Coronary microcirculation in the beating heart

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.

Vascularisation of pluripotent stem cell-derived myocardium: biomechanical insights for physiological relevance in cardiac tissue engineering

The myocardium is a diverse environment, requiring coordination between a variety of specialised cell types. Biochemical crosstalk between cardiomyocytes (CM) and microvascular endothelial cells (MVEC) is essential to maintain contractility and healthy tissue homeostasis. Yet, as myocytes beat, heterocellular communication occurs also through constantly fluctuating biomechanical stimuli, namely (1) compressive and tensile forces generated directly by the beating myocardium, and (2) pulsatile shear stress caused by intra-microvascular flow. Despite endothelial cells (EC) being highly mechanosensitive, the role of biomechanical stimuli from beating CM as a regulatory mode of myocardial-microvascular crosstalk is relatively unexplored. Given that cardiac biomechanics are dramatically altered during disease, and disruption of myocardial-microvascular communication is a known driver of pathological remodelling, understanding the biomechanical context necessary for healthy myocardial-microvascular interaction is of high importance. The current gap in understanding can largely be attributed to technical limitations associated with reproducing dynamic physiological biomechanics in multicellular in vitro platforms, coupled with limited in vitro viability of primary cardiac tissue. However, differentiation of CM from human pluripotent stem cells (hPSC) has provided an unlimited source of human myocytes suitable for designing in vitro models. This technology is now converging with the diverse field of tissue engineering, which utilises in vitro techniques designed to enhance physiological relevance, such as biomimetic extracellular matrix (ECM) as 3D scaffolds, microfluidic perfusion of vascularised networks, and complex multicellular architectures generated via 3D bioprinting. These strategies are now allowing researchers to design in vitro platforms which emulate the cell composition, architectures, and biomechanics specific to the myocardial-microvascular microenvironment. Inclusion of physiological multicellularity and biomechanics may also induce a more mature phenotype in stem cell-derived CM, further enhancing their value. This review aims to highlight the importance of biomechanical stimuli as determinants of CM-EC crosstalk in cardiac health and disease, and to explore emerging tissue engineering and hPSC technologies which can recapitulate physiological dynamics to enhance the value of in vitro cardiac experimentation.

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.

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.

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.

In vivo characterization of rodent cyclic myocardial perfusion variation at rest and during adenosine-induced stress using cine-ASL cardiovascular magnetic resonance

BACKGROUND

Assessment of cyclic myocardial blood flow (MBF) variations can be an interesting addition to the characterization of microvascular function and its alterations. To date, totally non-invasive in vivo methods with this capability are still lacking. As an original technique, a cine arterial spin labeling (ASL) cardiovascular magnetic resonance approach is demonstrated to be able to produce dynamic MBF maps across the cardiac cycle in rats.

METHOD

High-resolution MBF maps in left ventricular myocardium were computed from steady-state perfusion-dependent gradient-echo cine images produced by the cine-ASL sequence. Cyclic changes of MBF over the entire cardiac cycle in seven normal rats were analyzed quantitatively every 6 ms at rest and during adenosine-induced stress.

RESULTS

The study showed a significant MBF increase from end-systole (ES) to end-diastole (ED) in both physiological states. Mean MBF over the cardiac cycle within the group was 5.5 ± 0.6 mL g(-1) min(-1) at rest (MBFMin = 4.7 ± 0.8 at ES and MBFMax = 6.5 ± 0.6 mL g(-1) min(-1) at ED, P = 0.0007). Mean MBF during adenosine-induced stress was 12.8 ± 0.7mL g(-1) min(-1) (MBFMin = 11.7±1.0 at ES and MBFMax = 14.2 ± 0.7 mL g(-1) min(-1) at ED, P = 0.0007). MBF percentage relative variations were significantly different with 27.2 ± 9.3% at rest and 17.8 ± 7.1% during adenosine stress (P = 0.014). The dynamic analysis also showed a time shift of peak MBF within the cardiac cycle during stress.

CONCLUSION

The cyclic change of myocardial perfusion was examined by mapping MBF with a steady-pulsed ASL approach. Dynamic MBF maps were obtained with high spatial and temporal resolution (6 ms) demonstrating the feasibility of non-invasively mapping cyclic myocardial perfusion variation at rest and during adenosine stress. In a pathological context, detailed assessment of coronary responses to infused vasodilators may give valuable complementary information on microvascular functional defects in disease models.

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.

X-ray intravital microscopy for functional imaging in rat hearts using synchrotron radiation coronary microangiography

An X-ray intravital microscopy technique was developed to enable in vivo visualization of the coronary, cerebral, and pulmonary arteries in rats without exposure of organs and with spatial resolution in the micrometer range and temporal resolution in the millisecond range. We have refined the system continually in terms of the spatial resolution and exposure time. X-rays transmitted through an object are detected by an X-ray direct-conversion type detector, which incorporates an X-ray SATICON pickup tube. The spatial resolution has been improved to 6 μm, yielding sharp images of small arteries. The exposure time has been shortened to around 2 ms using a new rotating-disk X-ray shutter, enabling imaging of beating rat hearts. Quantitative evaluations of the X-ray intravital microscopy technique were extracted from measurements of the smallest-detectable vessel size and detection of the vessel function. The smallest-diameter vessel viewed for measurements is determined primarily by the concentration of iodinated contrast material. The iodine concentration depends on the injection technique. We used ex vivo rat hearts under Langendorff perfusion for accurate evaluation. After the contrast agent is injected into the origin of the aorta in an isolated perfused rat heart, the contrast agent is delivered directly into the coronary arteries with minimum dilution. The vascular internal diameter response of coronary arterial circulation is analyzed to evaluate the vessel function. Small blood vessels of more than about 50 μm diameters were visualized clearly at heart rates of around 300 beats/min. Vasodilation compared to the control was observed quantitatively using drug manipulation. Furthermore, the apparent increase in the number of small vessels with diameters of less than about 50 μm was observed after the vasoactive agents increased the diameters of invisible small blood vessels to visible sizes. This technique is expected to offer the potential for direct investigation of mechanisms of vascular dysfunctions.

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.

Ultrafast Doppler imaging of blood flow dynamics in the myocardium

Imaging intramyocardial vascular flows in real-time could strongly help to achieve better diagnostic of cardiovascular diseases. To date, no standard imaging modality allows describing accurately myocardial blood flow dynamics with good spatial and temporal resolution. We recently introduced a novel ultrasonic Doppler imaging technique based on compounded plane waves transmissions at ultrafast frame rate. The high sensitivity of this ultrafast Doppler technique permits to image the intramyocardial blood flow and its dynamics. A dedicated demodulation-filtering process is implemented to compensate for the large tissue velocity of the myocardium during the cardiac cycle. A signed power Doppler processing provides the discrimination between arterial and venous flows. Experiments were performed in vivo in a large animal open chest model ( N = 5 sheep) using a conventional ultrasonic probe placed at the surface of the heart. Results show the capability of the technique to image intramyocardial vascular flows in normal physiological conditions with good spatial (200 μm) and temporal resolution (10 ms). Flow dynamics over the cardiac cycle were investigated and the imaging method demonstrated a phase opposition of flow waveforms between arterial and venous flows. Finally, ultrafast Doppler combined with tissue motion compensation was found able to reveal vascular flow disruption in ischemic regions during occlusion of the main diagonal coronary artery.

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.

Cardioscopic observation of subendocardial microvessels in patients with coronary artery disease

Coronary microvessels play a direct and critical role in determining the extent and severity of myocardial ischemia and cardiac function. However, because direct observation has never been performed in vivo, the functional properties of the individual microvesssels in patients with coronary artery disease remain unknown. Subendocardial coronary microvessels were observed by cardioscopy in 149 successive patients with coronary artery disease (81 with stable angina and 68 with old myocardial infarction). Twenty-four arterial microvessels (AMs) and 27 venous microvessels (VMs) were observed in the left ventricular subendocardium. All 12 AMs and 13 of 14 VMs that were located in normokinetic-to-hypokinetic left ventricular wall segments were filled with blood during diastole and were collapsed during systole. In contrast, 8 of 12 AMs and 9 of 13 VMs that were located in akinetic-to-dyskinetic wall segments were filled with blood during systole and were collapsed during diastole. There were no significant correlations between the timing of blood filling and the severity of coronary stenosis and collateral development. In patients with coronary artery disease, the timing of blood filling of AMs and VMs was dependent on the regional left ventricular contractile state; during diastole when contraction was preserved and during systole when it was not. It remains to be elucidated whether and how blood filling is disturbed in other categories of heart disease.

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.

Orthostatic hypotension predicts all-cause mortality and coronary events in middle-aged individuals (The Malmo Preventive Project)

Aims

Orthostatic hypotension (OH) has been linked to increased mortality and incidence of cardiovascular disease in various risk groups, but determinants and consequences of OH in the general population are poorly studied.

Methods and results

Prospective data of the Swedish ‘Malmö Preventive Project’ (n = 33 346, 67.3% men, mean age 45.7 ± 7.4 years, mean follow-up 22.7 ± 6.0 years) were analysed. Orthostatic hypotension was found in 6.2% of study participants and was associated with age, female gender, hypertension, antihypertensive treatment, increased heart rate, diabetes, low BMI, and current smoking. In Cox regression analysis, individuals with OH had significantly increased all-cause mortality (in particular those aged less than 42 years) and coronary event (CE) risk. Mortality and CE risk were distinctly higher in those with systolic blood pressure (BP) fall ≥30 mmHg [hazard ratio (HR): 1.6, 95% CI 1.3–1.9, P < 0.0001 and 1.6, 95% CI 1.2–2.1, P = 0.001] and diastolic BP fall ≥15 mmHg (HR: 1.4, 95% CI 1.1–1.9, P = 0.024 and 1.7, 95% CI 1.1–2.5, P = 0.01). In addition, impaired diastolic BP response had relatively greater impact (per mmHg) on CE incidence than systolic reaction.

Conclusion

Orthostatic hypotension can be detected in ∼6% of middle-aged individuals and is often associated with such comorbidities as hypertension or diabetes. Presence of OH increases mortality and CE risk, independently of traditional risk factors. Although both impaired systolic and diastolic responses predict adverse events, the diastolic impairment shows stronger association with coronary disease.