Morphometric Reconstruction of Coronary Vasculature Incorporating Uniformity of Flow Dispersion

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.

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.

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.

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.