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.

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.

Colocalization of Coronary Plaque with Wall Shear Stress in Myocardial Bridge Patients

PURPOSE

Patients with myocardial bridges (MBs) have a higher prevalence of atherosclerosis. Wall shear stress (WSS) has previously been correlated with plaque in coronary artery disease patients, but such correlations have not been investigated in symptomatic MB patients. The aim of this paper was to use a multi-scale computational fluid dynamics (CFD) framework to simulate hemodynamics in MB patient, and investigate the co-localization of WSS and plaque.

METHODS

We identified N = 10 patients from a previously reported cohort of 50 symptomatic MB patients, all of whom had plaque in the proximal vessel. Dynamic 3D models were reconstructed from coronary computed tomography angiography (CCTA), intravascular ultrasound (IVUS) and catheter angiograms. CFD simulations were performed to compute WSS proximal to, within and distal to the MB. Plaque was quantified from IVUS images in 2 mm segments and registered to CFD model. Plaque area was compared to absolute and patient-normalized WSS.

RESULTS

WSS was lower in the proximal segment compared to the bridge segment (6.1 ± 2.9 vs. 16.0 ± 7.1 dynes/cm², p value < 0.01). Plaque area and plaque burden measured from IVUS peaked at 1-3 cm proximal to the MB entrance, coinciding with the first diagonal branch. Normalized WSS showed a statistically significant moderate correlation with plaque area (r = 0.41, p < 0.01).

CONCLUSION

WSS may be obtained non-invasively in MB patients and provides a surrogate marker of plaque area. Using CFD, it may be possible to non-invasively assess the extent of plaque area, and identify patients who could benefit from frequent monitoring or medical management.

Retinal Vascular Profile in Predicting Incident Cardiometabolic Diseases among Individuals with Diabetes

OBJECTIVE

To determine the longitudinal associations between retinal vascular profile (RVP) and four major cardiometabolic diseases; and to quantify the predictive improvements when adding RVP beyond traditional risk factors in individuals with diabetes.

METHODS

Subjects were enrolled from the Singapore Epidemiology of Eye Disease (SEED) study, a multi-ethnic population-based cohort. Four incident cardiometabolic diseases, calculated over a ~6-year period, were considered: cardiovascular disease (CVD), hypertension (HTN), diabetic kidney disease (DKD) and hyperlipidaemia (HLD). The RVP - vessel tortuosity, branching angle, branching coefficient, fractal dimension, vessel calibre, and DR status - was characterized at baseline using a computer-assisted program. Traditional risk factors at baseline included age, gender, ethnicity, smoking, blood pressure (BP), HbA1c, estimated glomerular filtration rate (eGFR) or cholesterol. The improvements in predictive performance when adding RVP (compared to only traditional risk factors) was calculated using several metrics including area under the receiver operating characteristics curve (AUC) and Net Reclassification Improvement (NRI).

RESULTS

Among 1,770 individuals with diabetes, incidences were 6.3% (n=79/1259) for CVD, 48.7% (n=166/341) for HTN, 14.6% (n=175/1199) for DKD, and 59.4% (n=336/566) for HLD. DR preceded the onset of CVD (RR 1.85[1.14;3.00]) and DKD (1.44 [1.06;1.96]). Narrower arteriolar calibre preceding the onset of HTN (0.84 [0.72;0.99]), and changes in arteriolar branching angle preceded the onset of CVD (0.78 [0.62;0.98]) and HTN (1.15 [1.03;1.29]). The largest predictive improvement was found for HTN with AUC increment of 3.4% (p=0.027) and better reclassification of 11.4% of the cases and 4.6% of the controls (p=0.008).

CONCLUSION

We found that RVPs improved the prediction of HTN in individuals with diabetes, but add limited information for CVD, DKD and HLD predictions.

Low Wall Shear Stress Is Associated with Saphenous Vein Graft Stenosis in Patients with Coronary Artery Bypass Grafting

Biomechanical forces may play a key role in saphenous vein graft (SVG) disease after coronary artery bypass graft (CABG) surgery. Computed tomography angiography (CTA) of 430 post-CABG patients were evaluated and 15 patients were identified with both stenosed and healthy SVGs for paired analysis. The stenosis was virtually removed, and detailed 3D models were reconstructed to perform patient-specific computational fluid dynamic (CFD) simulations. Models were processed to compute anatomic parameters, and hemodynamic parameters such as local and vessel-averaged wall shear stress (WSS), normalized WSS (WSS*), low shear area (LSA), oscillatory shear index (OSI), and flow rate. WSS* was significantly lower in pre-diseased SVG segments compared to corresponding control segments without disease (1.22 vs. 1.73, p = 0.012) and the area under the ROC curve was 0.71. No differences were observed in vessel-averaged anatomic or hemodynamic parameters between pre-stenosed and control whole SVGs. There are currently no clinically available tools to predict SVG failure post-CABG. CFD modeling has the potential to identify high-risk CABG patients who may benefit from more aggressive medical therapy and closer surveillance. Graphical Abstract.

Effect of stenosis and dilatation on the hemodynamic parameters associated with left coronary artery

BACKGROUND AND OBJECTIVE

The main objective of the work is to examine the curvature effects of stenosis/dilatation region pertaining to left coronary artery. The hemodymamic features during the cardiac cycle is thoroughly examined.

METHODS

A numerical fluid structure interaction model incorporating multi- layered elastic artery wall, non-Newtonian blood viscosity and pulsating boundary conditions is developed. The composite arterial wall consists of a thin layer tunica intima, atheroma and a thick wall. Higher stiffness of atheroma is captured by using higher Young's modulus. The CFD and FSI models are validated with available experimental and analytical data. Computations are done with five different non-Newtonian models and arterial wall with various elasticity levels. The local and time averaged WSS, velocity contours downstream of stenosis, wall pressure and pressure drop during various phases of cardiac cycle are provided in detail.

RESULTS

The influence of non-Newtonian effects of blood viscosity is found to be significant especially at stenosis regions. The flexible wall caused wall deformation and the associated flow and pressure wave propagation affecting WSS and pressure drop compared to the rigid wall. Flow recirculation is noticed at stenosis downstream locations and its strength increases with increased severity of the stenosis. A stenosis is characterised by a sudden drop in wall pressure and a slower two stage recovery during peak velocity periods of the cardiac cycle.

CONCLUSIONS

The pressure drop, local WSS at stenosis centre, and radial velocity increase are significantly higher for stenosis cases and the effect is severe during peak diastole. The variation in hemodynamic parameters is found to be less significant for dilatation. Significantly lower WSS is noticed for the recirculation regions downstream of stenosis which can enhance the tendency for monocytes to attach to the endothelium. The radius of curvature of the stenosis is found to be the most sensitive parameter affecting the hemodynamic characteristics rather than the detailed geometry of the stenosis. The main effect of variation of artery wall stiffness is noted at recirculation regions present downstream of stenosis. The results from the study may be useful for predicting wall shear stress signatures associated with stenosis/dilatation changes and the management of specific cases.

The role of vascular complexity on optimal junction exponents

We examine the role of complexity on arterial tree structures, determining globally optimal vessel arrangements using the Simulated AnneaLing Vascular Optimization algorithm, a computational method which we have previously used to reproduce features of cardiac and cerebral vasculatures. In order to progress computational methods for growing arterial networks, deeper understanding of the stability of computational arterial growth algorithms to complexity, variations in physiological parameters (such as metabolic costs for maintaining and pumping blood), and underlying assumptions regarding the value of junction exponents is needed. We determine the globally optimal structure of two-dimensional arterial trees; analysing how physiological parameters affect tree morphology and optimal bifurcation exponent. We find that considering the full complexity of arterial trees is essential for determining the fundamental properties of vasculatures. We conclude that optimisation-based arterial growth algorithms are stable against uncertainties in physiological parameters, while optimal bifurcation exponents (a key parameter for many arterial growth algorithms) are affected by the complexity of vascular networks and the boundary conditions dictated by organs.

Flow topology and targeted drug delivery in cardiovascular disease

Targeted drug delivery is a promising technique to direct the drug to the specific diseased region. Nanoparticles have provided an attractive approach for this purpose. In practice, the major focus of targeted delivery has been on targeting cell receptors. However, the complex fluid mechanics in diseased biomedical flows questions if a sufficient number of nanoparticles can reach the desired region. In this paper, we propose that hidden topological structures in cardiovascular flows identified with Lagrangian coherent structures (LCS) control drug transport and provide valuable information for optimizing targeted drug delivery efficiency. We couple image-based computational fluid dynamics (CFD) with continuum transport models to study nanoparticle transport in coronary artery disease. We simulate nanoparticle transport as well as the recently proposed shear targeted drug delivery system that couples micro-carriers with nanoparticle drugs. The role of the LCS formed near the stenosed artery in controlling drug transport is discussed. Our results motivate the design of smart micro-needles guided by flow topology, which could achieve optimal drug delivery efficiency.

The effects of clinically-derived parametric data uncertainty in patient-specific coronary simulations with deformable walls

Cardiovascular simulations are increasingly used for noninvasive diagnosis of cardiovascular disease, to guide treatment decisions, and in the design of medical devices. Quantitative assessment of the variability of simulation outputs due to input uncertainty is a key step toward further integration of cardiovascular simulations in the clinical workflow. In this study, we present uncertainty quantification in computational models of the coronary circulation to investigate the effect of uncertain parameters, including coronary pressure waveform, intramyocardial pressure, morphometry exponent, and the vascular wall Young's modulus. We employ a left coronary artery model with deformable vessel walls, simulated via an Arbitrary-Lagrangian-Eulerian framework for fluid-structure interaction, with a prescribed inlet pressure and open-loop lumped parameter network outlet boundary conditions. Stochastic modeling of the uncertain inputs is determined from intra-coronary catheterization data or gathered from the literature. Uncertainty propagation is performed using several approaches including Monte Carlo, Quasi Monte Carlo sampling, stochastic collocation, and multi-wavelet stochastic expansion. Variabilities in the quantities of interest, including branch pressure, flow, wall shear stress, and wall deformation are assessed. We find that uncertainty in inlet pressures and intramyocardial pressures significantly affect all resulting QoIs, while uncertainty in elastic modulus only affects the mechanical response of the vascular wall. Variability in the morphometry exponent used to distribute the total downstream vascular resistance to the single outlets, has little effect on coronary hemodynamics or wall mechanics. Finally, we compare convergence behaviors of statistics of QoIs using several uncertainty propagation methods on three model benchmark problems and the left coronary simulations. From the simulation results, we conclude that the multi-wavelet stochastic expansion shows superior accuracy and performance against Quasi Monte Carlo and stochastic collocation methods.

Reduced order models for transstenotic pressure drop in the coronary arteries

The efficacy of reduced order modeling for transstenotic pressure drop in the coronary arteries is presented. Coronary artery disease is a leading cause of death worldwide and the computation of fractional flow reserve from computed tomography (FFRct) has become a standard for evaluating the functional significance of a coronary stenosis. FFRct uses 3D computational fluid dynamics to simulate coronary blood flow in order to compute transstenotic pressure drop during simulated hyperemia. In this study, we evaluate different fidelity hydrodynamic models and their ability to compute transstenotic pressure drop and FFRct in the coronary arteries. Models range from simple algebraic formulae to 1D, 2D and 3D time-dependent computational fluid dynamic simulations. Although several algebraic pressure-drop formulae have been proposed in the literature, these models were found to exhibit wide variation in predictions. Nonetheless, we demonstrate an algebraic formula that provides reliable predictions over a range of stenosis severity, morphology, location and flow rate when compared to the current standard for FFRct. The accounting of viscous dissipation, flow separation and pulsatile inertial effects were found to be the most significant contributions to accurate reduce order modeling of transstenotic coronary hemodynamics.

Fractal characteristics of the microvascular network: A useful index to assess vascularization level of porous silk fibroin biomaterial

The neovascularization of biomaterials for tissue engineering is not only related to growth of capillaries but also involves appropriate hierarchy distribution of the microvessels. In this study, we proposed hierarchy distribution contrast method which can assess vascular transport capacity, in order to examine the hierarchy distribution of the neovessels during vascularization of the porous silk fibroin biomaterials implanted into rats and its evolution. The results showed that the fractal characteristics appeared toward the end of the vascularization stages, and the structure of the microvascular network after 3 weeks of implantation was similar to the fractal microvascular tree with bifurcation exponent x = 3 and fractal dimension D = 1.46, which became a sign of maturation of the regenerative vasculature. © 2017 Wiley Periodicals, Inc. J Biomed Mater Res Part A: 105A: 2276-2290, 2017.

Retinal microvasculature as a model to study the manifestations of hypertension

The retinal vasculature allows direct noninvasive visualization of the body's mircrovasculature. Because the retina and other end organs (brain and kidney) share similar anatomical features and physiological properties, the retinal vessels offer a unique and easily accessible window to study the health and disease of the human microcirculation. Advanced retinal vascular imaging technologies have been developed to allow a more objective and precise assessment of retinal vascular changes. The changes in the retinal vasculature associated with hypertension can be broadly divided into 3 groups: (1) classic retinal vascular changes in response to blood pressure (referred to as hypertensive retinopathy signs), (2) changes in retinal vascular caliber, and (3) changes in more global geometrical patterns of the retina. In this review, we summarize the current understanding of the relationship between retinal vascular changes and blood pressure, the evidence for the retinal vasculature as a biological model to study the manifestation and early pathogenic correlates of hypertension, the latest advances in retinal vascular imaging technologies, and the future opportunities and challenges of retinal vascular imaging. We suggest that further development of retinal vascular analyses and standardized measurement protocols, evaluation of the clinical use of retinal vascular imaging in assessing cardiovascular risk prediction, and using retinal vascular imaging to test antihypertensive treatments will allow the translation of retinal vascular imaging as a tool to improve the diagnosis, prognosis, and management of hypertension in clinical practice.

Blood Pressure and Retinal Microvascular Characteristics During Pregnancy

Changes in maternal blood pressure during pregnancy are associated with poor maternal and neonatal outcomes. We investigated whether maternal blood pressure during midpregnancy has an impact on the retinal microcirculation among pregnant Asian women. A total of 665 pregnant women aged 18 to 46 years were recruited from the Growing Up in Singapore Towards Healthy Outcomes Study. Blood pressure and retinal vascular parameters were both measured at 26 weeks' gestation following a standardized protocol. Blood pressure was measured by a digital automatic blood pressure monitor (Omron HEM 705 LP). Quantitative retinal vascular parameters were assessed by a semiautomated computer-based program (Singapore I Vessel Assessment, version 3.0). In multiple linear regression models, every 10-mm Hg increase in mean arterial blood pressure was associated with a 1.9-μm ( P <0.001) reduction in retinal arteriolar caliber, a 0.9° ( P =0.05) reduction in retinal arteriolar branching angle, and a 0.07 ( P <0.01) reduction in retinal arteriolar fractal dimension, respectively. Patients classified into a high-risk group in developing preeclampsia (mean arterial blood pressure ≥90 mm Hg) were twice as likely (odds ratio 2.1 [95% CI, 1.0–4.4]) to have generalized retinal arteriolar narrowing compared with those classified into a low-risk group (mean arterial blood pressure <90 mm Hg). Retinal venular caliber and vascular tortuosity were not associated with blood pressure measures. Elevated blood pressure is associated with a range of retinal arteriolar changes in pregnant women, providing evidence for an impact of blood pressure on the microcirculation during pregnancy.

Retinal vascular geometry in Asian persons with diabetes and retinopathy

PURPOSE

Our purpose was to examine the relationship of retinal vascular parameters with diabetes and retinopathy in an older Asian population.

METHODS

Retinal photographs from participants of a population-based survey of Asian Malay persons aged 40-80 years were analyzed. Specific retinal vascular parameters (tortuosity, branching angle, fractal dimension, and caliber) were measured using a semiautomated computer-based program. Diabetes was defined as random plasma glucose ≥ 11.1 mmol/liter, the use of diabetes medication, or physician-diagnosed diabetes. Retinopathy signs were graded from photographs using the modified Airlie House classification system.

RESULTS

A total of 2735 persons were included in the study. Persons with diabetes (n = 594) were more likely to have straighter (less tortuous) arterioles and wider arteriolar and venular caliber than those without diabetes (n = 2141). Among subjects with diabetes, those with retinopathy had wider venular caliber than those without retinopathy (211.3 versus 204.9 mm, p = .001). Among nondiabetic subjects, however, those with retinopathy had more tortuous venules than those without retinopathy [5.19(×10(4)) versus 4.27(×10(4)), p < .001].

CONCLUSIONS

Retinal vascular parameters varied by diabetes and retinopathy status in this older Asian cohort. Our findings suggest that subtle alterations in retinal vascular architecture are influenced by diabetes.

Are wet-induced wrinkled fingers primate rain treads?

Wet fingers and toes eventually wrinkle, and this is commonly attributed by lay opinion to local osmotic reactions. However, nearly a century ago surgeons observed that no wrinkling occurs if a nerve to the finger has been cut. Here we provide evidence that, rather than being an accidental side effect of wetness, wet-induced wrinkles have been selected to enhance grip in wet conditions. We show that their morphology has the signature properties of drainage networks, enabling efficient removal of water from the gripped surface.