Biophysical model of the spatial heterogeneity of myocardial flow

Noninvasive computed tomography derived fractional flow reserve simulation based on microvascular tree model reconstruction

To establish a novel method for noninvasive computed tomography derived fractional flow reserve (CT-FFR) simulation based on microvascular tree model reconstruction and to evaluate the feasibility and diagnostic performance of the novel method in coronary artery disease compared with invasive fractional flow reserve (FFR). Twenty patients (20 vessels) who underwent coronary computed tomography angiography (CCTA) and invasive FFR were retrospectively studied. The anatomic epicardial coronary artery model was reconstructed based on CCTA image, and the microvascular tree model was simulated based on patient-specific anatomical structures and physiological principles. Numerical simulation was subsequently performed using the CFD method with full consideration of the variation of viscosity in microvascular. Two patients with the FFR value of .80 were selected for adjusting the parameters of the model, while the remaining 18 patients were selected as a validation cohort. After simulation, CT-FFR was compared with invasive FFR with a threshold of .80. Eleven (55%) patients had an abnormal FFR that was less than or equal to .80. Compared with invasive FFR, sensitivity, specificity, positive predictive value, negative predictive value, and accuracy of CT-FFR with an optimal threshold of .80 were 100%, 77.8%, 81.8%, 100%, 88.89%, respectively. There were a good correlation and consistency between CT-FFR and invasive FFR. Time per patient of CT-FFR analysis was less than 15 min. CT-FFR based on microvascular tree model reconstruction is feasible with good diagnostic performance. It requires a short processing time with excellent accuracy. Large multicenter prospective studies are required for further demonstrating the diagnostic performance of this novel model in myocardium ischemia evaluation.

Coronary angiography-derived index for assessing microcirculatory resistance in patients with non-obstructed vessels: The FLASH IMR study

BACKGROUND

Assessing index of microcirculatory resistance (IMR) is customarily performed using intracoronary wires fitted with sensors by at least 3 intracoronary injections of 3 to 4 mL of room-temperature saline during sustained hyperemia, which is time- and cost-consuming.

METHODS

The FLASH IMR study is a prospective, multicenter, randomized study to assess the diagnostic performance of coronary angiography-derived IMR (caIMR) in patients with suspected myocardial ischemia with nonobstructive coronary arteries using wire-based IMR as a reference. The caIMR was calculated by an optimized computational fluid dynamics model simulating hemodynamics during diastole based on coronary angiograms. TIMI frame count and aortic pressure were included in computation. caIMR was determined onsite in real time and compared blind to wire-based IMR by an independent core laboratory, using wire-based IMR ≥25 units as indicative of abnormal coronary microcirculatory resistance. The primary endpoint was the diagnostic accuracy of caIMR, using wire-based IMR as a reference, with a pre-specified performance goal of 82%.

RESULTS

A total of 113 patients underwent paired caIMR and wire-based IMR measurements. Order of performance of tests was based on randomization. Diagnostic accuracy, sensitivity, specificity, positive and negative predictive values of caIMR were 93.8% (95% CI: 87.7%-97.5%), 95.1% (95% CI: 83.5%- 99.4%), 93.1% (95% CI: 84.5%-97.7%), 88.6% (95% CI: 75.4%-96.2%) and 97.1% (95% CI: 89.9%-99.7%). The receiver-operating curve for caIMR to diagnose abnormal coronary microcirculatory resistance had area under the curve of 0.963 (95% CI: 0.928-0.999).

CONCLUSIONS

Angiography-based caIMR has a good diagnostic yield with wire-based IMR.

CLINICALTRIALS

GOV IDENTIFIER

NCT05009667.

Coronary Angiography-Derived Index of Microvascular Resistance

A coronary angiography-derived index of microvascular resistance (caIMR) is proposed for physiological assessment of microvasular diseases in coronary circulation. The aim of the study is to assess diagnostic performance of caIMR, using wire-derived index of microvascular resistance (IMR) as the reference standard. IMR was demonstrated in 56 patients (57 vessels) with stable/unstable angina pectoris and no obstructive coronary arteries in three centers using the Certus pressure wire. Based on the aortic pressure wave and coronary angiograms from two projections, the caIMR was computed and assessed in blinded fashion against the IMR at an independent core laboratory. Diagnostic accuracy, sensitivity, specificity, positive predictive value and negative predictive value of the caIMR with a cutoff value of 25 were 84.2% (95% CI: 72.1% to 92.5%), 86.1% (95% CI: 70.5% to 95.3%), 81.0% (95% CI: 58.1% to 94.6%), 88.6% (95% CI: 76.1% to 95.0%), and 77.3% (95% CI: 59.5% to 88.7%) against the IMR with a cutoff value of 25. The receiver-operating curve had area under the curve of 0.919 and the correlation coefficient equaled to 0.746 between caIMR and wire-derived IMR. Hence, caIMR could eliminate the need of a pressure wire, reduce technical error, and potentially increase adoption of physiological assessment of microvascular diseases in patients with ischemic heart disease.

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.

Usefulness of Proximal Coronary Wave Speed for Wave Intensity Analysis in Diseased Coronary Vessels

Background: Wave speed is needed to separate net wave intensity into forward and backward traveling components. However, wave speed in diseased coronary arteries cannot be assessed from hemodynamic measurements obtained distal to a stenosis. Wave speed inherently depends on arterial wall properties which should be similar proximal and distal to a stenosis. Our hypothesis is that proximal wave speed can be used to separate net wave intensity obtained distal to a stenosis.

Methods: We assessed coronary wave speed using the sum-of-squares single-point technique (SPc) based on simultaneous intracoronary pressure and flow velocity measurements in human coronary arteries. SPc at resting flow was determined in diseased coronary vessels of 12 patients both proximal and distal to the stenosis. In seven of these vessels, distal measurements were additionally obtained after revascularization by stent placement. SPc was also assessed at two axial locations in 14 reference vessels without a stenosis.

Results: (1) No difference in SPc was present between proximal and distal locations in the reference vessels. (2) In diseased vessels with a focal stenosis, SPc at the distal location was paradoxically larger than SPc proximal to the stenosis (28.4 ± 3.7 m/s vs. 18.3 ± 1.8 m/s, p < 0.02), despite the lower distending pressure downstream of the stenosis. The corresponding separated wave energy tended to be underestimated when derived from SPc at the distal compared with the proximal location. (3) After successful revascularization, SPc at the distal location no longer differed from SPc at the proximal location prior to revascularization (21.9 ± 2.0 m/s vs. 20.8 ± 1.9 m/s, p = 0.48). Accordingly, no significant difference in separated wave energy was observed for forward or backward waves.

Conclusion: In diseased coronary vessels, SPc assessed from distal hemodynamic signals is erroneously elevated. Our findings suggest that proximal wave speed can be used to separate wave intensity profiles obtained downstream of a stenosis. This approach may extend the application of wave intensity analysis to diseased coronary vessels.

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.

Acute Tachycardia Increases Aortic Distensibility, but Reduces Total Arterial Compliance Up to a Moderate Heart Rate

Background: The differential effects of rapid cardiac pacing on small and large vessels have not been well-established. The objective of this study was to investigate the effect of pacing-induced acute tachycardia on hemodynamics and arterial stiffness.

Methods: The pressure and flow waves in ascending aorta and femoral artery of six domestic swine were recorded simultaneously at baseline and heart rates (HR) of 135 and 155 beats per minutes (bpm) and analyzed by the models of Windkessel and Womersley types. Accordingly, the flow waves were simultaneously measured at carotid and femoral arteries to quantify aortic pulse wave velocity (PWV). The arterial distensibility was identified in small branches of coronary, carotid and femoral arteries with diameters of 300–600 μm by ex vivo experiments.

Results: The rapid pacing in HR up to 135 bpm reduced the total arterial compliance, stroke volume, systemic pulse pressure, and central systolic pressure by 36 ± 17, 38 ± 26, 29 ± 16, and 23 ± 12%, respectively, despite no statistical difference of mean aortic pressure, cardiac output, peripheral resistance, and vascular flow patterns. The pacing also resulted in a decrease of distensibility of small muscular arteries, but an increase of aortic distensibility. Pacing from 135 to 155 bpm had negligible effects on systemic and local hemodynamics and arterial stiffness.

Conclusions: There is an acute mismatch in the response of aorta and small arteries to pacing from basal HR to 135 bpm, which may have important pathological implications under chronic tachycardia conditions.

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.

Bifurcation Asymmetry of Small Coronary Arteries in Juvenile and Adult Mice

Background: Microvascular bifurcation asymmetry is of significance for regulation of coronary flow heterogeneity during juvenile and adult growth. The aim of the study is to investigate the morphometric and hemodynamic variation of coronary arterial bifurcations in mice of different ages.

Methods: Pulsatile blood flows were computed from a Womersley-type model in the reconstructed left coronary arterial (LCA) trees from Micro-CT images in normal mice at ages of 3 weeks, 6 weeks, 12 weeks, 5-6 months, and >8 months. Diameter and flow ratios and bifurcation angles were determined in each bifurcation of the LCA trees.

Results: The blood volume and inlet flow rate of LCA trees increase and decrease during juvenile and adult growth, respectively. As vessel diameters decrease, the increased ratios of small to large daughter vessel diameters (D_s/D_l) result in more uniform flows and lower velocities. There are significant structure-functional changes of LCA trees in mice of >8 months compared with mice of < 8 months. As D_s/D_l increases, the variation trend of bifurcation angle during juvenile growth is different from that during adult growth.

Conclusions: Although inlet flows are different in adult vs. juvenile mice, the adult still have uniform flow and low velocity. This is accomplished through a decrease in diameter. The design ensures ordered dispersion of red cells through asymmetric branching patterns into the capillaries.

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.

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.

Myocardial Perfusion: Characteristics of Distal Intramyocardial Arteriolar Trees

A combination of experimental, theoretical, and imaging methodologies is used to examine the hierarchical structure and function of intramyocardial arteriolar trees in porcine hearts to provide a window onto a region of myocardial microvasculature which has been difficult to fully explore so far. A total of 66 microvascular trees from 6 isolated myocardial specimens were analyzed, with a cumulative number of 2438 arteriolar branches greater than or equal to 40 μm lumen diameter. The distribution of flow rates within each tree was derived from an assumed power law relationship for that tree between the diameter of vessel segments and flow rates that are consistent with that power law and subject to conservation of mass along hierarchical structure of the tree. The results indicate that the power law index increases at levels of arteriolar vasculature closer to the capillary level, consistent with a concomitant decrease in shear stress acting on endothelial tissue. These results resolve a long standing predicament which could not be resolved previously because of lack of data about the 3D, interconnected, arterioles. In the context of myocardial perfusion, the results indicate that the coefficient of variation of flow rate in pre-capillary distal arterioles is high, suggesting that heterogeneity of flow rate in these arterioles is not entirely random but may be due at least in part to active control.

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.

Microsphere skimming in the porcine coronary arteries: Implications for flow quantification

Particle skimming is a phenomenon where particles suspended in fluid flowing through vessels distribute disproportionately to bulk fluid volume at junctions. Microspheres are considered a gold standard of intra-organ perfusion measurements and are used widely in studies of flow distribution and quantification. It has previously been hypothesised that skimming at arterial junctions is responsible for a systematic over-estimation of myocardial perfusion from microspheres at the subendocardium. Our objective is to integrate coronary arterial structure and microsphere distribution, imaged at high resolution, to test the hypothesis of microsphere skimming in a porcine left coronary arterial (LCA) network. A detailed network was reconstructed from cryomicrotome imaging data and a Poiseuille flow model was used to simulate flow. A statistical approach using Clopper-Pearson confidence intervals was applied to determine the prevalence of skimming at bifurcations in the LCA. Results reveal that microsphere skimming is most prevalent at bifurcations in the larger coronary arteries, namely the epicardial and transmural arteries. Bifurcations at which skimming was identified have significantly more asymmetric branching parameters. This finding suggests that when using thin transmural segments to quantify flow from microspheres, a skimming-related deposition bias may result in underestimation of perfusion in the subepicardium, and overestimation in the subendocardium.

The role of capillary transit time heterogeneity in myocardial oxygenation and ischemic heart disease

Ischemic heart disease (IHD) is characterized by an imbalance between oxygen supply and demand, most frequently caused by coronary artery disease (CAD) that reduces myocardial perfusion. In some patients, IHD is ascribed to microvascular dysfunction (MVD): microcirculatory disturbances that reduce myocardial perfusion at the level of myocardial pre-arterioles and arterioles. In a minority of cases, chest pain and reductions in myocardial flow reserve may even occur in patients without any other demonstrable systemic or cardiac disease. In this topical review, we address whether these findings might be caused by impaired myocardial oxygen extraction, caused by capillary flow disturbances further downstream. Myocardial blood flow (MBF) increases approximately linearly with oxygen utilization, but efficient oxygen extraction at high MBF values is known to depend on the parallel reduction of capillary transit time heterogeneity (CTH). Consequently, changes in capillary wall morphology or blood viscosity may impair myocardial oxygen extraction by preventing capillary flow homogenization. Indeed, a recent re-analysis of oxygen transport in tissue shows that elevated CTH can reduce tissue oxygenation by causing a functional shunt of oxygenated blood through the tissue. We review the combined effects of MBF, CTH, and tissue oxygen tension on myocardial oxygen supply. We show that as CTH increases, normal vasodilator responses must be attenuated in order to reduce the degree of functional shunting and improve blood-tissue oxygen concentration gradients to allow sufficient myocardial oxygenation. Theoretically, CTH can reach levels such that increased metabolic demands cannot be met, resulting in tissue hypoxia and angina in the absence of flow-limiting CAD or MVD. We discuss these predictions in the context of MVD, myocardial infarction, and reperfusion injury.

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.

Compensatory remodeling of coronary microvasculature maintains shear stress in porcine left-ventricular hypertrophy

BACKGROUND

Hypertension-induced left-ventricular hypertrophy (LVH) is generally accompanied with coronary neovascularization. The extent of vascular growth or rarefaction depends on many factors (e.g. age, duration of hypertension, degree of hypertrophy). Here, we hypothesize that there is a compensatory vascular growth that maintains uniform wall shear stress (WSS) in perfusion arterioles (diameters of 8-60 μm) in LVH of young porcine.

METHOD

To test this hypothesis, we investigated LVH in young porcine after 5 weeks of supravalvular aortic stenosis (3 months of age). The morphometry (diameters, lengths, number and connectivity of vessels) of the entire left circumflex (LCx) arterial tree was determined and a hemodynamic network analysis was used to calculate the distribution of pressure, flow and WSS throughout the tree in the control and LVH groups.

RESULTS

It was found that the number of vessels and the weight of left ventricle (LV) in hypertrophy increased 1.5 and 1.2 times, respectively, and the length of the LCx main trunk increased by 3 cm (36% increase), as compared with those in control group. There were similar myocardial blood flows of 0.87 ± 0.24 and 0.94 ± 0.38 ml/min per g in control and LVH hearts, respectively. The compensatory remodeling in early LVH restores WSS in the smaller perfusion arterioles, but not in the larger epicardial branches.

CONCLUSION

The present findings quantify the structural and functional remodeling in the entire LCx arterial tree in response to LVH, which reflect heterogeneity in vascular morphometry and hemodynamics from small to large vessels. These conclusions enhance our understanding of compensatory vascular remodeling in LVH of pediatric heart.

Multiscale imaging and computational modeling of blood flow in the tumor vasculature

The evolution in our understanding of tumor angiogenesis has been the result of pioneering imaging and computational modeling studies spanning the endothelial cell, microvasculature and tissue levels. Many of these primary data on the tumor vasculature are in the form of images from pre-clinical tumor models that provide a wealth of qualitative and quantitative information in many dimensions and across different spatial scales. However, until recently, the visualization of changes in the tumor vasculature across spatial scales remained a challenge due to a lack of techniques for integrating micro- and macroscopic imaging data. Furthermore, the paucity of three-dimensional (3-D) tumor vascular data in conjunction with the challenges in obtaining such data from patients presents a serious hurdle for the development and validation of predictive, multiscale computational models of tumor angiogenesis. In this review, we discuss the development of multiscale models of tumor angiogenesis, new imaging techniques capable of reproducing the 3-D tumor vascular architecture with high fidelity, and the emergence of "image-based models" of tumor blood flow and molecular transport. Collectively, these developments are helping us gain a fundamental understanding of the cellular and molecular regulation of tumor angiogenesis that will benefit the development of new cancer therapies. Eventually, we expect this exciting integration of multiscale imaging and mathematical modeling to have widespread application beyond the tumor vasculature to other diseases involving a pathological vasculature, such as stroke and spinal cord injury.

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.

Effect of blood pressure on vascular hemodynamics in acute tachycardia

Paroxysmal supraventricular tachycardia is accompanied by hypotension, which can affect vascular hemodynamics. Here, we hypothesized that a fall in blood flow as a result of hypotension has a larger effect on hemodynamics in medium-sized peripheral arteries compared with increased pulsatility in rapid pacing. To test this hypothesis, we experimentally and theoretically investigated hemodynamic changes in femoral, carotid, and subclavian arteries at heart rates of 95-170 beats/min after acute pacing. The arterial pressure, blood flow, and other hemodynamic parameters remained statistically unchanged for heart rates ≤ 135 beats/min. Systemic pressure and flow velocities, however, showed an abrupt decrease, resulting in larger alteration of hemodynamic parameters for heart rates ≥ 155 beats/min after pacing (initial period) and then recovered close to baseline after several minutes of pacing (recovery period). During the initial period, the pressure dropped from 88 mmHg (baseline) to 44 mmHg, and the flow velocity decreased to about one-third of baseline at heart rate of 170 beats/min. A hemodynamic analysis showed a velocity profile with a near-wall retrograde flow or a fully reversed flow during the initial period, which vanished at the recovery period. It was concluded that the initial fall of blood flow due to pressure drop led to transient flow reversal and negative wall shear stress because this phenomena was not observed at the recovery period. This study underscores the significant effects of hypotension on vascular hemodynamics, which may have relevance to physiology and chronic pathophysiology in paroxysmal supraventricular tachycardia.

Extraction of morphometry and branching angles of porcine coronary arterial tree from CT images

The morphometry (diameters, length, and angles) of coronary arteries is related to their function. A simple, easy, and accurate image-based method to seamlessly extract the morphometry for coronary arteries is of significant value for understanding the structure-function relation. Here, the morphometry of large (> or = 1 mm in diameter) coronary arteries was extracted from computed tomography (CT) images using a recently validated segmentation algorithm. The coronary arteries of seven pigs were filled with Microfil, and the cast hearts were imaged with CT. The centerlines of the extracted vessels, the vessel radii, and the vessel lengths were identified for over 700 vessel segments. The extraction algorithm was based on a topological analysis of a vector field generated by normal vectors of the extracted vessel wall. The diameters, lengths, and angles of the right coronary artery, left anterior descending coronary artery, and left circumflex artery of all vessels > or = 1 mm in diameter were tabulated for the respective orders. It was found that bifurcations at orders 9-11 are planar ( approximately 90%). The relations between volume and length and area and length were also examined and found to scale as power laws. Furthermore, the bifurcation angles follow the minimum energy hypothesis but with significant scatter. Some of the applications of the semiautomated extraction of morphometric data in applications to coronary physiology and pathophysiology are highlighted.