Functional hierarchy of coronary circulation: direct evidence of a structure-function relation

The heart muscle is nourished by a complex system of blood vessels that make up the coronary circulation. Here we show that the design of the coronary circulation has a functional hierarchy. A full anatomic model of the coronary arterial tree, containing millions of blood vessels down to the capillary vessels, was simulated based on previously measured porcine morphometric data. A network analysis of blood flow through every vessel segment was carried out based on the laws of fluid mechanics and appropriate boundary conditions. Our results show an abrupt change in cross-sectional area that demarcates the transition from epicardial (EPCA) to intramyocardial (IMCA) coronary arteries. Furthermore, a similar pattern of blood flow was observed with a corresponding transition from EPCA to IMCA. These results suggest functional differences between the two types of vessels. An additional abrupt change occurs in the IMCA in relation to flow velocity. The velocity is fairly uniform proximal to these vessels but drops significantly distal to those vessels toward the capillary branches. This finding suggests functional differences between large and small IMCA. Collectively, these observations suggest a novel functional hierarchy of the coronary vascular tree and provide direct evidence of a structure-function relation.     

Analysis of blood flow in the entire coronary arterial tree

A hemodynamic analysis of coronary blood flow must be based on the measured branching pattern and vascular geometry of the coronary vasculature. We recently developed a computer reconstruction of the entire coronary arterial tree of the porcine heart based on previously measured morphometric data. In the present study, we carried out an analysis of blood flow distribution through a network of millions of vessels that includes the entire coronary arterial tree down to the first capillary branch. The pressure and flow are computed throughout the coronary arterial tree based on conservation of mass and momentum and appropriate pressure boundary conditions. We found a power law relationship between the diameter and flow of each vessel branch. The exponent is approximately 2.2, which deviates from Murray's prediction of 3.0. Furthermore, we found the total arterial equivalent resistance to be 0.93, 0.77, and 1.28 mmHg.ml(-1).s(-1).g(-1) for the right coronary artery, left anterior descending coronary artery, and left circumflex artery, respectively. The significance of the present study is that it yields a predictive model that incorporates some of the factors controlling coronary blood flow. The model of normal hearts will serve as a physiological reference state. Pathological states can then be studied in relation to changes in model parameters that alter coronary perfusion.     

Smaller, stiffer coronary bypass can moderate or reverse the adverse effects of wave reflections.

The question of whether the mechanical stiffness of a coronary bypass or that of a diseased coronary artery can have a significant effect on the hemodynamics in these vessels is addressed analytically, with emphasis on the effects of wave reflections. The analysis is based on a model of the vessels involved, and the results show the essential hemodynamic effects in each vessel. It is found that in the absence of a bypass graft, wave reflections resulting from a narrowing and stiffening of a diseased coronary artery have the effect of actually aiding the flow in the diseased vessel. In the presence of a bypass graft, however, the effects of wave reflections are reversed and become adverse to flow in both the bypass graft and the diseased coronary artery. A stiffer bypass moderates these effects and is therefore preferable to a more elastic bypass. The adverse effects also depend critically on the relative diameter of the bypass. Here the results indicate that a bypass of smaller diameter than that of the native coronary artery can moderate and even reverse the adverse effects of wave reflections resulting from the presence of the bypass.     

Heterogeneous mechanics of the mouse pulmonary arterial network

Individualized modeling and simulation of blood flow mechanics find applications in both animal research and patient care. Individual animal or patient models for blood vessel mechanics are based on combining measured vascular geometry with a fluid structure model coupling formulations describing dynamics of the fluid and mechanics of the wall. For example, one-dimensional fluid flow modeling requires a constitutive law relating vessel cross-sectional deformation to pressure in the lumen. To investigate means of identifying appropriate constitutive relationships, an automated segmentation algorithm was applied to micro-computerized tomography images from a mouse lung obtained at four different static pressures to identify the static pressure–radius relationship for four generations of vessels in the pulmonary arterial network. A shape-fitting function was parameterized for each vessel in the network to characterize the nonlinear and heterogeneous nature of vessel distensibility in the pulmonary arteries. These data on morphometric and mechanical properties were used to simulate pressure and flow velocity propagation in the network using one-dimensional representations of fluid and vessel wall mechanics. Moreover, wave intensity analysis was used to study effects of wall mechanics on generation and propagation of pressure wave reflections. Simulations were conducted to investigate the role of linear versus nonlinear formulations of wall elasticity and homogeneous versus heterogeneous treatments of vessel wall properties. Accounting for heterogeneity, by parameterizing the pressure/distention equation of state individually for each vessel segment, was found to have little effect on the predicted pressure profiles and wave propagation compared to a homogeneous parameterization based on average behavior. However, substantially different results were obtained using a linear elastic thin-shell model than were obtained using a nonlinear model that has a more physiologically realistic pressure versus radius relationship.     

Pulsatile blood flow in the entire coronary arterial tree: theory and experiment

The pulsatility of coronary circulation can be accurately simulated on the basis of the measured branching pattern, vascular geometry, and material properties of the coronary vasculature. A Womersley-type mathematical model is developed to analyze pulsatile blood flow in diastole in the absence of vessel tone in the entire coronary arterial tree on the basis of previously measured morphometric data. The model incorporates a constitutive equation of pressure and cross-section area relation based on our previous experimental data. The formulation enables the prediction of the impedance, the pressure distribution, and the pulsatile flow distribution throughout the entire coronary arterial tree. The model is validated by experimental measurements in six diastolic arrested, vasodilated porcine hearts. The agreement between theory and experiment is excellent. Furthermore, the present pulse wave results at low frequency agree very well with previously published steady-state model. Finally, the phase angle of flow is seen to decrease along the trunk of the major coronary artery and primary branches toward the capillary vessels. This study represents the first, most extensive validated analysis of Womersley-type pulse wave transmission in the entire coronary arterial tree down to the first segment of capillaries. The present model will serve to quantitatively test various hypotheses in the coronary circulation under pulsatile flow conditions.     

Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: clinical implications and therapeutic targeting strategies

Angiogenesis, the growth of a network of blood vessels, is a crucial component of solid tumour growth, linking the relatively harmless avascular growth phase and the potentially fatal vascular growth phase. As a process, angiogenesis is a well-orchestrated sequence of events involving endothelial cell migration, proliferation; degradation of tissue; new capillary vessel (sprout) formation; loop formation (anastomosis) and, crucially, blood flow through the network. Once there is blood flow associated with the nascent network, the subsequent growth of the network evolves both temporally and spatially in response to the combined effects of angiogenic factors, migratory cues via the extracellular matrix and perfusion-related haemodynamic forces in a manner that may be described as both adaptive and dynamic. In this paper we present a mathematical model which simultaneously couples vessel growth with blood flow through the vessels--dynamic adaptive tumour-induced angiogenesis (DATIA). This new mathematical model presents a theoretical and computational investigation of the process and highlights a number of important new targets for therapeutic intervention. In contrast to earlier flow models, where the effects of perfusion (blood flow) were essentially evaluated a posteriori, i.e. after generating a hollow network, blood flow in the model described in this paper has a direct impact during capillary growth, with radial adaptations and network remodelling occurring as immediate consequences of primary anastomoses. Capillary network architectures resulting from the dynamically adaptive model are found to differ radically from those obtained using earlier models. The DATIA model is used to examine the effects of changing various physical and biological model parameters on the developing vascular architecture and the delivery of chemotherapeutic drugs to the tumour. Subsequent simulations of chemotherapeutic treatments under different parameter regimes lead to the identification of a number of new therapeutic targets for tumour management.     

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.     

Numerical simulation of the flow field and mass transport pattern within the coronary artery

In this study, the steady and pulsatile flow field with mass transport analysis in an anatomically correct model of coronary artery is simulated numerically using a specific patient data from a 64-multislice computed tomography scanner. It is assumed that the blood flow is laminar and that the Navier-Stokes equations of motion are applied. Downstream of the bifurcation, a strong skewing occurs towards the flow divider walls as a result of branching. For the low-density lipoprotein (LDL) transport analysis where a specific boundary condition at the arterial walls is applied, LDL is generally elevated at locations where shear stress distribution is low, but it does not co-locate at whole domain. This numerical simulation gives an insight, as well as detailed quantitative data, of haemodynamic conditions in the left coronary artery as well as mass transfer patterns for a specific patient.     

A coupled hydrodynamic model of the cardiovascular and cerebrospinal fluid system

Coupling of the cardiovascular and cerebrospinal fluid (CSF) system is considered to be important to understand the pathophysiology of cerebrovascular and craniospinal disease and intrathecal drug delivery. A coupled cardiovascular and CSF system model was designed to examine the relation of spinal cord (SC) blood flow (SCBF) and CSF pulsations along the spinal subarachnoid space (SSS). A one-dimensional (1-D) cardiovascular tree model was constructed including a simplified SC arterial network. Connection between the cardiovascular and CSF system was accomplished by a transfer function based on in vivo measurements of CSF and cerebral blood flow. A 1-D tube model of the SSS was constructed based on in vivo measurements in the literature. Pressure and flow throughout the cardiovascular and CSF system were determined for different values of craniospinal compliance. SCBF results indicated that the cervical, thoracic, and lumbar SC each had a signature waveform shape. The cerebral blood flow to CSF transfer function reproduced an in vivo-like CSF flow waveform. The 1-D tube model of the SSS resulted in a distribution of CSF pressure and flow and a wave speed that were similar to those in vivo. The SCBF to CSF pulse delay was found to vary a great degree along the spine depending on craniospinal compliance and vascular anatomy. The properties and anatomy of the SC arterial network and SSS were found to have an important impact on pressure and flow and perivascular fluid movement to the SC. Overall, the coupled model provides predictions about the flow and pressure environment in the SC and SSS. More detailed measurements are needed to fully validate the model.     

Advances in percutaneous coronary intervention for chronic total occlusions: current antegrade dissection and reentry techniques and updated algorithm

Percutaneous coronary intervention (PCI) for chronic total occlusions (CTO) is considered relatively complex with low success rates and high complication rates. Treating a CTO with PCI using the hybrid algorithm increases success rates with acceptable complication rates. An essential part of the hybrid algorithm is antegrade dissection and reentry (ADR). In PCI of a non-CTO coronary lesion, the guidewire over which the stent is advanced and placed stays within the true lumen of the coronary artery. ADR techniques make it possible to cross the lesion through the wall of the coronary artery, the subintimal space, thus creating a small bypass within the architecture of the coronary artery and restoring antegrade blood flow. ADR increases success rates, especially in more difficult CTO procedures. In the last decade, new materials and techniques have been introduced in quick succession, which are summarised in this review. Consequently an updated ADR algorithm is presented, which can support the CTO operator during an ADR procedure.

     

<Emphasis Type="Italic">In silico</Emphasis> coronary wave intensity analysis: application of an integrated one-dimensional and poromechanical model of cardiac perfusion

Coronary wave intensity analysis (cWIA) is a diagnostic technique based on invasive measurement of coronary pressure and velocity waveforms. The theory of WIA allows the forward- and backward-propagating coronary waves to be separated and attributed to their origin and timing, thus serving as a sensitive and specific cardiac functional indicator. In recent years, an increasing number of clinical studies have begun to establish associations between changes in specific waves and various diseases of myocardium and perfusion. These studies are, however, currently confined to a trial-and-error approach and are subject to technological limitations which may confound accurate interpretations. In this work, we have developed a biophysically based cardiac perfusion model which incorporates full ventricular–aortic–coronary coupling. This was achieved by integrating our previous work on one-dimensional modelling of vascular flow and poroelastic perfusion within an active myocardial mechanics framework. Extensive parameterisation was performed, yielding a close agreement with physiological levels of global coronary and myocardial function as well as experimentally observed cumulative wave intensity magnitudes. Results indicate a strong dependence of the backward suction wave on QRS duration and vascular resistance, the forward pushing wave on the rate of myocyte tension development, and the late forward pushing wave on the aortic valve dynamics. These findings are not only consistent with experimental observations, but offer a greater specificity to the wave-originating mechanisms, thus demonstrating the value of the integrated model as a tool for clinical investigation.     

不仅是"益母"草:益母草的心脏保护作用

益母草作为一种传统的妇科中药,近年来的研究表明其作用是多方面的。在心血管方面,益母草能改善心肌缺血、增加冠状动脉血流、提高心功能,其机制主要是在氧化应激状态下通过清除氧自由基、抑制活性氧簇生成发挥抗氧化作用。益母草心脏保护作用的另一机制是促进血管发生。临床试验也表明,益母草能抑制冠心病人的血小板聚集,起抗凝、抗血栓形成作用,从而改善血流变学参数。本文根据目前研究进展,对益母草的心脏保护作用简要综述。     

The coronary circulation in exercise training

Exercise training (EX) induces increases in coronary transport capacity through adaptations in the coronary microcirculation including increased arteriolar diameters and/or densities and changes in the vasomotor reactivity of coronary resistance arteries. In large animals, EX increases capillary exchange capacity through angiogenesis of new capillaries at a rate matched to EX-induced cardiac hypertrophy so that capillary density remains normal. However, after EX coronary capillary exchange area is greater (i.e., capillary permeability surface area product is greater) at any given blood flow because of altered coronary vascular resistance and matching of exchange surface area and blood flow distribution. The improved coronary capillary blood flow distribution appears to be the result of structural changes in the coronary tree and alterations in vasoreactivity of coronary resistance arteries. EX also alters vasomotor reactivity of conduit coronary arteries in that after EX, α-adrenergic receptor responsiveness is blunted. Of interest, α- and β-adrenergic tone appears to be maintained in the coronary microcirculation in the presence of lower circulating catecholamine levels because of increased receptor responsiveness to adrenergic stimulation. EX also alters other vasomotor control processes of coronary resistance vessels. For example, coronary arterioles exhibit increased myogenic tone after EX, likely because of a calcium-dependent PKC signaling-mediated alteration in voltage-gated calcium channel activity in response to stretch. Conversely, EX augments endothelium-dependent vasodilation throughout the coronary arteriolar network and in the conduit arteries in coronary artery disease (CAD). The enhanced endothelium-dependent dilation appears to result from increased nitric oxide bioavailability because of changes in nitric oxide synthase expression/activity and decreased oxidant stress. EX also decreases extravascular compressive forces in the myocardium at rest and at comparable levels of exercise, mainly because of decreases in heart rate and duration of systole. EX does not stimulate growth of coronary collateral vessels in the normal heart. However, if exercise produces ischemia, which would be absent or minimal under resting conditions, there is evidence that collateral growth can be enhanced. While there is evidence that EX can decrease the progression of atherosclerotic lesions or even induce the regression of atherosclerotic lesions in humans, the evidence of this is not strong due to the fact that most prospective trials conducted to date have included other lifestyle changes and treatment strategies by necessity. The literature from large animal models of CAD also presents a cloudy picture concerning whether EX can induce the regression of or slow the progression of atherosclerotic lesions. Thus, while evidence from research using humans with CAD and animal models of CAD indicates that EX increases endothelium-dependent dilation throughout the coronary vascular tree, evidence that EX reverses or slows the progression of lesion development in CAD is not conclusive at this time. This suggests that the beneficial effects of EX in CAD may not be the result of direct effects on the coronary artery wall. If this suggestion is true, it is important to determine the mechanisms involved in these beneficial effects.     

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.     

Dynamics of flow velocities in endocardial and epicardial coronary arterioles

The subendocardium is the most vulnerable area of the left ventricle to the effects of hypoperfusion and ischemia. Despite this well-acknowledged observation, the mechanisms underlying this susceptibility are not elucidated, although numerous explanations including differences in transmural distribution of hemodynamics, metabolism, and wall stresses have been proposed. Our goal was to make dynamic measurements of endocardial and epicardial flow velocities, which reflect hemodynamic and wall stresses, to approach this problem. We measured blood flow velocities in subendocardial and subepicardial coronary arterioles of in vivo beating canine hearts using a high-speed, charge-coupled device, intravital videomicroscope with a rod-probe lens. Subendocardial flow was characterized by remarkable systolic flow-velocity reversal (systolic slosh ratio, 84%; measurable velocity of retrograde flow, faster than -40 mm/s), which contrasted to predominant forward-flow velocity during systole in the subepicardial arterioles (systolic slosh ratio, 25%; maximum velocity, approximately -20 mm/s; P < 0.0005 and 0.05 vs. subendocardial arterioles, respectively). We speculate that this retrograde flow is "wasteful," because this volume must be refilled during the subsequent diastole, which thereby detracts from the net perfusion as well as the time for perfusion. Accordingly, we also believe that the retrograde systolic blood flow contributes to the vulnerability of the subendocardium to ischemia.     

Modeling of Kidney Hemodynamics: Probability-Based Topology of an Arterial Network

Through regulation of the extracellular fluid volume, the kidneys provide important long-term regulation of blood pressure. At the level of the individual functional unit (the nephron), pressure and flow control involves two different mechanisms that both produce oscillations. The nephrons are arranged in a complex branching structure that delivers blood to each nephron and, at the same time, provides a basis for an interaction between adjacent nephrons. The functional consequences of this interaction are not understood, and at present it is not possible to address this question experimentally. We provide experimental data and a new modeling approach to clarify this problem. To resolve details of microvascular structure, we collected 3D data from more than 150 afferent arterioles in an optically cleared rat kidney. Using these results together with published micro-computed tomography (μCT) data we develop an algorithm for generating the renal arterial network. We then introduce a mathematical model describing blood flow dynamics and nephron to nephron interaction in the network. The model includes an implementation of electrical signal propagation along a vascular wall. Simulation results show that the renal arterial architecture plays an important role in maintaining adequate pressure levels and the self-sustained dynamics of nephrons.     

Evidence against significant resting alpha-adrenergic coronary vasoconstrictor tone

The importance of sympathetically mediated coronary vasoconstrictor tone as a determinant of resting coronary blood flow was assessed in the conscious dog by comparing blood flow and oxygen extraction in a normally innervated (I) and a previously sympathectomized (Sx) region of the same left ventricle. The regional ventricular sympathectomy was achieved by the topical application of phenol. The animals were well acclimated to the laboratory environment before regional myocardial blood flow was measured with microspheres or regional myocardial oxygen extraction was determined on blood sampled from chronically implanted coronary venous catheters. Results indicated that blood flow and oxygen extraction were not significantly different in I and Sx regions under these conditions. Regional blood flow data obtained after beta-adrenergic blockade or combined alpha- and beta-adrenergic blockade were not significantly different from control data. Thus we were unable to confirm previous evidence in the literature of significant resting sympathetic coronary vasoconstrictor tone in the conscious animal.     

Non-Newtonian effects of blood flow on hemodynamics in distal vascular graft anastomoses

Non-Newtonian fluid flow in a stenosed coronary bypass is investigated numerically using the Carreau-Yasuda model for the shear thinning behavior of the blood. End-to-side coronary bypass anastomosis is considered in a simplified model geometry where the host coronary artery has a 75% severity stenosis. Different locations of the bypass graft to the stenosis and different flow rates in the graft and in the host artery are studied. Particular attention is given to the non-Newtonian effect of the blood on the primary and secondary flow patterns in the host coronary artery and the wall shear stress (WSS) distribution there. Interaction between the jet flow from the stenosed artery and the flow from the graft is simulated by solving the three-dimensional Navier-Stokes equation coupled with the non-Newtonian constitutive model. Results for the non-Newtonian flow, the Newtonian flow and the rescaled Newtonian flow are presented. Significant differences in axial velocity profiles, secondary flow streamlines and WSS between the non-Newtonian and Newtonian fluid flows are revealed. However, reasonable agreement between the non-Newtonian and the rescaled Newtonian flows is found. Results from this study support the view that the residual flow in a partially occluded coronary artery interacts with flow in the bypass graft and may have significant hemodynamic effects in the host vessel downstream of the graft. Non-Newtonian property of the blood alters the flow pattern and WSS distribution and is an important factor to be considered in simulating hemodynamic effects of blood flow in arterial bypass grafts.