Fractal nature of regional myocardial blood flow heterogeneity

Differentiating Macrovascular and Microvascular Ischemia Using Fractal Analysis of Dynamic Myocardial Perfusion Stress-CT

OBJECTIVES

Fractal analysis of dynamic myocardial stress computed tomography perfusion imaging (4D-CTP) has shown potential to noninvasively differentiate obstructive coronary artery disease (CAD) and coronary microvascular disease (CMD). This study validates fractal analysis of 4D-CTP in a multicenter setting and assesses its diagnostic accuracy in subgroups with ischemia and nonobstructed coronary arteries (INOCA) and with mild to moderate stenosis.

MATERIALS AND METHODS

From the AMPLIFiED multicenter trial, patients with suspected or known chronic myocardial ischemia and an indication for invasive coronary angiography were included. Patients underwent dual-source CT angiography, 4D-CTP, and CT delayed-enhancement imaging. Coronary artery disease, CMD, and normal perfusion were defined by a combined reference standard comprising invasive coronary angiography with fractional flow reserve, and absolute or relative CT-derived myocardial blood flow. Nonobstructed coronary arteries were defined as ≤25% stenosis and mild to moderate stenosis as 26%-80%.

RESULTS

In 127 patients (27% female), fractal analysis accurately differentiated CAD (n = 61, 23% female), CMD (n = 23, 30% female), and normal perfusion (n = 34, 35% female) with a multiclass area under the receiver operating characteristic curve (AUC) of 0.92 and high agreement (multiclass κ = 0.89). In patients with ischemia (n = 84), fractal analysis detected CAD (n = 61) over CMD (n = 23) with sensitivity of 95%, specificity of 74%, accuracy of 89%, and AUC of 0.83. In patients with nonobstructed coronary arteries (n = 33), INOCA (n = 15) was detected with sensitivity of 100%, specificity of 78%, accuracy of 88%, and AUC of 0.94. In patients with mild to moderate stenosis (n = 27), fractal analysis detected CAD (n = 19) over CMD with sensitivity of 84%, specificity of 100%, accuracy of 89%, and AUC of 0.95.

CONCLUSIONS

In this multicenter study, fractal analysis of 4D-CTP accurately differentiated CAD and CMD including subgroups with INOCA and with mild to moderate stenosis.

Functional implications of microvascular heterogeneity for oxygen uptake and utilization

In the vascular system, an extensive network structure provides convective and diffusive transport of oxygen to tissue. In the microcirculation, parameters describing network structure, blood flow, and oxygen transport are highly heterogeneous. This heterogeneity can strongly affect oxygen supply and organ function, including reduced oxygen uptake in the lung and decreased oxygen delivery to tissue. The causes of heterogeneity can be classified as extrinsic or intrinsic. Extrinsic heterogeneity refers to variations in oxygen demand in the systemic circulation or oxygen supply in the lungs. Intrinsic heterogeneity refers to structural heterogeneity due to stochastic growth of blood vessels and variability in flow pathways due to geometric constraints, and resulting variations in blood flow and hematocrit. Mechanisms have evolved to compensate for heterogeneity and thereby improve oxygen uptake in the lung and delivery to tissue. These mechanisms, which involve long-term structural adaptation and short-term flow regulation, depend on upstream responses conducted along vessel walls, and work to redistribute flow and maintain blood and tissue oxygenation. Mathematically, the variance of a functional quantity such as oxygen delivery that depends on two or more heterogeneous variables can be reduced if one of the underlying variables is controlled by an appropriate compensatory mechanism. Ineffective regulatory mechanisms can result in poor oxygen delivery even in the presence of adequate overall tissue perfusion. Restoration of endothelial function, and specifically conducted responses, should be considered when addressing tissue hypoxemia and organ failure in clinical settings.

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.

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.

Effects of impaired microvascular flow regulation on metabolism-perfusion matching and organ function

Impaired tissue oxygen delivery is a major cause of organ damage and failure in critically ill patients, which can occur even when systemic parameters, including cardiac output and arterial hemoglobin saturation, are close to normal. This review addresses oxygen transport mechanisms at the microcirculatory scale, and how hypoxia may occur in spite of adequate convective oxygen supply. The structure of the microcirculation is intrinsically heterogeneous, with wide variations in vessel diameters and flow pathway lengths, and consequently also in blood flow rates and oxygen levels. The dynamic processes of structural adaptation and flow regulation continually adjust microvessel diameters to compensate for heterogeneity, redistributing flow according to metabolic needs to ensure adequate tissue oxygenation. A key role in flow regulation is played by conducted responses, which are generated and propagated by endothelial cells and signal upstream arterioles to dilate in response to local hypoxia. Several pathophysiological conditions can impair local flow regulation, causing hypoxia and tissue damage leading to organ failure. Therapeutic measures targeted to systemic parameters may not address or may even worsen tissue oxygenation at the microvascular level. Restoration of tissue oxygenation in critically ill patients may depend on restoration of endothelial cell function, including conducted responses.

Myocardial Perfusion Simulation for Coronary Artery Disease: A Coupled Patient-Specific Multiscale Model

Patient-specific models of blood flow are being used clinically to diagnose and plan treatment for coronary artery disease. A remaining challenge is bridging scales from flow in arteries to the micro-circulation supplying the myocardium. Previously proposed models are descriptive rather than predictive and have not been applied to human data. The goal here is to develop a multiscale patient-specific model enabling blood flow simulation from large coronary arteries to myocardial tissue. Patient vasculatures are segmented from coronary computed tomography angiography data and extended from the image-based model down to the arteriole level using a space-filling forest of synthetic trees. Blood flow is modeled by coupling a 1D model of the coronary arteries to a single-compartment Darcy myocardium model. Simulated results on five patients with non-obstructive coronary artery disease compare overall well to [\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{15}$$\end{document}15O]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {H}_{{2}}$$\end{document}H2O PET exam data for both resting and hyperemic conditions. Results on a patient with severe obstructive disease link coronary artery narrowing with impaired myocardial blood flow, demonstrating the model’s ability to predict myocardial regions with perfusion deficit. This is the first report of a computational model for simulating blood flow from the epicardial coronary arteries to the left ventricle myocardium applied to and validated on human data.

Topologic and Hemodynamic Characteristics of the Human Coronary Arterial Circulation

Background

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

Methods

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

Results

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

Conclusion

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

Krogh’s capillary recruitment hypothesis, 100 years on: Is the opening of previously closed capillaries necessary to ensure muscle oxygenation during exercise?

In 1919, August Krogh published his seminal work on skeletal muscle oxygenation. Krogh’s observations indicated that muscle capillary diameter is actively regulated, rather than a passive result of arterial blood flow regulation. Indeed, combining a mathematical model with the number of ink-filled capillaries he observed in muscle cross sections taken at different workloads, Krogh was able to account for muscle tissue’s remarkably efficient oxygen extraction during exercise in terms of passive diffusion from nearby capillaries. Krogh was awarded the 1920 Nobel Prize for his account of muscle oxygenation. Today, his observations are engrained in the notion of capillary recruitment: the opening of previously closed capillaries. While the binary distinction between “closed” and “open” was key to Krogh’s model argument, he did in fact report a continuum of capillary diameters, degrees of erythrocyte deformation, and perfusion states. Indeed, modern observations question the presence of closed muscle capillaries. We therefore examined whether changes in capillary flow patterns and hematocrit among open capillaries can account for oxygen extraction in muscle across orders-of-magnitude changes in blood flow. Our four-compartment model of oxygen extraction in muscle confirms this notion and provides a framework for quantifying the impact of changes in microvascular function on muscle oxygenation in health and disease. Our results underscore the importance of capillary function for oxygen extraction in muscle tissue as first proposed by Krogh. While Krogh’s model calculations still hold, our model predictions support that capillary recruitment can be viewed in the context of continuous, rather than binary, erythrocyte distributions among capillaries.

NEW & NOTEWORTHY Oxygen extraction in working muscle is extremely efficient in view of single capillaries properties. The underlying mechanisms have been widely debated. Here, we develop a four-compartment model to quantify the influence of each of the hypothesized mechanisms on muscle oxygenation. Our results show that changes in capillary flow pattern and hematocrit can account for the high oxygen extraction observed in working muscle, while capillary recruitment is not required to account for these extraction properties.

Biofabrication strategies for creating microvascular complexity

Design and fabrication of effective biomimetic vasculatures constitutes a relevant and yet unsolved challenge, lying at the heart of tissue repair and regeneration strategies. Even if cell growth is achieved in 3D tissue scaffolds or advanced implants, tissue viability inevitably requires vascularization, as diffusion can only transport nutrients and eliminate debris within a few hundred microns. This engineered vasculature may need to mimic the intricate branching geometry of native microvasculature, referred to herein as vascular complexity, to efficiently deliver blood and recreate critical interactions between the vascular and perivascular cells as well as parenchymal tissues. This review first describes the importance of vascular complexity in labs- and organs-on-chips, the biomechanical and biochemical signals needed to create and maintain a complex vasculature, and the limitations of current 2D, 2.5D, and 3D culture systems in recreating vascular complexity. We then critically review available strategies for design and biofabrication of complex vasculatures in cell culture platforms, labs- and organs-on-chips, and tissue engineering scaffolds, highlighting their advantages and disadvantages. Finally, challenges and future directions are outlined with the hope of inspiring researchers to create the reliable, efficient and sustainable tools needed for design and biofabrication of complex vasculatures.

Physiological Consequences of Coronary Arteriolar Dysfunction and Its Influence on Cardiovascular Disease

To date, the major focus of diagnostic modalities and interventions to treat coronary artery disease has been the large epicardial vessels. Despite substantial data showing that microcirculatory dysfunction is a strong predictor of future adverse cardiovascular events, very little research has gone into developing techniques for in vivo diagnosis and therapeutic interventions to improve microcirculatory function. In this review, we will discuss the pathophysiology of coronary arteriolar dysfunction, define its prognostic implications, evaluate the diagnostic modalities available, and provide speculation on current and potential therapeutic opportunities.

Rapid quantification of mitochondrial fractal dimension in individual cells

An improved technique for fractal characterization called the modified blanket method is introduced that can quantify surrounding fractal structures on a pixel by pixel basis without artifacts associated with scale-dependent image features such as object size. The method interprets images as topographical maps, obtaining information regarding the local surface area as a function of image resolution. Local fractal dimension (FD) can be quantified from the power law exponent derived from the surface area and image resolution relationship. We apply this technique on simulated cell images of known FD and compared the obtained values to power spectral density (PSD) analysis. Our method is sensitive to a wider FD range (2.0-4.5), having a mean error of 1.4% compared to 6% for PSD analysis. This increased sensitivity and an ability to compute regional FD properties enabled the discrimination of the differences in radiation resistant cancer cell responses that could not be detected using PSD analysis.

Morphometric Reconstruction of Coronary Vasculature Incorporating Uniformity of Flow Dispersion

Experimental limitations in measurements of coronary flow in the beating heart have led to the development of in silico models of reconstructed coronary trees. Previous coronary reconstructions relied primarily on anatomical data, including statistical morphometry (e.g., diameters, length, connectivity, longitudinal position). Such reconstructions are non-unique, however, often leading to unrealistic predicted flow features. Thus, it is necessary to impose physiological flow constraints to ensure realistic tree reconstruction. Since a vessel flow depends on its diameter to fourth power, diameters are the logical candidates to guide vascular reconstructions to achieve realistic flows. Here, a diameter assignment method was developed where each vessel diameter was determined depending on its downstream tree size, aimed to reduce flow dispersion to within measured range. Since the coronary micro-vessels are responsible for a major portion of the flow resistance, the auto regulated coronary flow was analyzed in a morphometry-based reconstructed 400 vessel arterial microvascular sub-tree spanning vessel orders 1–6. Diameters in this subtree were re-assigned based on the flow criteria. The results revealed that diameter re-assignment, while adhering to measured morphometry, significantly reduced the flow dispersion to realistic levels while adhering to measured morphometry. The resulting network flow has longitudinal pressure distribution, flow fractal nature, and near-neighboring flow autocorrelation, which agree with measured coronary flow characteristics. Collectively, these results suggest that a realistic coronary tree reconstruction should impose not only morphometric data but also flow considerations. The work is of broad significance in providing a novel computational framework in the field of coronary microcirculation. It is essential for the study of coronary circulation by model simulation, based on a realistic network structure.

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.

Quantitative Vascular Evaluation: From Laboratory Experiments to Point-of-Care Patient (Experimental Approach)

This paper illustrates the evolution of our knowledge of arterial mechanics from our initial research works up to the present time. Several techniques focusing on this topic in terms of our experience are dis-cussed. An interdisciplinary team composed by different institutions from Argentina, Uruguay, France and Spain was created to conduct research, to train human resources and to fulfill the inevitable social role of gaining access to technological inno-vation to improve public health.

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.

Myocardial Viability: Survival Mechanisms and Molecular Imaging Targets in Acute and Chronic Ischemia

Myocardial responses to acute ischemia/reperfusion and to chronic ischemic conditions have been studied extensively at all levels of organization. These include subcellular (eg, mitochondria in vitro); intact, large animal models (eg, swine with chronic coronary stenosis); as well as human subjects. Investigations in humans have used positron emission tomographic metabolic and myocardial blood flow measurements, assessment of gene expression and anatomic description of myocardium obtained at the time of coronary artery revascularization, ventricular assist device placement, or heart transplantation. A multitude of genetic, molecular, and metabolic pathways have been identified, which may promote either myocyte survival or death or, most interestingly, both. Many of these potential mediators in both acute ischemia/reperfusion and adaptations to chronic ischemic conditions involve the mitochondria, which play a central role in cellular energy production and homeostasis. The present review is focused on operative survival mechanisms and potential myocardial viability molecular imaging targets in acute and chronic ischemia, especially those which impact mitochondrial function.

Impact of motion and partial volume effects correction on PET myocardial perfusion imaging using simultaneous PET-MR

PET is an established modality for myocardial perfusion imaging (MPI) which enables quantification of absolute myocardial blood flow (MBF) using dynamic imaging and kinetic modeling. However, heart motion and partial volume effects (PVE) significantly limit the spatial resolution and quantitative accuracy of PET MPI. Simultaneous PET-MR offers a solution to the motion problem in PET by enabling MR-based motion correction of PET data. The aim of this study was to develop a motion and PVE correction methodology for PET MPI using simultaneous PET-MR, and to assess its impact on both static and dynamic PET MPI using 18F-Flurpiridaz, a novel 18F-labeled perfusion tracer. Two dynamic 18F-Flurpiridaz MPI scans were performed on healthy pigs using a PET-MR scanner. Cardiac motion was tracked using a dedicated tagged-MRI (tMR) sequence. Motion fields were estimated using non-rigid registration of tMR images and used to calculate motion-dependent attenuation maps. Motion correction of PET data was achieved by incorporating tMR-based motion fields and motion-dependent attenuation coefficients into image reconstruction. Dynamic and static PET datasets were created for each scan. Each dataset was reconstructed as (i) Ungated, (ii) Gated (end-diastolic phase), and (iii) Motion-Corrected (MoCo), each without and with point spread function (PSF) modeling for PVE correction. Myocardium-to-blood concentration ratios (MBR) and apparent wall thickness were calculated to assess image quality for static MPI. For dynamic MPI, segment- and voxel-wise MBF values were estimated by non-linear fitting of a 2-tissue compartment model to tissue time-activity-curves. MoCo and Gating respectively decreased mean apparent wall thickness by 15.1% and 14.4% and increased MBR by 20.3% and 13.6% compared to Ungated images (P  <  0.01). Combined motion and PSF correction (MoCo-PSF) yielded 30.9% (15.7%) lower wall thickness and 82.2% (20.5%) higher MBR compared to Ungated data reconstructed without (with) PSF modeling (P  <  0.01). For dynamic PET, mean MBF across all segments were comparable for MoCo (0.72  ±  0.21 ml/min/ml) and Gating (0.69  ±  0.18 ml/min/ml). Ungated data yielded significantly lower mean MBF (0.59  ±  0.16 ml/min/ml). Mean MBF for MoCo-PSF was 0.80  ±  0.22 ml/min/ml, which was 37.9% (25.0%) higher than that obtained from Ungated data without (with) PSF correction (P  <  0.01). The developed methodology holds promise to improve the image quality and sensitivity of PET MPI studies performed using PET-MR.

The fractal heart - embracing mathematics in the cardiology clinic

For clinicians grappling with quantifying the complex spatial and temporal patterns of cardiac structure and function (such as myocardial trabeculae, coronary microvascular anatomy, tissue perfusion, myocyte histology, electrical conduction, heart rate, and blood-pressure variability), fractal analysis is a powerful, but still underused, mathematical tool. In this Perspectives article, we explain some fundamental principles of fractal geometry and place it in a familiar medical setting. We summarize studies in the cardiovascular sciences in which fractal methods have successfully been used to investigate disease mechanisms, and suggest potential future clinical roles in cardiac imaging and time series measurements. We believe that clinical researchers can deploy innovative fractal solutions to common cardiac problems that might ultimately translate into advancements for patient care.

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.

Trees with random conductivities and the (reciprocal) inverse Gaussian distribution

Equipping the edges of a finite rooted tree with independent resistances that are inverse Gaussian for interior edges and reciprocal inverse Gaussian for terminal edges makes it possible, for suitable constellations of the parameters, to show that the total resistance is reciprocal inverse Gaussian (Barndorff-Nielsen 1994). This result is extended to infinite trees. Also, a connection to Brownian diffusion is established and, for the case of finite trees, an exact distributional and independence result is derived for the conditional model given the total resistance.

Trees with random conductivities and the (reciprocal) inverse Gaussian distribution

Equipping the edges of a finite rooted tree with independent resistances that are inverse Gaussian for interior edges and reciprocal inverse Gaussian for terminal edges makes it possible, for suitable constellations of the parameters, to show that the total resistance is reciprocal inverse Gaussian (Barndorff-Nielsen 1994). This result is extended to infinite trees. Also, a connection to Brownian diffusion is established and, for the case of finite trees, an exact distributional and independence result is derived for the conditional model given the total resistance.

The Human Microcirculation: Regulation of Flow and Beyond

The microcirculation is responsible for orchestrating adjustments in vascular tone to match local tissue perfusion with oxygen demand. Beyond this metabolic dilation, the microvasculature plays a critical role in modulating vascular tone by endothelial release of an unusually diverse family of compounds including nitric oxide, other reactive oxygen species, and arachidonic acid metabolites. Animal models have provided excellent insight into mechanisms of vasoregulation in health and disease. However, there are unique aspects of the human microcirculation that serve as the focus of this review. The concept is put forth that vasculoparenchymal communication is multimodal, with vascular release of nitric oxide eliciting dilation and preserving normal parenchymal function by inhibiting inflammation and proliferation. Likewise, in disease or stress, endothelial release of reactive oxygen species mediates both dilation and parenchymal inflammation leading to cellular dysfunction, thrombosis, and fibrosis. Some pathways responsible for this stress-induced shift in mediator of vasodilation are proposed. This paradigm may help explain why microvascular dysfunction is such a powerful predictor of cardiovascular events and help identify new approaches to treatment and prevention.

Fractal regional myocardial blood flows pattern according to metabolism, not vascular anatomy

Regional myocardial blood flows are markedly heterogeneous. Fractal analysis shows strong near-neighbor correlation. In experiments to distinguish control by vascular anatomy vs. local vasomotion, coronary flows were increased in open-chest dogs by stimulating myocardial metabolism (catecholamines + atropine) with and without adenosine. During control states mean left ventricular (LV) myocardial blood flows (microspheres) were 0.5-1 ml·g(-1)·min(-1) and increased to 2-3 ml·g(-1)·min(-1) with catecholamine infusion and to ∼4 ml·g(-1)·min(-1) with adenosine (Ado). Flow heterogeneity was similar in all states: relative dispersion (RD = SD/mean) was ∼25%, using LV pieces 0.1-0.2% of total. During catecholamine infusion local flows increased in proportion to the mean flows in 45% of the LV, "tracking" closely (increased proportionately to mean flow), while ∼40% trended toward the mean. Near-neighbor regional flows remained strongly spatially correlated, with fractal dimension D near 1.2 (Hurst coefficient 0.8). The spatial patterns remain similar at varied levels of metabolic stimulation inferring metabolic dominance. In contrast, adenosine vasodilation increased flows eightfold times control while destroying correlation with the control state. The Ado-induced spatial patterns differed from control but were self-consistent, inferring that with full vasodilation the relaxed arterial anatomy dominates the distribution. We conclude that vascular anatomy governs flow distributions during adenosine vasodilation but that metabolic vasoregulation dominates in normal physiological states.

Progressively heterogeneous mismatch of regional oxygen delivery to consumption during graded coronary stenosis in pig left ventricle

In normal hearts, myocardial perfusion is fairly well matched to regional metabolic demand, although both are distributed heterogeneously. Nonuniform regional metabolic vulnerability during coronary stenosis would help to explain nonuniform necrosis during myocardial infarction. In the present study, we investigated whether metabolism-perfusion correlation diminishes during coronary stenosis, indicating increasing mismatch of regional oxygen supply to demand. Thirty anesthetized male pigs were studied: controls without coronary stenosis ( n = 11); group I, left anterior descending (LAD) coronary stenosis leading to coronary perfusion pressure reduction to 70 mmHg ( n = 6); group II, stenosis with perfusion pressure of about 35 mmHg ( n = 6); and group III, stenosis with perfusion pressure of 45 mmHg combined with adenosine infusion ( n = 7). [2-13C]- and [1,2-13C]acetate infusion was used to calculate regional O2 consumption from glutamate NMR spectra measured for multiple tissue samples of about 100 mg dry mass in the LAD region. Blood flow was measured with microspheres in the same regions. In control hearts without stenosis, regional oxygen extraction did not correlate with basal blood flow. Average myocardial O2 delivery and consumption decreased during coronary stenosis, but vasodilation with adenosine counteracted this. Regional oxygen extraction was on average decreased during stenosis, suggesting adaptation of metabolism to lower oxygen supply after half an hour of ischemia. Whereas regional O2 delivery correlated with O2 consumption in controls, this relation was progressively lost with graded coronary hypotension but partially reestablished by adenosine infusion. Therefore, coronary stenosis leads to heterogeneous metabolic stress indicated by decreasing regional O2 supply to demand matching in myocardium during partial coronary obstruction.

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.

Early changes in myocardial microcirculation in asymptomatic hypercholesterolemic subjects: as detected by perfusion CT

Intramyocardial microvessels show functional changes in early stages of atherosclerosis prior to epicardial coronary artery stenosis. However, clinical CT does not have adequate spatial resolution to resolve the microvessels. To clinically detect changes in the function of the intramyocardial microcirculation, the spatial heterogeneity of the distribution of myocardial perfusion (F) and intramyocardial microcirculatory blood volume (Bv) was determined by perfusion CT. Two human subject groups were studied: (i) a "Control" group (24) with no risk factors nor evidence of coronary artery disease (CAD), and (ii) an "At-Risk" group (24) with hypercholesterolemia, but no evidence of CAD. In the perfusion CT image, a region of interest (ROI) covering the left ventricular myocardium was subdivided into multiple nested ROI (nROI) of equal size and used to compute F and Bv for each nROI. No significant differences between the groups were demonstrable in overall myocardial F, or Bv. The nROI data showed significantly increased spatial heterogeneity in the "At Risk" group when compared to "Control" subjects. This study demonstrates that subresolution distribution at the microcirculatory level can be quantified with myocardial perfusion CT and significant changes in these parameters occur in hypercholesterolemic subjects before they have developed significant changes in conventional perfusion parameters.

Nonlinear complexity analysis of brain FMRI signals in schizophrenia

We investigated the differences in brain fMRI signal complexity in patients with schizophrenia while performing the Cyberball social exclusion task, using measures of Sample entropy and Hurst exponent (H). 13 patients meeting diagnostic and Statistical Manual of Mental Disorders, 4th Edition (DSM IV) criteria for schizophrenia and 16 healthy controls underwent fMRI scanning at 1.5 T. The fMRI data of both groups of participants were pre-processed, the entropy characterized and the Hurst exponent extracted. Whole brain entropy and H maps of the groups were generated and analysed. The results after adjusting for age and sex differences together show that patients with schizophrenia exhibited higher complexity than healthy controls, at mean whole brain and regional levels. Also, both Sample entropy and Hurst exponent agree that patients with schizophrenia have more complex fMRI signals than healthy controls. These results suggest that schizophrenia is associated with more complex signal patterns when compared to healthy controls, supporting the increase in complexity hypothesis, where system complexity increases with age or disease, and also consistent with the notion that schizophrenia is characterised by a dysregulation of the nonlinear dynamics of underlying neuronal systems.

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.

Comparison of blood flow models and acquisitions for quantitative myocardial perfusion estimation from dynamic CT

Myocardial blood flow (MBF) can be estimated from dynamic contrast enhanced (DCE) cardiac CT acquisitions, leading to quantitative assessment of regional perfusion. The need for low radiation dose and the lack of consensus on MBF estimation methods motivates this study to refine the selection of acquisition protocols and models for CT-derived MBF. DCE cardiac CT acquisitions were simulated for a range of flow states (MBF = 0.5, 1, 2, 3 ml (min g)(-1), cardiac output = 3, 5, 8 L min(-1)). Patient kinetics were generated by a mathematical model of iodine exchange incorporating numerous physiological features including heterogenenous microvascular flow, permeability and capillary contrast gradients. CT acquisitions were simulated for multiple realizations of realistic x-ray flux levels. CT acquisitions that reduce radiation exposure were implemented by varying both temporal sampling (1, 2, and 3 s sampling intervals) and tube currents (140, 70, and 25 mAs). For all acquisitions, we compared three quantitative MBF estimation methods (two-compartment model, an axially-distributed model, and the adiabatic approximation to the tissue homogeneous model) and a qualitative slope-based method. In total, over 11 000 time attenuation curves were used to evaluate MBF estimation in multiple patient and imaging scenarios. After iodine-based beam hardening correction, the slope method consistently underestimated flow by on average 47.5% and the quantitative models provided estimates with less than 6.5% average bias and increasing variance with increasing dose reductions. The three quantitative models performed equally well, offering estimates with essentially identical root mean squared error (RMSE) for matched acquisitions. MBF estimates using the qualitative slope method were inferior in terms of bias and RMSE compared to the quantitative methods. MBF estimate error was equal at matched dose reductions for all quantitative methods and range of techniques evaluated. This suggests that there is no particular advantage between quantitative estimation methods nor to performing dose reduction via tube current reduction compared to temporal sampling reduction. These data are important for optimizing implementation of cardiac dynamic CT in clinical practice and in prospective CT MBF trials.

Anionic biopolyelectrolytes of the syndecan/perlecan superfamily: physicochemical properties and medical significance

In the review article presented here, we demonstrate that the connective tissue is more than just a matrix for cells and a passive scaffold to provide physical support. The extracellular matrix can be subdivided into proteins (collagen, elastin), glycoconjugates (structural glycoproteins, proteoglycans) and glycosaminoglycans (hyaluronan). Our main focus rests on the anionic biopolyelectrolytes of the perlecan/syndecan superfamily which belongs to extracellular matrix and cell membrane integral proteoglycans. Though the extracellular domain of the syndecans may well be performing a structural role within the extracellular matrix, a key function of this class of membrane intercalated proteoglycans may be to act as signal transducers across the plasma membrane and thus be more appropriately included in the group of cell surface receptors. Nevertheless, there is a continuum in functions of syndecans and perlecans, especially with respect to their structural role and biomedical significance. HS/CS proteoglycans are receptor sites for lipoprotein binding thus intervening directly in lipid metabolism. We could show that among all lipoproteins, HDL has the highest affinity to these proteoglycans and thus instals a feedforward forechecking loop against atherogenic apoB100 lipoprotein deposition on surface membranes and in subendothelial spaces. Therefore, HDL is not only responsible for VLDL/IDL/LDL cholesterol exit but also controls thoroughly the entry. This way, it inhibits arteriosclerotic nanoplaque formation. The ternary complex 'lipoprotein receptor (HS/CS-PG) - lipoprotein (LDL, oxLDL, Lp(a)) - calcium' may be interpreted as arteriosclerotic nanoplaque build-up on the molecular level before any cellular reactivity, possibly representing the arteriosclerotic primary lesion combined with endothelial dysfunction. With laser-based ellipsometry we could demonstrate that nanoplaque formation is a Ca(2+)-driven process. In an in vitro biosensor application of HS-PG coated silica surfaces we tested nanoplaque formation and size in clinical trials with cardiovascular high-risk patients who underwent treatment with ginkgo or fluvastatin. While ginkgo reduced nanoplaque formation (size) by 14.3% (23.4%) in the isolated apoB100 lipid fraction at a normal blood Ca(2+) concentration, the effect of the statin with a reduction of 44.1% (25.4%) was more pronounced. In addition, ginkgo showed beneficial effects on several biomarkers of oxidative stress and inflammation. Besides acting as peripheral lipoprotein binding receptor, HS/CS-PG is crucially implicated in blood flow sensing. A sensor molecule has to fulfil certain mechanochemical and mechanoelectrical requirements. It should possess viscoelastic and cation binding properties capable of undergoing conformational changes caused both mechanically and electrostatically. Moreover, the latter should be ion-specific. Under no-flow conditions, the viscoelastic polyelectrolyte at the endothelium - blood interface assumes a random coil form. Blood flow causes a conformational change from the random coil state to the directed filament structure state. This conformational transition effects a protein unfurling and molecular elongation of the GAG side chains like in a 'stretched' spring. This configuration is therefore combined with an increase in binding sites for Na(+) ions. Counterion migration of Na(+) along the polysaccharide chain is followed by transmembrane Na(+) influx into the endothelial cell and by endothelial cell membrane depolarization. The simultaneous Ca(2+) influx releases NO and PGI2, vasodilatation is the consequence. Decrease in flow reverses the process. Binding of Ca(2+) and/or apoB100 lipoproteins (nanoplaque formation) impairs the flow sensor function. The physicochemical and functional properties of proteoglycans are due to their amphiphilicity and anionic polyelectrolyte character. Thus, they potently interact with cations, albeit in a rather complex manner. Utilizing (23)Na(+) and (39)K(+) NMR techniques, we could show that, both in HS-PG solutions and in native vascular connective tissue, the mode of interaction for monovalent cations is competition. Mg(2+) and Ca(2+) ions, however, induced a conformational change leading to an increased allosteric, cooperative K(+) and Na(+) binding, respectively. Since extracellular matrices and basement membranes form a tight-fitting sheath around the cell membrane of muscle and Schwann cells, in particular around sinus node cells of the heart, and underlie all epithelial and endothelial cell sheets and tubes, a release of cations from or an adsorption to these polyanionic macromolecules can transiently lead to fast and drastic activity changes in these tiny extracellular tissue compartments. The ionic currents underlying pacemaker and action potential of sinus node cells are fundamentally modulated. Therefore, these polyelectrolytic ion binding characteristics directly contribute to and intervene into heart rhythm.

Oligometastasis as a predictor for occult disease

Oligometastasis can be defined as a state of limited metastases that is potentially amenable to ablative local therapy; the success of such therapy depends on whether or not additional occult metastases exist. A model is presented here to predict occult metastases given detectable oligometastases. Predictions were based on Bayes' theorem, in conjunction with descriptions of the statistical distributions for the sizes and numbers of hematogenous metastases. The background probability for occult metastases in individuals with oligometastases increased markedly with relatively minor increases in metastatic potential. With each additional metastasis detected the chance of further occult metastases increased. These latter increases were incremental and proportionately smaller with the more metastatic tumors. Long disease free intervals had a major effect to decrease in the probability of further occult disease. Demonstration of oligometastases depends heavily upon the sensitivity of radiological imaging techniques, where the proportion of detectable metastases relates to the position of the distribution of metastasis growth times with respect to the detection threshold. Given the limitations of radiological methods, and the possibility that the oligometastases detected may be the only disease, an aggressive approach appears indicated.

Quantifying left ventricular trabeculae function - application of image-based fractal analysis

The ventricular-blood interface is geometrically complex due to the presence of ventricular trabeculae carneae (VTC). We introduce a new image-based framework to quantify VTC function using high-resolution computed tomography (CT) imaging and offer new insights into the active role of VTCs during ejection. High-resolution Cine CT scans of a patient with normal cardiac function were acquired at a resolution of 0.77 mm per pixel at 10 phases of the cardiac cycle. The images were segmented and the VTC surface was obtained by triangulating the segmented data. Fractal dimension of the VTC surface was calculated for each cardiac phase as a function of scale size using the box-counting algorithm. The fractal dimension, D corresponding to VTCs ranged between 2.05 and 2.2 and varied as a function of time during the cardiac cycle. Fractal dimension is highest at diastole and lowest at peak systole with the change being significantly different (P < 0.003). This variation of D when plotted against stroke volume (i.e., D-V loop) revealed an active VTC role due to hysteresis in the loop. Physically the hysteresis in the D-V loop indicates a new mechanical function of VTCs as structures that provide mechanical leverage during early systolic ejection through contraction. VTC relaxation is noted to occur during late diastole at larger ventricular volume. D-V loop of VTCs quantifies VTC function. A new dynamic physical role of VTCs is suggested by way of mechanical leverage, as opposed to the traditionally accepted passive role.

Fractal analysis in radiological and nuclear medicine perfusion imaging: a systematic review

OBJECTIVES

To provide an overview of recent research in fractal analysis of tissue perfusion imaging, using standard radiological and nuclear medicine imaging techniques including computed tomography (CT), magnetic resonance imaging (MRI), ultrasound, positron emission tomography (PET) and single-photon emission computed tomography (SPECT) and to discuss implications for different fields of application.

METHODS

A systematic review of fractal analysis for tissue perfusion imaging was performed by searching the databases MEDLINE (via PubMed), EMBASE (via Ovid) and ISI Web of Science.

RESULTS

Thirty-seven eligible studies were identified. Fractal analysis was performed on perfusion imaging of tumours, lung, myocardium, kidney, skeletal muscle and cerebral diseases. Clinically, different aspects of tumour perfusion and cerebral diseases were successfully evaluated including detection and classification. In physiological settings, it was shown that perfusion under different conditions and in various organs can be properly described using fractal analysis.

CONCLUSIONS

Fractal analysis is a suitable method for quantifying heterogeneity from radiological and nuclear medicine perfusion images under a variety of conditions and in different organs. Further research is required to exploit physiologically proven fractal behaviour in the clinical setting.

KEY POINTS

• Fractal analysis of perfusion images can be successfully performed. • Tumour, pulmonary, myocardial, renal, skeletal muscle and cerebral perfusion have already been examined. • Clinical applications of fractal analysis include tumour and brain perfusion assessment. • Fractal analysis is a suitable method for quantifying perfusion heterogeneity. • Fractal analysis requires further research concerning the development of clinical applications.

Visualizing regional myocardial blood flow in the mouse

RATIONALE

The spatial distribution of blood flow in the hearts of genetically modified mice is a phenotype of interest because derangements in blood flow may precede detectable changes in organ function. However, quantifying the regional distribution of blood flow within organs of mice is challenging because of the small organ volume and the high resolution required to observe spatial differences in flow. Traditional microsphere methods in which the numbers of microspheres per region are indirectly estimated from radioactive counts or extracted fluorescence have been limited to larger organs for 2 reasons; to ensure statistical confidence in the measured flow per region and to be able to physically dissect the organ to acquire spatial information.

OBJECTIVE

To develop methods to quantify and statistically compare the spatial distribution of blood flow within organs of mice.

METHODS AND RESULTS

We developed and validated statistical methods to compare blood flow between regions and with the same regions over time using 15-µm fluorescent microspheres. We then tested this approach by injecting fluorescent microspheres into isolated perfused mice hearts, determining the spatial location of every microsphere in the hearts, and then visualizing regional flow patterns. We demonstrated application of these statistical and visualizing methods in a coronary artery ligation model in mice.

CONCLUSIONS

These new methods provide tools to investigate the spatial and temporal changes in blood flow within organs of mice at a much higher spatial resolution than currently available by other methods.

Validation of an axially distributed model for quantification of myocardial blood flow using ¹³N-ammonia PET

BACKGROUND

Estimation of myocardial blood flow (MBF) with cardiac PET is often performed with conventional compartmental models. In this study, we developed and evaluated a physiologically and anatomically realistic axially distributed model. Unlike compartmental models, this axially distributed approach models both the temporal and the spatial gradients in uptake and retention along the capillary.

METHODS

We validated PET-derived flow estimates with microsphere studies in 19 (9 rest, 10 stress) studies in five dogs. The radiotracer, (13)N-ammonia, was injected intravenously while microspheres were administered into the left atrium. A regional reduction in hyperemic flow was forced by an external occluder in five of the stress studies. The flow estimates from the axially distributed model were compared with estimates from conventional compartmental models.

RESULTS

The mean difference between microspheres and the axially distributed blood flow estimates in each of the 17 segments was 0.03 mL/g/minute (95% CI [-0.05, 0.11]). The blood flow estimates were highly correlated with each regional microsphere value for the axially distributed model (y = 0.98x + 0.06 mL/g/minute; r = 0.74; P < .001), for the two-compartment (y = 0.64x + 0.34; r = 0.74; P < .001), and for three-compartment model (y = 0.69x + 0.54; r = 0.74; P < .001). The variance of the error of the estimates is higher with the axially distributed model than the compartmental models (1.7 [1.3, 2.1] times higher).

CONCLUSION

The proposed axially distributed model provided accurate regional estimates of MBF. The axially distributed model estimated blood flow with more accuracy, but less precision, than the evaluated compartmental models.

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.

Modeling to link regional myocardial work, metabolism and blood flows

Given the mono-functional, highly coordinated processes of cardiac excitation and contraction, the observations that regional myocardial blood flows, rMBF, are broadly heterogeneous has provoked much attention, but a clear explanation has not emerged. In isolated and in vivo heart studies the total coronary flow is found to be proportional to the rate-pressure product (systolic mean blood pressure times heart rate), a measure of external cardiac work. The same relationship might be expected on a local basis: more work requires more flow. The validity of this expectation has never been demonstrated experimentally. In this article we review the concepts linking cellular excitation and contractile work to cellular energetics and ATP demand, substrate utilization, oxygen demand, vasoregulation, and local blood flow. Mathematical models of these processes are now rather well developed. We propose that the construction of an integrated model encompassing the biophysics, biochemistry and physiology of cardiomyocyte contraction, then combined with a detailed three-dimensional structuring of the fiber bundle and sheet arrangements of the heart as a whole will frame an hypothesis that can be quantitatively evaluated to settle the prime issue: Does local work drive local flow in a predictable fashion that explains the heterogeneity? While in one sense one can feel content that work drives flow is irrefutable, the are no cardiac contractile models that demonstrate the required heterogeneity in local strain-stress-work; quite the contrary, cardiac contraction models have tended toward trying to show that work should be uniform. The object of this review is to argue that uniformity of work does not occur, and is impossible in any case, and that further experimentation and analysis are necessary to test the hypothesis.

A quantitative pixel-wise measurement of myocardial blood flow by contrast-enhanced first-pass CMR perfusion imaging: microsphere validation in dogs and feasibility study in humans

OBJECTIVES

The aim of this study was to evaluate fully quantitative myocardial blood flow (MBF) at a pixel level based on contrast-enhanced first-pass cardiac magnetic resonance (CMR) imaging in dogs and in patients.

BACKGROUND

Microspheres can quantify MBF in subgram regions of interest, but CMR perfusion imaging may be able to quantify MBF and differentiate blood flow at a much higher resolution.

METHODS

First-pass CMR perfusion imaging was performed in a dog model with local hyperemia induced by intracoronary adenosine. Fluorescent microspheres were the reference standard for MBF validation. CMR perfusion imaging was also performed on patients with significant coronary artery disease (CAD) by invasive coronary angiography. Myocardial time-signal intensity curves of the images were quantified on a pixel-by-pixel basis using a model-constrained deconvolution analysis.

RESULTS

Qualitatively, color CMR perfusion pixel maps were comparable to microsphere MBF bull's-eye plots in all animals. Pixel-wise CMR MBF estimates correlated well against subgram (0.49 ± 0.14 g) microsphere measurements (r = 0.87 to 0.90) but showed minor underestimation of MBF. To reduce bias due to misregistration and minimize issues related to repeated measures, 1 hyperemic and 1 remote sector per animal were compared with the microsphere MBF, which improved the correlation (r = 0.97 to 0.98), and the bias was close to zero. Sector-wise and pixel-wise CMR MBF estimates also correlated well (r = 0.97). In patients, color CMR stress perfusion pixel maps showed regional blood flow decreases and transmural perfusion gradients in territories served by stenotic coronary arteries. MBF estimates in endocardial versus epicardial subsectors, and ischemic versus remote sectors, were all significantly different (p < 0.001 and p < 0.01, respectively).

CONCLUSIONS

Myocardial blood flow can be quantified at the pixel level (∼32 μl of myocardium) on CMR perfusion images, and results compared well with microsphere measurements. High-resolution pixel-wise CMR perfusion maps can quantify transmural perfusion gradients in patients with CAD.

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.

Imaging for lung physiology: what do we wish we could measure?

The role of imaging as a tool for investigating lung physiology is growing at an accelerating pace. Looking forward, we wished to identify unresolved issues in lung physiology that might realistically be addressed by imaging methods in development or imaging approaches that could be considered. The role of imaging is framed in terms of the importance of good spatial and temporal resolution and the types of questions that could be addressed as these technical capabilities improve. Recognizing that physiology is fundamentally a quantitative science, a recurring emphasis is on the need for imaging methods that provide reliable measurements of specific physiological parameters. The topics included necessarily reflect our perspective on what are interesting questions and are not meant to be a comprehensive review. Nevertheless, we hope that this essay will be a spur to physiologists to think about how imaging could usefully be applied in their research and to physical scientists developing new imaging methods to attack challenging questions imaging could potentially answer.

Modeling of angioadaptation: insights for vascular development

Vascular beds are generated by vasculogenesis and sprouting angiogenesis, and these processes have strong stochastic components. As a result, vascular patterns exhibit significant heterogeneity with respect to the topological arrangement of the individual vessel segments and the characteristics (length, number of segments) of different arterio-venous pathways. This structural heterogeneity tends to cause heterogeneous distributions of flow and oxygen availability in tissue. However, these quantities must be maintained within tolerable ranges to allow normal tissue function. This is achieved largely through adjustment of vascular flow resistance by control of vessel diameters. While short-term diameter control by changes in vascular tone in arterioles and small arteries plays an important role, in the long term an even more important role is played by structural adaptation (angioadaptation), occurring in response to metabolic and hemodynamic signals. The effectiveness, stability and robustness of this angioadaptation depend sensitively on the nature and strength of the vascular responses involved and their interactions with the network structure. Mathematical models are helpful in understanding these complex interactions, and can be used to simulate the consequences of failures in sensing or signal transmission mechanisms. For the tumor microcirculation, this strategy of combining experimental observations with theoretical models, has led to the hypothesis that dysfunctional information transport via vascular connexins is a major cause of the observed vascular pathology and increased heterogeneity in oxygen distribution.

Taylor's power law and fluctuation scaling explained by a central-limit-like convergence

A power function relationship observed between the variance and the mean of many types of biological and physical systems has generated much debate as to its origins. This Taylor's law (or fluctuation scaling) has been recently hypothesized to result from the second law of thermodynamics and the behavior of the density of states. This hypothesis is predicated on physical quantities like free energy and an external field; the correspondence of these quantities with biological systems, though, remains unproven. Questions can be posed as to the applicability of this hypothesis to the diversity of observed phenomena as well as the range of spatial and temporal scales observed with Taylor's law. We note that the cumulant generating functions derived from this thermodynamic model correspond to those derived over a quarter century earlier for a class of probabilistic models known as the Tweedie exponential dispersion models. These latter models are characterized by variance-to-mean power functions; their phenomenological basis rests with a central-limit-theorem-like property that causes many statistical systems to converge mathematically toward a Tweedie form. We review evaluations of the Tweedie Poisson-gamma model for Taylor's law and provide three further cases to test: the clustering of single nucleotide polymorphisms (SNPs) within the horse chromosome 1, the clustering of genes within human chromosome 8, and the Mertens function. This latter case is a number theoretic function for which a thermodynamic model cannot explain Taylor's law, but where Tweedie convergence remains applicable. The Tweedie models are applicable to diverse biological, physical, and mathematical phenomena that express power variance functions over a wide range of measurement scales; they provide a probabilistic description for Taylor's law that allows mechanistic insight into complex systems without the assumption of a thermodynamic mechanism.