The mechanical and metabolic basis of myocardial blood flow heterogeneity

Integrated modeling and simulation of recruitment of myocardial perfusion and oxygen delivery in exercise

While exercise-mediated vasoregulation in the myocardium is understood to be governed by autonomic, myogenic, and metabolic-mediated mechanisms, we do not yet understand the spatial heterogeneity of vasodilation or its effects on microvascular flow patterns and oxygen delivery. This study uses a simulation and modeling approach to explore the mechanisms underlying the recruitment of myocardial perfusion and oxygen delivery in exercise. The simulation approach integrates model components representing: whole-body cardiovascular hemodynamics, cardiac mechanics and myocardial work; myocardial perfusion; and myocardial oxygen transport. Integrating these systems together, model simulations reveal: (1.) To match expected flow and transmural flow ratios at increasing levels of exercise, a greater degree of vasodilation must occur in the subendocardium compared to the subepicardium. (2.) Oxygen extraction and venous oxygenation are predicted to substantially decrease with increasing exercise level preferentially in the subendocardium, suggesting that an oxygen-dependent error signal driving metabolic mediated recruitment of flow would be operative only in the subendocardium. (3.) Under baseline physiological conditions approximately 4% of the oxygen delivered to the subendocardium may be supplied via retrograde flow from coronary veins.

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.

Oxygen-sensing pathways below autoregulatory threshold act to sustain myocardial oxygen delivery during reductions in perfusion pressure

The coronary circulation has an innate ability to maintain constant blood flow over a wide range of perfusion pressures. However, the mechanisms responsible for coronary autoregulation remain a fundamental and highly contested question. This study interrogated the local metabolic hypothesis of autoregulation by testing the hypothesis that hypoxemia-induced exaggeration of the metabolic error signal improves the autoregulatory response. Experiments were performed on open-chest anesthetized swine during stepwise changes in coronary perfusion pressure (CPP) from 140 to 40 mmHg under normoxic (n = 15) and hypoxemic (n = 8) conditions, in the absence and presence of dobutamine-induced increases in myocardial oxygen consumption (MVO2) (n = 5-7). Hypoxemia (PaO2 < 40 mmHg) decreased coronary venous PO2 (CvPO2) ~ 30% (P < 0.001) and increased coronary blood flow ~ 100% (P < 0.001), sufficient to maintain myocardial oxygen delivery (P = 0.14) over a wide range of CPPs. Autoregulatory responsiveness during hypoxemia-induced reductions in CvPO2 were associated with increases of autoregulatory gain (Gc; P = 0.033) but not slope (P = 0.585) over a CPP range of 120 to 60 mmHg. Preservation of autoregulatory Gc (P = 0.069) and slope (P = 0.264) was observed during dobutamine administration ± hypoxemia. Reductions in coronary resistance in response to decreases in CPP predominantly occurred below CvPO2 values of ~ 25 mmHg, irrespective of underlying vasomotor reserve. These findings support the presence of an autoregulatory threshold under which oxygen-sensing pathway(s) act to preserve sufficient myocardial oxygen delivery as CPP is reduced during increases in MVO2 and/or reductions in arterial oxygen content.

Fractal Analysis of Dynamic Stress CT-Perfusion Imaging for Detection of Hemodynamically Relevant Coronary Artery Disease

BACKGROUND

Combined computed tomography-derived myocardial blood flow (CTP-MBF) and computed tomography angiography (CTA) has shown good diagnostic performance for detection of coronary artery disease (CAD). However, fractal analysis might provide additional insight into ischemia pathophysiology by characterizing multiscale perfusion patterns and, therefore, may be useful in diagnosing hemodynamically significant CAD.

OBJECTIVES

The purpose of this study was to investigate, in a multicenter setting, whether fractal analysis of perfusion improves detection of hemodynamically relevant CAD over myocardial blood flow quantification (CTP-MBF) using dynamic, 4-dimensional, dynamic stress myocardial computed tomography perfusion (CTP) imaging.

METHODS

In total, 7 centers participating in the prospective AMPLIFiED (Assessment of Myocardial Perfusion Linked to Infarction and Fibrosis Explored with Dual-source CT) study acquired CTP and CTA data in patients with suspected or known CAD. Hemodynamically relevant CAD was defined as ≥90% stenosis on invasive coronary angiography or fractional flow reserve <0.80. Both fractal analysis and CTP-MBF quantification were performed on CTP images and were combined with CTA results.

RESULTS

This study population included 127 participants, among them 61 patients, or 79 vessels, with CAD as per invasive reference standard. Compared with the combination of CTP-MBF and CTA, combined fractal analysis and CTA improved sensitivity on the per-patient level from 84% (95% CI: 72%-92%) to 95% (95% CI: 86%-99%; P = 0.01) and specificity from 70% (95% CI: 57%-82%) to 89% (95% CI: 78%-96%; P = 0.02). The area under the receiver-operating characteristic curve improved from 0.83 (95% CI: 0.75-0.90) to 0.92 (95% CI: 0.86-0.98; P = 0.01).

CONCLUSIONS

Fractal analysis constitutes a quantitative and pathophysiologically meaningful approach to myocardial perfusion analysis using dynamic stress CTP, which improved diagnostic performance over CTP-MBF when combined with anatomical information from CTA.

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

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

Fractal analysis of 4D dynamic myocardial stress-CT perfusion imaging differentiates micro- and macrovascular ischemia in a multi-center proof-of-concept study

Fractal analysis of dynamic, four-dimensional computed tomography myocardial perfusion (4D-CTP) imaging might have potential for noninvasive differentiation of microvascular ischemia and macrovascular coronary artery disease (CAD) using fractal dimension (FD) as quantitative parameter for perfusion complexity. This multi-center proof-of-concept study included 30 rigorously characterized patients from the AMPLIFiED trial with nonoverlapping and confirmed microvascular ischemia (n_micro = 10), macrovascular CAD (n_macro = 10), or normal myocardial perfusion (n_normal = 10) with invasive coronary angiography and fractional flow reserve (FFR) measurements as reference standard. Perfusion complexity was comparatively high in normal perfusion (FD_normal = 4.49, interquartile range [IQR]:4.46-4.53), moderately reduced in microvascular ischemia (FD_micro = 4.37, IQR:4.36-4.37), and strongly reduced in macrovascular CAD (FD_macro = 4.26, IQR:4.24-4.27), which allowed to differentiate both ischemia types, p < 0.001. Fractal analysis agreed excellently with perfusion state (κ = 0.96, AUC = 0.98), whereas myocardial blood flow (MBF) showed moderate agreement (κ = 0.77, AUC = 0.78). For detecting CAD patients, fractal analysis outperformed MBF estimation with sensitivity and specificity of 100% and 85% versus 100% and 25%, p = 0.02. In conclusion, fractal analysis of 4D-CTP allows to differentiate microvascular from macrovascular ischemia and improves detection of hemodynamically significant CAD in comparison to MBF estimation.

Prediction of prostate cancer grade using fractal analysis of perfusion MRI: retrospective proof-of-principle study

OBJECTIVES

Multiparametric MRI has high diagnostic accuracy for detecting prostate cancer, but non-invasive prediction of tumor grade remains challenging. Characterizing tumor perfusion by exploiting the fractal nature of vascular anatomy might elucidate the aggressive potential of a tumor. This study introduces the concept of fractal analysis for characterizing prostate cancer perfusion and reports about its usefulness for non-invasive prediction of tumor grade.

METHODS

We retrospectively analyzed the openly available PROSTATEx dataset with 112 cancer foci in 99 patients. In all patients, histological grading groups specified by the International Society of Urological Pathology (ISUP) were obtained from in-bore MRI-guided biopsy. Fractal analysis of dynamic contrast-enhanced perfusion MRI sequences was performed, yielding fractal dimension (FD) as quantitative descriptor. Two-class and multiclass diagnostic accuracy was analyzed using area under the curve (AUC) receiver operating characteristic analysis, and optimal FD cutoffs were established. Additionally, we compared fractal analysis to conventional apparent diffusion coefficient (ADC) measurements.

RESULTS

Fractal analysis of perfusion allowed accurate differentiation of non-significant (group 1) and clinically significant (groups 2-5) cancer with a sensitivity of 91% (confidence interval [CI]: 83-96%) and a specificity of 86% (CI: 73-94%). FD correlated linearly with ISUP groups (r² = 0.874, p < 0.001). Significant groupwise differences were obtained between low, intermediate, and high ISUP group 1-4 (p ≤ 0.001) but not group 5 tumors. Fractal analysis of perfusion was significantly more reliable than ADC in predicting non-significant and clinically significant cancer (AUC_FD = 0.97 versus AUC_ADC = 0.77, p < 0.001).

CONCLUSION

Fractal analysis of perfusion MRI accurately predicts prostate cancer grading in low-, intermediate-, and high-, but not highest-grade, tumors.

KEY POINTS

• In 112 prostate carcinomas, fractal analysis of MR perfusion imaging accurately differentiated low-, intermediate-, and high-grade cancer (ISUP grade groups 1-4). • Fractal analysis detected clinically significant prostate cancer with a sensitivity of 91% (83-96%) and a specificity of 86% (73-94%). • Fractal dimension of perfusion at the tumor margin may provide an imaging biomarker to predict prostate cancer grading.

Therapeutic Hypothermia Reduces Peritoneal Dialysis Induced Myocardial Blood Flow Heterogeneity and Arrhythmia

Background: Moderate therapeutic hypothermia (TH) is a well-recognized cardio-protective strategy. The instillation of fluid into the peritoneum provides an opportunity to deliver moderate hypothermia as primary prevention against cardiovascular events. We aimed to to investigate both cardiac perfusion consequences (overall blood flow and detailed assessment of perfusion heterogeneity) and subsequently simulate the associated arrhythmic risk for patients undergoing peritoneal dialysis (PD) induced TH. Methods: Patients underwent high resolution myocardial perfusion scanning using high resolution 256 slice CT scanning, at rest and with adenosine stress. The first visit using the patient's usual PD regimen, on the second visit the same regime was utilized but with cooled peritoneal dialysate at 32°C. Myocardial blood flow (MBF) was quantified from generated perfusion maps, reconstructed in 3D. MBF heterogeneity was assessed by fractal dimension (FD) measurement on the 3D left ventricular reconstruction. Arrhythmogenicity was quantified from a sophisticated computational simulation using a multi-scale human 3D ventricle wedge electrophysiological computational model. Results: We studied 7 PD patients, mean age of 60 ± 7 and mean vintage dialysis of 23.6 ± 17.6 months. There were no significant different in overall segmental MBF between normothermic condition (NT) and TH. MBF heterogeneity was significantly decreased (-14%, p = 0.03) at rest and after stress (-14%, p = 0.03) when cooling was applied. Computational simulation showed that TH allowed a normalization of action potential, QT duration and T wave. Conclusion: TH-PD results in moderate hypothermia leading to a reduction in perfusion heterogeneity and simulated risk of non-terminating malignant ventricular arrhythmias.

Development of Novel Fractal Method for Characterizing the Distribution of Blood Flow in Multi-Scale Vascular Tree

Blood perfusion is an important index for the function of the cardiovascular system and it can be indicated by the blood flow distribution in the vascular tree. As the blood flow in a vascular tree varies in a large range of scales and fractal analysis owns the ability to describe multi-scale properties, it is reasonable to apply fractal analysis to depict the blood flow distribution. The objective of this study is to establish fractal methods for analyzing the blood flow distribution which can be applied to real vascular trees. For this purpose, the modified methods in fractal geometry were applied and a special strategy was raised to make sure that these methods are applicable to an arbitrary vascular tree. The validation of the proposed methods on real arterial trees verified the ability of the produced parameters (fractal dimension and multifractal spectrum) in distinguishing the blood flow distribution under different physiological states. Furthermore, the physiological significance of the fractal parameters was investigated in two situations. For the first situation, the vascular tree was set as a perfect binary tree and the blood flow distribution was adjusted by the split ratio. As the split ratio of the vascular tree decreases, the fractal dimension decreases and the multifractal spectrum expands. The results indicate that both fractal parameters can quantify the degree of blood flow heterogeneity. While for the second situation, artificial vascular trees with different structures were constructed and the hemodynamics in these vascular trees was simulated. The results suggest that both the vascular structure and the blood flow distribution affect the fractal parameters for blood flow. The fractal dimension declares the integrated information about the heterogeneity of vascular structure and blood flow distribution. In contrast, the multifractal spectrum identifies the heterogeneity features in blood flow distribution or vascular structure by its width and height. The results verified that the proposed methods are capable of depicting the multi-scale features of the blood flow distribution in the vascular tree and further are potential for investigating vascular physiology.

Fractal analysis of the ischemic transition region in chronic ischemic heart disease using magnetic resonance imaging

OBJECTIVES

To introduce a novel hypothesis and method to characterise pathomechanisms underlying myocardial ischemia in chronic ischemic heart disease by local fractal analysis (FA) of the ischemic myocardial transition region in perfusion imaging.

METHODS

Vascular mechanisms to compensate ischemia are regulated at various vascular scales with their superimposed perfusion pattern being hypothetically self-similar. Dedicated FA software ("FraktalWandler") has been developed. Fractal dimensions during first-pass (FD_first-pass) and recirculation (FD_{recirculation}) are hypothesised to indicate the predominating pathomechanism and ischemic severity, respectively.

RESULTS

Twenty-six patients with evidence of myocardial ischemia in 108 ischemic myocardial segments on magnetic resonance imaging (MRI) were analysed. The 40th and 60th percentiles of FD_first-pass were used for pathomechanical classification, assigning lesions with FD_first-pass ≤ 2.335 to predominating coronary microvascular dysfunction (CMD) and ≥2.387 to predominating coronary artery disease (CAD). Optimal classification point in ROC analysis was FD_first-pass = 2.358. FD_{recirculation} correlated moderately with per cent diameter stenosis in invasive coronary angiography in lesions classified CAD (r = 0.472, p = 0.001) but not CMD (r = 0.082, p = 0.600).

CONCLUSIONS

The ischemic transition region may provide information on pathomechanical composition and severity of myocardial ischemia. FA of this region is feasible and may improve diagnosis compared to traditional noninvasive myocardial perfusion analysis.

KEY POINTS

• A novel hypothesis and method is introduced to pathophysiologically characterise myocardial ischemia. • The ischemic transition region appears a meaningful diagnostic target in perfusion imaging. • Fractal analysis may characterise pathomechanical composition and severity of myocardial ischemia.

Myocardial Po2 does not limit aerobic metabolism in the postischemic heart

Reperfused hypertrophic hearts are prone to develop reflow abnormalities, which are likely to impair O2 return to the myocardium. Yet, reflow deficit may not be the only factor determining postischemic oxygenation in the hypertrophic heart. Altered O2 demand may also contribute to hypoxia. In addition, the extent to which myocardial Po2 dictates energy and functional recovery in the reperfused heart remains uncertain. In the present study, moderately hypertrophied hearts from spontaneously hypertensive rats were subjected to ischemia-reperfusion, and the recovery time courses of pH and high-energy phosphates were followed by (31)P NMR. (1)H NMR measurement of intracellular myoglobin assessed tissue O2 levels. The present study found that the exacerbation of hypoxia in the postischemic spontaneously hypertensive rat heart arises mostly from impaired microvascular supply of O2. However, postischemic myocardial Po2, at least when it exceeds ∼18% of the preischemic level, does not limit mitochondrial respiration and high-energy phosphate resynthesis. It only passively reflects changes in the O2 supply-demand balance.

Normal range and regional heterogeneity of myocardial perfusion in healthy human myocardium: assessment on dynamic perfusion CT using 128-slice dual-source CT

Information about myocardial perfusion in healthy hearts is essential for evaluating patients with ischemic heart disease. The purpose of this study was to determine the range and regional variability of myocardial perfusion in normal volunteers on dynamic perfusion computed tomography (CT). Myocardial perfusion was assessed in 19 healthy volunteers (age 33-60 years; 11 men) at rest and during adenosine-induced hyperemia using a 128-slice dual-source CT scanner. Data were quantified as cc/cc/min for the transmural myocardium based on a 17-segment American Heart Association model. Mean myocardial blood flows (MBF) were 1.73 ± 0.33 cc/cc/min during adenosine-induced hyperemia, 0.83 ± 0.21 cc/cc/min at rest, and perfusion reserve was 2.20 ± 0.53. Regional variability was 17 ± 5% for hyperemic perfusion, 18 ± 7% for resting, and 21 ± 6 % for perfusion reserve. Although statistically insignificant, perfusion in the septum was lower at rest and during hyperemia than in other regions. Women tended to have lower perfusion during hyperemia (1.65 ± 0.40 vs. 1.79 ± 0.28 cc/cc/min, P = 0.40), and higher perfusion at rest than men (0.91 ± 0.27 vs. 0.77 ± 0.15 cc/cc/min, P = 0.23), resulting in lower perfusion reserve (1.86 ± 0.31 vs. 2.45 ± 0.53, P = 0.11). This small cohort of healthy volunteers study reveals normal myocardial perfusion parameter on dynamic perfusion CT as follows: mean MBF is 1.73 ± 0.33 cc/cc/min during hyperemia, 0.83 ± 0.21 cc/cc/min at rest, and perfusion reserve is 2.20 ± 0.53. And the study also demonstrates considerable regional heterogeneity of the myocardial perfusion.

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.

Left-ventricular shape determines intramyocardial mechanical heterogeneity

Left-ventricular remodeling is considered to be an important mechanism of disease progression leading to mechanical dysfunction of the heart. However, the interaction between the physiological changes in the remodeling process and the associated mechanical dysfunction is still poorly understood. Clinically, it has been observed that the left ventricle often undergoes large shape changes, but the importance of left-ventricular shape as a contributing factor to alterations in mechanical function has not been clearly determined. Therefore, the interaction between left-ventricular shape and systolic mechanical function was examined in a computational finite-element study. Hereto, finite-element models were constructed with varying shapes, ranging from an elongated ellipsoid to a sphere. A realistic transmural gradient in fiber orientation was considered. The passive myocardium was described by an incompressible hyperelastic material law with transverse isotropic symmetry. Activation was governed by the eikonal-diffusion equation. Contraction was incorporated using a Hill model. For each shape, simulations were performed in which passive filling was followed by isovolumic contraction and ejection. It was found that the intramyocardial distributions of fiber stress, strain, and stroke work density were shape dependent. Ejection performance was reduced with increasing sphericity, which was regionally related to a reduction in the active fiber stress development, fiber shortening, and stroke work in the midwall and subepicardial region at the midheight level in the left-ventricular wall. Based on these results, we conclude that a significant interaction exists between left-ventricular shape and regional myofiber mechanics, but the importance for left-ventricular remodeling requires further investigation.

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.

Biophysical model of the spatial heterogeneity of myocardial flow

The blood flow in the myocardium has significant spatial heterogeneity. The objective of this study was to develop a biophysical model based on detailed anatomical data to determine the heterogeneity of regional myocardial flow during diastole. The model predictions were compared with experimental measurements in a diastolic porcine heart in the absence of vessel tone using nonradioactive fluorescent microsphere measurements. The results from the model and experimental measurements showed good agreement. The relative flow dispersion in the arrested, vasodilated heart was found to be 44% and 48% numerically and experimentally, respectively. Furthermore, the flow dispersion was found to have fractal characteristics with fractal dimensions (D) of 1.25 and 1.27 predicted by the model and validated by the experiments, respectively. This validated three-dimensional model of normal diastolic heart will play an important role in elucidating the spatial heterogeneity of coronary blood flow, and serve as a foundation for understanding the interplay between cardiac mechanics and coronary hemodynamics.

Origins of heterogeneity in tissue perfusion and metabolism

AIMS

In the heart and other tissues, perfusion and metabolic activity are heterogeneous and spatially correlated. The goal of this work is to investigate the causes of this behaviour. Theoretical simulations are used to examine the effects on flow distribution and oxygen levels in terminal vascular beds of inherent irregularity in network structure, considering structural adaptation of vessel diameters to haemodynamic and metabolic stimuli, and adaptation of oxygen demand to local oxygen availability.

METHODS AND RESULTS

A mathematical model based on experimentally observed microvascular network structures (rat mesentery and m. sartorius) is used to simulate blood flow, oxygen transport, and adaptation of vessel diameters and tissue oxygen demand. Inherent geometric heterogeneities of vascular networks cause heterogeneity of blood flow and oxygen levels that cannot be eliminated by increasing metabolic sensitivity of diameter adaptation. Adaptation of oxygen demand to differences in oxygen availability causes increased oxygen extraction, implying improved functional capacity, and establishes a correlation between local oxygen demand and flow rate, as observed experimentally. Such a correlation is not predicted if the heterogeneity of oxygen demand is assumed to be an intrinsic tissue property.

CONCLUSION

A central mechanism generating heterogeneous perfusion is the inevitable structural heterogeneity of terminal vascular beds, which cannot be fully compensated by structural adaptation of vessel diameters. Heterogeneity of metabolism may result from adaptation of tissue function to the heterogeneous oxygen availability. These findings are of interest for the understanding of tissue function, including the heart, and of results obtained by corresponding imaging approaches.

Computational biology of cardiac myocytes: proposed standards for the physiome

Predicting information about human physiology and pathophysiology from genomic data is a compelling, but unfulfilled goal of post-genomic biology. This is the aim of the so-called Physiome Project and is, undeniably, an ambitious goal. Yet if we can exploit even a small proportion of the rich and varied experimental data currently available, significant insights into clinically important aspects of human physiology will follow. To achieve this requires the integration of data from disparate sources into a common framework. Extrapolation of available data across species, laboratory techniques and conditions requires a quantitative approach. Mathematical models allow us to integrate molecular information into cellular, tissue and organ-level, and ultimately clinically relevant scales. In this paper we argue that biophysically detailed computational modelling provides the essential tool for this process and, furthermore, that an appropriate framework for annotating, databasing and critiquing these models will be essential for the development of integrative computational biology.

Regional sympathetic denervation affects the relation between canine local myocardial blood flow and oxygen consumption

Myocardial blood flow and oxygen consumption are heterogeneously distributed. Perfusion and myocardial oxygen consumption are closely correlated in the normal heart. It is unknown how this metabolism-perfusion relation is influenced by sympathetic denervation. We investigated this question in seven chloralose-anaesthetized dogs, 3-4 weeks after regional sympathetic denervation of the left circumflex coronary artery area of supply of the left ventricle. Measurements were made of local myocardial blood flow (MBF, in ml min(-1) (g dry wt)(-1)), measured with microspheres, and myocardial oxygen consumption ( , in mumol min(-1) (g dry wt)(-1)) in the same location, calculated from the (13)C spectrum of tissue extracts after intracoronary infusion of 3-(13)C-lactate. Since both innervated and denervated regions are subject to the same arterial pressure, lower blood flow indicates higher resistance. Mean MBF was 5.56 ml min(-1) (g dry wt)(-1) (heterogeneity of 3.47 ml min(-1) (g dry wt)(-1)) innervated, 7.48 ml min(-1) (g dry wt)(-1) (heterogeneity of 3.62 ml min(-1) (g dry wt)(-1)) denervated (n.s.). Significant linear relations were found between MBF and M Vo2 of individual samples within the innervated and denervated regions. The slopes of these relations were not significantly different, but the adjusted mean was significantly higher in the denervated regions (+1.92 ml min(-1) (g dry wt)(-1), an increase of 38% of the mean MBF at the pooled mean M Vo2, P = 0.028, ANCOVA). The ratio MBF/M Vo2(in ml micromol(-1)) was significantly higher, being 0.296 +/- 0.167 ml micromol(-1) in the denervated region compared with the innervated region, 0.216 +/- 0.126 ml micromol(-1), P = 0.0182, Mann-Whitney U test. These results indicate that sympathetic tone under chloralose anaesthesia imposes a moderate vasoconstrictive effect in the myocardium that is not detected by comparison of the mean blood flow or resistance.

Dependence of intramyocardial pressure and coronary flow on ventricular loading and contractility: a model study

The phasic coronary arterial inflow during the normal cardiac cycle has been explained with simple (waterfall, intramyocardial pump) models, emphasizing the role of ventricular pressure. To explain changes in isovolumic and low afterload beats, these models were extended with the effect of three-dimensional wall stress, nonlinear characteristics of the coronary bed, and extravascular fluid exchange. With the associated increase in the number of model parameters, a detailed parameter sensitivity analysis has become difficult. Therefore we investigated the primary relations between ventricular pressure and volume, wall stress, intramyocardial pressure and coronary blood flow, with a mathematical model with a limited number of parameters. The model replicates several experimental observations: the phasic character of coronary inflow is virtually independent of maximum ventricular pressure, the amplitude of the coronary flow signal varies about proportionally with cardiac contractility, and intramyocardial pressure in the ventricular wall may exceed ventricular pressure. A parameter sensitivity analysis shows that the normalized amplitude of coronary inflow is mainly determined by contractility, reflected in ventricular pressure and, at low ventricular volumes, radial wall stress. Normalized flow amplitude is less sensitive to myocardial coronary compliance and resistance, and to the relation between active fiber stress, time, and sarcomere shortening velocity.

Cross-Talk Between Cardiac Muscle and Coronary Vasculature

The cardiac muscle and the coronary vasculature are in close proximity to each other, and a two-way interaction, called cross-talk, exists. Here we focus on the mechanical aspects of cross-talk including the role of the extracellular matrix. Cardiac muscle affects the coronary vasculature. In diastole, the effect of the cardiac muscle on the coronary vasculature depends on the (changes in) muscle length but appears to be small. In systole, coronary artery inflow is impeded, or even reversed, and venous outflow is augmented. These systolic effects are explained by two mechanisms. The waterfall model and the intramyocardial pump model are based on an intramyocardial pressure, assumed to be proportional to ventricular pressure. They explain the global effects of contraction on coronary flow and the effects of contraction in the layers of the heart wall. The varying elastance model, the muscle shortening and thickening model, and the vascular deformation model are based on direct contact between muscles and vessels. They predict global effects as well as differences on flow in layers and flow heterogeneity due to contraction. The relative contributions of these two mechanisms depend on the wall layer (epi- or endocardial) and type of contraction (isovolumic or shortening). Intramyocardial pressure results from (local) muscle contraction and to what extent the interstitial cavity contracts isovolumically. This explains why small arterioles and venules do not collapse in systole. Coronary vasculature affects the cardiac muscle. In diastole, at physiological ventricular volumes, an increase in coronary perfusion pressure increases ventricular stiffness, but the effect is small. In systole, there are two mechanisms by which coronary perfusion affects cardiac contractility. Increased perfusion pressure increases microvascular volume, thereby opening stretch-activated ion channels, resulting in an increased intracellular Ca2+transient, which is followed by an increase in Ca2+sensitivity and higher muscle contractility (Gregg effect). Thickening of the shortening cardiac muscle takes place at the expense of the vascular volume, which causes build-up of intracellular pressure. The intracellular pressure counteracts the tension generated by the contractile apparatus, leading to lower net force. Therefore, cardiac muscle contraction is augmented when vascular emptying is facilitated. During autoregulation, the microvasculature is protected against volume changes, and the Gregg effect is negligible. However, the effect is present in the right ventricle, as well as in pathological conditions with ineffective autoregulation. The beneficial effect of vascular emptying may be reduced in the presence of a stenosis. Thus cardiac contraction affects vascular diameters thereby reducing coronary inflow and enhancing venous outflow. Emptying of the vasculature, however, enhances muscle contraction. The extracellular matrix exerts its effect mainly on cardiac properties rather than on the cross-talk between cardiac muscle and coronary circulation.

Nitric oxide and prostaglandins influence local skeletal muscle blood flow during exercise in humans: coupling between local substrate uptake and blood flow

Synergic action of nitric oxide (NO) and prostaglandins (PG) in the regulation of muscle blood flow during exercise has been demonstrated. In the present study, we investigated whether these vasodilators also regulate local blood flow, flow heterogeneity, and glucose uptake within the exercising skeletal muscle. Skeletal muscle blood flow was measured in seven healthy young men using near-infrared spectroscopy and indocyanine green and muscle glucose uptake using positron emission tomography and 2-fluoro-2-deoxy-d-[18F]glucose without and with local blockade of NO and PG at rest and during one-legged dynamic knee-extension exercise. Local blockade was produced by infusing nitro-l-arginine methyl ester and indomethacin directly in the muscle via a microdialysis catheter. Blood flow and glucose uptake were measured in the region of blockade and in two additional regions of vastus lateralis muscle 1 and 4 cm away from the infusion of blockers. Local blockade during exercise at 25 and 40 watts significantly decreased blood flow in the infusion region and in the region 1 cm away from the site of infusion but not in the region 4 cm away. During exercise, muscle glucose uptake did not show any regional differences in response to blockade. These results show that NO and PG synergistically contribute to the local regulation of blood flow in skeletal muscle independently of muscle glucose uptake in healthy young men. Thus these vasodilators can play a role in regulating microvascular blood flow in localized regions of vastus lateralis muscle but do not influence regional glucose uptake. The findings suggest that local substrate uptake in skeletal muscle can be regulated independently of regional changes in blood flow.

Modeling of oxygen transport and cellular energetics explains observations on in vivo cardiac energy metabolism

Observations on the relationship between cardiac work rate and the levels of energy metabolites adenosine triphosphate (ATP), adenosine diphosphate (ADP), and phosphocreatine (CrP) have not been satisfactorily explained by theoretical models of cardiac energy metabolism. Specifically, the in vivo stability of ATP, ADP, and CrP levels in response to changes in work and respiratory rate has eluded explanation. Here a previously developed model of mitochondrial oxidative phosphorylation, which was developed based on data obtained from isolated cardiac mitochondria, is integrated with a spatially distributed model of oxygen transport in the myocardium to analyze data obtained from several laboratories over the past two decades. The model includes the components of the respiratory chain, the F₀F₁-ATPase, adenine nucleotide translocase, and the mitochondrial phosphate transporter at the mitochondrial level; adenylate kinase, creatine kinase, and ATP consumption in the cytoplasm; and oxygen transport between capillaries, interstitial fluid, and cardiomyocytes. The integrated model is able to reproduce experimental observations on ATP, ADP, CrP, and inorganic phosphate levels in canine hearts over a range of workload and during coronary hypoperfusion and predicts that cytoplasmic inorganic phosphate level is a key regulator of the rate of mitochondrial respiration at workloads for which the rate of cardiac oxygen consumption is less than or equal to approximately 12 μmol per minute per gram of tissue. At work rates corresponding to oxygen consumption higher than 12 μmol min⁻¹ g⁻¹, model predictions deviate from the experimental data, indicating that at high work rates, additional regulatory mechanisms that are not currently incorporated into the model may be important. Nevertheless, the integrated model explains metabolite levels observed at low to moderate workloads and the changes in metabolite levels and tissue oxygenation observed during graded hypoperfusion. These findings suggest that the observed stability of energy metabolites emerges as a property of a properly constructed model of cardiac substrate transport and mitochondrial metabolism. In addition, the validated model provides quantitative predictions of changes in phosphate metabolites during cardiac ischemia.

To function properly over a range of work rates, the heart must maintain its metabolic energy level within a range that is narrow relative to changes in the rate of energy utilization. Decades of observations have revealed that in cardiac muscle cells, the supply of adenosine triphosphate (ATP)—the primary currency of intracellular energy transfer—is controlled to maintain intracellular concentrations of ATP and related compounds within narrow ranges. Yet the development of a mechanistic understanding of this tight control has lagged behind experimental observation. This paper introduces a computational model that links ATP synthesis in a subcellular body called the mitochondrion with ATP utilization in the cytoplasm, and reveals that the primary control mechanism operating in the system is feedback of substrate concentrations for ATP synthesis. In other words, changes in the concentrations of the products generated by the utilization of ATP in the cell (adenosine diphosphate and inorganic phosphate) effect changes in the rate at which mitochondria utilize those products to resynthesize ATP.

Simultaneous blood-tissue exchange of oxygen, carbon dioxide, bicarbonate, and hydrogen ion

A detailed nonlinear four-region (red blood cell, plasma, interstitial fluid, and parenchymal cell) axially distributed convection-diffusion-permeation-reaction-binding computational model is developed to study the simultaneous transport and exchange of oxygen (O2) and carbon dioxide (CO2) in the blood-tissue exchange system of the heart. Since the pH variation in blood and tissue influences the transport and exchange of O2 and CO2 (Bohr and Haldane effects), and since most CO2 is transported as HCO3(-) (bicarbonate) via the CO2 hydration (buffering) reaction, the transport and exchange of HCO3(-) and H+ are also simulated along with that of O2 and CO2. Furthermore, the model accounts for the competitive nonlinear binding of O2 and CO2 with the hemoglobin inside the red blood cells (nonlinear O2-CO2 interactions, Bohr and Haldane effects), and myoglobin-facilitated transport of O2 inside the parenchymal cells. The consumption of O2 through cytochrome-c oxidase reaction inside the parenchymal cells is based on Michaelis-Menten kinetics. The corresponding production of CO2 is determined by respiratory quotient (RQ), depending on the relative consumption of carbohydrate, protein, and fat. The model gives a physiologically realistic description of O2 transport and metabolism in the microcirculation of the heart. Furthermore, because model solutions for tracer transients and steady states can be computed highly efficiently, this model may be the preferred vehicle for routine data analysis where repetitive solutions and parameter optimization are required, as is the case in PET imaging for estimating myocardial O2 consumption.

Large-scale 3-D geometric reconstruction of the porcine coronary arterial vasculature based on detailed anatomical data

The temporal and spatial distribution of coronary blood flow, pressure, and volume are determined by the branching pattern and three-dimensional (3-D) geometry of the coronary vasculature, and by the mechanics of heart wall and vascular tone. Consequently, a realistic simulation of coronary blood flow requires, as a first step, an accurate representation of the coronary vasculature in a 3-D model of the beating heart. In the present study, a large-scale stochastic reconstruction of the asymmetric coronary arterial trees (right coronary artery, RCA; left anterior descending, LAD; and left circumflex, LCx) of the porcine heart has been carried out to set the stage for future hemodynamic analysis. The model spans the entire coronary arterial tree down to the capillary vessels. The 3-D tree structure was reconstructed initially in rectangular slab geometry by means of global geometrical optimization using parallel simulated annealing (SA) algorithm. The SA optimization was subject to constraints prescribed by previously measured morphometric features of the coronary arterial trees. Subsequently, the reconstructed trees were mapped onto a prolate spheroid geometry of the heart. The transformed geometry was determined through least squares minimization of the related changes in both segments lengths and their angular characteristics. Vessel diameters were assigned based on a novel representation of diameter asymmetry along bifurcations. The reconstructed RCA, LAD and LCx arterial trees show qualitative resemblance to native coronary networks, and their morphological statistics are consistent with the measured data. The present model constitutes the first most extensive reconstruction of the entire coronary arterial system which will serve as a geometric foundation for future studies of flow in an anatomically accurate 3-D coronary vascular model.

Multiscale modeling of cardiac cellular energetics

Multiscale modeling is essential to integrating knowledge of human physiology starting from genomics, molecular biology, and the environment through the levels of cells, tissues, and organs all the way to integrated systems behavior. The lowest levels concern biophysical and biochemical events. The higher levels of organization in tissues, organs, and organism are complex, representing the dynamically varying behavior of billions of cells interacting together. Models integrating cellular events into tissue and organ behavior are forced to resort to simplifications to minimize computational complexity, thus reducing the model's ability to respond correctly to dynamic changes in external conditions. Adjustments at protein and gene regulatory levels shortchange the simplified higher-level representations. Our cell primitive is composed of a set of subcellular modules, each defining an intracellular function (action potential, tricarboxylic acid cycle, oxidative phosphorylation, glycolysis, calcium cycling, contraction, etc.), composing what we call the "eternal cell," which assumes that there is neither proteolysis nor protein synthesis. Within the modules are elements describing each particular component (i.e., enzymatic reactions of assorted types, transporters, ionic channels, binding sites, etc.). Cell subregions are stirred tanks, linked by diffusional or transporter-mediated exchange. The modeling uses ordinary differential equations rather than stochastic or partial differential equations. This basic model is regarded as a primitive upon which to build models encompassing gene regulation, signaling, and long-term adaptations in structure and function. During simulation, simpler forms of the model are used, when possible, to reduce computation. However, when this results in error, the more complex and detailed modules and elements need to be employed to improve model realism. The processes of error recognition and of mapping between different levels of model form complexity are challenging but are essential for successful modeling of large-scale systems in reasonable time. Currently there is to this end no established methodology from computational sciences.

Left bundle branch block induces ventricular remodelling and functional septal hypoperfusion

AIMS

Left ventricular (LV) dilatation, hypertrophy, and septal perfusion defects are frequently observed in patients with left bundle branch block (LBBB). We investigated whether isolated LBBB causes these abnormalities.

METHODS AND RESULTS

In eight dogs, LBBB was induced by radio frequency ablation. Two-dimensional echocardiography showed that 16 weeks of LBBB decreased LV ejection fraction (by 23+/-14%) and increased LV cavity volume (by 25+/-19%) and wall mass (by 17+/-16%). The LV septal-to-lateral wall mass ratio decreased by 6+/-9%, indicating asymmetric hypertrophy. After onset of LBBB, myocardial blood flow (MBF, fluorescent microspheres) and systolic circumferential shortening [CS(sys), magnetic resonance (MR) tagging] decreased in the septum to 83+/-16% and -11+/-20% of baseline, respectively, and increased in LV lateral wall to 118+/-12% and 180+/-90% of baseline, respectively. MBF and CS(sys) values did not change over 16 weeks of LBBB. Changes in external mechanical work paralleled those in CS(sys). Glycogen content was not significantly different between septum and LV lateral wall of LBBB hearts (16 weeks) and control samples, indicating absence of hibernation.

CONCLUSIONS

The asynchronous ventricular activation during LBBB leads to redistribution of circumferential shortening and myocardial blood flow and, in the long run, LV remodelling. Septal hypoperfusion during LBBB appears to be primarily determined by reduced septal workload.

Regional differences of myocardial infarct development and ischemic preconditioning

The spatial and temporal development of myocardial infarction depends on the area at risk (AAR), the severity and duration of blood flow reduction (energy supply) as well as on heart rate and regional wall function (energy demand). Both supply and demand can vary within the AAR of a given heart, potentially resulting in differences in infarct development. We therefore retrospectively analyzed infarct size (IS, %AAR, TTC) in 24 anesthetized pigs in vivo following 90 min hypoperfusion and 120 min reperfusion of the LAD coronary artery, which supplies parts of the LV septum (LVS) and anterior free wall (LVAFW). The total LAD perfusion territory averaged 49.8 +/- 14.2 (SD) g (49.2 +/- 8.4% of LV); 61.4 +/- 8.1% of the AAR was LVAFW. IS within the LVS was 25.3 +/- 15.1%, while IS within the LVAFW was 16.6 +/-10.1% (p<0.05). While ischemic blood flow (radiolabeled microspheres) did not differ between LVS (0.05 +/- 0.02 ml/min/g) and LVAFW (0.05 +/- 0.03 ml/min/g), perivascular connective tissue (56 +/- 9 vs. 38+/-7 microm(2), p < 0.05) and the capillary-to-myocyte distance (1.65 +/- 0.23 vs. 1.18 +/- 0.23 mm, p < 0.05) were larger in LVS than in LVAFW. Interestingly, IS in LVS (9.3 +/- 9.6%, n = 24) and LVAFW (9.2 +/- 9.1%) were reduced to the same absolute extent by ischemic preconditioning with one cycle of 10 min ischemia and 15 min reperfusion, suggesting that a similar regional difference exists also in the protection afforded by ischemic preconditioning. The mechanism(s) for that remain(s) to be established.

CONCLUSION

In pigs, regional differences in infarct development and protection from it exist in the LAD perfusion territory, which are independent of ischemic blood flow but apparently related to pre-existing structural differences.

Fractal properties of perfusion heterogeneity in optimized arterial trees: a model study

Regional blood flows in the heart muscle are remarkably heterogeneous. It is very likely that the most important factor for this heterogeneity is the metabolic need of the tissue rather than flow dispersion by the branching network of the coronary vasculature. To model the contribution of tissue needs to the observed flow heterogeneities we use arterial trees generated on the computer by constrained constructive optimization. This method allows to prescribe terminal flows as independent boundary conditions, rather than obtaining these flows by the dispersive effects of the tree structure. We study two specific cases: equal terminal flows (model 1) and terminal flows set proportional to the volumes of Voronoi polyhedra used as a model for blood supply regions of terminal segments (model 2). Model 1 predicts, depending on the number Nterm of end-points, fractal dimensions D of perfusion heterogeneities in the range 1.20 to 1.40 and positively correlated nearest-neighbor regional flows, in good agreement with experimental data of the normal heart. Although model 2 yields reasonable terminal flows well approximated by a lognormal distribution, it fails to predict D and nearest-neighbor correlation coefficients r1 of regional flows under normal physiologic conditions: model 2 gives D = 1.69 +/- 0.02 and r1 = -0.18 +/- 0.03 (n = 5), independent of Nterm and consistent with experimental data observed under coronary stenosis and under the reduction of coronary perfusion pressure. In conclusion, flow heterogeneity can be modeled by terminal positions compatible with an existing tree structure without resorting to the flow-dispersive effects of a specific branching tree model to assign terminal flows.

In vivo study of microcirculation in canine myocardium using the IVIM method

The intravoxel incoherent motion (IVIM) method was implemented in closed-chest dogs to obtain measurements on microcirculation in the left ventricular wall in vivo. Specifically, it enabled us to measure the mean microflow velocity (400 +/- 40 microm/s) and the vascular volume fraction (VVF) (11.1% +/- 2.2%), and observe the directional preference of capillary orientation. The apparent diffusion coefficients (ADCs) of water along and perpendicular to myofibers were also measured. With vasodilatation by adenosine infusion, a 25% increase in the VVF and a 7% increase in the mean microflow velocity were observed, while no change in the ADC was detected. A 28.5% decrease of the ADC was observed postmortem.

Flow heterogeneity following global no-flow ischemia in isolated rabbit heart

The purpose of this study was to evaluate flow heterogeneity and impaired reflow during reperfusion after 60-min global no-flow ischemia in the isolated rabbit heart. Radiolabeled microspheres were used to measure relative flow in small left ventricular (LV) segments in five ischemia + reperfused hearts and in five nonischemic controls. Relative flow heterogeneity was expressed as relative dispersion (RD) and computed as standard deviation/mean. In postischemic vs. preischemic hearts, RD was increased for the whole LV (0.92 +/- 0.41 vs. 0.37 +/- 0.07, P < 0.05) as well as the subendocardium (Endo) and subepicardium considered separately (1.28 +/- 0.74 vs. 0.30 +/- 0.09 and 0.69 +/- 0.22 vs. 0.38 +/- 0.08; P < 0.05 for both comparisons, respectively) during early reperfusion. During late reperfusion, the increased RD for the whole LV and Endo remained significant (0.70 +/- 0.22 vs. 0.37 +/- 0.07 and 1.06 +/- 0.55 vs. 0.30 +/- 0.09; P < 0.05 for both comparisons, respectively). In addition to the increase in postischemic flow heterogeneity, there were some regions demonstrating severely impaired reflow, indicating that regional ischemia can persist despite restoration of normal global flow. Also, the relationship between regional and global flow was altered by the increased postischemic flow heterogeneity, substantially reducing the significance of measured global LV reflow. These observations emphasize the need to quantify regional flow during reperfusion after sustained no-flow ischemia in the isolated rabbit heart.