Mechanisms of myocardium-coronary vessel interaction

Modeling cardiac microcirculation for the simulation of coronary flow and 3D myocardial perfusion

Accurate modeling of blood dynamics in the coronary microcirculation is a crucial step toward the clinical application of in silico methods for the diagnosis of coronary artery disease. In this work, we present a new mathematical model of microcirculatory hemodynamics accounting for microvasculature compliance and cardiac contraction; we also present its application to a full simulation of hyperemic coronary blood flow and 3D myocardial perfusion in real clinical cases. Microvasculature hemodynamics is modeled with a compliant multi-compartment Darcy formulation, with the new compliance terms depending on the local intramyocardial pressure generated by cardiac contraction. Nonlinear analytical relationships for vessels distensibility are included based on experimental data, and all the parameters of the model are reformulated based on histologically relevant quantities, allowing a deeper model personalization. Phasic flow patterns of high arterial inflow in diastole and venous outflow in systole are obtained, with flow waveforms morphology and pressure distribution along the microcirculation reproduced in accordance with experimental and in vivo measures. Phasic diameter change for arterioles and capillaries is also obtained with relevant differences depending on the depth location. Coronary blood dynamics exhibits a disturbed flow at the systolic onset, while the obtained 3D perfusion maps reproduce the systolic impediment effect and show relevant regional and transmural heterogeneities in myocardial blood flow (MBF). The proposed model successfully reproduces microvasculature hemodynamics over the whole heartbeat and along the entire intramural vessels. Quantification of phasic flow patterns, diameter changes, regional and transmural heterogeneities in MBF represent key steps ahead in the direction of the predictive simulation of cardiac perfusion.

Simulation of coronary fractional flow reserve and whole-cycle flow based on optical coherence tomography in individual patients with coronary artery disease

Computer simulations of coronary fractional flow reserve (FFR) based on coronary imaging have emerged as an attractive alternative to invasive measurements. However, most methods are proprietary and employ non-physiological assumptions. Our aims were to develop and validate a physiologically realistic open-source simulation model for coronary flow, and to use this model to predict FFR based on intracoronary optical coherence tomography (OCT) data in individual patients. We included patients undergoing elective coronary angiography with angiographic borderline coronary stenosis. Invasive measurements of coronary hyperemic pressure and absolute flow and OCT imaging were performed. A computer model of coronary flow incorporating pulsatile flow and the effect of left ventricular contraction was developed and calibrated, and patient-specific flow simulation was performed. Forty-eight coronary arteries from 41 patients were included in the analysis. Average FFR was 0.79 ± 0.14, and 50% had FFR ≤ 0.80. Correlation between simulated and measured FFR was high (r = 0.83, p < 0.001). Average difference between simulated FFR and observed FFR in individual patients was - 0.009 ± 0.076. Overall diagnostic accuracy for simulated FFR ≤ 0.80 in predicting observed FFR ≤ 0.80 was 0.88 (0.75-0.95) with sensitivity 0.79 (0.58-0.93) and specificity 0.96 (0.79-1.00). The positive predictive value was 0.95 (0.75-1.00) and the negative predictive value was 0.82 (0.63-0.94). In conclusion, realistic simulations of whole-cycle coronary flow can be produced based on intracoronary OCT data with a new, computationally simple simulation model. Simulated FFR had moderate numerical agreement with observed FFR and a good diagnostic accuracy for predicting hemodynamic significance of coronary stenoses.

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.

A multi-scale computational model for the passive mechanical behavior of right ventricular myocardium

We have previously demonstrated the importance of myofiber-collagen mechanical interactions in modeling the passive mechanical behavior of right ventricle free wall (RVFW) myocardium. To gain deeper insights into these coupling mechanisms, we developed a high-fidelity, micro-anatomically realistic 3D finite element model of right ventricle free wall (RVFW) myocardium by combining high-resolution imaging and supercomputer-based simulations. We first developed a representative tissue element (RTE) model at the sub-tissue scale by specializing the hyperelastic anisotropic structurally-based constitutive relations for myofibers and ECM collagen, and equi-biaxial and non-equibiaxial loading conditions were simulated using the open-source software FEniCS to compute the effective stress-strain response of the RTE. To estimate the model parameters of the RTE model, we first fitted a 'top-down' biaxial stress-strain behavior with our previous structurally based (tissue-scale) model, informed by the measured myofiber and collagen fiber composition and orientation distributions. Next, we employed a multi-scale approach to determine the tissue-level (5 x 5 x 0.7 mm specimen size) RVFW biaxial behavior via 'bottom-up' homogenization of the fitted RTE model, recapitulating the histologically measured myofiber and collagen orientation to the biaxial mechanical data. Our homogenization approach successfully reproduced the tissue-level mechanical behavior of our previous studies in all biaxial deformation modes, suggesting that the 3D micro-anatomical arrangement of myofibers and ECM collagen is indeed a primary mechanism driving myofiber-collagen interactions.

Mechanism of exercise intolerance in heart diseases predicted by a computer model of myocardial demand-supply feedback system

BACKGROUND AND OBJECTIVE

The myocardial demand-supply feedback system plays an important role in augmenting blood supply in response to exercise-induced increased myocardial demand. During this feedback process, the myocardium and coronary blood flow interact bidirectionally at many different levels.

METHODS

To investigate these interactions, a novel computational framework that considers the closed myocardial demand-supply feedback system was developed. In the framework coupling the systemic circulation of the left ventricle and coronary perfusion with regulation, myocardial work affects coronary perfusion via flow regulation mechanisms (e.g., metabolic regulation) and myocardial-vessel interactions, whereas coronary perfusion affects myocardial contractility in a closed feedback system. The framework was calibrated based on the measurements from healthy subjects under graded exercise conditions, and then was applied to simulate the effects of graded exercise on myocardial demand-supply under different physiological and pathological conditions.

RESULTS

We found that the framework can recapitulate key features found during exercise in clinical and animal studies. We showed that myocardial blood flow is increased but maximum hyperemia is reduced during exercise, which led to a reduction in coronary flow reserve. For coronary stenosis and myocardial inefficiency, the model predicts that an increase in heart rate is necessary to maintain the baseline cardiac output. Correspondingly, the resting coronary flow reserve is exhausted and the range of heart rate before exhaustion of coronary flow reserve is reduced. In the presence of metabolic regulation dysfunction, the model predicts that the metabolic vasodilator signal is higher at rest, saturates faster during exercise, and as a result, causes quicker exhaustion of coronary flow reserve.

CONCLUSIONS

Model predictions showed that the coronary flow reserve deteriorates faster during graded exercise, which in turn, suggests a decrease in exercise tolerance for patients with stenosis, myocardial inefficiency and metabolic flow regulation dysfunction. The findings in this study may have clinical implications in diagnosing cardiovascular diseases.

Three-dimensional visualization of heart-wide myocardial architecture and vascular network simultaneously at single-cell resolution

Obtaining various structures of the entire mature heart at single-cell resolution is highly desired in cardiac studies; however, effective methodologies are still lacking. Here, we propose a pipeline for labeling and imaging myocardial and vascular structures. In this pipeline, the myocardium is counterstained using fluorescent dyes and the cardiovasculature is labeled using transgenic markers. High-definition dual-color fluorescence micro-optical sectioning tomography is used to perform heart-wide tissue imaging, enabling the acquisition of whole-heart data at a voxel resolution of 0.32 × 0.32 × 1 μm³. Obtained structural data demonstrated the superiority of the pipeline. In particular, the three-dimensional morphology and spatial arrangement of reconstructed cardiomyocytes were revealed, and high-resolution vascular data helped determine differences in the features of endothelial cells and complex coiled capillaries. Our pipeline can be used in cardiac studies for examining the structures of the entire heart at the single-cell level.

Numerical Analysis on Effect of Coronary Supply-Demand Equilibrium on Varying Coronary Blockage and Stress Conditions

In this paper, we present a computational fluid dynamic (CFD) analysis to capture the effect of physical stress and stenosis severity in coronary arteries leading to changes in coronary supply demand oxygen equilibrium. We propose a coupled Od-3d coronary vessel model to predict the variation in flow dynamics of coronary as well as arterial system, modeled using an in-silico model replicating cardiovascular hemodynamics. CFD simulation were solved using subject specific CT scan for coronary and arterial flow and pressure along with metrics related to arterial wall shear stress. Simulations were performed for three heart rates (75, 90 and 120 bpm) and four stenosis states representing different stages of Coronary artery disease (CAD) namely healthy, 50%, 75%, 90% blockage in left anterior descending artery (LAD). Myocardial oxygen supply demand equilibrium were calculated for each cases using hemodynamic surrogate markers naming Diastolic pressure time index for supply and Tension time index for demand. The proposed 0d-3d coupled hemodynamic model of the coronary vessel bed along with supply-demand equilibrium estimated for different stress level and stenosis severity may provide useful insights on the dynamics of CAD manifestation and predict vulnerable regions in coronary bed for early screening and interventions.

Multiscale model of the physiological control of myocardial perfusion to delineate putative metabolic feedback mechanisms

Coronary blood flow is tightly regulated to ensure that myocardial oxygen delivery meets local metabolic demand via the concurrent action of myogenic, neural and metabolic mechanisms. Although several competing hypotheses exist, the specific nature of the local metabolic mechanism(s) remains poorly defined. To gain insights into the viability of putative metabolic feedback mechanisms and into the co-ordinated action of parallel regulatory mechanisms, we applied a multiscale modelling framework to analyse experimental data on coronary pressure, flow and myocardial oxygen delivery in the porcine heart in vivo. The modelling framework integrates a previously established lumped-parameter model of myocardial perfusion used to account for transmural haemodynamic variations and a simple vessel mechanics model used to simulate the vascular tone in each of three myocardial layers. Vascular tone in the resistance vessel mechanics model is governed by input stimuli from the myogenic, metabolic and autonomic control mechanisms. Seven competing formulations of the metabolic feedback mechanism are implemented in the modelling framework, and associated model simulations are compared with experimental data on coronary pressures and flows under a range of experimental conditions designed to interrogate the governing control mechanisms. Analysis identifies a maximally probable metabolic mechanism among the seven tested models, in which production of a metabolic signalling factor is proportional to myocardial oxygen consumption and delivery is proportional to flow. Finally, the identified model is validated based on comparisons of simulations with data on the myocardial perfusion response to conscious exercise that were not used for model identification. KEY POINTS: Although several competing hypotheses exist, we lack knowledge of specific nature of the metabolic mechanism(s) governing regional myocardial perfusion. Moreover, we lack an understanding of how parallel myogenic, adrenergic/autonomic and metabolic mechanisms work together to regulatory oxygen delivery in the beating heart. We have developed a multiscale modelling framework to test competing hypotheses against experimental data on coronary pressure, flow and myocardial oxygen delivery in the porcine heart in vivo. The analysis identifies a maximally probable metabolic mechanism among seven tested models, in which the production of a metabolic signalling factor is proportional to myocardial oxygen consumption and delivery is proportional to flow.

A Closed-Loop Modeling Framework for Cardiac-to-Coronary Coupling

The mechanisms by which cardiac mechanics effect coronary perfusion (cardiac-to-coronary coupling) remain incompletely understood. Several coronary models have been proposed to deepen our understanding of coronary hemodynamics, but possibilities for in-depth studies on cardiac-to-coronary coupling are limited as mechanical properties like myocardial stress and strain are most often neglected. To overcome this limitation, a mathematical model of coronary mechanics and hemodynamics was implemented in the previously published multi-scale CircAdapt model of the closed-loop cardiovascular system. The coronary model consisted of a relatively simple one-dimensional network of the major conduit arteries and veins as well as a lumped parameter model with three transmural layers for the microcirculation. Intramyocardial pressure was assumed to arise from transmission of ventricular cavity pressure into the myocardial wall as well as myocardial stiffness, based on global pump mechanics and local myofiber mechanics. Model-predicted waveforms of global epicardial flow velocity, as well as of intramyocardial flow and diameter were qualitatively and quantitatively compared with reported data. Versatility of the model was demonstrated in a case study of aortic valve stenosis. The reference simulation correctly described the phasic pattern of coronary flow velocity, arterial flow impediment, and intramyocardial differences in coronary flow and diameter. Predicted retrograde flow during early systole in aortic valve stenosis was in agreement with measurements obtained in patients. In conclusion, we presented a powerful multi-scale modeling framework that enables realistic simulation of coronary mechanics and hemodynamics. This modeling framework can be used as a research platform for in-depth studies of cardiac-to-coronary coupling, enabling study of the effect of abnormal myocardial tissue properties on coronary hemodynamics.

Transmural Distribution of Coronary Perfusion and Myocardial Work Density Due to Alterations in Ventricular Loading, Geometry and Contractility

Myocardial supply changes to accommodate the variation of myocardial demand across the heart wall to maintain normal cardiac function. A computational framework that couples the systemic circulation of a left ventricular (LV) finite element model and coronary perfusion in a closed loop is developed to investigate the transmural distribution of the myocardial demand (work density) and supply (perfusion) ratio. Calibrated and validated against measurements of LV mechanics and coronary perfusion, the model is applied to investigate changes in the transmural distribution of passive coronary perfusion, myocardial work density, and their ratio in response to changes in LV contractility, preload, afterload, wall thickness, and cavity volume. The model predicts the following: (1) Total passive coronary flow varies from a minimum value at the endocardium to a maximum value at the epicardium transmurally that is consistent with the transmural distribution of IMP; (2) Total passive coronary flow at different transmural locations is increased with an increase in either contractility, afterload, or preload of the LV, whereas is reduced with an increase in wall thickness or cavity volume; (3) Myocardial work density at different transmural locations is increased transmurally with an increase in either contractility, afterload, preload or cavity volume of the LV, but is reduced with an increase in wall thickness; (4) Myocardial work density-perfusion mismatch ratio at different transmural locations is increased with an increase in contractility, preload, wall thickness or cavity volume of the LV, and the ratio is higher at the endocardium than the epicardium. These results suggest that an increase in either contractility, preload, wall thickness, or cavity volume of the LV can increase the vulnerability of the subendocardial region to ischemia.

Role of coronary flow regulation and cardiac-coronary coupling in mechanical dyssynchrony associated with right ventricular pacing

Mechanical dyssynchrony (MD) affects left ventricular (LV) mechanics and coronary perfusion. To understand the multifactorial effects of MD, we developed a computational model that bidirectionally couples the systemic circulation with the LV and coronary perfusion with flow regulation. In the model, coronary flow in the left anterior descending (LAD) and left circumflex (LCX) arteries affects the corresponding regional contractility based on a prescribed linear LV contractility-coronary flow relationship. The model is calibrated with experimental measurements of LV pressure and volume, as well as LAD and LCX flow rate waveforms acquired under regulated and fully dilated conditions from a swine under right atrial (RA) pacing. The calibrated model is applied to simulate MD. The model can simultaneously reproduce the reduction in mean LV pressure (39.3%), regulated flow (LAD: 7.9%; LCX: 1.9%), LAD passive flow (21.6%), and increase in LCX passive flow (15.9%). These changes are associated with right ventricular pacing compared with RA pacing measured in the same swine only when LV contractility is affected by flow alterations with a slope of 1.4 mmHg/mL² in a contractility-flow relationship. In sensitivity analyses, the model predicts that coronary flow reserve (CFR) decreases and increases in the LAD and LCX with increasing delay in LV free wall contraction. These findings suggest that asynchronous activation associated with MD impacts 1) the loading conditions that further affect the coronary flow, which may explain some of the changes in CFR, and 2) the coronary flow that reduces global contractility, which contributes to the reduction in LV pressure.NEW & NOTEWORTHY A computational model that couples the systemic circulation of the left ventricular (LV) and coronary perfusion with flow regulation is developed to study the effects of mechanical dyssynchrony. The delayed contraction in the LV free wall with respect to the septum has a significant effect on LV function and coronary flow reserve.

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.

Cardiac T2 mapping: robustness and homogeneity of standardized in-line analysis

BACKGROUND AND PURPOSE

Interpretation of T2 values remains difficult due to limited comparability across hardware and software systems and the lack of validated measurement recommendations for the number and orientation of mandatory slices. Our aims were to provide a standardized comparison of intra- and inter-individual T2 values in the short and long axes and to investigate inter-scanner reproducibility.

METHOD AND MATERIALS

Ninety cardiovascular magnetic resonance (CMR) studies in 30 healthy subjects were performed with three identical 1.5 T CMR scanners (same hardware and software) using a balanced steady-state free precession (bSSFP) gradient echo sequence in three short axis (SAx) and three long axis (LAx) views. A commercially available T2 mapping software package of the latest generation with automatic in-line motion correction was used for acquisition. Regions of interest were manually drawn in each of the 16 myocardial segments according to the American Heart Association (AHA) model in three SAx and three LAx acquisitions. Analysis of inter-scanner, inter-segmental, intra-segmental, inter-regional and inter-level differences was performed.

RESULTS

Inter-scanner reproducibility was high and the mean myocardial T2 value for all evaluated segments was 45.7 ± 3.4 ms. Significant inter-segmental variations of mean T2 values were found. Mean intra-segmental T2 values were comparable between LAx and SAx acquisitions in 72%. Significantly higher T2 values were found in apical segments and a significant disparity among different regions was found for SAx and LAx orientations.

CONCLUSION

Standardized cardiac T2 mapping is highly reproducible on identical CMR systems. T2 values vary significantly between single heart segments, regions, levels, and axes in young, healthy subjects.

Overview of mathematical modeling of myocardial blood flow regulation

The oxygen consumption by the heart and its extraction from the coronary arterial blood are the highest among all organs. Any increase in oxygen demand due to a change in heart metabolic activity requires an increase in coronary blood flow. This functional requirement of adjustment of coronary blood flow is mediated by coronary flow regulation to meet the oxygen demand without any discomfort, even under strenuous exercise conditions. The goal of this article is to provide an overview of the theoretical and computational models of coronary flow regulation and to reveal insights into the functioning of a complex physiological system that affects the perfusion requirements of the myocardium. Models for three major control mechanisms of myogenic, flow, and metabolic control are presented. These explain how the flow regulation mechanisms operating over multiple spatial scales from the precapillaries to the large coronary arteries yield the myocardial perfusion characteristics of flow reserve, autoregulation, flow dispersion, and self-similarity. The review not only introduces concepts of coronary blood flow regulation but also presents state-of-the-art advances and their potential to impact the assessment of coronary microvascular dysfunction (CMD), cardiac-coronary coupling in metabolic diseases, and therapies for angina and heart failure. Experimentalists and modelers not trained in these models will have exposure through this review such that the nonintuitive and highly nonlinear behavior of coronary physiology can be understood from a different perspective. This survey highlights knowledge gaps, key challenges, future research directions, and novel paradigms in the modeling of coronary flow regulation.

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.

Coronary Microcirculation in Aortic Stenosis

Aortic stenosis is a heterogeneous disorder. Variations in the pathological and physiological responses to pressure overload are incompletely understood and generate a range of flow and pressure gradient patterns, which ultimately cause varying microvascular effects. The impact of cardiac-coronary coupling depends on these pressure and flow effects. In this article, we explore important concepts concerning cardiac physiology and the coronary microcirculation in aortic stenosis and their impact on myocardial remodeling, aortic valve flow patterns, and clinical progression.

A One-Dimensional Hemodynamic Model of the Coronary Arterial Tree

One-dimensional (1D) hemodynamic models of arteries have increasingly been applied to coronary circulation. In this study, we have adopted flow and pressure profiles in Olufsen's 1D structured tree as coronary boundary conditions, with terminals coupled to the dynamic pressure feedback resulting from the intra-myocardial stress because of ventricular contraction. We model a trifurcation structure of the example coronary tree as two adjacent bifurcations. The estimated results of blood pressure and flow rate from our simulation agree well with the clinical measurements and published data. Furthermore, the 1D model enables us to use wave intensity analysis to simulate blood flow in the developed coronary model. Six characteristic waves are observed in both left and right coronary flows, though the waves' magnitudes differ from each other. We study the effects of arterial wall stiffness on coronary blood flow in the left circumflex artery (LCX). Different diseased cases indicate that distinct pathological reactions of the cardiovascular system can be better distinguished through Wave Intensity analysis, which shows agreement with clinical observations. Finally, the feedback pressure in terminal vessels and measurement deviation are also investigated by changing parameters in the LCX. We find that larger feedback pressure increases the backward wave and decreases the forward one. Although simplified, this 1D model provides new insight into coronary hemodynamics in healthy and diseased conditions. We believe that this approach offers reference resources for studies on coronary circulation disease diagnosis, treatment and simulation.

Studying The Sensitivity Of Coronary Blood Flow Using Nondimensional Analysis

Nondimensional analysis was used to develop a novel model of coronary blood flow. In addition to general hemodynamics, the model was used to study the sensitivity of the arterial flow to variations in characteristic lumped parameters. Experimental hemodynamic data obtained from four normal healthy pigs were used in the current study. The results suggest that the mean coronary arterial flow is primarily sensitive to the flow and elasticity parameters of the coronary vasculature. Other flow features were also studied, and it was shown that the sensitivities of the general flow waveforms are influenced to different extents by the perturbations of these parameters. More specifically, the flow coefficient affects the systolic inflow more than the diastolic portion; conversely, the elasticity coefficient has more impact on the diastolic period.

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.

Role of Coronary Myogenic Response in Pressure-Flow Autoregulation in Swine: A Meta-Analysis With Coronary Flow Modeling

Myogenic responses (pressure-dependent contractions) of coronary arterioles play a role in autoregulation (relatively constant flow vs. pressure). Publications on myogenic reactivity in swine coronaries vary in caliber, analysis, and degree of responsiveness. Further, data on myogenic responses and autoregulation in swine have not been completely compiled, compared, and modeled. Thus, it has been difficult to understand these physiological phenomena. Our purpose was to: (a) analyze myogenic data with standard criteria; (b) assign results to diameter categories defined by morphometry; and (c) use our novel multiscale flow model to determine the extent to which ex vivo myogenic reactivity can explain autoregulation in vivo. When myogenic responses from the literature are an input for our model, the predicted coronary autoregulation approaches in vivo observations. More complete and appropriate data are now available to investigate the regulation of coronary blood flow in swine, a highly relevant model for human physiology and disease.

Major influence of a 'smoke and mirrors' effect caused by wave reflection on early diastolic coronary arterial wave intensity

KEY POINTS

Coronary wave intensity analysis (WIA) is an emerging technique for assessing upstream and downstream influences on myocardial perfusion. It is thought that a dominant backward decompression wave (BDW_dia ) is generated by a distal suction effect, while early-diastolic forward decompression (FDW_dia ) and compression (FCW_dia ) waves originate in the aorta. We show that wave reflection also makes a substantial contribution to FDW_dia , FCW_dia and BDW_dia , as quantified by a novel method. In 18 sheep, wave reflection accounted for ∼70% of BDW_dia , whereas distal suction dominated in a computer model representing a hypertensive human. Non-linear addition/subtraction of mechanistically distinct waves (e.g. wave reflection and distal suction) obfuscates the true contribution of upstream and downstream forces on measured waves (the 'smoke and mirrors' effect). The mechanisms underlying coronary WIA are more complex than previously thought and the impact of wave reflection should be considered when interpreting clinical and experimental data.

ABSTRACT

Coronary arterial wave intensity analysis (WIA) is thought to provide clear insight into upstream and downstream forces on coronary flow, with a large early-diastolic surge in coronary flow accompanied by a prominent backward decompression wave (BDW_dia ), as well as a forward decompression wave (FDW_dia ) and forward compression wave (FCW_dia ). The BDW_dia is believed to arise from distal suction due to release of extravascular compression by relaxing myocardium, while FDW_dia and FCW_dia are thought to be transmitted from the aorta into the coronary arteries. Based on an established multi-scale computational model and high-fidelity measurements from the proximal circumflex artery (Cx) of 18 anaesthetized sheep, we present evidence that wave reflection has a major impact on each of these three waves, with a non-linear addition/subtraction of reflected waves obscuring the true influence of upstream and downstream forces through concealment and exaggeration, i.e. a 'smoke and mirrors' effect. We also describe methods, requiring additional measurement of aortic WIA, for unravelling the separate influences of wave reflection versus active upstream/downstream forces on coronary waves. Distal wave reflection accounted for ∼70% of the BDW_dia in sheep, but had a lesser influence (∼25%) in the computer model representing a hypertensive human. Negative reflection of the BDW_dia at the coronary-aortic junction attenuated the Cx FDW_dia (by ∼40% in sheep) and augmented Cx FCW_dia (∼5-fold), relative to the corresponding aortic waves. We conclude that wave reflection has a major influence on early-diastolic WIA, and thus needs to be considered when interpreting coronary WIA profiles.

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.

The impact of the aortic valve impairment on the distant coronary arteries hemodynamics: a fluid-structure interaction study

Atherosclerosis is still the leading cause of death in the developed world. Although its initiation and progression is a complex multifactorial process, it is well known that blood flow-induced wall shear stress (WSS) is an important factor involved in early atherosclerotic plaque initiation. In recent clinical studies, it was established that the regional pathologies of the aortic valve can be involved in the formation of atherosclerotic plaques. However, the impact of hemodynamic effects is not yet fully elucidated for disease initiation and progression. In this study, our developed 3D global fluid-structure interaction model of the aortic root incorporating coronary arteries is used to investigate the possible interaction between coronary arteries and aortic valve pathologies. The coronary hemodynamics was examined and quantified for different degrees of aortic stenosis varying from nonexistent to severe. For the simulated healthy model, the calculated WSS varied between 0.41 and 1.34 Pa which is in the atheroprotective range. However, for moderate and severe aortic stenoses, wide regions of the coronary structures, especially the proximal sections around the first bifurcation, were exposed to lower values of WSS and therefore they were prone to atherosclerosis even in the case of healthy coronary arteries.

Regulation of Coronary Blood Flow

The heart is uniquely responsible for providing its own blood supply through the coronary circulation. Regulation of coronary blood flow is quite complex and, after over 100 years of dedicated research, is understood to be dictated through multiple mechanisms that include extravascular compressive forces (tissue pressure), coronary perfusion pressure, myogenic, local metabolic, endothelial as well as neural and hormonal influences. While each of these determinants can have profound influence over myocardial perfusion, largely through effects on end-effector ion channels, these mechanisms collectively modulate coronary vascular resistance and act to ensure that the myocardial requirements for oxygen and substrates are adequately provided by the coronary circulation. The purpose of this series of Comprehensive Physiology is to highlight current knowledge regarding the physiologic regulation of coronary blood flow, with emphasis on functional anatomy and the interplay between the physical and biological determinants of myocardial oxygen delivery. © 2017 American Physiological Society. Compr Physiol 7:321-382, 2017.

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.

Influence of anatomical dominance and hypertension on coronary conduit arterial and microcirculatory flow patterns: a multiscale modeling study

Coronary hemodynamics are known to be affected by intravascular and extravascular factors that vary regionally and transmurally between the perfusion territories of left and right coronary arteries. However, despite clinical evidence that left coronary arterial dominance portends greater cardiovascular risk, relatively little is known about the effects of left or right dominance on regional conduit arterial and microcirculatory blood flow patterns, particularly in the presence of systemic or pulmonary hypertension. We addressed this issue using a multiscale numerical model of the human coronary circulation situated in a closed-loop cardiovascular model. The coronary model represented left or right dominant anatomies and accounted for transmural and regional differences in vascular properties and extravascular compression. Regional coronary flow dynamics of the two anatomical variants were compared under normotensive conditions, raised systemic or pulmonary pressures with maintained flow demand, and after accounting for adaptations known to occur in acute and chronic hypertensive states. Key findings were that 1) right coronary arterial flow patterns were strongly influenced by dominance and systemic/pulmonary hypertension; 2) dominance had minor effects on left coronary arterial and all microvascular flow patterns (aside from mean circumflex flow); 3) although systemic hypertension favorably increased perfusion pressure, this benefit varied regionally and transmurally and was offset by increased left ventricular and septal flow demands; and 4) pulmonary hypertension had a substantial negative effect on right ventricular and septal flows, which was exacerbated by greater metabolic demands. These findings highlight the importance of interactions between coronary arterial dominance and hypertension in modulating coronary hemodynamics.

In silico coronary wave intensity analysis: application of an integrated one-dimensional and poromechanical model of cardiac perfusion

Coronary wave intensity analysis (cWIA) is a diagnostic technique based on invasive measurement of coronary pressure and velocity waveforms. The theory of WIA allows the forward- and backward-propagating coronary waves to be separated and attributed to their origin and timing, thus serving as a sensitive and specific cardiac functional indicator. In recent years, an increasing number of clinical studies have begun to establish associations between changes in specific waves and various diseases of myocardium and perfusion. These studies are, however, currently confined to a trial-and-error approach and are subject to technological limitations which may confound accurate interpretations. In this work, we have developed a biophysically based cardiac perfusion model which incorporates full ventricular–aortic–coronary coupling. This was achieved by integrating our previous work on one-dimensional modelling of vascular flow and poroelastic perfusion within an active myocardial mechanics framework. Extensive parameterisation was performed, yielding a close agreement with physiological levels of global coronary and myocardial function as well as experimentally observed cumulative wave intensity magnitudes. Results indicate a strong dependence of the backward suction wave on QRS duration and vascular resistance, the forward pushing wave on the rate of myocyte tension development, and the late forward pushing wave on the aortic valve dynamics. These findings are not only consistent with experimental observations, but offer a greater specificity to the wave-originating mechanisms, thus demonstrating the value of the integrated model as a tool for clinical investigation.

Remodeling of left circumflex coronary arterial tree in pacing-induced heart failure

Congestive heart failure (CHF) is a very serious heart disease that manifests an imbalance between left ventricle supply and demand. Although the mechanical demand of the failing heart has been well characterized, the systematic remodeling of the entire coronary arterial tree that constitutes the supply of the myocardium is lacking. We hypothesize that the well-known increase in ventricle wall stress during CHF causes coronary vascular rarefaction to increase the vascular flow resistance, which in turn compromises the perfusion of the heart. Morphometric (diameters, length, and numbers) data of the swine left circumflex (LCx) arterial tree were measured in both CHF (n = 6) and control (n = 6) groups, from which a computer reconstruction of the entire LCx tree was implemented down to the capillary level to enable a hemodynamic analysis of coronary circulation. The vascular flow resistance was increased by ∼75% due to a significant decrease of vessel numbers (∼45%) and diameters in the first capillary segments (∼10%) of the LCx arterial tree after 3-4 wk of pacing. The structural remodeling significantly changed the wall shear stress in vessel segments of the entire LCx arterial tree of CHF animals. This study enhances our knowledge of coronary arterial tree remodeling in heart failure, which provides a deeper understanding of the deterioration of supply-demand relation in left ventricle.

Scalability and in vivo validation of a multiscale numerical model of the left coronary circulation

Multiscale modeling is a promising tool for the study of coronary hemodynamics. A key strength of this approach is that it accounts for microvascular properties and extravascular forces that differ regionally and transmurally, as well as wave propagation effects in the conduit arteries. However, little validation of such models has been reported and no models of the newborn coronary circulation have been described. We therefore validated a multiscale model of the left coronary circulation using high-fidelity data from nine adult sheep and nine newborn lambs and investigated whether wave propagation effects are more prominent in adults, whose body size (and hence wave transit distance) is greater. The model consisted of a one-dimensional (1D) network of the major conduit arteries and a lumped parameter model of microvascular beds. Intramyocardial pressure was considered to arise via contraction-related myocyte thickening and transmission of ventricular cavity pressure into the heart wall. 1D network geometry from published human anatomical data was scaled using myocardial weights, while subject-specific aortic pressure/flow and ventricular pressure formed model inputs. Total vascular resistance was determined iteratively from measured mean circumflex coronary flow (CxQ), but no fitting of phasic aspects of the waveform was performed. Excellent agreement was obtained between simulated and measured CxQ waveforms in most cases. Detailed flow waveform analysis did not clearly reveal a greater prominence of wave propagation effects in adults compared with newborns. This multiscale model is likely to be useful for investigating wave phenomena and phasic aspects of coronary flow in adults and during development.

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).

Validation of a multi-scale model of the coronary circulation in adult sheep and newborn lambs

We validated a multi-scale model of a left-dominant coronary circulation using high fidelity pressure and flow data acquired in adult sheep and newborn lambs. The model incorporated a one-dimensional representation of the major left conduit coronary arteries, allowing for the study of wave propagation effects. The coronary microvasculature was represented by regional instances of a lumped parameter model consisting of three transmural layers, each with two serial compartments accounting for compliance, resistance and intramyocardial pressure effects. Model inputs comprised measured aortic pressure/flow and ventricular pressure. Minimal data fitting was employed, with only measured mean coronary flow used to iteratively adjust total coronary resistance. The model was adapted to different heart sizes via allometric scaling. Excellent agreement was observed between model and experimental flow waveforms in the proximal circumflex artery, both in terms of the degree of systolic flow impediment and transient waveform features. The proposed multi-scale modelling approach is likely to be useful for studying phasic features of the coronary flow waveform, including coronary waves in different coronary anatomies and throughout development.

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.

Modeling to link regional myocardial work, metabolism and blood flows

Given the mono-functional, highly coordinated processes of cardiac excitation and contraction, the observations that regional myocardial blood flows, rMBF, are broadly heterogeneous has provoked much attention, but a clear explanation has not emerged. In isolated and in vivo heart studies the total coronary flow is found to be proportional to the rate-pressure product (systolic mean blood pressure times heart rate), a measure of external cardiac work. The same relationship might be expected on a local basis: more work requires more flow. The validity of this expectation has never been demonstrated experimentally. In this article we review the concepts linking cellular excitation and contractile work to cellular energetics and ATP demand, substrate utilization, oxygen demand, vasoregulation, and local blood flow. Mathematical models of these processes are now rather well developed. We propose that the construction of an integrated model encompassing the biophysics, biochemistry and physiology of cardiomyocyte contraction, then combined with a detailed three-dimensional structuring of the fiber bundle and sheet arrangements of the heart as a whole will frame an hypothesis that can be quantitatively evaluated to settle the prime issue: Does local work drive local flow in a predictable fashion that explains the heterogeneity? While in one sense one can feel content that work drives flow is irrefutable, the are no cardiac contractile models that demonstrate the required heterogeneity in local strain-stress-work; quite the contrary, cardiac contraction models have tended toward trying to show that work should be uniform. The object of this review is to argue that uniformity of work does not occur, and is impossible in any case, and that further experimentation and analysis are necessary to test the hypothesis.

Slackness between vessel and myocardium is necessary for coronary flow reserve

Tone regulation in coronary microvessels has largely been studied in isolated vessels in the absence of myocardial tethering. Here, the potential effect of radial tethering and interstitial space connective tissue (ISCT) between coronary microvessels and the surrounding myocardium was studied. We hypothesized that rigid tethering between microvessels and the myocardium would constrain the active contraction of arterioles and is not compatible with the observed tone regulation. The ISCT between coronary microvessels and myocardium in five swine was found to increase exponentially from 0.22 ± 0.02 μm in capillaries (modified Strahler order 0) of the endocardium to 34.9 ± 7.1 μm in epicardial vessels (order 10). Microvessels with both soft tethering and ISCT gap were capable of significant changes in vessel resistance (up to an ∼1,600% increase), consistent with experimental measurements of high coronary flow reserve. Additionally, the mechanical energy required for myogenic contraction was estimated. The results indicate that rigid tethering requires up to four times more mechanical energy than soft tethering in the absence of a gap. Hence, the experimental measurements and model predictions suggest that effectiveness and efficiency in tone regulation can be achieved only if the vessel is both softly tethered to and separated from the myocardium in accordance with the experimental findings of ISCT gap. These results have fundamental implications on future simulations of coronary circulation.

Coronary pressure-flow relations as basis for the understanding of coronary physiology

Recent technological advancements in the area of intracoronary physiology, as well as non-invasive contrast perfusion imaging, allow to make clinical decisions with respect to percutaneous coronary interventions and to identify microcirculatory coronary pathophysiology. The basic characteristics of coronary hemodynamics, as described by pressure-flow relations in the normal and diseased heart, need to be understood for a proper interpretation of these physiological measurements. Especially the hyperemic coronary pressure-flow relation, as well as the influence of cardiac function on it, bears great clinical significance. The interaction of a coronary stenosis with the coronary pressure-flow relation can be understood from the stenosis pressure drop-flow velocity relationship. Based on these relationships the clinically applied concepts of coronary flow velocity reserve, fractional flow reserve, stenosis resistance and microvascular resistance are discussed. Attention is further paid to the heterogeneous nature of myocardial perfusion, the vulnerability of the subendocardium and the role of collateral flow on hyperemic coronary pressure-flow relations. This article is part of a Special Issue entitled "Coronary Blood Flow".

Heart rate: a forgotten link in coronary artery disease?

A considerable body of evidence indicates that elevated resting heart rate is an independent, modifiable risk factor for cardiovascular events and mortality in patients with coronary artery disease. Elevated heart rate can produce adverse effects in several ways. Firstly, myocardial oxygen consumption is increased at high heart rates, but the time available for myocardial perfusion is reduced, increasing the likelihood of myocardial ischemia. Secondly, exposure of the large elastic arteries to cyclical stretch is increased at high heart rates. This effect can increase the rate at which components of the arterial wall deteriorate. Elastin fibers, which have an extremely slow rate of turnover in adult life, might be particularly vulnerable. Thirdly, elevated heart rate can predispose the myocardium to arrhythmias, and favor the development and progression of coronary atherosclerosis, by adversely affecting the balance between systolic and diastolic flow. Comparisons of the effects of the specific heart-rate-lowering drug ivabradine with those of β-blockers could help clarify the pathophysiological effects of elevated heart rate. Effective heart rate control among patients with coronary artery disease is uncommon in clinical practice, representing a missed therapeutic opportunity.

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.

Why is the subendocardium more vulnerable to ischemia? A new paradigm

Myocardial ischemia is transmurally heterogeneous where the subendocardium is at higher risk. Stenosis induces reduced perfusion pressure, blood flow redistribution away from the subendocardium, and consequent subendocardial vulnerability. We propose that the flow redistribution stems from the higher compliance of the subendocardial vasculature. This new paradigm was tested using network flow simulation based on measured coronary anatomy, vessel flow and mechanics, and myocardium-vessel interactions. Flow redistribution was quantified by the relative change in the subendocardial-to-subepicardial perfusion ratio under a 60-mmHg perfusion pressure reduction. Myocardial contraction was found to induce the following: 1) more compressive loading and subsequent lower transvascular pressure in deeper vessels, 2) consequent higher compliance of the subendocardial vasculature, and 3) substantial flow redistribution, i.e., a 20% drop in the subendocardial-to-subepicardial flow ratio under the prescribed reduction in perfusion pressure. This flow redistribution was found to occur primarily because the vessel compliance is nonlinear (pressure dependent). The observed thinner subendocardial vessel walls were predicted to induce a higher compliance of the subendocardial vasculature and greater flow redistribution. Subendocardial perfusion was predicted to improve with a reduction of either heart rate or left ventricular pressure under low perfusion pressure. In conclusion, subendocardial vulnerability to a acute reduction in perfusion pressure stems primarily from differences in vascular compliance induced by transmural differences in both extravascular loading and vessel wall thickness. Subendocardial ischemia can be improved by a reduction of heart rate and left ventricular pressure.

Significance of microvascular remodelling for the vascular flow reserve in hypertension

Vascular flow reserve (VFR) is the relative increase in tissue perfusion from the resting state to a state with maximum vasodilatation. Longstanding hypertension reduces the VFR, which in turn reduces the maximum working capacity of the tissue. In principle, both inward arteriolar remodelling and rarefaction of the microvascular network may contribute to this reduction. These processes are known to occur simultaneously in the microcirculation of the hypertensive individual and both cause a reduction in the luminal trans-sectional area available for perfusion. Which of them is the main factor responsible for the reduction in VFR is, however, not known. Here we present simulations performed on large microvascular networks to assess the VFR in various situations. Particular attention is paid to the VFR in networks in which the vessels have structurally adapted to a sustained increase in pressure by inward eutrophic remodelling (IER), i.e. by redistributing the same amount of wall material around a smaller lumen. Collectively, the results indicate that the IER may not per se be the main factor responsible for the hypertensive reduction in VFR. Rather, it may be explained by the presence of arteriolar and capillary rarefaction.

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.