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

Computer model coupling hemodynamics and oxygen transport in the coronary capillary network: Pulsatile vs. non-pulsatile analysis

BACKGROUND AND OBJECTIVE

Oxygen transport in the heart is crucial, and its impairment can lead to pathological conditions such as hypoxia, ischemia, and heart failure. However, investigating oxygen transport in the heart using in vivo measurements is difficult due to the small size of the coronary capillaries and their deep embedding within the heart wall.

METHODS

In this study, we developed a novel computational modeling framework that integrates a 0-D hemodynamic model with a 1-D mass transport model to simulate oxygen transport in/across the coronary capillary network.

RESULTS

The model predictions agree with analytical solutions and experimental measurements. The framework is used to simulate the effects of pulsatile vs. non-pulsatile behavior of the capillary hemodynamics on oxygen-related metrics such as the myocardial oxygen consumption (MVO2) and oxygen extraction ratio (OER). Compared to simulations that consider (physiological) pulsatile behaviors of the capillary hemodynamics, the OER is underestimated by less than 9% and the MVO2 is overestimated by less than 5% when the pulsatile behaviors are ignored in the simulations. Statistical analyses show that model predictions of oxygen-related quantities and spatial distribution of oxygen without consideration of the pulsatile behaviors do not significantly differ from those that considered such behaviors (p-values >0.05).

CONCLUSIONS

This finding provides the basis for reducing the model complexity by ignoring the pulsatility of coronary capillary hemodynamics in the computational framework without a substantial loss of accuracy when predicting oxygen-related metrics.

Unraveling the Gordian knot of coronary pressure-flow autoregulation

The coronary circulation has the inherent ability to maintain myocardial perfusion constant over a wide range of perfusion pressures. The phenomenon of pressure-flow autoregulation is crucial in response to flow-limiting atherosclerotic lesions which diminish coronary driving pressure and increase risk of myocardial ischemia and infarction. Despite well over half a century of devoted research, understanding of the mechanisms responsible for autoregulation remains one of the most fundamental and contested questions in the field today. The purpose of this review is to highlight current knowledge regarding the complex interrelationship between the pathways and mechanisms proposed to dictate the degree of coronary pressure-flow autoregulation. Our group recently likened the intertwined nature of the essential determinants of coronary flow control to the symbolically unsolvable "Gordian knot". To further efforts to unravel the autoregulatory "knot", we consider recent challenges to the local metabolic and myogenic hypotheses and the complicated dynamic structural and functional heterogeneity unique to the heart and coronary circulation. Additional consideration is given to interrogation of putative mediators, role of K+ and Ca2+ channels, and recent insights from computational modeling studies. Improved understanding of how specific vasoactive mediators, pathways, and underlying disease states influence coronary pressure-flow relations stands to significantly reduce morbidity and mortality for what remains the leading cause of death worldwide.

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.

Mechanisms of coronary sinus reducer for treatment of myocardial ischemia: in silico study

The coronary sinus reducer (CSR) is an emerging medical device for treating patients with refractory angina, often associated with myocardial ischemia. Patients implanted with CSR have shown positive outcomes, but the underlying mechanisms are unclear. This study sought to understand the mechanisms of CSR by investigating its effects on coronary microcirculation hemodynamics that may help explain the therapy's efficacy. We applied a validated computer model of the coronary microcirculation to investigate how CSR affects hemodynamics under different degrees of coronary artery stenosis. With moderate coronary stenosis, an increase in capillary transit time (CTT) [up to 69% with near-complete coronary sinus (CS) occlusion] is the key change associated with CSR. Because capillaries in the microcirculation can still receive oxygenated blood from the upstream artery with moderate stenosis, the increase in CTT allows more time for the exchange of gases and nutrients, aiding tissue oxygenation. With severe coronary stenosis; however, the redistribution of blood draining from the nonischemic region to the ischemic region (up to 96% with near-complete CS occlusion) and the reduction in capillary flow heterogeneity are the key changes associated with CSR. Because blood draining from the nonischemic region is not completely devoid of O2, the redistribution of blood to the capillaries in the ischemic region by CSR is beneficial especially when little or no oxygenated blood reaches these capillaries. This simulation study provides insights into the mechanisms of CSR in improving clinical symptoms. The mechanisms differ with the severity of the upstream stenosis.NEW & NOTEWORTHY Emerging coronary venous retroperfusion treatments, particularly coronary sinus reducer (CSR) for refractory angina linked to myocardial ischemia, show promise; however, their mechanisms of action are not well understood. We find that CSR's effectiveness varies with the severity of coronary stenosis. In moderate stenosis, CSR improves tissue oxygenation by increasing capillary transit time, whereas in severe stenosis, it redistributes blood from nonischemic to ischemic regions and reduces capillary flow heterogeneity.

Investigation into the two-way interaction of coronary flow and heart function in coronary artery disease predicted by a computational model of autoregulation of coronary flow

This study presents a closed-loop computational model to investigate the interplay between heart function, coronary flow, and systemic circulation during exercise, with a specific focus on the impact of coronary artery stenosis. The model incorporates a lumped representation of the heart, main arteries, and coronary arteries, establishing a closed circulatory system. The simulation investigates the autoregulation of coronary flow in response to myocardial oxygen demands during physical exercise by incorporating sympathetic and parasympathetic functions. This study establishes a closed supply-demand loop and investigates the effect of coronary flow deficiency on heart function and systemic circulation in coronary artery diseases during exercise. In coronary artery diseases with low stenosis, heart function and systemic flow resemble those of a healthy person. However, as stenosis intensifies with physical exercise, an additional regulatory mechanism (reg2) is activated. This mechanism adjusts coronary flow by reducing myocardial contractility (E) and increasing heart rate (HR) while maintaining cardiac output (CO). The study results indicate that, at the highest exercise intensity for a healthy individual (HR = 150), the value of E increases from 6 to 8.65mmHg/ml. Meanwhile, for a patient with 85 % coronary artery stenosis in the same exercise intensity, the HR increases to 200, and the value of E decreases to 3.45mmHg/ml. The results also demonstrate that the initiation of the (reg2) mechanism at rest occurs at 83 % stenosis, while at the highest exercise intensity, this mechanism commences at 67 % stenosis.

Simulation of coronary capillary transit time based on full vascular model of the heart

Capillary transit time (CTT) is a fundamental determinant of gas exchange between blood and tissues in the heart and other organs. Despite advances in experimental techniques, it remains difficult to measure coronary CTT in vivo. Here, we developed a novel computational framework that couples coronary microcirculation with cardiac mechanics in a closed-loop system that enables prediction of hemodynamics in the entire coronary network, including arteries, veins, and capillaries. We also developed a novel "particle-tracking" approach for computing CTT where "virtual tracers" are individually tracked as they traverse the capillary network. Model predictions compare well with blood pressure and flow rate distributions in the arterial network reported in previous studies. Model predictions of transit times in the capillaries (1.21 ± 1.5 s) and entire coronary network (11.8 ± 1.8 s) also agree with measurements. We show that, with increasing coronary artery stenosis (as quantified by fractional flow reserve, FFR), intravascular pressure and flow rate downstream are reduced but remain non-stationary even at 100 % stenosis because some flow (∼3 %) is redistributed from the non-occluded to the occluded territories. Importantly, the model predicts that occlusion of a large artery results in higher CTT. For moderate stenosis (FFR > 0.6), the increase in CTT (from 1.21 s without stenosis to 2.23 s at FFR=0.6) is caused by a decrease in capillary flow rate. In severe stenosis (FFR = 0.1), the increase in CTT to 14.2 s is due to both a decrease in flow rate and an increase in path length taken by "virtual tracers" in the capillary network.

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.

Morphological importance of coronary ostia in sheep and swine

The aortic valve was investigated in 58 sheep and 60 swine without heart disease. After fixation in 4% formalin, the distance between the ostia and the elements of the right/left aortic sinuses was measured. For the left coronary ostium (LCO), it was found that in sheep 81% were below and 19% at the level of intercomissural line (IL). In pigs, 88.3% were below and 11.7% at the IL level. In sheep, the OCL was close to the right valve commissure (CVR) in 98.3% and close to the left valve commissure (CVV) in 1.7%. In pigs, it was close to RVC at 83.3% and close to LVC at 16.7%. Regarding to RCO, it was found that in sheep 69% was below, 1.7% was above and 29.3% at the IL level. In pigs, 20% were below, 15% above and 65% at the IL level. The distance of the RCO in relation to the valve commissures was 56.9% close to LVC and 43.1% close to RVC in sheep. In pigs, 81.7% were close to LVC and 18.3% close to RVC. The position of LCO was balanced between sheep and swine, while the RCO in swine was closer to CVE when compared with sheep. The accessory coronary ostium was observed in 18.6% of sheep and 10% of pigs. Thus, it is concluded that in sheep and swine the left coronary artery is perfused only in ventricular diastole. Perfusion of the right coronary artery occurs more frequently in diastole and less frequently in ventricular systole.

Predicting pregnancy specific uterine vascular reactivity: A data driven computational model of shear-dependent, myogenic, and mechanical radial artery features

The entire maternal circulation adapts to pregnancy, and this adaption is particularly extensive in the uterine circulation where the major vessels double in size to facilitate an approximately 15-fold increase in blood supply to this organ over the course of pregnancy. Several factors may play a role in both the remodelling and biomechanical function of the uterine vasculature including the paracrine microenvironment, passive properties of the vessel wall, and active components of vascular function (incorporating the myogenic response and response to shear stress induced by intravascular blood flow). However, the interplay between these factors, and how this plays out in an organ-specific manner to induce the extent of remodelling observed in the uterus is not well understood. Here we present an integrated assessment of the uterine radial arteries, likely rate-limiters to flow of oxygenated maternal blood to the placental surface, via computational modelling and pressure myography. We show that uterine radial arteries behave differently to other systemic vessels (higher compliance and shear mediated constriction) and that their properties change with the adaptation to pregnancy (higher myogenic tone, higher compliance, and ability to tolerate higher flow rates before constricting). Together, this provides a useful tool to improve our understanding of the role of uterine vascular adaptation in normal and abnormal pregnancies and highlights the need for vascular bed specific investigations of vascular function in health and disease.

Optimization of cardiac resynchronization therapy based on a cardiac electromechanics-perfusion computational model

Cardiac resynchronization therapy (CRT) is an established treatment for left bundle branch block (LBBB) resulting in mechanical dyssynchrony. Approximately 1/3 of patients with CRT, however, are non-responders. To understand factors affecting CRT response, an electromechanics-perfusion computational model based on animal-specific left ventricular (LV) geometry and coronary vascular networks located in the septum and LV free wall is developed. The model considers contractility-flow and preload-activation time relationships, and is calibrated to simultaneously match the experimental measurements in terms of the LV pressure, volume waveforms and total coronary flow in the left anterior descending and left circumflex territories from 2 swine models under right atrium and right ventricular pacing. The model is then applied to investigate the responses of CRT indexed by peak LV pressure and (dP/dt)max at multiple pacing sites with different degrees of perfusion in the LV free wall. Without the presence of ischemia, the model predicts that basal-lateral endocardial region is the optimal pacing site that can best improve (dP/dt)max by 20%, and is associated with the shortest activation time. In the presence of ischemia, a non-ischemic region becomes the optimal pacing site when coronary flow in the ischemic region fell below 30% of its original value. Pacing at the ischemic region produces little response at that perfusion level. The optimal pacing site is associated with one that optimizes the LV activation time. These findings suggest that CRT response is affected by both pacing site and coronary perfusion, which may have clinical implication in improving CRT responder rates.

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.

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.

Topologic and Hemodynamic Characteristics of the Human Coronary Arterial Circulation

Background

Many processes contributing to the functional and structural regulation of the coronary circulation have been identified. A proper understanding of the complex interplay of these processes requires a quantitative systems approach that includes the complexity of the coronary network. The purpose of this study was to provide a detailed quantification of the branching characteristics and local hemodynamics of the human coronary circulation.

Methods

The coronary arteries of a human heart were filled post-mortem with fluorescent replica material. The frozen heart was alternately cut and block-face imaged using a high-resolution imaging cryomicrotome. From the resulting 3D reconstruction of the left coronary circulation, topological (node and loop characteristics), topographic (diameters and length of segments), and geometric (position) properties were analyzed, along with predictions of local hemodynamics (pressure and flow).

Results

The reconstructed left coronary tree consisted of 202,184 segments with diameters ranging from 30 μm to 4 mm. Most segments were between 100 μm and 1 mm long. The median segment length was similar for diameters ranging between 75 and 200 μm. 91% of the nodes were bifurcations. These bifurcations were more symmetric and less variable in smaller vessels. Most of the pressure drop occurred in vessels between 200 μm and 1 mm in diameter. Downstream conductance variability affected neither local pressure nor median local flow and added limited extra variation of local flow. The left coronary circulation perfused 358 cm³ of myocardium. Median perfused volume at a truncation level of 100 to 200 μm was 20 mm³ with a median perfusion of 5.6 ml/min/g and a high local heterogeneity.

Conclusion

This study provides the branching characteristics and hemodynamic analysis of the left coronary arterial circulation of a human heart. The resulting model can be deployed for further hemodynamic studies at the whole organ and local level.

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.

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

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