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

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.

Review of cardiac-coronary interaction and insights from mathematical modeling

Cardiac-coronary interaction is fundamental to the function of the heart. As one of the highest metabolic organs in the body, the cardiac oxygen demand is met by blood perfusion through the coronary vasculature. The coronary vasculature is largely embedded within the myocardial tissue which is continually contracting and hence squeezing the blood vessels. The myocardium-coronary vessel interaction is two-ways and complex. Here, we review the different types of cardiac-coronary interactions with a focus on insights gained from mathematical models. Specifically, we will consider the following: (1) myocardial-vessel mechanical interaction; (2) metabolic-flow interaction and regulation; (3) perfusion-contraction matching, and (4) chronic interactions between the myocardium and coronary vasculature. We also provide a discussion of the relevant experimental and clinical studies of different types of cardiac-coronary interactions. Finally, we highlight knowledge gaps, key challenges, and limitations of existing mathematical models along with future research directions to understand the unique myocardium-coronary coupling in the heart. This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Biomedical Engineering Cardiovascular Diseases > Molecular and Cellular Physiology.

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.

Extended-volume image-derived models of coronary microcirculation

OBJECTIVE

Recent advances in tissue clearing and high-throughput imaging have enabled the acquisition of extended-volume microvasculature images at a submicron resolution. The objective of this study was to extract information from this type of images by integrating a sequence of 3D image processing steps on Terabyte scale datasets.

METHODS

We acquired coronary microvasculature images throughout an entire short-axis slice of a 3-month-old Wistar-Kyoto rat heart. This dataset covered 13 × 10 × 0.6 mm at a resolution of 0.933 × 0.933 × 1.866 μm and occupied 700 Gigabytes of disk space. We used chunk-based image segmentation, combined with an efficient graph generation technique, to quantify the microvasculature in the large-scale images. Specifically, we focused on the microvasculature with a vessel diameter up to 15 μm.

RESULTS

Morphological data for the complete short-axis ring were extracted within 16 h using this pipeline. From the analyses, we identified that microvessel lengths in the rat coronary microvasculature varied from 6 to 300 μm. However, their distribution was heavily skewed toward shorter lengths, with a mode of 16.5 μm. In contrast, vessel diameters ranged from 3 to 15 μm and had an approximately normal distribution of 6.5 ± 2 μm.

CONCLUSION

The tools and techniques from this study will serve other investigations into the microcirculation, and the wealth of data from this study will enable the analysis of biophysical mechanisms using computer models.

Investigation of intravoxel incoherent motion tensor imaging for the characterization of the in vivo human heart

PURPOSE

To investigate intravoxel incoherent motion (IVIM) tensor imaging of the in vivo human heart and elucidate whether the estimation of IVIM tensors is affected by the complexity of pseudo-diffusion components in myocardium.

METHODS

The cardiac IVIM data of 10 healthy subjects were acquired using a diffusion weighted spin-echo echo-planar imaging sequence along 6 gradient directions with 10 b values (0~400 s/mm² ). The IVIM data of left ventricle myocardium were fitted to the IVIM tensor model. The complexity of myocardial pseudo-diffusion components was reduced through exclusion of low b values (0 and 5 s/mm² ) from the IVIM curve-fitting analysis. The fractional anisotropy, mean fraction/mean diffusivity, and Westin measurements of pseudo-diffusion tensors (f_p and D*) and self-diffusion tensor (D), as well as the angle between the main eigenvector of f_p (or D*) and that of D, were computed and compared before and after excluding low b values.

RESULTS

The fractional anisotropy values of f_p and D* without low b value participation were significantly higher (P < .001) than those with low b value participation, but an opposite trend was found for the mean fraction/diffusivity values. Besides, after removing low b values, the angle between the main eigenvector of f_p (or D*) and that of D became small, and both f_p and D* tensors presented significant decrease of spherical components and significant increase of linear components.

CONCLUSION

The presence of multiple pseudo-diffusion components in myocardium indeed influences the estimation of IVIM tensors. The IVIM tensor model needs to be further improved to account for the complexity of myocardial microcirculatory network and blood flow.

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.

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.

Development of a globally optimised model of the cerebral arteries

The cerebral arteries are difficult to reproduce from first principles, featuring interwoven territories, and intricate layers of grey and white matter with differing metabolic demand. The aim of this study was to identify the ideal configuration of arteries required to sustain an entire brain hemisphere based on minimisation of the energy required to supply the tissue. The 3D distribution of grey and white matter within a healthy human brain was first segmented from magnetic resonance images. A novel simulated annealing algorithm was then applied to determine the optimal configuration of arteries required to supply brain tissue. The model was validated through comparison of this ideal, entirely optimised, brain vasculature with the structure and properties of real arteries. This analysis established that the human cerebral vasculature is highly optimised; closely resembling the most energy efficient arrangement of vessels. In addition to local adherence to fluid dynamical optimisation principles, the optimised vasculature reproduced expected brain perfusion territories, featuring well-defined boundaries between anterior, middle and posterior regions. This validated brain vascular model and algorithm can be used for patient-specific modelling of stroke and cerebral haemodynamics, identification of sub-optimal conditions associated with vascular disease, and optimising vascular structures for tissue engineering applications and artificial organ design.

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.

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.

Intraspecific scaling laws are preserved in ventricular hypertrophy but not in heart failure

It is scientifically and clinically important to understand the structure-function scaling of coronary arterial trees in compensatory (e.g., left and right ventricular hypertrophy, LVH and RVH) and decompensatory vascular remodeling (e.g., congestive heart failure, CHF). This study hypothesizes that intraspecific scaling power laws of vascular trees are preserved in hypertrophic hearts but not in CHF swine hearts. To test the hypothesis, we carried out the scaling analysis based on morphometry and hemodynamics of coronary arterial trees in moderate LVH, severe RVH, and CHF compared with age-matched respective control hearts. The scaling exponents of volume-diameter, length-volume, and flow-diameter power laws in control hearts were consistent with the theoretical predictions (i.e., 3, 7/9, and 7/3, respectively), which remained unchanged in LVH and RVH hearts. The scaling exponents were also preserved with an increase of body weight during normal growth of control animals. In contrast, CHF increased the exponents of volume-diameter and flow-diameter scaling laws to 4.25 ± 1.50 and 3.15 ± 1.49, respectively, in the epicardial arterial trees. This study validates the predictive utility of the scaling laws to diagnose vascular structure and function in CHF hearts to identify the borderline between compensatory and decompensatory remodeling.

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.

Toward an optimal design principle in symmetric and asymmetric tree flow networks

Fluid flow in tree-shaped networks plays an important role in both natural and engineered systems. This paper focuses on laminar flows of Newtonian and non-Newtonian power law fluids in symmetric and asymmetric bifurcating trees. Based on the constructal law, we predict the tree-shaped architecture that provides greater access to the flow subjected to the total network volume constraint. The relationships between the sizes of parent and daughter tubes are presented both for symmetric and asymmetric branching tubes. We also approach the wall-shear stresses and the flow resistance in terms of first tube size, degree of asymmetry between daughter branches, and rheological behavior of the fluid. The influence of tubes obstructing the fluid flow is also accounted for. The predictions obtained by our theory-driven approach find clear support in the findings of previous experimental studies.

Measurement and modeling of coronary blood flow

Ischemic heart disease that comprises both coronary artery disease and microvascular disease is the single greatest cause of death globally. In this context, enhancing our understanding of the interaction of coronary structure and function is not only fundamental for advancing basic physiology but also crucial for identifying new targets for treating these diseases. A central challenge for understanding coronary blood flow is that coronary structure and function exhibit different behaviors across a range of spatial and temporal scales. While experimental studies have sought to understand this feature by isolating specific mechanisms, in tandem, computational modeling is increasingly also providing a unique framework to integrate mechanistic behaviors across different scales. In addition, clinical methods for assessing coronary disease severity are continuously being informed and updated by findings in basic physiology. Coupling these technologies, computational modeling of the coronary circulation is emerging as a bridge between the experimental and clinical domains, providing a framework to integrate imaging and measurements from multiple sources with mathematical descriptions of governing physical laws. State-of-the-art computational modeling is being used to combine mechanistic models with data to provide new insight into coronary physiology, optimization of medical technologies, and new applications to guide clinical practice.

A one-dimensional mathematical model for studying the pulsatile flow in microvascular networks

Techniques that model microvascular hemodynamics have been developed for decades. While the physiological significance of pressure pulsatility is acknowledged, most of the microcirculatory models use steady flow approaches. To theoretically study the extent and transmission of pulsatility in microcirculation, dynamic models need to be developed. In this paper, we present a one-dimensional model to describe the dynamic behavior of microvascular blood flow. The model is applied to a microvascular network from a rat mesentery. Intravital microscopy was used to record the morphology and flow velocities in individual vessel segments, and boundaries are defined according to the experimental data. The system of governing equations constituting the model is solved numerically using the discontinuous Galerkin method. An implicit integration scheme is adopted to increase computing efficiency. The model allows the simulation of the dynamic properties of blood flow in microcirculatory networks, including the pressure pulsatility (quantified by a pulsatility index) and pulse wave velocity (PWV). From the main input arteriole to the main output venule, the pulsatility index decreases by 66.7%. PWV obtained along arterioles declines with decreasing diameters, with mean values of 77.16, 25.31, and 8.30 cm/s for diameters of 26.84, 17.46, and 13.33 μm, respectively. These results suggest that the 1D model developed is able to simulate the characteristics of pressure pulsatility and wave propagation in complex microvascular networks.

Perfusion territories subtended by penetrating coronary arteries increase in size and decrease in number toward the subendocardium

Blood flow distribution within the myocardium and the location and extent of areas at risk in case of coronary artery disease are dependent on the distribution and morphology of intramural vascular crowns. Knowledge of the intramural vasculature is essential in novel multiscale and multiphysics modeling of the heart. For this study, eight canine hearts were analyzed with an imaging cryomicrotome, developed to acquire high-resolution spatial data on three-dimensional vascular structures. The obtained vasculature was skeletonized, and for each penetrating artery starting from the epicardium, the dependent vascular crown was defined. Three-dimensional Voronoi tessellation was applied with the end points of the terminal segments as center points. The centroid of end points in each branch allowed classification of the corresponding perfusion territories in subendocardial, midmyocardial, and subepicardial. Subendocardial regions have relatively few territories of about 0.5 ml in volume having their own penetrating artery at the epicardium, whereas the subepicardium is perfused by a multitude of small perfusion territories, in the order of 0.01 ml. Vascular volume density of small arteries up till 400 μm was 3.2% at the subendocardium territories but only 0.8% in the subepicardium territories. Their higher volume density corresponds to compensation for flow impeding forces by cardiac contraction. These density differences result in different scaling law properties of vascular volume and tissue mass per territory type. This novel three-dimensional quantitative analysis may form the basis for patient-specific computational models on coronary perfusion and aid the interpretation of image-based clinical methods for assessing the transmural perfusion distribution.

Flow restoration post revascularization predicted by stenosis indexes: sensitivity to hemodynamic variability

The expected blood flow improvement following a coronary intervention is inversely related to the stenotic-to-normal flow ratio Qs/Qn. Since Qn cannot be measured prior to intervention, treatment decisions rely on stenosis-severity indexes, e.g., area stenosis (%AS), hyperemic stenosis resistance (HSR), and fractional flow reserve (FFR), where treatment cut-off levels have been established for each index based on presence of inducible ischemia. Here, we studied the dependence of these indexes-predicted Qs/Qn under physiological perturbations of stenosis features and of hemodynamic and mechanical conditions. Dynamic coronary flow was simulated based on measured coronary morphometric data and a physics-based computational model. Simulations were used to evaluate the relationship between each index level and Qs/Qn. Under each perturbation, an independence measure (IM) was calculated for each index based on the relative change in Qs/Qn associated with each perturbation. The results show that while %AS prediction of Qs/Qn is largely independent (IM > 90%) of physiological changes in heart rate, venous pressure, and lesion length and location on the epicardial tree, HSR is also independent of changes in left ventricle pressure. FFR-predicted Qs/Qn is also independent of changes in aortic pressure, blood hematocrit, and stenotic vessel stiffness. Nevertheless, independence of all indexes is substantially compromised (IM < 70%) under changes in vasculature stiffness. Specifically, a physiological stiffening elevates Qs/Qn value by 21% at the FFR cut-off value (0.75). These findings suggest that the current FFR cut-off value for treatment of stenotic lesions overestimates the benefit of coronary intervention in patients with a stiffer coronary vasculature (e.g., diabetics, hypertensives).

Network remodeling of intramural coronary resistance arteries in the aged rat: a statistical analysis of geometry

AIMS

To identify the geometrical alterations in the age-remodeled rat coronary artery network and to develop a useful technique to analyze network properties in the rat heart.

METHODS AND RESULTS

We analyzed the networks of the left anterior descendent coronary arteries on in situ perfused hearts of young (3 months) and old (18 months) male rats. All segments and branching over >80 μm diameter were analyzed using 50 μm long cylindrical ring units of the networks. Arterial widening and paucity, increased tortuosity were typical features in the old network. In addition, axis angles deviated more from the mother branches in the old, whereas the diameters of daughter branches fit the Murray law in both groups. The detected changes in the old network resulted in a longer blood flow route for the same direct distance.

CONCLUSION

We developed a useful method to investigate arterial network property changes in the rat heart. Ageing resulted in longer, more tortuous flow route in the LAD network that might be hemodynamically disadvantageous.

3D Imaging of vascular networks for biophysical modeling of perfusion distribution within the heart

One of the main determinants of perfusion distribution within an organ is the structure of its vascular network. Past studies were based on angiography or corrosion casting and lacked quantitative three dimensional, 3D, representation. Based on branching rules and other properties derived from such imaging, 3D vascular tree models were generated which were rather useful for generating and testing hypotheses on perfusion distribution in organs. Progress in advanced computational models for prediction of perfusion distribution has raised the need for more realistic representations of vascular trees with higher resolution. This paper presents an overview of the different methods developed over time for imaging and modeling the structure of vascular networks and perfusion distribution, with a focus on the heart. The strengths and limitations of these different techniques are discussed. Episcopic fluorescent imaging using a cryomicrotome is presently being developed in different laboratories. This technique is discussed in more detail, since it provides high-resolution 3D structural information that is important for the development and validation of biophysical models but also for studying the adaptations of vascular networks to diseases. An added advantage of this method being is the ability to measure local tissue perfusion. Clinically, indices for patient-specific coronary stenosis evaluation derived from vascular networks have been proposed and high-resolution noninvasive methods for perfusion distribution are in development. All these techniques depend on a proper representation of the relevant vascular network structures.

Wall structures of myocardial precapillary arterioles and postcapillary venules reexamined and reconstructed in vitro for studies on barrier functions

The barrier functions of myocardial precapillary arteriolar and postcapillary venular walls (PCA or PCV, respectively) are of considerable scientific and clinical interest (regulation of blood flow and recruitment of immune defense). Using enzyme histochemistry combined with confocal microscopy, we reexamined the cell architecture of human PCA and PVC and reconstructed appropriate in vitro models for studies of their barrier functions. Contrary to current opinion, the PCA endothelial tube is encompassed not by smooth muscle cells but rather by a concentric layer of pericytes cocooned in a thick, microparticle-containing extracellular matrix (ECM) that contributes substantially to the tightness of the arteriolar wall. This core tube extends upstream into the larger arterioles, there additionally enwrapped by smooth muscle. PCV consist of an inner layer of large, contractile endothelial cells encompassed by a fragile, wide-meshed pericyte network with a weakly developed ECM. Pure pericyte and endothelial cell preparations were isolated from PCA and PCV and grown in sandwich cultures. These in vitro models of the PCA and PCV walls exhibited typical histological and functional features. In both plasma-like (PLM) and serum-containing (SCM) media, the PCA model (including ECM) maintained its low hydraulic conductivity (L(P) = 3.24 ± 0.52·10(-8)cm·s(-1)·cmH(2)O(-1)) and a high selectivity index for transmural passage of albumin (SI(Alb) = 0.95 ± 0.02). In contrast, L(P) and SI(Alb) in the PCV model (almost no ECM) were 2.55 ± 0.32·10(-7)cm·s(-1)·cmH(2)O(-1) and 0.88 ± 0.03, respectively, in PLM, and 1.39 ± 0.10·10(-6)cm·s(-1)·cmH(2)O(-1) and 0.49 ± 0.04 in SCM. With the use of these models, systematic, detailed studies on the regulation of microvascular barrier properties now appear to be feasible.

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.

Endotoxemia decreases matching of regional blood flow and O2 delivery to O2 uptake in the porcine left ventricle

Heterogeneity of regional coronary blood flow is caused in part by heterogeneity in O(2) demand in the normal heart. We investigated whether myocardial O(2) supply/demand mismatching is associated with the myocardial depression of sepsis. Regional blood flow (microspheres) and O(2) uptake ([(13)C]acetate infusion and analysis of resultant NMR spectra) were measured in about nine contiguous tissue samples from the left ventricle (LV) in each heart. Endotoxemic pigs (n = 9) showed hypotension at unchanged cardiac output with a fall in LV stroke work and first derivative of LV pressure relative to controls (n = 4). Global coronary blood flow and O(2) delivery were maintained. Lactate accumulated in arterial blood, but net lactate extraction across the coronary bed was unchanged during endotoxemia. When LV O(2) uptake based on blood gas versus NMR data were compared, the correlation was 0.73 (P = 0.007). While stable over time in controls, regional blood flows were strongly redistributed during endotoxin shock, with overall flow heterogeneity unchanged. A stronger redistribution of blood flow with endotoxin was associated with a larger fall in LV function parameters. Moreover, the correlation of regional O(2) delivery to uptake fell from r = 0.73 (P < 0.001) in control to r = 0.18 (P = 0.25, P = 0.009 vs. control) in endotoxemic hearts. The results suggest a redistribution of LV regional coronary blood flow during endotoxin shock in pigs, with regional O(2) delivery mismatched to O(2) demand. Mismatching may underlie, at least in part, the myocardial depression of sepsis.