-stenosed human right coronary arteries (RCAs). They were compared with maps of fatty streak prevalence derived from a previous study of 1852 RCAs.

RESULTS

Time average WSS (TAWSS), OSI, transWSS and the cross-flow index (CFI), a non-dimensional form of the transWSS, gave non-significant or significant but low spatial correlations with lesion prevalence. The highest correlation coefficient (0.71) was for the relative residence time (RRT), a metric that decreases with TAWSS and increases with OSI. The coefficient was not changed if RRT was calculated using CFI, which captures multidirectional WSS only, rather than OSI, which encompasses both multidirectional and oscillatory WSS.

CONCLUSION

Contrary to our earlier findings in the aorta, low WSS in combination with highly multidirectional flow correlates best with lesion location in the RCA, explaining approximately half of its anatomical variation.

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 ([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.

Plant-Based Decellularization: A Novel Approach for Perfusion-Compatible Tissue Engineering Structures

This study explores the potential of plant-based decellularization in regenerative medicine, a pivotal development in tissue engineering focusing on scaffold development, modification, and vascularization. Plant decellularization involves removing cellular components from plant structures, offering an eco-friendly and cost-effective alternative to traditional scaffold materials. The use of plant-derived polymers is critical, presenting both benefits and challenges, notably in mechanical properties. Integration of plant vascular networks represents a significant bioengineering breakthrough, aligning with natural design principles. The paper provides an in-depth analysis of development protocols, scaffold fabrication considerations, and illustrative case studies showcasing plant-based decellularization applications. This technique is transformative, offering sustainable scaffold design solutions with readily available plant materials capable of forming perfusable structures. Ongoing research aims to refine protocols, assess long-term implications, and adapt the process for clinical use, indicating a path toward widespread adoption. Plant-based decellularization holds promise for regenerative medicine, bridging biological sciences with engineering through eco-friendly approaches. Future perspectives include protocol optimization, understanding long-term impacts, clinical scalability, addressing mechanical limitations, fostering collaboration, exploring new research areas, and enhancing education. Collectively, these efforts envision a regenerative future where nature and scientific innovation converge to create sustainable solutions, offering hope for generations to come.

Evaluation of models of sequestration flow in coronary arteries-Physiology versus anatomy?

BACKGROUND

Myocardial ischaemia results from insufficient coronary blood flow. Computed virtual fractional flow reserve (vFFR) allows quantification of proportional flow loss without the need for invasive pressure-wire testing. In the current study, we describe a novel, conductivity model of side branch flow, referred to as 'leak'. This leak model is a function of taper and local pressure, the latter of which may change radically when focal disease is present. This builds upon previous techniques, which either ignore side branch flow, or rely purely on anatomical factors. This study aimed to describe a new, conductivity model of side branch flow and compare this with established anatomical models.

METHODS AND RESULTS

The novel technique was used to quantify vFFR, distal absolute flow (Qd) and microvascular resistance (CMVR) in 325 idealised 1D models of coronary arteries, modelled from invasive clinical data. Outputs were compared to an established anatomical model of flow. The conductivity model correlated and agreed with the reference model for vFFR (r = 0.895, p < 0.0001; ＋0.02, 95% CI 0.00 to ＋ 0.22), Qd (r = 0.959, p < 0.0001; -5.2 mL/min, 95% CI -52.2 to ＋13.0) and CMVR (r = 0.624, p < 0.0001; ＋50 Woods Units, 95% CI -325 to ＋2549).

CONCLUSION

Agreement between the two techniques was closest for vFFR, with greater proportional differences seen for Qd and CMVR. The conductivity function assumes vessel taper was optimised for the healthy state and that CMVR was not affected by local disease. The latter may be addressed with further refinement of the technique or inferred from complementary image data. The conductivity technique may represent a refinement of current techniques for modelling coronary side-branch flow. Further work is needed to validate the technique against invasive clinical data.

Sex differences in coronary microvascular resistance measured by a computational fluid dynamics model

Background

Increased coronary microvascular resistance (CMVR) is associated with coronary microvascular dysfunction (CMD). Although CMD is more common in women, sex-specific differences in CMVR have not been demonstrated previously.

Aim

To compare CMVR between men and women being investigated for chest pain.

Methods and results

We used a computational fluid dynamics (CFD) model of human coronary physiology to calculate absolute CMVR based on invasive coronary angiographic images and pressures in 203 coronary arteries from 144 individual patients. CMVR was significantly higher in women than men (860 [650-1,205] vs. 680 [520-865] WU, Z = -2.24, p = 0.025). None of the other major subgroup comparisons yielded any differences in CMVR.

Conclusion

CMVR was significantly higher in women compared with men. These sex-specific differences may help to explain the increased prevalence of CMD in women.

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

Aims

Ischaemic heart disease results from insufficient coronary blood flow. Direct measurement of absolute flow (mL/min) is feasible, but has not entered routine clinical practice in most catheterization laboratories. Interventional cardiologists, therefore, rely on surrogate markers of flow. Recently, we described a computational fluid dynamics (CFD) method for predicting flow that differentiates inlet, side branch, and outlet flows during angiography. In the current study, we evaluate a new method that regionalizes flow along the length of the artery.

Methods and results

Three-dimensional coronary anatomy was reconstructed from angiograms from 20 patients with chronic coronary syndrome. All flows were computed using CFD by applying the pressure gradient to the reconstructed geometry. Side branch flow was modelled as a porous wall boundary. Side branch flow magnitude was based on morphometric scaling laws with two models: a homogeneous model with flow loss along the entire arterial length; and a regionalized model with flow proportional to local taper. Flow results were validated against invasive measurements of flow by continuous infusion thermodilution (Coroventis™, Abbott). Both methods quantified flow relative to the invasive measures: homogeneous (r 0.47, P 0.006; zero bias; 95% CI -168 to +168 mL/min); regionalized method (r 0.43, P 0.013; zero bias; 95% CI -175 to +175 mL/min).

Conclusion

During angiography and pressure wire assessment, coronary flow can now be regionalized and differentiated at the inlet, outlet, and side branches. The effect of epicardial disease on agreement suggests the model may be best targeted at cases with a stenosis close to side branches.

Computing intracoronary blood flow rate under incomplete boundary conditions: Combing coronary anatomy and fractional flow reserve

BACKGROUND

Accurate measurement of intracoronary blood flow rate is of great significance for the diagnosis of ischemic heart disease (IHD). Computational fluid dynamic (CFD) method, combining coronary angiography images and fractional flow reserve (FFR), provides a new way to calculate the mean flow rate. However, due to the incomplete boundary conditions obtained by FFR, side branches were ignored which was likely to have a significant impact on the accuracy. In this paper, a novel CFD based method for calculating the mean intracoronary flow rate under incomplete pressure boundary conditions was proposed, in order to improve the accuracy by including the side branches.

METHODS

A pressure-flow curve based flow resistance model was employed to model resistance of the epicardial arteries. A series of steady flow simulations were performed to extract the parameters of the flow resistance model, which implicitly specified constraints for splitting flow between branches and thus enabled the mean intracoronary blood flow rate to be calculated in two or more branches under incomplete pressure boundary conditions. Simulation experiments were designed to validate the proposed method in both idealized and reconstructed 3D models of coronary branches, and the impact of the assumed coefficient of the Murray's Law for splitting flow between branches was also investigated.

RESULTS

The mean percentage error of the proposed method was +2.05%±0.04% for idealized models and +2.24%±0.01% for reconstructed models, and it was much lower than that of the method ignoring side branches (+38.48%±10.45% for idealized models and +30.54%±6.12% for reconstructed models). When the assumed coefficient of the Murray's Law was inconsistent with the real blood flow condition, the percentage errors still maintained less than about 3.00%.

CONCLUSIONS

The proposed method provided an easy and accurate way to measure the mean intracoronary flow rate and would facilitate the accurate diagnosis of IHD.

Shared decision-making in the realm of uncertainty: The example of coronary artery disease through an EBM and complexity science lens

Patients look to their clinicians for explanations and treatments that achieve predictable cures with certainty. Clinicians usually respond accordingly. Acknowledging uncertainty, while necessary, is difficult, anxiety-provoking and at times overwhelming for patients and clinicians alike. We here present three case studies to illustrate the uncertainties of managing patients with potentially life-threatening illnesses. Research aims to provide answers to clinical problems. But, conducting research almost inevitably entails a reduction of real-world complexities. Research ultimately can only provide 'partial or in general answers' mostly revealing new questions. Due to the complexity of clinical care, research cannot really achieve certainty and predictability for an individual within his specific living context and values. In an unavoidably uncertain environment, instead of oversimplifying, clinicians like patients-as far as possible-ought to better embrace a complexity thinking frame. This provides a deeper understanding how living bodies function as-a-whole within their living contexts. Uncertainty and unpredictability, being inherent elements of complexity thinking, cannot be overcome. However, it may be made easier to cope with uncertainty by at least adopting the thinking in probabilities for benefits and harms of patient related outcomes as introduced in Sackett's Evidence-Based Medicine framework. Through the lenses of evidence-based medicine and complexity sciences this paper critically explores the clinical management of three patients diagnosed as having coronary artery disease. They all received the same treatment even though they presented with very different clinical complaints arising from different disease manifestations. Looking at these case studies the authors reflect on the reasons behind this astonishing, but widely seen medical behaviour of 'one size fits all'. They critically reflect the importance of research and evidence in view of a person-centred solution.