Large-scale 3-D geometric reconstruction of the porcine coronary arterial vasculature based on detailed anatomical data

A comprehensive experimental analysis of the local passive response across the healthy porcine left ventricle

This work provides a comprehensive characterization of porcine myocardial tissue, combining true biaxial (TBx), simple triaxial shear (STS) and confined compression (CC) tests to analyze its elastic behavior under cyclic loads. We expanded this study to different zones of the ventricular free wall, providing insights into the local behavior along the longitudinal and radial coordinates. The aging impact was also assessed by comparing two age groups (4 and 8 months). Resulting data showed that the myocardium exhibits a highly nonlinear hyperelastic and incompressible behavior. We observed an anisotropy ratio of 2-2.4 between averaged peak stresses in TBx tests and 1-0.59-0.40 orthotropy ratios for normalised fiber-sheet-normal peak stresses in STS tests. We obtained a highly incompressible response, reaching volumetric pressures of 2-7 MPa for perfused tissue in CC tests, with notable differences when fluid drainage was allowed, suggesting a high permeability. Regional analysis showed reduced stiffness and anisotropy (20-25%) at the apical region compared to the medial, which we attributed to differences in the fiber field dispersion. Compressibility also increased towards the epicardium and apical regions. Regarding age-related variations, 8-month animals showed stiffer response (at least 25% increase), particularly in directions where the mechanical stress is absorbed by collagenous fibers (more than 90%), as supported by a histological analysis. Although compressibility of perfused tissue remained unchanged, permeability significantly reduced in 8-month-old animals. Our findings offer new insights into myocardial properties, emphasizing on local variations, which can help to get a more realistic understanding of cardiac mechanics in this common animal model. STATEMENT OF SIGNIFICANCE: In this work, we conducted a comprehensive analysis of the passive mechanical behavior of porcine myocardial tissue through biaxial, triaxial shear, and confined compression tests. Unlike previous research, we investigated the variation in mechanical response across the left ventricular free wall, conventionally assumed homogeneous, revealing differences in terms of stiffness and compressibility. Additionally, we evaluated age-related effects on mechanical properties by comparing two age groups, observing significant variations in stiffness and permeability. To date, there has been no such in-depth exploration of myocardial elastic response and compressibility considering regional variations along the wall and may contribute to a better understanding of the cardiac tissue's passive mechanical response.

Modelling coronary flow and myocardial perfusion by integrating a structured-tree coronary flow model and a hyperelastic left ventricle model

BACKGROUND AND OBJECTIVE

There is an increasing demand to establish integrated computational models that facilitate the exploration of coronary circulation in physiological and pathological contexts, particularly concerning interactions between coronary flow dynamics and myocardial motion. The field of cardiology has also demonstrated a trend toward personalised medicine, where these integrated models can be instrumental in integrating patient-specific data to improve therapeutic outcomes. Notably, incorporating a structured-tree model into such integrated models is currently absent in the literature, which presents a promising prospect. Thus, the goal here is to develop a novel computational framework that combines a 1D structured-tree model of coronary flow in human coronary vasculature with a 3D left ventricle model utilising a hyperelastic constitutive law, enabling the physiologically accurate simulation of coronary flow dynamics.

METHODS

We adopted detailed geometric information from previous studies of both coronary vasculature and left ventricle to construct the coronary flow model and the left ventricle model. The structured-tree model for coronary flow was expanded to encompass the effect of time-varying intramyocardial pressure on intramyocardial blood vessels. Simultaneously, the left ventricle model served as a robust foundation for the calculation of intramyocardial pressure and subsequent quantitative evaluation of myocardial perfusion. A one-way coupling framework between the two models was established to enable the evaluation and examination of coronary flow dynamics and myocardial perfusion.

RESULTS

Our predicted coronary flow waveforms aligned well with published experimental data. Our model precisely captured the phasic pattern of coronary flow, including impeded or even reversed flow during systole. Moreover, our assessment of coronary flow, considering both globally and regionally averaged intramyocardial pressure, demonstrated that elevated intramyocardial pressure corresponds to increased impeding effects on coronary flow. Furthermore, myocardial blood flow simulated from our model was comparable with MRI perfusion data at rest, showcasing the capability of our model to predict myocardial perfusion.

CONCLUSIONS

The integrated model introduced in this study presents a novel approach to achieving physiologically accurate simulations of coronary flow and myocardial perfusion. It holds promise for its clinical applicability in diagnosing insufficient myocardial perfusion.

A multiscale framework for defining homeostasis in distal vascular trees: applications to the pulmonary circulation

Pulmonary arteries constitute a low-pressure network of vessels, often characterized as a bifurcating tree with heterogeneous vessel mechanics. Understanding the vascular complexity and establishing homeostasis is important to study diseases such as pulmonary arterial hypertension (PAH). The onset and early progression of PAH can be traced to changes in the morphometry and structure of the distal vasculature. Coupling hemodynamics with vessel wall growth and remodeling (G&R) is crucial for understanding pathology at distal vasculature. Accordingly, the goal of this study is to provide a multiscale modeling framework that embeds the essential features of arterial wall constituents coupled with the hemodynamics within an arterial network characterized by an extension of Murray's law. This framework will be used to establish the homeostatic baseline characteristics of a pulmonary arterial tree, including important parameters such as vessel radius, wall thickness and shear stress. To define the vascular homeostasis and hemodynamics in the tree, we consider two timescales: a cardiac cycle and a longer period of vascular adaptations. An iterative homeostatic optimization, which integrates a metabolic cost function minimization, the stress equilibrium, and hemodynamics, is performed at the slow timescale. In the fast timescale, the pulsatile blood flow dynamics is described by a Womersley's deformable wall analytical solution. Illustrative examples for symmetric and asymmetric trees are presented that provide baseline characteristics for the normal pulmonary arterial vasculature. The results are compared with diverse literature data on morphometry, structure, and mechanics of pulmonary arteries. The developed framework demonstrates a potential for advanced parametric studies and future G&R and hemodynamics modeling of PAH.

Tissue-growth-based synthetic tree generation and perfusion simulation

Biological tissues receive oxygen and nutrients from blood vessels by developing an indispensable supply and demand relationship with the blood vessels. We implemented a synthetic tree generation algorithm by considering the interactions between the tissues and blood vessels. We first segment major arteries using medical image data and synthetic trees are generated originating from these segmented arteries. They grow into extensive networks of small vessels to fill the supplied tissues and satisfy the metabolic demand of them. Further, the algorithm is optimized to be executed in parallel without affecting the generated tree volumes. The generated vascular trees are used to simulate blood perfusion in the tissues by performing multiscale blood flow simulations. One-dimensional blood flow equations were used to solve for blood flow and pressure in the generated vascular trees and Darcy flow equations were solved for blood perfusion in the tissues using a porous model assumption. Both equations are coupled at terminal segments explicitly. The proposed methods were applied to idealized models with different tree resolutions and metabolic demands for validation. The methods demonstrated that realistic synthetic trees were generated with significantly less computational expense compared to that of a constrained constructive optimization method. The methods were then applied to cerebrovascular arteries supplying a human brain and coronary arteries supplying the left and right ventricles to demonstrate the capabilities of the proposed methods. The proposed methods can be utilized to quantify tissue perfusion and predict areas prone to ischemia in patient-specific geometries.

Prediction of myocardial blood flow under stress conditions by means of a computational model

PURPOSE

Quantification of myocardial blood flow (MBF) and functional assessment of coronary artery disease (CAD) can be achieved through stress myocardial computed tomography perfusion (stress-CTP). This requires an additional scan after the resting coronary computed tomography angiography (cCTA) and administration of an intravenous stressor. This complex protocol has limited reproducibility and non-negligible side effects for the patient. We aim to mitigate these drawbacks by proposing a computational model able to reproduce MBF maps.

METHODS

A computational perfusion model was used to reproduce MBF maps. The model parameters were estimated by using information from cCTA and MBF measured from stress-CTP (MBF_CTP) maps. The relative error between the computational MBF under stress conditions (MBF_COMP) and MBF_CTP was evaluated to assess the accuracy of the proposed computational model.

RESULTS

Applying our method to 9 patients (4 control subjects without ischemia vs 5 patients with myocardial ischemia), we found an excellent agreement between the values of MBF_COMP and MBF_CTP. In all patients, the relative error was below 8% over all the myocardium, with an average-in-space value below 4%.

CONCLUSION

The results of this pilot work demonstrate the accuracy and reliability of the proposed computational model in reproducing MBF under stress conditions. This consistency test is a preliminary step in the framework of a more ambitious project which is currently under investigation, i.e., the construction of a computational tool able to predict MBF avoiding the stress protocol and potential side effects while reducing radiation exposure.

Analysis of the passive biomechanical behavior of a sheep-specific aortic artery in pulsatile flow conditions

In this work, a novel numerical-experimental procedure is proposed, through the use of the Cardiac Simulation Test (CST), device that allows the exposure of the arterial tissue to in-vitro conditions, mimicking cardiac cycles generated by the heart. The main goal is to describe mechanical response of the arterial wall under physiological conditions, when it is subjected to a variable pressure wave over time, which causes a stress state affecting the biomechanical behavior of the artery wall. In order to get information related to stress and strain states, numerical simulation via finite element method, is performed under a condition of systolic and diastolic pressure. The description of this methodological procedure is performed with a sample corresponding to a sheep aorta without cardiovascular pathologies. There are two major findings: the evaluation of the mechanical properties of the sheep aorta through the above-mentioned tests and, the numerical simulation of the mechanical response under the conditions present in the CST. The results state that differences between numerical and experimental circumferential stretch in diastole and systole to distinct zones studied do not exceed 1%. However, greater discrepancies can be seen in the distensibility and incremental modulus, two main indicators, which are in the order of 30%. In addition, numerical results determine an increase of the principal maximum stress and strain between the case of systolic and diastolic pressure, corresponding to 31.1% and 14.9% for the stress and strain measurement respectively; where maximum values of these variables are located in the zone of the ascending aorta and the aortic arch.

Effects of Mechanical Dyssynchrony on Coronary Flow: Insights From a Computational Model of Coupled Coronary Perfusion With Systemic Circulation

Mechanical dyssynchrony affects left ventricular (LV) mechanics and coronary perfusion. Due to the confounding effects of their bi-directional interactions, the mechanisms behind these changes are difficult to isolate from experimental and clinical studies alone. Here, we develop and calibrate a closed-loop computational model that couples the systemic circulation, LV mechanics, and coronary perfusion. The model is applied to simulate the impact of mechanical dyssynchrony on coronary flow in the left anterior descending artery (LAD) and left circumflex artery (LCX) territories caused by regional alterations in perfusion pressure and intramyocardial pressure (IMP). We also investigate the effects of regional coronary flow alterations on regional LV contractility in mechanical dyssynchrony based on prescribed contractility-flow relationships without considering autoregulation. The model predicts that LCX and LAD flows are reduced by 7.2%, and increased by 17.1%, respectively, in mechanical dyssynchrony with a systolic dyssynchrony index of 10% when the LAD's IMP is synchronous with the arterial pressure. The LAD flow is reduced by 11.6% only when its IMP is delayed with respect to the arterial pressure by 0.07 s. When contractility is sensitive to coronary flow, mechanical dyssynchrony can affect global LV mechanics, IMPs and contractility that in turn, further affect the coronary flow in a feedback loop that results in a substantial reduction of dP_LV/dt, indicative of ischemia. Taken together, these findings imply that regional IMPs play a significant role in affecting regional coronary flows in mechanical dyssynchrony and the changes in regional coronary flow may produce ischemia when contractility is sensitive to the changes in coronary flow.

Multiscale modeling of human cerebrovasculature: A hybrid approach using image-based geometry and a mathematical algorithm

The cerebral vasculature has a complex and hierarchical network, ranging from vessels of a few millimeters to superficial cortical vessels with diameters of a few hundred micrometers, and to the microvasculature (arteriole/venule) and capillary beds in the cortex. In standard imaging techniques, it is difficult to segment all vessels in the network, especially in the case of the human brain. This study proposes a hybrid modeling approach that determines these networks by explicitly segmenting the large vessels from medical images and employing a novel vascular generation algorithm. The framework enables vasculatures to be generated at coarse and fine scales for individual arteries and veins with vascular subregions, following the personalized anatomy of the brain and macroscale vasculatures. In this study, the vascular structures of superficial cortical (pial) vessels before they penetrate the cortex are modeled as a mesoscale vasculature. The validity of the present approach is demonstrated through comparisons with partially observed data from existing measurements of the vessel distributions on the brain surface, pathway fractal features, and vascular territories of the major cerebral arteries. Additionally, this validation provides some biological insights: (i) vascular pathways may form to ensure a reasonable supply of blood to the local surface area; (ii) fractal features of vascular pathways are not sensitive to overall and local brain geometries; and (iii) whole pathways connecting the upstream and downstream entire-scale cerebral circulation are highly dependent on the local curvature of the cerebral sulci.

Cerebral autoregulation in the complex vascular networks of the brain is an amazing achievement. We believe that numerical analysis of the cerebral blood circulation using an anatomically precise vascular model provides a powerful tool for evaluating the direct relationships between local- and global-scale blood flows. However, there is a lack of information about the overall vascular pathways in the human brain, preventing a monolithic model of the human cerebrovasculature from being established. This paper presents a multiscale model of human cerebrovasculature based on a hybrid approach that uses image-based geometries and a newly developed mathematical algorithm. One important argument of this paper is the validity of the cerebrovasculature represented in the model, which reflects anatomical features of major cerebral vasculatures and brain shape, and has strong similarities with available data for human superficial cortical vessels. Investigations of the reconstructed model allow us to derive some biological insights and associated hypotheses for the cerebral vasculature. The authors believe the present cerebrovascular model can be applied to numerical simulations of the entire-scale cerebral blood flow.

Effects of myocardial function and systemic circulation on regional coronary perfusion

Cardiac-coronary interaction and the effects of its pathophysiological variations on spatial heterogeneity of coronary perfusion and myocardial work are still poorly understood. This hypothesis-generating study predicts spatial heterogeneities in both regional cardiac work and perfusion that offer a new paradigm on the vulnerability of the subendocardium to ischemia, particularly at the apex. We propose a mathematical and computational modeling framework to simulate the interaction of left ventricular mechanics, systemic circulation, and coronary microcirculation. The computational simulations revealed that the relaxation rate of the myocardium has a significant effect whereas the contractility has a marginal effect on both the magnitude and transmural distribution of coronary perfusion. The ratio of subendocardial to subepicardial perfusion density (Q_endo/Q_epi) changed by -12 to +6% from a baseline value of 1.16 when myocardial contractility was varied by +25 and -10%, respectively; Q_endo/Q_epi changed by 37% when sarcomere relaxation rate, b, was faster and increased by 10% from the baseline value. The model predicts axial differences in regional myocardial work and perfusion density across the wall thickness. Regional myofiber work done at the apex is 30-50% lower than at the center region, whereas perfusion density in the apex is lower by only 18% compared with the center. There are large axial differences in coronary flow and myocardial work at the subendocardial locations, with the highest differences located at the apex region. A mismatch exists between perfusion density and regional work done at the subendocardium. This mismatch is speculated to be compensated by coronary autoregulation.NEW & NOTEWORTHY We present a model of left ventricle perfusion based on an anatomically realistic coronary tree structure that includes its interaction with the systemic circulation. Left ventricular relaxation rate has a significant effect on the regional distribution of coronary flow and myocardial work.

Delayed Transplantation of Autologous Mitochondria for Cardioprotection in a Porcine Model

BACKGROUND

We have previously demonstrated the efficacy of mitochondrial transplantation (MT) for the treatment of ischemia-reperfusion injury (IRI). We now investigate the efficacy of delayed MT by intracoronary administration in a model of regional IRI as a strategy for cardioprotection.

METHODS

Female Yorkshire pigs (40-50 kg; n = 16) underwent 30 minutes of ischemia by snaring of the left anterior descending artery, and the hearts were then reperfused for 120 minutes. At that point, vehicle only or autologous mitochondria (1 × 10⁹ in 5 mL of vehicle) were delivered as a bolus to the left coronary ostium, followed by a further 120-minute reperfusion.

RESULTS

Echocardiographic analysis demonstrated that hearts receiving delayed MT after regional IRI had enhanced ejection fraction (P = .019), fractional shortening (P = .022), and fractional area change (P = .011) at 240 minutes of reperfusion compared with the untreated pigs. At the end of reperfusion there was a difference between the groups in measures of global left ventricular (LV) function such as LV end-diastolic pressure (P = .015) and rate of rise of LV pressure (P = .021). No significant differences were found between the groups in the area at risk (P = .48). Infarct size (% area at risk) was significantly decreased in hearts receiving MT compared with hearts receiving vehicle only (P < .001).

CONCLUSIONS

Delayed MT by intracoronary injection appreciably decreases myocardial infarct size, increasing regional and global myocardial function. These results suggest that this can be a viable treatment modality in IRI, thus reducing long-term morbidity and mortality in cardiac surgical patients.

Mechanical Identification of Materials and Structures with Optical Methods and Metaheuristic Optimization

This study presents a hybrid framework for mechanical identification of materials and structures. The inverse problem is solved by combining experimental measurements performed by optical methods and non-linear optimization using metaheuristic algorithms. In particular, we develop three advanced formulations of Simulated Annealing (SA), Harmony Search (HS) and Big Bang-Big Crunch (BBBC) including enhanced approximate line search and computationally cheap gradient evaluation strategies. The rationale behind the new algorithms-denoted as Hybrid Fast Simulated Annealing (HFSA), Hybrid Fast Harmony Search (HFHS) and Hybrid Fast Big Bang-Big Crunch (HFBBBC)-is to generate high quality trial designs lying on a properly selected set of descent directions. Besides hybridizing SA/HS/BBBC metaheuristic search engines with gradient information and approximate line search, HS and BBBC are also hybridized with an enhanced 1-D probabilistic search derived from SA. The results obtained in three inverse problems regarding composite and transversely isotropic hyperelastic materials/structures with up to 17 unknown properties clearly demonstrate the validity of the proposed approach, which allows to significantly reduce the number of structural analyses with respect to previous SA/HS/BBBC formulations and improves robustness of metaheuristic search engines.

Morphometric Reconstruction of Coronary Vasculature Incorporating Uniformity of Flow Dispersion

Experimental limitations in measurements of coronary flow in the beating heart have led to the development of in silico models of reconstructed coronary trees. Previous coronary reconstructions relied primarily on anatomical data, including statistical morphometry (e.g., diameters, length, connectivity, longitudinal position). Such reconstructions are non-unique, however, often leading to unrealistic predicted flow features. Thus, it is necessary to impose physiological flow constraints to ensure realistic tree reconstruction. Since a vessel flow depends on its diameter to fourth power, diameters are the logical candidates to guide vascular reconstructions to achieve realistic flows. Here, a diameter assignment method was developed where each vessel diameter was determined depending on its downstream tree size, aimed to reduce flow dispersion to within measured range. Since the coronary micro-vessels are responsible for a major portion of the flow resistance, the auto regulated coronary flow was analyzed in a morphometry-based reconstructed 400 vessel arterial microvascular sub-tree spanning vessel orders 1–6. Diameters in this subtree were re-assigned based on the flow criteria. The results revealed that diameter re-assignment, while adhering to measured morphometry, significantly reduced the flow dispersion to realistic levels while adhering to measured morphometry. The resulting network flow has longitudinal pressure distribution, flow fractal nature, and near-neighboring flow autocorrelation, which agree with measured coronary flow characteristics. Collectively, these results suggest that a realistic coronary tree reconstruction should impose not only morphometric data but also flow considerations. The work is of broad significance in providing a novel computational framework in the field of coronary microcirculation. It is essential for the study of coronary circulation by model simulation, based on a realistic network structure.

Coronary Blood Flow Is Increased in RV Hypertrophy, but the Shape of Normalized Waves Is Preserved Throughout the Arterial Tree

A pulsatile hemodynamic analysis was carried out in the right coronary arterial (RCA) tree of control and RV hypertrophy (RVH) hearts. The shape of flow and wall shear stress (WSS) waves was hypothesized to be maintained throughout the RCA tree in RVH (i.e., similar patterns of normalized flow and WSS waves in vessels of various sizes). Consequently, we reconstructed the entire RCA tree down to the first capillary bifurcation of control and RVH hearts based on measured morphometric data. A Womersley-type model was used to compute the flow and WSS waves in the tree. The hemodynamic parameters obtained from experimental measurements were incorporated into the numerical model. Given an increased number of arterioles, the mean and amplitude of flow waves at the inlet of RCA tree in RVH was found to be two times larger than that in control, but no significant differences (p > 0.05) were found in precapillary arterioles. The increase of stiffness in RCA of RVH preserved the shape of normalized flow and WSS waves, but increased the PWV in coronary arteries and reduced the phase angle difference for the waves between the most proximal RCA and the most distal precapillary arteriole. The study is important for understanding pulsatile coronary blood flow in ventricular hypertrophy.

Computational Assessment of Blood Flow Heterogeneity in Peritoneal Dialysis Patients' Cardiac Ventricles

Dialysis prolongs life but augments cardiovascular mortality. Imaging data suggests that dialysis increases myocardial blood flow (BF) heterogeneity, but its causes remain poorly understood. A biophysical model of human coronary vasculature was used to explain the imaging observations, and highlight causes of coronary BF heterogeneity. Post-dialysis CT images from patients under control, pharmacological stress (adenosine), therapy (cooled dialysate), and adenosine and cooled dialysate conditions were obtained. The data presented disparate phenotypes. To dissect vascular mechanisms, a 3D human vasculature model based on known experimental coronary morphometry and a space filling algorithm was implemented. Steady state simulations were performed to investigate the effects of altered aortic pressure and blood vessel diameters on myocardial BF heterogeneity. Imaging showed that stress and therapy potentially increased mean and total BF, while reducing heterogeneity. BF histograms of one patient showed multi-modality. Using the model, it was found that total coronary BF increased as coronary perfusion pressure was increased. BF heterogeneity was differentially affected by large or small vessel blocking. BF heterogeneity was found to be inversely related to small blood vessel diameters. Simulation of large artery stenosis indicates that BF became heterogeneous (increase relative dispersion) and gave multi-modal histograms. The total transmural BF as well as transmural BF heterogeneity reduced due to large artery stenosis, generating large patches of very low BF regions downstream. Blocking of arteries at various orders showed that blocking larger arteries results in multi-modal BF histograms and large patches of low BF, whereas smaller artery blocking results in augmented relative dispersion and fractal dimension. Transmural heterogeneity was also affected. Finally, the effects of augmented aortic pressure in the presence of blood vessel blocking shows differential effects on BF heterogeneity as well as transmural BF. Improved aortic blood pressure may improve total BF. Stress and therapy may be effective if they dilate small vessels. A potential cause for the observed complex BF distributions (multi-modal BF histograms) may indicate existing large vessel stenosis. The intuitive BF heterogeneity methods used can be readily used in clinical studies. Further development of the model and methods will permit personalized assessment of patient BF status.

Integrative model of coronary flow in anatomically based vasculature under myogenic, shear, and metabolic regulation

Coronary blood flow is regulated to match the oxygen demand of myocytes in the heart wall. Flow regulation is essential to meet the wide range of cardiac workload. The blood flows through a complex coronary vasculature of elastic vessels having nonlinear wall properties, under transmural heterogeneous myocardial extravascular loading. To date, there is no fully integrative flow analysis that incorporates global and local passive and flow control determinants. Here, we provide an integrative model of coronary flow regulation that considers the realistic asymmetric morphology of the coronary network, the dynamic myocardial loading on the vessels embedded in it, and the combined effects of local myogenic effect, local shear regulation, and conducted metabolic control driven by venous O₂ saturation level. The model predicts autoregulation (approximately constant flow over a wide range of coronary perfusion pressures), reduced heterogeneity of regulated flow, and presence of flow reserve, in agreement with experimental observations. Furthermore, the model shows that the metabolic and myogenic regulations play a primary role, whereas shear has a secondary one. Regulation was found to have a significant effect on the flow except under extreme (high and low) inlet pressures and metabolic demand. Novel outcomes of the model are that cyclic myocardial loading on coronary vessels enhances the coronary flow reserve except under low inlet perfusion pressure, increases the pressure range of effective autoregulation, and reduces the network flow in the absence of metabolic regulation. Collectively, these findings demonstrate the utility of the present biophysical model, which can be used to unravel the underlying mechanisms of coronary physiopathology.

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.

Flow velocity is relatively uniform in the coronary sinusal venous tree: structure-function relation

The structure and function of coronary venous vessels are different from those of coronary arteries and are much less understood despite the therapeutic significance of coronary sinus interventions. Here we aimed to perform a hemodynamic analysis in the entire coronary sinusal venous tree, which enhances the understanding of coronary venous circulation. A hemodynamic model was developed in the entire coronary sinusal venous tree reconstructed from casts and histological data of five swine hearts. Various morphometric and hemodynamic parameters were determined in each vessel and analyzed in the diameter-defined Strahler system. The findings demonstrate an area preservation between the branches of the coronary venous system that leads to relatively uniform flow velocity in different orders of the venous tree. Pressure and circumferential and wall shear stresses decreased abruptly from the smallest venules toward vessels of order -5 (80.4 ± 39.1 µm) but showed a more modest change toward the coronary sinus. The results suggest that vessels of order -5 denote a hemodynamic transition from the venular bed to the transmural subnetwork. In contrast with the coronary arterial tree, which obeys the minimum energy hypothesis, the coronary sinusal venous system complies with the area-preserving rule for efficient venous return, i.e., da Vinci's rule. The morphometric and hemodynamic model serves as a physiological reference state to test various therapeutic rationales through the venous route.

NEW & NOTEWORTHY

A hemodynamic model is developed in the entire coronary sinusal venous tree of the swine heart. A key finding is that the coronary sinusal venous system complies with the area preservation rule for efficient venous return while the coronary arterial tree obeys the minimum energy hypothesis. This model can also serve as a physiological reference state to test various therapeutic rationales through the venous route.

Simulated annealing approach to vascular structure with application to the coronary arteries

Do the complex processes of angiogenesis during organism development ultimately lead to a near optimal coronary vasculature in the organs of adult mammals? We examine this hypothesis using a powerful and universal method, built on physical and physiological principles, for the determination of globally energetically optimal arterial trees. The method is based on simulated annealing, and can be used to examine arteries in hollow organs with arbitrary tissue geometries. We demonstrate that the approach can generate in silico vasculatures which closely match porcine anatomical data for the coronary arteries on all length scales, and that the optimized arterial trees improve systematically as computational time increases. The method presented here is general, and could in principle be used to examine the arteries of other organs. Potential applications include improvement of medical imaging analysis and the design of vascular trees for artificial organs.

Design of vascular networks: a mathematical model approach

In this paper, methods for the modeling of a realistic vascular tree in 3D space and for hemodynamic calculating throughout the simulated tree structure have been developed. Vascular trees are generated based on the power law relationship. Variations in branching asymmetry and segment length of the vasculature are precisely controlled by the designed gaussian distributions. The resolution limit of current imaging techniques for vessel detectability is simulated by designed pruning technique. On the basis of the generated diameters and lengths, the space locations of the vessel segments are calculated by optimizing the out-of-plane angles of two daughter branches. The generated vascular tree not only follows the power law relationship, but also maximizes the filling volume of the tree structure in 3D space. From the hemodynamic calculation in the simulated vasculature, the processes for which structural changes affect hemodynamic distributions are studied in detail. And also, the fractal nature and resistance of the vascular trees are quantified and compared. The developed method provides some insight into the design of the vascular trees in biology and may be used as a reference for the study of vascular diseases.

Quantification of absolute coronary flow reserve and relative fractional flow reserve in a swine animal model using angiographic image data

Coronary flow reserve (CFR) and fractional flow reserve (FFR) are important physiological indexes for coronary disease. The purpose of this study was to validate the CFR and FFR measurement techniques using only angiographic image data. Fifteen swine were instrumented with an ultrasound flow probe on the left anterior descending artery (LAD). Microspheres were gradually injected into the LAD to create microvascular disruption. An occluder was used to produce stenosis. Contrast material injections were made into the left coronary artery during image acquisition. Volumetric blood flow from the flow probe (Q(q)) was continuously recorded. Angiography-based blood flow (Q(a)) was calculated by using a time-density curve based on the first-pass analysis technique. Flow probe-based CFR (CFR(q)) and angiography-based CFR (CFR(a)) were calculated as the ratio of hyperemic to baseline flow using Q(q) and Q(a), respectively. Relative angiographic FFR (relative FFR(a)) was calculated as the ratio of the normalized Q(a) in LAD to the left circumflex artery (LC(X)) during hyperemia. Flow probe-based FFR (FFR(q)) was measured from the ratio of hyperemic flow with and without disease. CFR(a) showed a strong correlation with the gold standard CFR(q) (CFR(a) = 0.91 CFR(q) + 0.30; r = 0.90; P < 0.0001). Relative FFR(a) correlated linearly with FFR(q) (relative FFR(a) = 0.86 FFR(q) + 0.05; r = 0.90; P < 0.0001). The quantification of CFR and relative FFR(a) using angiographic image data was validated in a swine model. This angiographic technique can potentially be used for coronary physiological assessment during routine cardiac catheterization.

Development of a model of the coronary arterial tree for the 4D XCAT phantom

A detailed three-dimensional (3D) model of the coronary artery tree with cardiac motion has great potential for applications in a wide variety of medical imaging research areas. In this work, we first developed a computer-generated 3D model of the coronary arterial tree for the heart in the extended cardiac-torso (XCAT) phantom, thereby creating a realistic computer model of the human anatomy. The coronary arterial tree model was based on two datasets: (1) a gated cardiac dual-source computed tomography (CT) angiographic dataset obtained from a normal human subject and (2) statistical morphometric data of porcine hearts. The initial proximal segments of the vasculature and the anatomical details of the boundaries of the ventricles were defined by segmenting the CT data. An iterative rule-based generation method was developed and applied to extend the coronary arterial tree beyond the initial proximal segments. The algorithm was governed by three factors: (1) statistical morphometric measurements of the connectivity, lengths and diameters of the arterial segments; (2) avoidance forces from other vessel segments and the boundaries of the myocardium, and (3) optimality principles which minimize the drag force at the bifurcations of the generated tree. Using this algorithm, the 3D computational model of the largest six orders of the coronary arterial tree was generated, which spread across the myocardium of the left and right ventricles. The 3D coronary arterial tree model was then extended to 4D to simulate different cardiac phases by deforming the original 3D model according to the motion vector map of the 4D cardiac model of the XCAT phantom at the corresponding phases. As a result, a detailed and realistic 4D model of the coronary arterial tree was developed for the XCAT phantom by imposing constraints of anatomical and physiological characteristics of the coronary vasculature. This new 4D coronary artery tree model provides a unique simulation tool that can be used in the development and evaluation of instrumentation and methods for imaging normal and pathological hearts with myocardial perfusion defects.

euHeart: personalized and integrated cardiac care using patient-specific cardiovascular modelling

The loss of cardiac pump function accounts for a significant increase in both mortality and morbidity in Western society, where there is currently a one in four lifetime risk, and costs associated with acute and long-term hospital treatments are accelerating. The significance of cardiac disease has motivated the application of state-of-the-art clinical imaging techniques and functional signal analysis to aid diagnosis and clinical planning. Measurements of cardiac function currently provide high-resolution datasets for characterizing cardiac patients. However, the clinical practice of using population-based metrics derived from separate image or signal-based datasets often indicates contradictory treatments plans owing to inter-individual variability in pathophysiology. To address this issue, the goal of our work, demonstrated in this study through four specific clinical applications, is to integrate multiple types of functional data into a consistent framework using multi-scale computational modelling.

Theoretical models for coronary vascular biomechanics: progress & challenges

A key aim of the cardiac Physiome Project is to develop theoretical models to simulate the functional behaviour of the heart under physiological and pathophysiological conditions. Heart function is critically dependent on the delivery of an adequate blood supply to the myocardium via the coronary vasculature. Key to this critical function of the coronary vasculature is system dynamics that emerge via the interactions of the numerous constituent components at a range of spatial and temporal scales. Here, we focus on several components for which theoretical approaches can be applied, including vascular structure and mechanics, blood flow and mass transport, flow regulation, angiogenesis and vascular remodelling, and vascular cellular mechanics. For each component, we summarise the current state of the art in model development, and discuss areas requiring further research. We highlight the major challenges associated with integrating the component models to develop a computational tool that can ultimately be used to simulate the responses of the coronary vascular system to changing demands and to diseases and therapies.

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.

Towards organ printing: engineering an intra-organ branched vascular tree

IMPORTANCE OF THE FIELD

Effective vascularization of thick three-dimensional engineered tissue constructs is a problem in tissue engineering. As in native organs, a tissue-engineered intra-organ vascular tree must be comprised of a network of hierarchically branched vascular segments. Despite this requirement, current tissue-engineering efforts are still focused predominantly on engineering either large-diameter macrovessels or microvascular networks.

AREAS COVERED IN THIS REVIEW

We present the emerging concept of organ printing or robotic additive biofabrication of an intra-organ branched vascular tree, based on the ability of vascular tissue spheroids to undergo self-assembly.

WHAT THE READER WILL GAIN

The feasibility and challenges of this robotic biofabrication approach to intra-organ vascularization for tissue engineering based on organ-printing technology using self-assembling vascular tissue spheroids including clinically relevantly vascular cell sources are analyzed.

TAKE HOME MESSAGE

It is not possible to engineer 3D thick tissue or organ constructs without effective vascularization. An effective intra-organ vascular system cannot be built by the simple connection of large-diameter vessels and microvessels. Successful engineering of functional human organs suitable for surgical implantation will require concomitant engineering of a 'built in' intra-organ branched vascular system. Organ printing enables biofabrication of human organ constructs with a 'built in' intra-organ branched vascular tree.

Branching patterns for arterioles and venules of the human cerebral cortex

Branching patterns of microvascular networks influence vascular resistance and allow control of peripheral flow distribution. The aim of this paper was to analyze these branching patterns in human cerebral cortex. Digital three-dimensional images of the microvascular network were obtained from thick sections of India ink-injected human brain by confocal laser microscopy covering a large zone of secondary cortex. A novel segmentation method was used to extract the skeletons of 228 vascular trees (152 arterioles and 76 venules) and measure the diameter at every vertex. The branching patterns (area ratios and angles of bifurcations) of nearly 10,000 bifurcations of cortical vascular trees were analyzed, establishing their statistical properties and structural variations as a function of the vessel nature (arterioles versus venules), the parent vessel topological order or the bifurcation type. We also describe their connectivity and discuss the relevance of the assumed optimal design of vascular branching to account for the complex nature of microvascular architecture. The functional implications of some of these structural variations are considered. The branching patterns established from a large database of a human organ contributes to a better understanding of the bifurcation design and provides an essential reference both for diagnosis and for a future large reconstruction of cerebral microvascular network.

Mechanisms of myocardium-coronary vessel interaction

The mechanisms by which the contracting myocardium exerts extravascular forces (intramyocardial pressure, IMP) on coronary blood vessels and by which it affects the coronary flow remain incompletely understood. Several myocardium-vessel interaction (MVI) mechanisms have been proposed, but none can account for all the major flow features. In the present study, we hypothesized that only a specific combination of MVI mechanisms can account for all observed coronary flow features. Three basic interaction mechanisms (time-varying elasticity, myocardial shortening-induced intracellular pressure, and ventricular cavity-induced extracellular pressure) and their combinations were analyzed based on physical principles (conservation of mass and force equilibrium) in a realistic data-based vascular network. Mechanical properties of both vessel wall and myocardium were coupled through stress analysis to simulate the response of vessels to internal blood pressure and external (myocardial) mechanical loading. Predictions of transmural dynamic vascular pressure, diameter, and flow velocity were determined under each MVI mechanism and compared with reported data. The results show that none of the three basic mechanisms alone can account for the measured data. Only the combined effect of the cavity-induced extracellular pressure and the shortening-induced intramyocyte pressure provides good agreement with the majority of measurements. These findings have important implications for elucidating the physical basis of IMP and for understanding coronary phasic flow and coronary artery and microcirculatory disease.

Extraction of morphometry and branching angles of porcine coronary arterial tree from CT images

The morphometry (diameters, length, and angles) of coronary arteries is related to their function. A simple, easy, and accurate image-based method to seamlessly extract the morphometry for coronary arteries is of significant value for understanding the structure-function relation. Here, the morphometry of large (> or = 1 mm in diameter) coronary arteries was extracted from computed tomography (CT) images using a recently validated segmentation algorithm. The coronary arteries of seven pigs were filled with Microfil, and the cast hearts were imaged with CT. The centerlines of the extracted vessels, the vessel radii, and the vessel lengths were identified for over 700 vessel segments. The extraction algorithm was based on a topological analysis of a vector field generated by normal vectors of the extracted vessel wall. The diameters, lengths, and angles of the right coronary artery, left anterior descending coronary artery, and left circumflex artery of all vessels > or = 1 mm in diameter were tabulated for the respective orders. It was found that bifurcations at orders 9-11 are planar ( approximately 90%). The relations between volume and length and area and length were also examined and found to scale as power laws. Furthermore, the bifurcation angles follow the minimum energy hypothesis but with significant scatter. Some of the applications of the semiautomated extraction of morphometric data in applications to coronary physiology and pathophysiology are highlighted.

Biophysical model of the spatial heterogeneity of myocardial flow

The blood flow in the myocardium has significant spatial heterogeneity. The objective of this study was to develop a biophysical model based on detailed anatomical data to determine the heterogeneity of regional myocardial flow during diastole. The model predictions were compared with experimental measurements in a diastolic porcine heart in the absence of vessel tone using nonradioactive fluorescent microsphere measurements. The results from the model and experimental measurements showed good agreement. The relative flow dispersion in the arrested, vasodilated heart was found to be 44% and 48% numerically and experimentally, respectively. Furthermore, the flow dispersion was found to have fractal characteristics with fractal dimensions (D) of 1.25 and 1.27 predicted by the model and validated by the experiments, respectively. This validated three-dimensional model of normal diastolic heart will play an important role in elucidating the spatial heterogeneity of coronary blood flow, and serve as a foundation for understanding the interplay between cardiac mechanics and coronary hemodynamics.

Estimation of regional myocardial mass at risk based on distal arterial lumen volume and length using 3D micro-CT images

The determination of regional myocardial mass at risk distal to a coronary occlusion provides valuable prognostic information for a patient with coronary artery disease. The coronary arterial system follows a design rule which allows for the use of arterial branch length and lumen volume to estimate regional myocardial mass at risk. Image processing techniques, such as segmentation, skeletonization and arterial network tracking, are presented for extracting anatomical details of the coronary arterial system using micro-computed tomography (micro-CT). Moreover, a method of assigning tissue voxels to their corresponding arterial branches is presented to determine the dependent myocardial region. The proposed micro-CT technique was utilized to investigate the relationship between the sum of the distal coronary arterial branch lengths and volumes to the dependent regional myocardial mass using a polymer cast of a porcine heart. The correlations of the logarithm of the total distal arterial lengths (L) to the logarithm of the regional myocardial mass (M) for the left anterior descending (LAD), left circumflex (LCX) and right coronary (RCA) arteries were log(L)=0.73log(M)+0.09 (R=0.78), log(L)=0.82log(M)+0.05 (R=0.77) and log(L)=0.85log(M)+0.05 (R=0.87), respectively. The correlation of the logarithm of the total distal arterial lumen volumes (V) to the logarithm of the regional myocardial mass for the LAD, LCX and RCA were log(V)=0.93log(M)-1.65 (R=0.81), log(V)=1.02log(M)-1.79 (R=0.78) and log(V)=1.17log(M)-2.10 (R=0.82), respectively. These morphological relations did not change appreciably for diameter truncations of 600-1400microm. The results indicate that the image processing procedures successfully extracted information from a large 3D dataset of the coronary arterial tree to provide prognostic indications in the form of arterial tree parameters and anatomical area at risk.

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 procedure to simulate coronary artery bypass graft surgery

In coronary artery bypass graft (CABG) surgery the involved tissues are overstretched, which may lead to intimal hyperplasia and graft failure. We propose a computational methodology for the simulation of traditional CABG surgery, and analyze the effect of two clinically relevant parameters on the artery and graft responses, i.e., incision length and insertion angle for a given graft diameter. The computational structural analyses are based on actual three-dimensional vessel dimensions of a human coronary artery and a human saphenous vein. The analyses consider the structure of the end-to-side anastomosis, the residual stresses and the typical anisotropic and nonlinear vessel behaviors. The coronary artery is modeled as a three-layer thick-walled tube. The finite element method is employed to predict deformation and stress distribution at various stages of CABG surgery. Small variations of the arterial incision have relatively big effects on the size of the arterial opening, which depends solely on the residual stress state. The incision length has a critical influence on the graft shape and the stress in the graft wall. Stresses at the heel region are higher than those at the toe region. The changes in the mechanical environment are severe along all transitions between the venous tissue and the host artery. Particular stress concentrations occur at the incision ends. The proposed computational methodology may be useful in designing a coronary anastomotic device for reducing surgical trauma. It may improve the quantitative knowledge of vessel diseases and serve as a tool for virtual planning of vascular surgery.

Automatic segmentation of 3D micro-CT coronary vascular images

Although there are many algorithms available in the literature aimed at segmentation and model reconstruction of 3D angiographic images, many are focused on characterizing only a part of the vascular network. This study is motivated by the recent emerging prospects of whole-organ simulations in coronary hemodynamics, autoregulation and tissue oxygen delivery for which anatomically accurate vascular meshes of extended scale are highly desirable. The key requirements of a reconstruction technique for this purpose are automation of processing and sub-voxel accuracy. We have designed a vascular reconstruction algorithm which satisfies these two criteria. It combines automatic seeding and tracking of vessels with radius detection based on active contours. The method was first examined through a series of tests on synthetic data, for accuracy in reproduced topology and morphology of the network and was shown to exhibit errors of less than 0.5 voxel for centerline and radius detections, and 3 degrees for initial seed directions. The algorithm was then applied on real-world data of full rat coronary structure acquired using a micro-CT scanner at 20 microm voxel size. For this, a further validation of radius quantification was carried out against a partially rescanned portion of the network at 8 microm voxel size, which estimated less than 10% radius error in vessels larger than 2 voxels in radius.

A Novel Method for Visualization of Entire Coronary Arterial Tree

The complexity of the coronary circulation especially in the deep layers largely evades experimental investigations. Hence, virtual/computational models depicting structure-function relation of the entire coronary vasculature including the deep layer are imperative. In order to interpret such anatomically based models, fast and efficient visualization algorithms are essential. The complexity of such models, which include vessels from the large proximal coronary arteries and veins down to the capillary level (3 orders of magnitude difference in diameter), is a challenging visualization problem since the resulting geometrical representation consists of millions of vessel segments. In this study, a novel method for rendering the entire porcine coronary arterial tree down to the first segments of capillaries interactively is described which employs geometry reduction and occlusion culling techniques. Due to the tree-shaped nature of the vasculature, these techniques exploit the geometrical topology of the object to achieve a faster rendering speed while still handling the full complexity of the data. We found a significant increase in performance combined with a more accurate, gap-less representation of the vessel segments resulting in a more interactive visualization and analysis tool for the entire coronary arterial tree. The proposed techniques can also be applied to similar data structures, such as neuronal trees, airway structures, bile ducts, and other tree-like structures. The utility and future applications of the proposed algorithms are explored.

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.

Relation between branching patterns and perfusion in stochastic generated coronary arterial trees

Biological variation in branching patterns is likely to affect perfusion of tissue. To assess the fundamental consequences of branching characteristics, 50 stochastic asymmetrical coronary trees and one non-stochastic symmetrical branching tree were generated. In the stochastic trees, area growth, A, at branching points was varied: A = random; 1.00; 1.10; 1.13 and 1.15 and symmetry, S, was varied: S = random; 1.00; 0.70; 0.58; 0.50 and 0.48. With random S and A values, a large variation in flow and volume was found, linearly related to the number of vessels in the trees. Large A values resulted in high number of vessels and high flow and volume values, indicating vessels connected in parallel. Lowering symmetry values increased the number of vessels, however, without changing flow, indicating a dominant connection of vessels in series. Both large A and small S values gave more realistic gradual pressure drops compared to the symmetrical non-stochastic branching tree. This study showed large variations in tree realizations, which may reflect real biological variations in tree anatomies. Furthermore, perfusion of tissue clearly depends on the branching rules applied.

Spiral Wave Attachment to Millimeter-Sized Obstacles

Background— Functional reentry in the heart takes the form of spiral waves. Drifting spiral waves can become pinned to anatomic obstacles and thus attain stability and persistence. Lidocaine is an antiarrhythmic agent commonly used to treat ventricular tachycardia clinically. We examined the ability of small obstacles to anchor spiral waves and the effect of lidocaine on their attachment.

Methods and Results— Spiral waves were electrically induced in confluent monolayers of cultured, neonatal rat cardiomyocytes. Small, circular anatomic obstacles (0.6 to 2.6 mm in diameter) were situated in the center of the monolayers to provide an anchoring site. Eighty reentry episodes consisting of at least 4 revolutions were studied. In 36 episodes, the spiral wave attached to the obstacle and became stationary and sustained, with a shorter reentry cycle length and higher rate. Spiral waves could attach to obstacles as small as 0.6 mm, with a likelihood for attachment that increased with obstacle size. After attachment, both conduction velocity of the wave-front tip and wavelength near the obstacle adapted from their pre-reentry values and increased linearly with obstacle size. In contrast, reentry cycle length did not correlate significantly with obstacle size. Addition of lidocaine 90 μmol/L depressed conduction velocity, increased reentry cycle length, and caused attached spiral waves to become quasi- attached to the obstacle or terminate.

Conclusions— Anchored spiral waves exhibit properties of both unattached spiral waves and anatomic reentry. Their behavior may be representative of functional reentry dynamics in cardiac tissue, particularly in the setting of monomorphic tachyarrhythmias.

Comparing microsphere deposition and flow modeling in 3D vascular trees

Blood perfusion in organs has been shown to be heterogeneous in a number of cases. At the same time, a number of models of vascular structure and flow have been proposed that also generate heterogeneous perfusion. Although a relationship between local perfusion and vascular structure has to exist, no model has yet been validated as an accurate description of this relationship. A study of perfusion and three-dimensional (3D) arterial structure in individual rat kidneys is presented, which allows comparison between local measurements of perfusion and model-based predictions. High-resolution computed tomography is used to obtain images of both deposited microspheres and of an arterial cast in the same organ. Microsphere deposition is used as an estimate of local perfusion. A 3D cylindrical pipe model of the arterial tree is generated based on an image of the arterial cast. Results of a flow model are compared with local microsphere deposition. High correlation (r(2) > 0.94) was observed between measured and modeled flows through the vascular tree segments. However, the relative dispersion of the microsphere perfusion measurement was two- to threefold higher than perfusion heterogeneity calculated in the flow model. Also, there was no correlation in the residual deviations between the methods. This study illustrates the importance of comparing models of local perfusion with in vivo measurements of perfusion in the same biologically realistic vascular tree.