Bifurcation asymmetry of the porcine coronary vasculature and its implications on coronary flow heterogeneity

Efficacy of catheter-based drug delivery in a hybrid in vitro model of cardiac microvascular obstruction with porcine microthrombi

Microvascular obstruction (MVO) often occurs in ST-elevation myocardial infarction (STEMI) patients after percutaneous coronary intervention (PCI). Diagnosis and treatment of MVO lack appropriate and established procedures. This study focused on two major points by using an in vitro multiscale flow model, which comprised an aortic root model with physiological blood flow and a microfluidic model of the microcirculation with vessel diameters down to 50 μm. First, the influence of porcine microthrombi (MT), injected into the fluidic microchip, on perfusion was investigated. We found that only 43 % of all injected MT were fully occlusive. Second, it could also be shown that the maximal concentration of a dye (representing therapeutic agent) during intracoronary infusion could be increased on average by 58 % , when proximally occluding the coronary artery by a balloon during drug infusion. The obtained results and insights enhance the understanding of perfusion in MVO-affected microcirculation and could lead to improved treatment methods for MVO patients.

Numerical assessment of recellularization conditions to vessel occlusion

To ensure the functional properties of an organ generated by the process of decellularization and recellularization, the initial density and distribution of seeding cells in the parenchymal space should be maximized. However, achieving a uniform distribution of cells across the entire organ is not straightforward because of vessel occlusion. This study assessed vessel occlusion during recellularization under different conditions. A combination of the electrical analog permeability (EPA) model, computational fluid dynamics (CFD), and discrete element method (DEM) was employed to describe the vessel occlusion phenomenon. In particular, realistic flow distributions in vascular trees of the decellularized organ were indicated by the EPA model. The cell suspension flow was modeled by a coupled CFD-DEM model, whereby living cells were presented as a discrete phase (solved by the DEM solver), and the culture medium was modeled as the fluid phase (solved by CFD solver). The cell suspension velocity was reduced up to 47% after decellularization, which directly affected cell movement. Simulation results also indicate that the occurrence of vessel occlusion was promoted by gravity direction in the asymmetric bifurcation and increased as the cell concentration increased. The assessment of vessel occlusion under different conditions was quantitatively investigated. The model provides insights into the dynamics of cells in the vessel compartment, allowing for the selection of optimum seeding parameters for the recellularization process.

Enhanced Drug Delivery for Cardiac Microvascular Obstruction with an Occlusion-Infusion-Catheter

Microvascular Obstruction (MVO) is a common consequence of acute myocardial infarction. MVO is underdiagnosed and treatment is often nonspecific and ineffective. A multi-scale in-vitro benchtop model was established to investigate drug perfusion in MVO affected microcirculation. The central element of the benchtop model was a fluidic microchip containing channels with diameters between [Formula: see text] and 50 μm representing [Formula: see text] of the microvascular tree fed by the left anterior descending artery (LAD). The outlets of the chip could be closed to mimic MVO. Two methods for intracoronary infusion of pharmacologic agents (simulated by dye) to regions with MVO were investigated using an occlusion-infusion catheter. The first case was a simple, bolus-like infusion into the LAD, whereas the second case consisted of infusion with concomitant proximal occlusion of the LAD phantom with a balloon. Results show that local dye concentration maxima in the chip with MVO were 2.2-3.2 times higher for the case with proximal balloon occlusion than for the conventional infusion method. The cumulated dose could be raised by a factor 4.6-5.2. These results suggest that drug infusion by catheter is more effective if the blood supply to the treated vascular bed is temporarily blocked by a balloon catheter.

Contemporary Management of Isolated Ostial Side Branch Disease: An Evidence-based Approach to Medina 001 Bifurcations

The optimal management of bifurcation lesions has received significant interest in recent years and remains a matter of debate among the interventional cardiology community. Bifurcation lesions are encountered in approximately 21% of percutaneous coronary intervention procedures and are associated with an increased risk of major adverse cardiac events. The Medina classification has been developed in an attempt to standardise the terminology when describing bifurcation lesions. The focus of this article is on the management of the Medina 0,0,1 lesion (‘Medina 001’), an uncommon lesion encountered in <5% of all bifurcations. Technical considerations, management options and interventional techniques relating to the Medina 001 lesion are discussed. In addition, current published data supporting the various proposed interventional treatment strategies are examined in an attempt to delineate an evidence-based approach to this uncommon lesion.

Considering intrauterine location in a model of fetal growth restriction after maternal titanium dioxide nanoparticle inhalation

Fetal growth restriction (FGR) is a condition with several underlying etiologies including gestational disease (e.g., preeclampsia, gestational diabetes) and xenobiotic exposure (e.g., environmental contaminants, pharmaceuticals, recreational drugs). Rodent models allow study of FGR pathogenesis. However, given the multiparous rodent pregnancy, fetal growth variability within uterine horns may arise. To ascertain whether intrauterine position is a determinant of fetal growth, we redesigned fetal weight analysis to include litter size and maternal weight. Our FGR model is produced by exposing pregnant Sprague Dawley rats to aerosolized titanium dioxide nanoparticles at 9.44 ± 0.26 mg/m3 on gestational day (GD) 4, GD 12 or GD 17 or 9.53 ± 1.01 mg/m3 between GD 4-GD 19. In this study fetal weight data was reorganized by intrauterine location [i.e., right/left uterine horn and ovarian/middle/vaginal position] and normalized by maternal weight and number of feti per uterine horn. A significant difference in fetal weight in the middle location in controls (0.061g ± 0.001 vs. 0.055g ± 0.002), GD 4 (0.033g ± 0.003 vs. 0.049g ± 0.004), and GD 17 (0.047g ± 0.002 vs. 0.038g ± 0.002) exposed animals was identified. Additionally, GD 4 exposure produced significantly smaller feti in the right uterine horn at the ovarian end (0.052g ± 0.003 vs. 0.029g ± 0.003) and middle of the right uterine horn (0.060g ± 0.001 vs. 0.033g ± 0.003). GD 17 exposure produced significantly smaller feti in the left uterine horn middle location (0.055g ± 0.002 vs. 0.033 ± 0.002). Placental weights were unaffected, and placental efficiency was reduced in the right uterine horn middle location after GD 17 exposure (5.74g ± 0.16 vs. 5.09g ± 0.14). These findings identified: 1) differences in fetal weight of controls between the right and left horns in the middle position, and 2) differential effects of single whole-body pulmonary exposure to titanium dioxide nanoparticles on fetal weight by position and window of maternal exposure. In conclusion, these results indicate that consideration for intrauterine position, maternal weight, and number of feti per horn provides a more sensitive assessment of FGR from rodent reproductive and developmental studies.

Vascular Patterning as Integrative Readout of Complex Molecular and Physiological Signaling by VESsel GENeration Analysis

The molecular signaling cascades that regulate angiogenesis and microvascular remodeling are fundamental to normal development, healthy physiology, and pathologies such as inflammation and cancer. Yet quantifying such complex, fractally branching vascular patterns remains difficult. We review application of NASA's globally available, freely downloadable VESsel GENeration (VESGEN) Analysis software to numerous examples of 2D vascular trees, networks, and tree-network composites. Upon input of a binary vascular image, automated output includes informative vascular maps and quantification of parameters such as tortuosity, fractal dimension, vessel diameter, area, length, number, and branch point. Previous research has demonstrated that cytokines and therapeutics such as vascular endothelial growth factor, basic fibroblast growth factor (fibroblast growth factor-2), transforming growth factor-beta-1, and steroid triamcinolone acetonide specify unique "fingerprint" or "biomarker" vascular patterns that integrate dominant signaling with physiological response. In vivo experimental examples described here include vascular response to keratinocyte growth factor, a novel vessel tortuosity factor; angiogenic inhibition in humanized tumor xenografts by the anti-angiogenesis drug leronlimab; intestinal vascular inflammation with probiotic protection by Saccharomyces boulardii, and a workflow programming of vascular architecture for 3D bioprinting of regenerative tissues from 2D images. Microvascular remodeling in the human retina is described for astronaut risks in microgravity, vessel tortuosity in diabetic retinopathy, and venous occlusive disease.

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.

Bioprinting Vasculature: Materials, Cells and Emergent Techniques

Despite the great advances that the tissue engineering field has experienced over the last two decades, the amount of in vitro engineered tissues that have reached a stage of clinical trial is limited. While many challenges are still to be overcome, the lack of vascularization represents a major milestone if tissues bigger than approximately 200 µm are to be transplanted. Cell survival and homeostasis is to a large extent conditioned by the oxygen and nutrient transport (as well as waste removal) by blood vessels on their proximity and spontaneous vascularization in vivo is a relatively slow process, leading all together to necrosis of implanted tissues. Thus, in vitro vascularization appears to be a requirement for the advancement of the field. One of the main approaches to this end is the formation of vascular templates that will develop in vitro together with the targeted engineered tissue. Bioprinting, a fast and reliable method for the deposition of cells and materials on a precise manner, appears as an excellent fabrication technique. In this review, we provide a comprehensive background to the fields of vascularization and bioprinting, providing details on the current strategies, cell sources, materials and outcomes of these studies.

Simulation study of Hemodynamic in Bifurcations for Cerebral Arteriovenous Malformation using Electrical Analogy

BACKGROUND AND OBJECTIVE

Cerebral Arteriovenous Malformation (CAVM) hemodynamic is disease condition, results changes in the flow and pressure level in cerebral blood vessels. Measuring flow and pressure without catheter intervention along the vessel is big challenge due to vessel bifurcations/complex bifurcations in Arteriovenous Malformation patients. The vessel geometry in CAVM patients are complex, composed of varying diameters, lengths, and bifurcations of various angles. The variations in the vessel diameter and bifurcation angle complicate the measurement and analysis of blood flow features invasively or non-invasively.

METHODS

In this paper, we proposed a lumped model for the bifurcation for symmetrical and asymmetrical networks in CAVM patients. The models are created using MATLAB Simulation software for various bifurcation angles. Each bifurcation angle created using electrical network- RLC. The segmentation and pre-processing of bifurcation vessels are implemented using adaptive segmentation. The proposed network address clinicians problem by measuring hemodynamic non-invasively. The method is applicable for any types of bifurcation networks with different bifurcation angles in CAVM patients.

RESULTS

In this work, we constructed a mathematical model, measured hemodynamic for 23 patients (actual and simulated cases) with 60 vessel bifurcation angles variations. The results indicate that comparisons evidenced highly significant correlations between values computed by the lumped model and simulated mechanical model for both networks with p < 0.0001. A P value of less than 0.05 considered statistically significant.

CONCLUSION

In this paper, we have modelled different bifurcation types and automatically display pressure and flow non-invasively at different node and at different angles of bifurcation in the complex vessel with help of bifurcation parameters, using lumped parameter model. We have simulated for different bifurcation angles and diameters of vessel for various imaging modality and model extend for different organs. This will help clinicians to measure haemodynamic parameters noninvasively at various bifurcations, where even catheter cannot be reached.

Personalized blood flow computations: A hierarchical parameter estimation framework for tuning boundary conditions

We propose a hierarchical parameter estimation framework for performing patient-specific hemodynamic computations in arterial models, which use structured tree boundary conditions. A calibration problem is formulated at each stage of the hierarchical framework, which seeks the fixed point solution of a nonlinear system of equations. Common hemodynamic properties, like resistance and compliance, are estimated at the first stage in order to match the objectives given by clinical measurements of pressure and/or flow rate. The second stage estimates the parameters of the structured trees so as to match the values of the hemodynamic properties determined at the first stage. A key feature of the proposed method is that to ensure a large range of variation, two different structured tree parameters are personalized for each hemodynamic property. First, the second stage of the parameter estimation framework is evaluated based on the properties of the outlet boundary conditions in a full body arterial model: the calibration method converges for all structured trees in less than 10 iterations. Next, the proposed framework is successfully evaluated on a patient-specific aortic model with coarctation: only six iterations are required for the computational model to be in close agreement with the clinical measurements used as objectives, and overall, there is a good agreement between the measured and computed quantities. Copyright © 2016 John Wiley & Sons, Ltd.

Do Vascular Networks Branch Optimally or Randomly across Spatial Scales?

Modern models that derive allometric relationships between metabolic rate and body mass are based on the architectural design of the cardiovascular system and presume sibling vessels are symmetric in terms of radius, length, flow rate, and pressure. Here, we study the cardiovascular structure of the human head and torso and of a mouse lung based on three-dimensional images processed via our software Angicart. In contrast to modern allometric theories, we find systematic patterns of asymmetry in vascular branching, potentially explaining previously documented mismatches between predictions (power-law or concave curvature) and observed empirical data (convex curvature) for the allometric scaling of metabolic rate. To examine why these systematic asymmetries in vascular branching might arise, we construct a mathematical framework to derive predictions based on local, junction-level optimality principles that have been proposed to be favored in the course of natural selection and development. The two most commonly used principles are material-cost optimizations (construction materials or blood volume) and optimization of efficient flow via minimization of power loss. We show that material-cost optimization solutions match with distributions for asymmetric branching across the whole network but do not match well for individual junctions. Consequently, we also explore random branching that is constrained at scales that range from local (junction-level) to global (whole network). We find that material-cost optimizations are the strongest predictor of vascular branching in the human head and torso, whereas locally or intermediately constrained random branching is comparable to material-cost optimizations for the mouse lung. These differences could be attributable to developmentally-programmed local branching for larger vessels and constrained random branching for smaller vessels.

The architecture of vascular networks must balance complex demands to efficiently deliver oxygen and resources throughout the entire body. These demands constrain the possible forms of vasculature. Because of these constraints and the indispensable role of vasculature for much of life, scientists have sought to identify systematic patterns in the structural properties of vascular networks and whether these patterns can be predicted from models based on biological and physical principles. These studies have been limited by the lack of extensive, detailed data. Using high-quality vascular network data obtained via our software, Angicart, we identify novel, systematic patterns of asymmetry in sizes and branching angles among sibling vessels from mouse lung and human head and torso. To examine what constraints might underlie these patterns, we investigate several explanations, including various types of optimal branching as well as random branching. The optimal branchings were derived locally with respect to constraints on material costs or power loss. For random branching we allowed the degree of randomness to vary from local to global spatial scales. By comparing predictions with real data, our study suggests that a key component in determining vascular branching is material cost with some randomness at local to intermediate spatial scales.

Neointimal response to everolimus-eluting bioresorbable scaffolds implanted at bifurcating coronary segments: insights from optical coherence tomography

Heterogeneity of neointimal thickness is observed after drug-eluting stents implantation in bifurcation lesions (BL). We evaluated the vascular response of everolimus-eluting bioresorbable scaffold (BRS) struts deployed at BL using optical coherence tomography (OCT). 50 patients (64 scaffolds) underwent follow-up OCT after BRS implantation. Cross-sectional areas of each BL with a side branch more than 1.5 mm were analyzed using OCT every 200 µm. All images were divided into three regions according to shear stress: the 1/2 circumference of the vessel opposite to the ostium (OO), the vessel wall adjacent to the ostium (AO) and the side-branch ostium (SO). The %uncovered strut and the averaged neointimal thickness (NIT) were calculated. Overall, there were significant differences in both NIT and %uncovered strut among the three regions (OO, 119.2 ± 68.5 μm vs. AO, 94.2 ± 35.7 μm vs. SO, 80.5 ± 41.4 μm, p = 0.03; OO, 0.4 %vs. AO, 1.4 %vs. SO, 4.8 %, p = 0.02). Scaffolds were divided into two groups: a large-ratio side-branch group (LRSB; n = 32) and a small-ratio side-branch group (SRSB; n = 32), based on the median value of the ratio of the diameter of side branch ostium (Ds) to that of the main branch (Dm). In the LRSB alone, there were significant differences in both NIT and %uncovered strut among the three regions (OO, 128.0 ± 61.1 μm vs. AO, 97.3 ± 34.3 μm vs. SO, 75.9 ± 39.4 μm, p < 0.01; OO, 0.3 % vs. AO, 2.3 % vs. SO, 8.7 %, p < 0.01). After BRS implantation in BL, neointimal response was pronounced at the vessel wall opposite to the side branch ostium, especially in those with large side branches.

Microsphere skimming in the porcine coronary arteries: Implications for flow quantification

Particle skimming is a phenomenon where particles suspended in fluid flowing through vessels distribute disproportionately to bulk fluid volume at junctions. Microspheres are considered a gold standard of intra-organ perfusion measurements and are used widely in studies of flow distribution and quantification. It has previously been hypothesised that skimming at arterial junctions is responsible for a systematic over-estimation of myocardial perfusion from microspheres at the subendocardium. Our objective is to integrate coronary arterial structure and microsphere distribution, imaged at high resolution, to test the hypothesis of microsphere skimming in a porcine left coronary arterial (LCA) network. A detailed network was reconstructed from cryomicrotome imaging data and a Poiseuille flow model was used to simulate flow. A statistical approach using Clopper-Pearson confidence intervals was applied to determine the prevalence of skimming at bifurcations in the LCA. Results reveal that microsphere skimming is most prevalent at bifurcations in the larger coronary arteries, namely the epicardial and transmural arteries. Bifurcations at which skimming was identified have significantly more asymmetric branching parameters. This finding suggests that when using thin transmural segments to quantify flow from microspheres, a skimming-related deposition bias may result in underestimation of perfusion in the subepicardium, and overestimation in the subendocardium.

Impedance boundary conditions for general transient hemodynamics

We discuss the implementation and calibration of a new generalized structured tree boundary condition for hemodynamics. The main idea is to approximate the impedance corresponding to the vessels downstream from a specific outlet. Unlike previous impedance conditions, the one considered here is applicable to general transient flows as opposed to periodic ones only. The physiological character of the approach significantly simplifies calibration. We also describe a novel way to incorporate autoregulation mechanisms in structured arterial trees at minimal computational cost. The strength of the approach is illustrated and validated on several examples through comparison with clinical data.

Deviation from Murray's law is associated with a higher degree of calcification in coronary bifurcations

OBJECTIVE

Murray's law describes the optimal branching anatomy of vascular bifurcations. If Murray's law is obeyed, shear stress is constant over the bifurcation. Associations between Murray's law and intravascular ultrasound (IVUS) assessed plaque composition near coronary bifurcations have not been investigated previously.

METHODS

In 253 patients plaque components (fibrous, fibro-fatty, necrotic core, and dense calcium) were identified by IVUS in segments proximal and distal to the bifurcation of a coronary side branch. The ratio of mother to daughter vessels was calculated according to Murray's law (Murray ratio) with a high Murray ratio indicating low shear stress. Analysis of variance was used to detect independent associations of Murray ratio and plaque composition.

RESULTS

Patients with a high Murray ratio exhibited a higher relative amount of dense calcium and a lower amount of fibrous and fibro-fatty tissue than those with a low Murray ratio. After adjustment for age, sex, cardiovascular risk factors or concomitant medications, the Murray ratio remained significantly associated with fibrous volume distal (F-ratio 4.90, P=0.028) to the bifurcation, fibro-fatty volume distal (F-ratio 4.76, P=0.030) to the bifurcation, and dense calcium volume proximal (F-ratio 5.93, P=0.016) and distal (F-ratio 5.16, P=0.024) to the bifurcation.

CONCLUSION

This study shows that deviation from Murray's law is associated with a high degree of calcification near coronary bifurcations. Individual deviations from Murray's law may explain why some patients are prone to plaque formation near vessel bifurcations.

Relating function to branching geometry: a micro-CT study of the hepatic artery, portal vein, and biliary tree

Utilizing micro-computed tomography images, the hierarchical structure, interbranch segment lengths and diameters of a hepatic artery, a portal vein, and two biliary trees from intact rat liver lobes were characterized. The data were investigated by analyzing the geometric properties of the vascular structures, such as how interbranch segment diameters change at bifurcation points. In the case of the hepatic artery and portal vein trees (in which the flow rate is high by comparison with that in the biliary tree), the vascular geometry is consistent with a fluid transport system which aims to simultaneously minimize both the power loss of laminar flow, and a cost function proportional to the total volume of material needed to maintain the system (lumenal contents). In comparison, the biliary tree (which has a low flow rate and an opposite flow direction to that of the hepatic artery and portal vein) was found to have a geometry in which the lumen cross-sectional area is maintained at bifurcations. These findings imply that the histological makeup and therefore the pathophysiology of biliary tree vasculature are likely very different from that of the vasculature within the systemic arterial tree. The extent to which the characteristic variability/scatter in the data may have resulted from imaging and/or measurement errors was examined by simulating such errors in a theoretical tree model and comparing the results with the measured data.

Assessment by optical coherence tomography of stent struts across side branch. -Comparison of bare-metal stents and drug-elution stents.-

BACKGROUND

Late stent thrombosis (LST) after drug-eluting stent (DES) implantation is a major clinical problem that has not been fully explained. Incomplete neointimal coverage of stent struts is an important morphometric predictor of LST, which may be associated with impaired healing and the absence of full coverage of struts at branch-point ostia. Optical coherence tomography (OCT) was performed to compare 3 types of stents placed across side branches.

METHODS AND RESULTS

At 9-month follow-up, the neointimal coverage of the struts of 58 stents across a side branch was measured by OCT (bare metal (BMS), n = 20; sirolimus-eluting (SES), n = 23; paclitaxel-eluting (PES), n = 15). According to the diameter ratio of side branch to main vessel, the side branches were classified as either large (ratio > 0.33) or small (ratio ≤ 0.33). BMS had the lowest frequency of uncovered struts (29.4%) and the greatest neointimal thickness on the struts (123 ± 33 µm). Neointimal thickness on the struts was less for SES than for PES (72 ± 16 vs. 91 ± 22 µm, P = 0.009), but there was no difference in the frequency of uncovered struts (66.1% vs. 58.6%, P=0.493). For large side branches, the frequency of uncovered struts was greater than in the small group for SES (87.5% vs. 40.7%, P = 0.0002) and PES (83.3% vs. 18.2%; P = 0.0013); there was no significant difference for BMS (43.8% vs. 16.7%, P = 0.138).

CONCLUSIONS

Neointimal coverage on struts across a side branch was less frequently observed in DES than in BMS, particularly in large side branches.

A full 3-D reconstruction of the entire porcine coronary vasculature

We have previously reconstructed the entire coronary arterial tree of the porcine heart down to the first segment of capillaries. Here, we extend the vascular model through the capillary bed and the entire coronary venous system. The reconstruction was based on comprehensive morphometric data previously measured in the porcine heart. The reconstruction was formulated as a large-scale optimization process, subject to both global constraints relating to the location of the larger veins and to local constraints of measured morphological features. The venous network was partitioned into epicardial, transmural, and perfusion functional subnetworks. The epicardial portion was generated by a simulated annealing search for the optimal coverage of the area perfused by the arterial epicardial vessels. The epicardial subnetwork and coronary arterial capillary network served as boundary conditions for the reconstruction of the in-between transmural and perfusion networks, which were generated to optimize vascular homogeneity. Five sets of full coronary trees, which spanned the entire network down to the capillary level, were reconstructed. The total number of reconstructed venous segments was 17,148,946 ± 1,049,498 (n = 5), which spanned the coronary sinus (order -12) to the first segment of the venous capillary (order 0v). Combined with the reconstructed arterial network, the number of vessel segments for the entire coronary network added up to 27,307,376 ± 1,155,359 (n = 5). The reconstructed full coronary vascular network agreed with the gross anatomy of coronary networks in terms of structure, location of major vessels, and measured morphometric statistics of native coronary networks. This is the first full model of the entire coronary vasculature, which can serve as a foundation for realistic large-scale coronary flow analysis.

Accuracy of microvascular measurements obtained from micro-CT images

Early changes in branching geometry of microvasculature and its associated impact on the perfusion distribution in diseases, especially those in which different branching generations are affected differently, require the ability to analyze intact vascular trees over a wide range of scales. Micro-CT offers an excellent framework to analyze the microvascular branching geometry. Such an analysis requires methods to be developed that can accurately characterize branching properties, such as branch diameter, length, branching angle, and branch interconnectivity of the microvasculature. The purpose of this article is to report the results of a study of two human intramyocardial coronary vascular tree casts in which the accuracy of micro-CT vascular imaging and its analysis are tested against measurements made through an optical microscope (used as the "gold-standard"). Methods related to image segmentation of the vascular lumen, vessel tree centerline extraction, individual branch segment measurement, and compensating for the non-ideal modulation transfer function of micro-CT scanners are presented. The extracted centerline accurately characterized the hierarchical structure of the vascular tree casts in terms of "parent-branch" relationships which allowed each interbranch segments' dimensions to be compared to the optical measurement method. The comparison results show a close to ideal 1:1 relationship for both length and diameter measurements made by the two methods. Combining the results from both specimens, the standard deviation of the difference between measurement methods was 19 microm for the measurement of interbranch segment diameters (ranging from 12 to 769 microm), and 172 microm for the measurement of interbranch segment lengths (ranging from 14 to 3252 microm). These results suggest that our micro-CT image analysis method can be used to characterize a vascular tree's hierarchical structure, and accurately measure interbranch segment lengths and diameters.

Diameter asymmetry of porcine coronary arterial trees: structural and functional implications

The coronary vasculature is characterized by highly asymmetric diameters at bifurcations, which may be an important determinant of flow distribution. To facilitate accurate reconstruction of the coronary network for hemodynamic analysis, we introduce a statistical data set of the diameter asymmetry at bifurcations based on morphometric data of the porcine coronary arterial and venous trees. The bifurcation asymmetry data were represented by the diameter ratio of the daughters relative to mother vessel and by an area expansion ratio (AER) at each bifurcation. A novel asymmetry ratio matrix was introduced to describe the diameter asymmetry of daughters to mother vessels. The relations between AER and flow velocity, and asymmetry ratio matrix and flow distribution, were considered. The results indicate that the ratio of large daughter to mother vessel has a minimum value at order 5 (mean diameter of approximately 70 microm), whereas the ratio of small daughter to mother vessel decreases monotonically with increase in order number. The AER was found to be fairly uniform for larger vessels and to increase from order 5 toward the capillaries. At order 5, we observe a transition in asymmetric bifurcation pattern that may mark a hemodynamic transition from transmural to perfusion subnetworks. The functional implications of these structural transitions are considered.

A hybrid one-dimensional/Womersley model of pulsatile blood flow in the entire coronary arterial tree

Using a frequency-domain Womersley-type model, we previously simulated pulsatile blood flow throughout the coronary arterial tree. Although this model represents a good approximation for the smaller vessels, it does not take into account the nonlinear convective energy losses in larger vessels. Here, using Womersley's theory, we present a hybrid model that considers the nonlinear effects for the larger epicardial arteries while simulating the distal vessels (down to the 1st capillary segments) with the use of Womersley's Theory. The main trunk and primary branches were discretized and modeled with one-dimensional Navier-Stokes equations, while the smaller-diameter vessels were treated as Womersley-type vessels. Energy losses associated with vessel bifurcations were incorporated in the present analysis. The formulation enables prediction of impedance and pressure and pulsatile flow distribution throughout the entire coronary arterial tree down to the first capillary segments in the arrested, vasodilated state. We found that the nonlinear convective term is negligible and the loss of energy at a bifurcation is small in the larger epicardial vessels of an arrested heart. Furthermore, we found that the flow waves along the trunk or at the primary branches tend to scale (normalized with respect to their mean values) to a single curve, except for a small phase angle difference. Finally, the model predictions for the inlet pressure and flow waves are in excellent agreement with previously published experimental results. This hybrid one-dimensional/Womersley model is an efficient approach that captures the essence of the hemodynamics of a complex large-scale vascular network. The present model has numerous applications to understanding the dynamics of coronary circulation.

Cross-Talk Between Cardiac Muscle and Coronary Vasculature

The cardiac muscle and the coronary vasculature are in close proximity to each other, and a two-way interaction, called cross-talk, exists. Here we focus on the mechanical aspects of cross-talk including the role of the extracellular matrix. Cardiac muscle affects the coronary vasculature. In diastole, the effect of the cardiac muscle on the coronary vasculature depends on the (changes in) muscle length but appears to be small. In systole, coronary artery inflow is impeded, or even reversed, and venous outflow is augmented. These systolic effects are explained by two mechanisms. The waterfall model and the intramyocardial pump model are based on an intramyocardial pressure, assumed to be proportional to ventricular pressure. They explain the global effects of contraction on coronary flow and the effects of contraction in the layers of the heart wall. The varying elastance model, the muscle shortening and thickening model, and the vascular deformation model are based on direct contact between muscles and vessels. They predict global effects as well as differences on flow in layers and flow heterogeneity due to contraction. The relative contributions of these two mechanisms depend on the wall layer (epi- or endocardial) and type of contraction (isovolumic or shortening). Intramyocardial pressure results from (local) muscle contraction and to what extent the interstitial cavity contracts isovolumically. This explains why small arterioles and venules do not collapse in systole. Coronary vasculature affects the cardiac muscle. In diastole, at physiological ventricular volumes, an increase in coronary perfusion pressure increases ventricular stiffness, but the effect is small. In systole, there are two mechanisms by which coronary perfusion affects cardiac contractility. Increased perfusion pressure increases microvascular volume, thereby opening stretch-activated ion channels, resulting in an increased intracellular Ca2+transient, which is followed by an increase in Ca2+sensitivity and higher muscle contractility (Gregg effect). Thickening of the shortening cardiac muscle takes place at the expense of the vascular volume, which causes build-up of intracellular pressure. The intracellular pressure counteracts the tension generated by the contractile apparatus, leading to lower net force. Therefore, cardiac muscle contraction is augmented when vascular emptying is facilitated. During autoregulation, the microvasculature is protected against volume changes, and the Gregg effect is negligible. However, the effect is present in the right ventricle, as well as in pathological conditions with ineffective autoregulation. The beneficial effect of vascular emptying may be reduced in the presence of a stenosis. Thus cardiac contraction affects vascular diameters thereby reducing coronary inflow and enhancing venous outflow. Emptying of the vasculature, however, enhances muscle contraction. The extracellular matrix exerts its effect mainly on cardiac properties rather than on the cross-talk between cardiac muscle and coronary circulation.

Functional hierarchy of coronary circulation: direct evidence of a structure-function relation

The heart muscle is nourished by a complex system of blood vessels that make up the coronary circulation. Here we show that the design of the coronary circulation has a functional hierarchy. A full anatomic model of the coronary arterial tree, containing millions of blood vessels down to the capillary vessels, was simulated based on previously measured porcine morphometric data. A network analysis of blood flow through every vessel segment was carried out based on the laws of fluid mechanics and appropriate boundary conditions. Our results show an abrupt change in cross-sectional area that demarcates the transition from epicardial (EPCA) to intramyocardial (IMCA) coronary arteries. Furthermore, a similar pattern of blood flow was observed with a corresponding transition from EPCA to IMCA. These results suggest functional differences between the two types of vessels. An additional abrupt change occurs in the IMCA in relation to flow velocity. The velocity is fairly uniform proximal to these vessels but drops significantly distal to those vessels toward the capillary branches. This finding suggests functional differences between large and small IMCA. Collectively, these observations suggest a novel functional hierarchy of the coronary vascular tree and provide direct evidence of a structure-function relation.

A computer reconstruction of the entire coronary arterial tree based on detailed morphometric data

A rigorous analysis of blood flow must be based on the branching pattern and vascular geometry of the full vascular circuit of interest. It is experimentally difficult to reconstruct the entire vascular circuit of any organ because of the enormity of the vessels. The objective of the present study was to develop a novel method for the reconstruction of the full coronary vascular tree from partial measurements. Our method includes the use of data on those parts of the tree that are measured to extrapolate the data on those parts that are missing. Specifically, a two-step approach was employed in the reconstruction of the entire coronary arterial tree down to the capillary level. Vessels > 40 microm were reconstructed from cast data while vessels < 40 microm were reconstructed from histological data. The cast data were reconstructed one-bifurcation at a time while histological data were reconstructed one-sub-tree at a time by "cutting" and "pasting" of data from measured to missing vessels. The reconstruction algorithm yielded a full arterial tree down to the first capillary bifurcation with 1.9, 2.04 and 1.15 million vessel segments for the right coronary artery (RCA), left anterior descending (LAD) and left circumflex (LCx) trees, respectively. The node-to-node connectivity along with the diameter and length of every vessel segment was determined. Once the full tree was reconstructed, we automated the assignment of order numbers, according to the diameter-defined Strahler system, to every vessel segment in the tree. Consequently, the diameters, lengths, number of vessels, segments-per-element ratio, connectivity and longitudinal matrices were determined for every order number. The present model establishes a morphological foundation for future analysis of blood flow in the coronary circulation.