Scaling laws of coronary circulation in health and disease

Static and dynamic analysis of cerebral blood flow in fifty-six large arterial vessel networks

Objective.The cerebral vasculature is formed of an intricate network of blood vessels over many different length scales. Changes in their structure and connection are implicated in multiple cerebrovascular and neurological disorders. In this study, we present a novel approach to the quantitative analysis of the cerebral macrovasculature using computational and mathematical tools in a large dataset.Approach.We analysed a publicly available vessel dataset from a cohort of 56 (32/24F/M) healthy subjects. This dataset includes digital reconstructions of human brain macrovasculatures. We then propose a new mathematical model to compute blood flow dynamics and pressure distributions within these 56-representative cerebral macrovasculatures and quantify the results across this cohort.Main results.Statistical analysis showed that the steady state level of cerebrovascular resistance (CVR) gradually increases with age in both men and women. These age-related changes in CVR are in good agreement with previously reported values. All subjects were found to have only small phase angles (<6°) between blood pressure and blood flow at the cardiac frequency.Significance.These results showed that the dynamic component of blood flow adds very little phase shift at the cardiac frequency, which implies that the cerebral macrocirculation can be regarded as close to steady state in its behaviour, at least in healthy populations, irrespective of age or sex. This implies that the phase shift observed in measurements of blood flow in cerebral vessels is caused by behaviour further down the vascular bed. This behaviour is important for future statistical models of the dynamic maintenance of oxygen and nutrient supply to the brain.

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.

Definitions and Standardized Endpoints for Treatment of Coronary Bifurcations

The Bifurcation Academic Research Consortium (Bif-ARC) project originated from the need to overcome the paucity of standardization and comparability between studies involving bifurcation coronary lesions. This document is the result of a collaborative effort between academic research organizations and the most renowned interventional cardiology societies focused on bifurcation lesions in Europe, the United States, and Asia. This consensus provides standardized definitions for bifurcation lesions; the criteria to judge the side branch relevance; the procedural, mechanistic, and clinical endpoints for every type of bifurcation study; and the follow-up methods. Considering the complexity of bifurcation lesions and their evaluation, detailed instructions and technical aspects for site and core laboratory analysis of bifurcation lesions are also reported. The recommendations included within this consensus will facilitate pooled analyses and the effective comparison of data in the future, improving the clinical relevance of trials in bifurcation lesions, and the quality of care in this subset of patients.

A novel technique of proximal optimization with kissing balloon inflation in bifurcation lesions

BACKGROUND

Percutaneous coronary interventions (PCI) of bifurcation lesions poses a technical challenge with a high complication rate. Kissing balloon inflation (KBI) and proximal optimization technique (POT) are used to correct bifurcation carina after stenting. However, both may still lead to uncomplete strut apposition to the side branch (SB) lateral wall. Proposed herein, is a new stent-optimization technique following bifurcation stenting consisting of a combination of POT and KBI called proximal optimization with kissing balloon inflation (POKI).

METHODS

Bench and in-vivo evaluations were performed. For the bench visualization bifurcated silicone mock vessel was used. The POKI technique was simulated using a 3.5 mm POT balloon. For the in-vivo evaluation patients with angiographic bifurcation lesions in a native coronary artery with diameter ≥ 2.5 mm and ≤ 4.5 mm, SB diameter ≥ 2.0 mm, and percentage diameter stenosis (%DS) more than 50% in the main vessel (MV) were included. Provisional stenting was the default strategy.

RESULTS

In total 41 vessels were evaluated. The target vessel was left main in 9 (22.0%) patients, left anterior descending artery - in 26 (63.4%), left circumflex artery - in 4 (9.8%) and right coronary artery - in 2 (4.9%). The predominant type of bifurcation was Medina 1-1-1 (61.8%). Baseline proximal MV DS% was 60.0 ± 23.7%, distal MV DS% - 58.8 ± 28.9% and SB DS% 53.0 ± 32.0%. The application of POKI was feasible in 41 (100%) of the vessels. Post-PCI residual DS at proximal MV was 11.5 ± 15.4%, distal MV - 6.6 ± 9.3%, and SB - 22.9 ± 28.5%. Both procedural and angiographic success was 100%.

CONCLUSIONS

POKI is a novel stent-optimization technique for bifurcation lesions. It showed excellent feasibility and success rate both in bench and in-vivo evaluation.

Definitions and Standardized Endpoints for Treatment of Coronary Bifurcations

The Bifurcation Academic Research Consortium (Bif-ARC) project originated from the need to overcome the paucity of standardization and comparability between studies involving bifurcation coronary lesions. This document is the result of a collaborative effort between academic research organizations and the most renowned interventional cardiology societies focused on bifurcation lesions in Europe, the United States, and Asia. This consensus provides standardized definitions for bifurcation lesions; the criteria to judge the side branch relevance; the procedural, mechanistic, and clinical endpoints for every type of bifurcation study; and the follow-up methods. Considering the complexity of bifurcation lesions and their evaluation, detailed instructions and technical aspects for site and core laboratory analysis of bifurcation lesions are also reported. The recommendations included within this consensus will facilitate pooled analyses and the effective comparison of data in the future, improving the clinical relevance of trials in bifurcation lesions, and the quality of care in this subset of patients.

Correlation and mechanism between cardiac magnetic resonance imaging and oral streptococcus count in patients with primary microvascular angina pectoris

BACKGROUND

Although primary microvascular angina (PMVA) can be diagnosed clinically, the etiology and pathophysiology of PMVA remain unclear. The effects of conventional clinical medications (aspirin, statins, and nitrates) are unsatisfactory, and PMVA can lead to serious cardiovascular events. The present study was designed to analyze the correlation between the load perfusion cardiovascular magnetic resonance imaging (CMR) results and the Streptococcus sanguinis(S sanguinis) count and the correlations between the S sanguinis count in oral cavity subgingival plaque and changes in the plasma levels of platelet alpha-granule membrane glycoprotein 140 (GMP-140), fibrinopeptide A (FPA), von Willebrand factor (vWF), and homocysteine (Hcy) in patients with PMVA after increased anti-infective treatment of the oral cavity. This study also discusses the pathogenesis of PMVA from this perspective. The differences in the S sanguinis count in oral cavity subgingival plaque and oral health status between healthy people and PMVA patients will be compared, and the correlation between the oral cavity health status and disease in PMVA patients will be analyzed.

METHODS

The present randomized controlled trial with a parallel control group will be conducted in 68 PMVA patients diagnosed by the in-patient cardiology department. The selected patients will be randomly divided into 2 groups, one receiving routine drug treatment and the other a combination of anti-infective treatments. The normal control group will comprise 30 healthy people with no infectious oral cavity disease matched by age and sex. We will conduct CMR, and the presence of S sanguinis in subgingival plaques will be used to determine the bacterial count in PMVA patients. Blood samples will also be collected to determine the levels of GMP-140, FPA, vWF, and Hcy. S sanguinis in the subgingival plaque of PMVA patients will be further analyzed after increasing the oral cavity anti-infective treatment; the resulting changes and their correlations with changes in GMP-140, FPA, vWF, and Hcy levels will be assessed. Additionally, the differences in the S sanguinis count and the oral cavity health status of oral cavity dental plaque between healthy people and PMVA patients will be determined, and the correlation between the oral cavity conditions and PMVA will be analyzed. The relationship between the perfusion CMR results and the oral cavity S sanguinis count of PMVA patients, and the potential pathogenesis, will be explored. We will use the SPSS19.0 statistical software package to analyze the data. The measurements will be expressed as means±standard deviation. Student t test will be used for intergroup comparisons, a relative number description will be used for the count data, and the chi-square test will be used for intergroup comparisons. Multivariate logistic regression will be performed to identify associations. A P value < .05 will be considered significant.

DISCUSSION

In this study, the correlation between the perfusion CMR results and the S sanguinis count in oral cavity subgingival plaque of PMVA patients will be analyzed. Changes in the levels of GMP-140, FPA, vWF, and Hcy of PMVA patients after receiving increased oral cavity anti-infective treatment will be explored, and the difference in the S sanguinis count in oral cavity subgingival plaque and the oral cavity health status between healthy people and PMVA patients will be compared.

ATRIAL REGISTRATION

Chinese Clinical Trial Registry, (http://www.chictr.org.cn/showprojen.aspx?proj=45091).

Development of Novel Fractal Method for Characterizing the Distribution of Blood Flow in Multi-Scale Vascular Tree

Blood perfusion is an important index for the function of the cardiovascular system and it can be indicated by the blood flow distribution in the vascular tree. As the blood flow in a vascular tree varies in a large range of scales and fractal analysis owns the ability to describe multi-scale properties, it is reasonable to apply fractal analysis to depict the blood flow distribution. The objective of this study is to establish fractal methods for analyzing the blood flow distribution which can be applied to real vascular trees. For this purpose, the modified methods in fractal geometry were applied and a special strategy was raised to make sure that these methods are applicable to an arbitrary vascular tree. The validation of the proposed methods on real arterial trees verified the ability of the produced parameters (fractal dimension and multifractal spectrum) in distinguishing the blood flow distribution under different physiological states. Furthermore, the physiological significance of the fractal parameters was investigated in two situations. For the first situation, the vascular tree was set as a perfect binary tree and the blood flow distribution was adjusted by the split ratio. As the split ratio of the vascular tree decreases, the fractal dimension decreases and the multifractal spectrum expands. The results indicate that both fractal parameters can quantify the degree of blood flow heterogeneity. While for the second situation, artificial vascular trees with different structures were constructed and the hemodynamics in these vascular trees was simulated. The results suggest that both the vascular structure and the blood flow distribution affect the fractal parameters for blood flow. The fractal dimension declares the integrated information about the heterogeneity of vascular structure and blood flow distribution. In contrast, the multifractal spectrum identifies the heterogeneity features in blood flow distribution or vascular structure by its width and height. The results verified that the proposed methods are capable of depicting the multi-scale features of the blood flow distribution in the vascular tree and further are potential for investigating vascular physiology.

Morphological and hemodynamic analysis of the patient-specific renal cell carcinoma models

Although the morbidity of renal cell carcinoma (RCC) has been increasing as the seventh most common tumours, to our knowledge, there is few studies foucsing on the hemodynamics of the renal artery (RA) with RCC. The objective of this study is to perform morphological and hemodynamic analysis of the RA and abdominal aorta artery (AAA) in the control healthy and RCC patient groups. Three-dimensional (3D) geometries are reconstructed from 18 control healthy subjects and 15 RCC patients based on Computed Tomography Angiography (CTA) images. There is higer in the lumen diameter of the RA (6.21 ± 0.89 mm) and curvature of the RA (1.2 ± 0.07) in the RCC patient group compared with the control healthy group (4.29 ± 1.08 mm, 1.1 ± 0.1), respectively. In the hemodynamic analysis, the surface area ratio (%) of low time-averaged wall shear stress (SAR-TAWSS) at the RA (10.65 ± 11.65) and AAA (48.49 ± 12.79) in the RCC patient group is significantly higher than that in the control healthy group (0.23 ± 0.22, 21.57 ± 20.5), respectively. It is found that RCC altered the morphology of the RA in the RCC patient group, which could deteriorate the hemodynamic environment of the RA and AAA. The finding in this study could enhance us to understand the progression of vascular disease caused by RCC.

Cardiovascular magnetic resonance image analysis and mechanism study for the changes after treatments for primary microvascular angina pectoris

ABSTRACT

Most cases of primary microvascular angina pectoris (PMVA) are diagnosed clinically, but the etiology and pathological mechanisms are unknown. The effect of routine clinical medications is minimal, and PMVA can progress to serious cardiovascular events. To improve the diagnosis and effective treatment of this disease, this study was designed to diagnose PMVA via cardiovascular magnetic resonance (CMR) and the coronary angiography thrombolysis in myocardial infarction (TIMI) blood flow grade, as well as to analyze vascular endothelial function to elucidate the pathogenesis of PMVA and compare the effects of routine clinical medications.The present randomized controlled trial including a parallel control group will be conducted on 63 PMVA patients in our cardiovascular department. The patients will be selected and randomly divided into the control, diltiazem, and nicorandil groups. The control group will be administered routine drug treatments (aspirin, atorvastatin, betaloc ZOK, perindopril, and isosorbidemononitrate sustained-release tablets). The diltiazem group will be additionally treated with 90 mg qd diltiazem sustained-release capsules. The nicorandil group was additionally given 5 mg tid nicorandil tablets. Coronary angiography will be performed before treatment, the severity and frequency of chest pain will be evaluated before and after 9 months of treatment, and homocysteine and von Willebrand factor levels will be measured. Electrocardiography, echocardiography, dynamic electrocardiography, a treadmill exercise test, and CMR will be performed. Sex, age, body mass index, complications, smoking, and family history will also be recorded. The SPSS19.0 statistical software package will be used to analyze the data. The measurements will be expressed as the mean ± standard deviation. Measurement data will be compared between the groups using Student's t-test. A relative number description will be used for the counting data, and the chi-squaretest will be used to compare the groups. A multivariate logistic regression analysis will be performed A P-value < .05 will be considered significant.The direct indices (CMR and coronary angiographic TIMI blood flow grade) may improve after adding diltiazem or nicorandil during routine drug treatments (such as aspirin, statins, and nitrates) in PMVA patients, and indirect indices (homocysteine and von Willebrand factor levels) may be reduced.

TRIAL REGISTRATION

Chinese Clinical Trial Registry (http://www.chictr.org.cn/showprojen.aspx?proj=41894), No. CHiCTR1900025319, Registered on August 23, 2019; pre initiation.

On deriving Murray's law from constrained minimization of flow resistance

Murray's law, which states that the cube of the radius of a parent vessel equals the sum of the cubes of the radii of the daughter vessels, was originally derived by minimizing the cost of operation of blood flow in a single cylindrical tube. An alternative widely cited derivation by Sherman is based upon the optimization problem of minimizing the total flow resistance subject to a material constraint, and that study claimed that "Conservation of the sum of the cubes of the radii is the condition for minimal resistance whether the parent vessel divides symmetrically or asymmetrically, and whether it divides into two, three, four, or, presumably, any number of daughter vessels." In this paper we show that Sherman's analysis is flawed, since with N daughter vessels there are 2^N-N-1 sets of vessel radii which satisfy Murray's law but which do not yield minimal total flow resistance. Moreover, we show that when there are N daughter vessels, each with the same radius, the minimal total flow resistance is an increasing function of N for N⩾1. Since N=1 corresponds to the degenerate case of no branching at all, our result implies that bifurcation (N=2) achieves the minimal total flow resistance. Our analysis thus offers an explanation for the preponderance of bifurcations (as opposed to trifurcations or higher level branchings) in many biological systems.

Topologic and Hemodynamic Characteristics of the Human Coronary Arterial Circulation

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.

Blood flow rate and wall shear stress in seven major cephalic arteries of humans

Blood flow rate ( Q ˙ ) in relation to arterial lumen radius (r_i ) is commonly modelled according to theoretical equations and paradigms, including Murray's Law ( Q ˙ ∝ r i 3 ) and da Vinci's Rule ( Q ˙ ∝ r i 2 ). Wall shear stress (τ) is independent of r_i with Murray's Law (τ ∝  r i 0 ) and decreases with da Vinci's Rule (τ ∝  r i - 1 ). These paradigms are tested empirically with a meta-analysis of the relationships between Q ˙ and r_i in seven major arteries of the human cephalic circulation from 19 imaging studies in which both variables were presented. The analysis shows that Q ˙ ∝ r i 2.16 and τ ∝  r i - 1.02 , more consistent with da Vinci's Rule than Murray's Law. This meta-analysis provides standard values for Q ˙ , r_i and τ in the human cephalic arteries that may be a useful baseline in future investigations. On average, the paired internal carotid arteries supply 75%, and the vertebral arteries supply 25%, of total brain blood flow. The internal carotid arteries contribute blood entirely to the anterior and middle cerebral arteries and also partly to the posterior cerebral arteries via the posterior communicating arteries of the circle of Willis. On average, the internal carotid arteries provide 88% of the blood flow to the cerebrum and the vertebral arteries only 12%.

A healthy dose of chaos: Using fractal frameworks for engineering higher-fidelity biomedical systems

Optimal levels of chaos and fractality are distinctly associated with physiological health and function in natural systems. Chaos is a type of nonlinear dynamics that tends to exhibit seemingly random structures, whereas fractality is a measure of the extent of organization underlying such structures. Growing bodies of work are demonstrating both the importance of chaotic dynamics for proper function of natural systems, as well as the suitability of fractal mathematics for characterizing these systems. Here, we review how measures of fractality that quantify the dose of chaos may reflect the state of health across various biological systems, including: brain, skeletal muscle, eyes and vision, lungs, kidneys, tumours, cell regulation, skin and wound repair, bone, vasculature, and the heart. We compare how reports of either too little or too much chaos and fractal complexity can be damaging to normal biological function, and suggest that aiming for the healthy dose of chaos may be an effective strategy for various biomedical applications. We also discuss rising examples of the implementation of fractal theory in designing novel materials, biomedical devices, diagnostics, and clinical therapies. Finally, we explain important mathematical concepts of fractals and chaos, such as fractal dimension, criticality, bifurcation, and iteration, and how they are related to biology. Overall, we promote the effectiveness of fractals in characterizing natural systems, and suggest moving towards using fractal frameworks as a basis for the research and development of better tools for the future of biomedical engineering.

Biofabrication strategies for creating microvascular complexity

Design and fabrication of effective biomimetic vasculatures constitutes a relevant and yet unsolved challenge, lying at the heart of tissue repair and regeneration strategies. Even if cell growth is achieved in 3D tissue scaffolds or advanced implants, tissue viability inevitably requires vascularization, as diffusion can only transport nutrients and eliminate debris within a few hundred microns. This engineered vasculature may need to mimic the intricate branching geometry of native microvasculature, referred to herein as vascular complexity, to efficiently deliver blood and recreate critical interactions between the vascular and perivascular cells as well as parenchymal tissues. This review first describes the importance of vascular complexity in labs- and organs-on-chips, the biomechanical and biochemical signals needed to create and maintain a complex vasculature, and the limitations of current 2D, 2.5D, and 3D culture systems in recreating vascular complexity. We then critically review available strategies for design and biofabrication of complex vasculatures in cell culture platforms, labs- and organs-on-chips, and tissue engineering scaffolds, highlighting their advantages and disadvantages. Finally, challenges and future directions are outlined with the hope of inspiring researchers to create the reliable, efficient and sustainable tools needed for design and biofabrication of complex vasculatures.

Interspecific scaling of blood flow rates and arterial sizes in mammals

This meta-study investigated the relationships between blood flow rate (Q̇; cm³ s^-1), wall shear stress (τ_w; dyn cm^-2) and lumen radius (r _i; cm) in 20 named systemic arteries of nine species of mammals, ranging in mass from 23 g mice to 652 kg cows, at rest. In the dataset, derived from 50 studies, lumen radius varied between 3.7 µm in a cremaster artery of a rat and 11.2 mm in the aorta of a human. The 92 logged data points of [Formula: see text] and r _i are described by a single second-order polynomial curve with the equation: [Formula: see text] The slope of the curve increased from approximately 2 in the largest arteries to approximately 3 in the smallest ones. Thus, da Vinci's rule ([Formula: see text]) applies to the main arteries and Murray's law ([Formula: see text]) applies to the microcirculation. A subset of the data, comprising only cephalic arteries in which [Formula: see text] is fairly constant, yielded the allometric power equation: [Formula: see text] These empirical equations allow calculation of resting perfusion rates from arterial lumen size alone, without reliance on theoretical models or assumptions on the scaling of wall shear stress in relation to body mass. As expected, [Formula: see text] of individual named arteries is strongly affected by body mass; however, [Formula: see text] of the common carotid artery from six species (mouse to horse) is also sensitive to differences in whole-body basal metabolic rate, independent of the effect of body mass.

FFRCT derived from computed tomography angiography: the experience in the UK

INTRODUCTION

Non-invasive fractional flow reserve derived from CT coronary angiography (FFR_CT) represents a novel technology to investigate coronary artery disease. The application of computational flow dynamics to anatomical data provides the clinician with a further functional assessment to inform decision-making in patients with coronary artery disease. In the UK FFR_CT has received medical technology approval for use since February 2017. Areas covered: This article discusses the mathematical and physiological principles underpinning calculation of non-invasive fractional flow reserve (FFR), as well as discussing the differences between the commercially available technologies. Diagnostic accuracy, cost effectiveness and safety of non-invasive FFR from the early clinical trials is examined. Further to this the potential implications of the use of non-invasive FFR in clinical practice in the UK are discussed. Expert commentary: Non-invasive FFR represents a promising comprehensive imaging technology providing both anatomical and physiological data to accurately diagnose obstructive coronary artery disease. The technology has yet to prove to be cost effective in 'real world' cohorts before becoming integrated into everyday clinical practice and guidelines in the United Kingdom.

Bifurcation Asymmetry of Small Coronary Arteries in Juvenile and Adult Mice

Background: Microvascular bifurcation asymmetry is of significance for regulation of coronary flow heterogeneity during juvenile and adult growth. The aim of the study is to investigate the morphometric and hemodynamic variation of coronary arterial bifurcations in mice of different ages.

Methods: Pulsatile blood flows were computed from a Womersley-type model in the reconstructed left coronary arterial (LCA) trees from Micro-CT images in normal mice at ages of 3 weeks, 6 weeks, 12 weeks, 5-6 months, and >8 months. Diameter and flow ratios and bifurcation angles were determined in each bifurcation of the LCA trees.

Results: The blood volume and inlet flow rate of LCA trees increase and decrease during juvenile and adult growth, respectively. As vessel diameters decrease, the increased ratios of small to large daughter vessel diameters (D_s/D_l) result in more uniform flows and lower velocities. There are significant structure-functional changes of LCA trees in mice of >8 months compared with mice of < 8 months. As D_s/D_l increases, the variation trend of bifurcation angle during juvenile growth is different from that during adult growth.

Conclusions: Although inlet flows are different in adult vs. juvenile mice, the adult still have uniform flow and low velocity. This is accomplished through a decrease in diameter. The design ensures ordered dispersion of red cells through asymmetric branching patterns into the capillaries.

Hepatic Hemangiomas Alter Morphometry and Impair Hemodynamics of the Abdominal Aorta and Primary Branches From Computer Simulations

Background: The formation of hepatic hemangiomas (HH) is associated with VEGF and IL-7 that alter conduit arteries and small arterioles. To our knowledge, there are no studies to investigate the effects of HH on the hemodynamics in conduit arteries. The aim of the study is to perform morphometric and hemodynamic analysis in abdominal conduit arteries and bifurcations of HH patients and controls.

Methods: Based on morphometry reconstructed from CT images, geometrical models were meshed with prismatic elements for the near wall region and tetrahedral and hexahedral elements for the core region. Simulations were performed for computation of the non-Newtonian blood flow using the Carreau-Yasuda model, based on which multiple hemodynamic parameters were determined.

Results: There was an increase of the lumen size, diameter ratio, and curvature in the abdominal arterial tree of HH patients as compared with controls. This significantly increased the surface area ratio of low time-averaged wall shear stress (i.e., SAR-TAWSS =Surface  areaTAWSS≤4 dynes·cm−2Total  surface  area× 100%) (24.1 ± 7.9 vs. 5 ± 6%, 11.6 ± 12.8 vs. < 0.1%, and 44.5 ± 9.2 vs. 21 ± 24% at hepatic bifurcations, common hepatic arteries, and abdominal aortas, respectively, between HH and control patients).

Conclusions: Morphometric changes caused by HH significantly deteriorated the hemodynamic environment in abdominal conduit arteries and bifurcations, which could be an important risk factor for the incidence and progression of vascular diseases.

Patient-Specific Modeling of Stented Coronary Arteries Reconstructed from Optical Coherence Tomography: Towards a Widespread Clinical Use of Fluid Dynamics Analyses

The recent widespread application of optical coherence tomography (OCT) in interventional cardiology has improved patient-specific modeling of stented coronary arteries for the investigation of local hemodynamics. In this review, the workflow for the creation of fluid dynamics models of stented coronary arteries from OCT images is presented. The algorithms for lumen contours and stent strut detection from OCT as well as the reconstruction methods of stented geometries are discussed. Furthermore, the state of the art of studies that investigate the hemodynamics of OCT-based stented coronary artery geometries is reported. Although those studies analyzed few patient-specific cases, the application of the current reconstruction methods of stented geometries to large populations is possible. However, the improvement of these methods and the reduction of the time needed for the entire modeling process are crucial for a widespread clinical use of the OCT-based models and future in silico clinical trials.

Quantitative angiography methods for bifurcation lesions: a consensus statement update from the European Bifurcation Club

Bifurcation lesions represent one of the most challenging lesion subsets in interventional cardiology. The European Bifurcation Club (EBC) is an academic consortium whose goal has been to assess and recommend the appropriate strategies to manage bifurcation lesions. The quantitative coronary angiography (QCA) methods for the evaluation of bifurcation lesions have been subject to extensive research. Single-vessel QCA has been shown to be inaccurate for the assessment of bifurcation lesion dimensions. For this reason, dedicated bifurcation software has been developed and validated. These software packages apply the principles of fractal geometry to address the "step-down" in the bifurcation and to estimate vessel diameter accurately. This consensus update provides recommendations on the QCA analysis and reporting of bifurcation lesions based on the most recent scientific evidence from in vitro and in vivo studies and delineates future advances in the field of QCA dedicated bifurcation analysis.

Planar cell polarity genes frizzled4 and frizzled6 exert patterning influence on arterial vessel morphogenesis

Quantitative analysis of the vascular network anatomy is critical for the understanding of the vasculature structure and function. In this study, we have combined microcomputed tomography (microCT) and computational analysis to provide quantitative three-dimensional geometrical and topological characterization of the normal kidney vasculature, and to investigate how 2 core genes of the Wnt/planar cell polarity, Frizzled4 and Frizzled6, affect vascular network morphogenesis. Experiments were performed on frizzled4 (Fzd4^-/-) and frizzled6 (Fzd6^-/-) deleted mice and littermate controls (WT) perfused with a contrast medium after euthanasia and exsanguination. The kidneys were scanned with a high-resolution (16 μm) microCT imaging system, followed by 3D reconstruction of the arterial vasculature. Computational treatment includes decomposition of 3D networks based on Diameter-Defined Strahler Order (DDSO). We have calculated quantitative (i) Global scale parameters, such as the volume of the vasculature and its fractal dimension (ii) Structural parameters depending on the DDSO hierarchical levels such as hierarchical ordering, diameter, length and branching angles of the vessel segments, and (iii) Functional parameters such as estimated resistance to blood flow alongside the vascular tree and average density of terminal arterioles. In normal kidneys, fractal dimension was 2.07±0.11 (n = 7), and was significantly lower in Fzd4^-/- (1.71±0.04; n = 4), and Fzd6^-/- (1.54±0.09; n = 3) kidneys. The DDSO number was 5 in WT and Fzd4^-/-, and only 4 in Fzd6^-/-. Scaling characteristics such as diameter and length of vessel segments were altered in mutants, whereas bifurcation angles were not different from WT. Fzd4 and Fzd6 deletion increased vessel resistance, calculated using the Hagen-Poiseuille equation, for each DDSO, and decreased the density and the homogeneity of the distal vessel segments. Our results show that our methodology is suitable for 3D quantitative characterization of vascular networks, and that Fzd4 and Fzd6 genes have a deep patterning effect on arterial vessel morphogenesis that may determine its functional efficiency.