Microvascular blood flow: evidence indicating a cubic dependence on arteriolar diameter

Cerebral perfusion simulation using realistically generated synthetic trees for healthy and stroke patients

BACKGROUND AND OBJECTIVE

Cerebral vascular diseases are among the most burdensome diseases faced by society. However, investigating the pathophysiology of diseases as well as developing future treatments still relies heavily on expensive in-vivo and in-vitro studies. The generation of realistic, patient-specific models of the cerebrovascular system capable of simulating hemodynamics and perfusion promises the ability to simulate diseased states, therefore accelerating development cycles using in silico studies and opening opportunities for the individual assessment of diseased states, treatment planning, and the prediction of outcomes. By providing a patient-specific, anatomically detailed and validated model of the human cerebral vascular system, we aim to provide the basis for future in silico investigations of the cerebral physiology and pathology.

METHODS

In this retrospective study, a processing pipeline for patient-specific quantification of cerebral perfusion was developed and applied to healthy individuals and a stroke patient. Major arteries are segmented from 3T MR angiography data. A synthetic tree generation algorithm titled tissue-growth based optimization (GBO)1 is used to extend vascular trees beyond the imaging resolution. To investigate the anatomical accuracy of the generated trees, morphological parameters are compared against those of 7 T MRI, 9.4 T MRI, and dissection data. Using the generated vessel model, hemodynamics and perfusion are simulated by solving one-dimensional blood flow equations combined with Darcy flow equations.

RESULTS

Morphological data of three healthy individuals (mean age 47 years ± 15.9 [SD], 2 female) was analyzed. Bifurcation and physiological characteristics of the synthetically generated vessels are comparable to those of dissection data. The inability of MRI based segmentation to resolve small branches and the small volume investigated cause a mismatch in the comparison to MRI data. Cerebral perfusion was estimated for healthy individuals and a stroke patient. The simulated perfusion is compared against Arterial-Spin-Labeling MRI perfusion data. Good qualitative agreement is found between simulated and measured cerebral blood flow (CBF)2. Ischemic regions are predicted well, however ischemia severity is overestimated.

CONCLUSIONS

GBO successfully generates detailed cerebral vascular models with realistic morphological parameters. Simulations based on the resulting networks predict perfusion territories and ischemic regions successfully.

Transport of nitrite from large arteries modulates regional blood flow during stress and exercise

Background

Acute cardiovascular stress increases systemic wall shear stress (WSS)-a frictional force exerted by the flow of blood on vessel walls-which raises plasma nitrite concentration due to enhanced endothelial nitric oxide synthase (eNOS) activity. Upstream eNOS inhibition modulates distal perfusion, and autonomic stress increases both the consumption and vasodilatory effects of endogenous nitrite. Plasma nitrite maintains vascular homeostasis during exercise and disruption of nitrite bioavailability can lead to intermittent claudication.

Hypothesis

During acute cardiovascular stress or strenuous exercise, we hypothesize enhanced production of nitric oxide (NO) by vascular endothelial cells raises nitrite concentrations in near-wall layers of flowing blood, resulting in cumulative NO concentrations in downstream arterioles sufficient for vasodilation.

Confirmation and implications

Utilizing a multiscale model of nitrite transport in bifurcating arteries, we tested the hypothesis for femoral artery flow under resting and exercised states of cardiovascular stress. Results indicate intravascular transport of nitrite from upstream endothelium could result in vasodilator-active levels of nitrite in downstream resistance vessels. The hypothesis could be confirmed utilizing artery-on-a-chip technology to measure NO production rates directly and help validate numerical model predictions. Further characterization of this mechanism may improve our understanding of symptomatic peripheral artery occlusive disease and exercise physiology.

Shear stress and intravascular pressure effects on vascular dynamics: two-phase blood flow in elastic microvessels accounting for the passive stresses

We study the steady hemodynamics in physiological elastic microvessels proposing an advanced fluid-structure interaction model. The arteriolar tissue is modeled as a two-layer fiber-reinforced hyperelastic material representing its Media and Adventitia layers. The constitutive model employed (Holzapfel et al. in J Elast 61:1-48, 2000) is parametrized via available data on stress-strain experiments for arterioles. The model is completed by simulating the blood/plasma flow in the lumen, using the thixotropic elasto-viscoplastic model in its core, and the linear Phan-Thien and Tanner viscoelastic model in its annular part. The Cell-Free Layer (CFL) and the Fåhraeus and Fåhraeus-Lindqvist effects are considered via analytical expressions based on experimental data (Giannokostas et al. in Materials (Basel) 14:367, 2021b). The coupling between tissue deformation and blood flow is achieved through the experimentally verified pressure-shear hypothesis (Pries et al. Circ Res 77:1017-1023, 1995). Our calculations confirm that the increase in the reference inner radius produces larger expansion. Also, by increasing the intraluminal pressure, the thinning of the walls is more pronounced and it may reach 40% of the initial thickness. Comparing our predictions with those in rigid-wall microtubes, we conclude that apart from the vital importance of vasodilation, there is an up to 25% reduction in wall shear stress. The passive vasodilation contributes to the decrease in the tissue stress fields and affects the hemodynamic features such as the CFL thickness, reducing the plasma layer when blood flows in vessels with elastic walls, in quantitative agreement with previous experiments. Our calculations verify the correctness of the pressure-shear hypothesis but not that of the Laplace law.

Dependence of red blood cell dynamics in microvessel bifurcations on the endothelial surface layer's resistance to flow and compression

Red blood cells (RBCs) make up 40-45% of blood and play an important role in oxygen transport. That transport depends on the RBC distribution throughout the body, which is highly heterogeneous. That distribution, in turn, depends on how RBCs are distributed or partitioned at diverging vessel bifurcations where blood flows from one vessel into two. Several studies have used mathematical modeling to consider RBC partitioning at such bifurcations in order to produce useful insights. These studies, however, assume that the vessel wall is a flat impenetrable homogeneous surface. While this is a good first approximation, especially for larger vessels, the vessel wall is typically coated by a flexible, porous endothelial glycocalyx or endothelial surface layer (ESL) that is on the order of 0.5-1 µm thick. To better understand the possible effects of this layer on RBC partitioning, a diverging capillary bifurcation is analyzed using a flexible, two-dimensional model. In addition, the model is also used to investigate RBC deformation and RBC penetration of the ESL region when ESL properties are varied. The RBC is represented using interconnected viscoelastic elements. Stokes flow equations (viscous flow) model the surrounding fluid. The flow in the ESL is modeled using the Brinkman approximation for porous media with a corresponding hydraulic resistivity. The ESL's resistance to compression is modeled using an osmotic pressure difference. One cell passes through the bifurcation at a time, so there are no cell-cell interactions. A range of physiologically relevant hydraulic resistivities and osmotic pressure differences are explored. Decreasing hydraulic resistivity and/or decreasing osmotic pressure differences (ESL resistance to compression) produced four behaviors: (1) RBC partitioning nonuniformity increased slightly; (2) RBC deformation decreased; (3) RBC velocity decreased relative to blood flow velocity; and (4) RBCs penetrated more deeply into the ESL. Decreasing the ESL's resistance to flow and/or compression to pathological levels could lead to more frequent cell adhesion and clotting as well as impaired vascular regulation due to weaker ATP and nitric oxide release. Potential mechanisms that can contribute to these behaviors are also discussed.

Analysis of flow resistance in the pulmonary arterial circulation: implications for hypoxic pulmonary vasoconstriction

Hypoxic pulmonary vasoconstriction (HPV) plays an essential role in distributing blood in the lung to enhance ventilation-perfusion matching and blood oxygenation. In this study, a theoretical model of the pulmonary vasculature is used to predict the effects of vasoconstriction over specified ranges of vessel diameters on pulmonary vascular resistance (PVR). The model is used to evaluate the ability of hypothesized mechanisms of HPV to account for observed levels of PVR elevation during hypoxia. The vascular structure from pulmonary arteries to capillaries is represented using scaling laws. Vessel segments are modeled as resistive elements and blood flow rates are computed from physical principles. Direct vascular responses to intravascular oxygen levels have been proposed as a mechanism of HPV. In the lung, significant changes in oxygen level occur only in vessels less than 60 μm in diameter. The model shows that observed levels of hypoxic vasoconstriction in these vessels alone cannot account for the elevation of PVR associated with HPV. However, the elevation in PVR associated with HPV can be accounted for if larger upstream vessels also constrict. These results imply that upstream signaling by conducted responses to engage constriction of arterioles plays an essential role in the elevation of PVR during HPV.NEW & NOTEWORTHY A theoretical model of the pulmonary vasculature is used to predict the effects of vasoconstriction over specified ranges of vessel diameters on pulmonary vascular resistance (PVR). The model shows that observed levels of hypoxic vasoconstriction in terminal vessels cannot account for the elevation of PVR associated with hypoxic pulmonary vasoconstriction (HPV). Upstream signaling by conducted responses to engage constriction of arterioles, therefore, plays an essential role in the elevation of PVR during HPV.

Automated vessel diameter quantification and vessel tracing for OCT angiography

Optical coherence tomography angiography (OCTA) is capable of non-invasively imaging the vascular networks within circulatory tissue beds in vivo. Following improvements in OCTA image quality, it is now possible to extract vascular parameters from imaging data to potentially facilitate the diagnosis and treatment of human disease. In this paper, we present a method for automated mapping of vessel diameter down to the individual capillary level, through gradient-guided minimum radial distance (MRD). During validation using well-characterized microfluidic flow phantoms, this method demonstrated superior consistency and a nearly threefold decrease in error when compared to currently accepted techniques. In addition, the MRD technique exhibited a high tolerance to rotation of the vasculature pattern. We also incorporated a modified A* path searching algorithm to trace vessel branches and calculate the diameter of each branch from the OCTA images. After validation in vitro, we applied these algorithms to the in vivo setting through analysis of mouse cortical vasculature. Our algorithm returned results that followed Murray's law, until reaching the capillary level, agreeing well with known physiological data. From our tracing process, vessel tortuosity and branching angle could also be measured. Our techniques provide a platform for the automated evaluation of the vasculature and may aid in diagnosis of vascular diseases, especially those resulting in regional early-stage morphological changes.

The effects of clinically-derived parametric data uncertainty in patient-specific coronary simulations with deformable walls

Cardiovascular simulations are increasingly used for noninvasive diagnosis of cardiovascular disease, to guide treatment decisions, and in the design of medical devices. Quantitative assessment of the variability of simulation outputs due to input uncertainty is a key step toward further integration of cardiovascular simulations in the clinical workflow. In this study, we present uncertainty quantification in computational models of the coronary circulation to investigate the effect of uncertain parameters, including coronary pressure waveform, intramyocardial pressure, morphometry exponent, and the vascular wall Young's modulus. We employ a left coronary artery model with deformable vessel walls, simulated via an Arbitrary-Lagrangian-Eulerian framework for fluid-structure interaction, with a prescribed inlet pressure and open-loop lumped parameter network outlet boundary conditions. Stochastic modeling of the uncertain inputs is determined from intra-coronary catheterization data or gathered from the literature. Uncertainty propagation is performed using several approaches including Monte Carlo, Quasi Monte Carlo sampling, stochastic collocation, and multi-wavelet stochastic expansion. Variabilities in the quantities of interest, including branch pressure, flow, wall shear stress, and wall deformation are assessed. We find that uncertainty in inlet pressures and intramyocardial pressures significantly affect all resulting QoIs, while uncertainty in elastic modulus only affects the mechanical response of the vascular wall. Variability in the morphometry exponent used to distribute the total downstream vascular resistance to the single outlets, has little effect on coronary hemodynamics or wall mechanics. Finally, we compare convergence behaviors of statistics of QoIs using several uncertainty propagation methods on three model benchmark problems and the left coronary simulations. From the simulation results, we conclude that the multi-wavelet stochastic expansion shows superior accuracy and performance against Quasi Monte Carlo and stochastic collocation methods.

Aortic stiffness is associated with changes in retinal arteriole flow pulsatility mediated by local vasodilation in healthy young/middle-age adults

Aortic stiffness is associated with augmented pressure pulsatility in large conduit arteries and remodeling of the microcirculation. However, studies in humans examining the relation between aortic stiffness and end-organ microvascular flow pulsatility are limited. Therefore, we used the retinal microvasculature as an end-organ in vivo model to examine the hypothesis that aortic stiffness would be positively associated with microvascular flow pulsatility index (PI) (flow pulse amplitude/mean flow) in humans. In 40 young/middle-age healthy adults (25-60 yr old, 50% women), aortic stiffness (carotid-femoral pulse wave velocity, CFPWV) and retinal arteriole flow (laser speckle flowgraphy) were examined at rest and during metabolic vasodilation (light flicker). CFPWV and related increases in central pulse pressure (PP) were inversely correlated with arteriole lumen diameter independent of age (CFPWV: R = -0.52, P = 0.001; Central PP: R = -0.39, P = 0.014). Accordingly, microvascular resistance was positively related to CFPWV independent of age (R = 0.35, P = 0.031). Multiple linear regression showed that CFPWV was not a significant determinant of resting arteriole flow PI (β = -0.10, P = 0.64). However, during reduced retinal microvascular resistance using light flicker (P < 0.001), CFPWV was a significant determinant of the percent change in arteriole flow PI (β = 0.58, P = 0.046), but not mean flow (β = -0.17, P = 0.54), where reductions in arteriole flow PI were associated with lower CFPWV. In summary, our findings suggest that higher aortic stiffness and the related increase in central PP in healthy young/middle-age adults are associated with retinal arteriole narrowing and smaller reductions in arteriole flow pulsatility in response to dynamic conditions such as local metabolic vasodilation.NEW & NOTEWORTHY By using the human retinal microvasculature as an end-organ in vivo model, we confirm that aortic stiffness and related increases in central pulse pressure are inversely correlated with retinal arteriole lumen diameter and increased microvascular resistance among heathy young/middle-age adults. Additionally, higher aortic stiffness is not associated with excessive flow pulsatility in the retinal microvasculature under tonic conditions but may be related to limited reductions in retinal arteriole flow pulsatility in response to local vasodilation.

Epigenetic regulators of the revascularization response to chronic arterial occlusion

Peripheral arterial disease (PAD) is the leading cause of lower limb amputation and estimated to affect over 202 million people worldwide. PAD is caused by atherosclerotic lesions that occlude large arteries in the lower limbs, leading to insufficient blood perfusion of distal tissues. Given the severity of this clinical problem, there has been long-standing interest in both understanding how chronic arterial occlusions affect muscle tissue and vasculature and identifying therapeutic approaches capable of restoring tissue composition and vascular function to a healthy state. To date, the most widely utilized animal model for performing such studies has been the ischaemic mouse hindlimb. Despite not being a model of PAD per se, the ischaemic hindlimb model does recapitulate several key aspects of PAD. Further, it has served as a valuable platform upon which we have built much of our understanding of how chronic arterial occlusions affect muscle tissue composition, muscle regeneration and angiogenesis, and collateral arteriogenesis. Recently, there has been a global surge in research aimed at understanding how gene expression is regulated by epigenetic factors (i.e. non-coding RNAs, histone post-translational modifications, and DNA methylation). Thus, perhaps not unexpectedly, many recent studies have identified essential roles for epigenetic factors in regulating key responses to chronic arterial occlusion(s). In this review, we summarize the mechanisms of action of these epigenetic regulators and highlight several recent studies investigating the role of said regulators in the context of hindlimb ischaemia. In addition, we focus on how these recent advances in our understanding of the role of epigenetics in regulating responses to chronic arterial occlusion(s) can inform future therapeutic applications to promote revascularization and perfusion recovery in the setting of PAD.

Blood flow rate and wall shear stress in seven major cephalic arteries of humans

Blood flow rate ( Q ˙ ) in relation to arterial lumen radius (r_i ) is commonly modelled according to theoretical equations and paradigms, including Murray's Law ( Q ˙ ∝ r i 3 ) and da Vinci's Rule ( Q ˙ ∝ r i 2 ). Wall shear stress (τ) is independent of r_i with Murray's Law (τ ∝  r i 0 ) and decreases with da Vinci's Rule (τ ∝  r i - 1 ). These paradigms are tested empirically with a meta-analysis of the relationships between Q ˙ and r_i in seven major arteries of the human cephalic circulation from 19 imaging studies in which both variables were presented. The analysis shows that Q ˙ ∝ r i 2.16 and τ ∝  r i - 1.02 , more consistent with da Vinci's Rule than Murray's Law. This meta-analysis provides standard values for Q ˙ , r_i and τ in the human cephalic arteries that may be a useful baseline in future investigations. On average, the paired internal carotid arteries supply 75%, and the vertebral arteries supply 25%, of total brain blood flow. The internal carotid arteries contribute blood entirely to the anterior and middle cerebral arteries and also partly to the posterior cerebral arteries via the posterior communicating arteries of the circle of Willis. On average, the internal carotid arteries provide 88% of the blood flow to the cerebrum and the vertebral arteries only 12%.

Fluid flow rate dictates the efficacy of low-intensity anti-vascular ultrasound therapy in a microfluidic model

OBJECTIVE

Low-intensity anti-vascular ultrasound therapy is an effective means of disrupting the blood supply in the tumor microenvironment. Its diminished effect on the surrounding vasculature is thought to be due to higher blood flow rates outside the tumor that decreases the interaction time between the endothelial lining and the microbubbles, which transduce acoustic energy to thermal heat. However, investigating the effect of circulation rate on the response to low-intensity ultrasound is complicated by the heterogeneity of the in vivo vascular microenvironment. Here, a 3D microfluidic model is used to directly interrogate the dynamics of ultrasound stimulation.

METHODS

A 3D in vitro vessel consisting of LifeACT transfected endothelial cells facilitate real-time analysis of actin dynamics during ultrasound treatment. Using an integrated testing platform, both the flow rate of microbubbles within the vessel and the magnitude of insonation can be varied.

RESULTS

Morphological measurements and dextran transport assays indicate that lower flow rates exacerbate the effect of low-intensity ultrasound on vessel integrity. Additionally, immunostaining for VE-cadherin and transmission electron microscopy provide further insight into structural changes in cell-cell junctions following insonation.

CONCLUSIONS

Overall, these results reveal that blood flow rate is an important parameter to consider during the refinement of anti-vascular low-intensity ultrasound therapies.

Interspecific scaling of blood flow rates and arterial sizes in mammals

This meta-study investigated the relationships between blood flow rate (Q̇; cm³ s^-1), wall shear stress (τ_w; dyn cm^-2) and lumen radius (r _i; cm) in 20 named systemic arteries of nine species of mammals, ranging in mass from 23 g mice to 652 kg cows, at rest. In the dataset, derived from 50 studies, lumen radius varied between 3.7 µm in a cremaster artery of a rat and 11.2 mm in the aorta of a human. The 92 logged data points of [Formula: see text] and r _i are described by a single second-order polynomial curve with the equation: [Formula: see text] The slope of the curve increased from approximately 2 in the largest arteries to approximately 3 in the smallest ones. Thus, da Vinci's rule ([Formula: see text]) applies to the main arteries and Murray's law ([Formula: see text]) applies to the microcirculation. A subset of the data, comprising only cephalic arteries in which [Formula: see text] is fairly constant, yielded the allometric power equation: [Formula: see text] These empirical equations allow calculation of resting perfusion rates from arterial lumen size alone, without reliance on theoretical models or assumptions on the scaling of wall shear stress in relation to body mass. As expected, [Formula: see text] of individual named arteries is strongly affected by body mass; however, [Formula: see text] of the common carotid artery from six species (mouse to horse) is also sensitive to differences in whole-body basal metabolic rate, independent of the effect of body mass.

The Shape Effect on Polymer Nanoparticle Transport in a Blood Vessel

Nanoparticle therapeutic delivery is influenced by many factors including physical, chemical, and biophysical properties along with local vascular conditions. In recent years, nanoparticles of various shapes have been fabricated and have shown significant impact on transport efficiency. Identification of which nanoparticle shape helps to improve the therapeutic delivery process allows for enhanced therapeutic effects, yet is hard to be quantified in vivo due to the complex nature of the in vivo environment. In this work, we turn to biological models as a guide for informing improved nanoparticle therapeutic delivery, and quantify the contribution of various factors on delivery efficiency. Here we show that with a mimetic blood vessel, improved therapeutic delivery is achieved using long filamentous rod nanoparticles under low pressure conditions. When considering medium pressure conditions, a combination of nanoparticle shapes presents improved therapeutic delivery over the treatment time-course starting with long filamentous rod nanoparticles, followed by short rod nanoparticles. Conditions of high pressure required a combination of short rod nanoparticles, followed by spherical nanoparticles to achieve enhanced therapeutic delivery. Overall, improvement of therapeutic delivery via nanoparticle carriers is likely to require a combination of nanoparticle shapes administered at different times over the treatment time-course, given patient specific conditions.

Microfluidic platform analysis of therapeutic carrier delivery to cancerous sites for optimization of drug delivery efficiency over time-course treatment plans.

Transport of drugs from blood vessels to tumour tissue

The effectiveness of anticancer drugs in treating a solid tumour is dependent on delivery of the drug to virtually all cancer cells in the tumour. The distribution of drug in tumour tissue depends on the plasma pharmacokinetics, the structure and function of the tumour vasculature and the transport properties of the drug as it moves through microvessel walls and in the extravascular tissue. The aim of this Review is to provide a broad, balanced perspective on the current understanding of drug transport to tumour cells and on the progress in developing methods to enhance drug delivery. First, the fundamental processes of solute transport in blood and tissue by convection and diffusion are reviewed, including the dependence of penetration distance from vessels into tissue on solute binding or uptake in tissue. The effects of the abnormal characteristics of tumour vasculature and extravascular tissue on these transport properties are then discussed. Finally, methods for overcoming limitations in drug transport and thereby achieving improved therapeutic results are surveyed.

Myocardial Perfusion: Characteristics of Distal Intramyocardial Arteriolar Trees

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

Hematocrit dispersion in asymmetrically bifurcating vascular networks

Quantitative modeling of physiological processes in vasculatures requires an accurate representation of network topology, including vessel branching. We propose a new approach for reconstruction of vascular network, which determines how vessel bifurcations distribute red blood cells (RBC) in the microcirculation. Our method follows the foundational premise of Murray's law in postulating the existence of functional optimality of such networks. It accounts for the non-Newtonian behavior of blood by allowing the apparent blood viscosity to vary with discharge hematocrit and vessel radius. The optimality criterion adopted in our approach is the physiological cost of supplying oxygen to the tissue surrounding a blood vessel. Bifurcation asymmetry is expressed in terms of the amount of oxygen consumption associated with the respective tissue volumes being supplied by each daughter vessel. The vascular networks constructed with our approach capture a number of physiological characteristics observed in in vivo studies. These include the nonuniformity of wall shear stress in the microcirculation, the significant increase in pressure gradients in the terminal sections of the network, the nonuniformity of both the hematocrit partitioning at vessel bifurcations and hematocrit across the capillary bed, and the linear relationship between the RBC flux fraction and the blood flow fraction at bifurcations.

Radius exponent in elastic and rigid arterial models optimized by the least energy principle

It was analyzed in normal physiological arteries whether the least energy principle would suffice to account for the radius exponent x. The mammalian arterial system was modeled as two types, the elastic or the rigid, to which Bernoulli's and Hagen-Poiseuille's equations were applied, respectively. We minimized the total energy function E, which was defined as the sum of kinetic, pressure, metabolic and thermal energies, and loss of each per unit time in a single artery transporting viscous incompressible blood. Assuming a scaling exponent α between the vessel radius (r) and length (l) to be 1.0, x resulted in 2.33 in the elastic model. The rigid model provided a continuously changing x from 2.33 to 3.0, which corresponded to Uylings' and Murray's theories, respectively, through a function combining Reynolds number with a proportional coefficient of the l - r relationship. These results were expanded to an asymmetric arterial fractal tree with the blood flow preservation rule. While x in the optimal elastic model accounted for around 2.3 in proximal systemic (r >1 mm) and whole pulmonary arteries (r ≥0.004 mm), optimal x in the rigid model explained 2.7 in elastic-muscular (0.1 < r ≤1 mm) and 3.0 in peripheral resistive systemic arteries (0.004 ≤ r ≤0.1 mm), in agreement with data obtained from angiographic, cast-morphometric, and in vivo experimental studies in the literature. The least energy principle on the total energy basis provides an alternate concept of optimality relating to mammalian arterial fractal dimensions under α = 1.0.

Vascularity of myocardium and gastrocnemius muscle in rats selectively bred for endurance running capacity

We tested the hypothesis that changes in the arteriolar branching architecture contributed to increased running capacity of rats subjected to two-way artificial selection for intrinsic aerobic endurance treadmill running capacity resulting in strains of low-capacity and high-capacity endurance rats. Hearts and gastrocnemius muscles were harvested from each strain, and the microvasculature's branching geometry measured from micro-CT images. The vascular branching geometry of the hearts and skeletal muscle from the high capacity was indistinguishable from low-capacity rats. Our hypothesis was not supported. Neither remodeling nor an increase in arteriolar microvasculature branching appears to play a role in the enhanced performance of the high capacity rats. We are led to speculate that endothelial tolerance for shear stress and/or increased coupling of myocardial muscle fiber metabolic-to-contractile function is increased in the high-capacity runner strain to the effect of allowing either higher flow rate per unit volume of muscle or more efficient use of oxygen and nutrients in the high-capacity endurance rats.

Assessment of Energy Requirement for the Retinal Arterial Network in Normal and Hypertensive Subjects

The retinal arterial network structure can be altered by systemic diseases such as hypertension and diabetes. In order to compare the energy requirement for maintaining retinal blood flow and vessel wall metabolism between normal and hypertensive subjects, 3D hypothetical models of a representative retinal arterial bifurcation were constructed based on topological features derived from retinal images. Computational analysis of blood flow was performed, which accounted for the non-Newtonian rheological properties of blood and peripheral vessel resistance. The results suggested that the rate of energy required to maintain the blood flow and wall metabolism is much lower for normal subjects than for hypertensives, with the latter requiring 49.2% more energy for an entire retinal arteriolar tree. Among the several morphological factors, length-to-diameter ratio was found to have the most significant influence on the overall energy requirement.

Structural adaptation of normal and tumour vascular networks

Vascular networks are dynamic structures, adapting to changing conditions by structural remodelling of vessel diameters and by growth of new vessels and regression of existing vessels. The vast number of blood vessels in the circulatory system, more than 10⁹, implies that vessels' arrangement and structure are not under individual genetic control but emerge as a result of generic responses of each segment to the various stimuli that it experiences. To obtain insight into the types of response that are needed, a network-oriented approach has been used, in which theoretical models are used to simulate structural adaptation in vascular networks, and the results are compared with experimental observations. With regard to the structural control of vessel diameters, this approach shows that responses to both haemodynamic and metabolic stimuli are needed for the formation of functionally adequate and efficient network structures. Furthermore, information transfer in both upstream and downstream directions is essential for balancing flows between long and short flow pathways. Otherwise, functional shunting occurs, that is, short pathways become enlarged and flow bypasses longer pathways. Information transfer in the upstream direction is achieved by conducted responses communicated along vessel walls. Simulations of structural adaptation in tumour microvascular networks indicate that impaired vascular communication, resulting in functional shunting, may be an important factor causing the dysfunctional microcirculation and local hypoxia typically observed in tumours. Anti-angiogenic treatment of tumours may restore vascular communication and thereby improve or normalize flow distribution in tumour vasculature.

Extension of Murray's law using a non-Newtonian model of blood flow

Background

So far, none of the existing methods on Murray's law deal with the non-Newtonian behavior of blood flow although the non-Newtonian approach for blood flow modelling looks more accurate.

Modeling

In the present paper, Murray's law which is applicable to an arterial bifurcation, is generalized to a non-Newtonian blood flow model (power-law model). When the vessel size reaches the capillary limitation, blood can be modeled using a non-Newtonian constitutive equation. It is assumed two different constraints in addition to the pumping power: the volume constraint or the surface constraint (related to the internal surface of the vessel). For a seek of generality, the relationships are given for an arbitrary number of daughter vessels. It is shown that for a cost function including the volume constraint, classical Murray's law remains valid (i.e. ΣR^c = cste with c = 3 is verified and is independent of n, the dimensionless index in the viscosity equation; R being the radius of the vessel). On the contrary, for a cost function including the surface constraint, different values of c may be calculated depending on the value of n.

Results

We find that c varies for blood from 2.42 to 3 depending on the constraint and the fluid properties. For the Newtonian model, the surface constraint leads to c = 2.5. The cost function (based on the surface constraint) can be related to entropy generation, by dividing it by the temperature.

Conclusion

It is demonstrated that the entropy generated in all the daughter vessels is greater than the entropy generated in the parent vessel. Furthermore, it is shown that the difference of entropy generation between the parent and daughter vessels is smaller for a non-Newtonian fluid than for a Newtonian fluid.

Wall shear stress as measured in vivo: consequences for the design of the arterial system

Based upon theory, wall shear stress (WSS), an important determinant of endothelial function and gene expression, has been assumed to be constant along the arterial tree and the same in a particular artery across species. In vivo measurements of WSS, however, have shown that these assumptions are far from valid. In this survey we will discuss the assessment of WSS in the arterial system in vivo and present the results obtained in large arteries and arterioles. In vivo WSS can be estimated from wall shear rate, as derived from non-invasively recorded velocity profiles, and whole blood viscosity in large arteries and plasma viscosity in arterioles, avoiding theoretical assumptions. In large arteries velocity profiles can be recorded by means of a specially designed ultrasound system and in arterioles via optical techniques using fluorescent flow velocity tracers. It is shown that in humans mean WSS is substantially higher in the carotid artery (1.1–1.3 Pa) than in the brachial (0.4–0.5 Pa) and femoral (0.3–0.5 Pa) arteries. Also in animals mean WSS varies substantially along the arterial tree. Mean WSS in arterioles varies between about 1.0 and 5.0 Pa in the various studies and is dependent on the site of measurement in these vessels. Across species mean WSS in a particular artery decreases linearly with body mass, e.g., in the infra-renal aorta from 8.8 Pa in mice to 0.5 Pa in humans. The observation that mean WSS is far from constant along the arterial tree implies that Murray’s cube law on flow-diameter relations cannot be applied to the whole arterial system. Because blood flow velocity is not constant along the arterial tree either, a square law also does not hold. The exponent in the power law likely varies along the arterial system, probably from 2 in large arteries near the heart to 3 in arterioles. The in vivo findings also imply that in in vitro studies no average shear stress value can be taken to study effects on endothelial cells derived from different vascular areas or from the same artery in different species. The cells have to be studied under the shear stress conditions they are exposed to in real life.

Theoretical model of metabolic blood flow regulation: roles of ATP release by red blood cells and conducted responses

A proposed mechanism for metabolic flow regulation involves the saturation-dependent release of ATP by red blood cells, which triggers an upstream conducted response signal and arteriolar vasodilation. To analyze this mechanism, a theoretical model is used to simulate the variation of oxygen and ATP levels along a flow pathway of seven representative segments, including two vasoactive arteriolar segments. The conducted response signal is defined by integrating the ATP concentration along the vascular pathway, assuming exponential decay of the signal in the upstream direction with a length constant of approximately 1 cm. Arteriolar tone depends on the conducted metabolic signal and on local wall shear stress and wall tension. Arteriolar diameters are calculated based on vascular smooth muscle mechanics. The model predicts that conducted responses stimulated by ATP release in venules and propagated to arterioles can account for increases in perfusion in response to increased oxygen demand that are consistent with experimental findings at low to moderate oxygen consumption rates. Myogenic and shear-dependent responses are found to act in opposition to this mechanism of metabolic flow regulation.

Simulated two-dimensional red blood cell motion, deformation, and partitioning in microvessel bifurcations

Movement, deformation, and partitioning of mammalian red blood cells (RBCs) in diverging microvessel bifurcations are simulated using a two-dimensional, flexible-particle model. A set of viscoelastic elements represents the RBC membrane and the cytoplasm. Motion of isolated cells is considered, neglecting cell-to-cell interactions. Center-of-mass trajectories deviate from background flow streamlines due to migration of flexible cells towards the mother vessel centerline upstream of the bifurcation and due to flow perturbations caused by cell obstruction in the neighborhood of the bifurcation. RBC partitioning in the bifurcation is predicted by determining the RBC fraction entering each branch, for a given partition of total flow and for a given upstream distribution of RBCs. Typically, RBCs preferentially enter the higher-flow branch, leading to unequal discharge hematocrits in the downstream branches. This effect is increased by migration toward the centerline but decreased by the effects of obstruction. It is stronger for flexible cells than for rigid circular particles of corresponding size, and decreases with increasing parent vessel diameter. For unequally sized daughter vessels, partitioning is asymmetric, with RBCs tending to enter the smaller vessel. Partitioning is not significantly affected by branching angles. Model predictions are consistent with previous experimental results.

Microvascular endothelial cells exhibit optimal aspect ratio for minimizing flow resistance

A recent analytical solution of the three-dimensional Stokes flow through a bumpy tube predicts that for a given bump area, there exists an optimal circumferential wavenumber which minimizes flow resistance. This study uses measurements of microvessel endothelial cell morphology to test whether this prediction holds in the microvasculature. Endothelial cell (EC) morphology was measured in blood perfused in situ microvessels in anesthetized mice using confocal intravital microscopy. EC borders were identified by immunofluorescently labeling the EC surface molecule ICAM-1 which is expressed on the surface but not in the EC border regions. Comparison of this theory with extensive in situ measurements of microvascular EC geometry in mouse cremaster muscle using intravital microscopy reveals that the spacing of EC nuclei in venules ranging from 27 to 106 microm in diameter indeed lies quite close to this predicted optimal configuration. Interestingly, arteriolar ECs are configured to minimize flow resistance not in the resting state, but at the dilated vessel diameter. These results raise the question of whether less organized circulatory systems, such as that found in newly formed solid tumors or in the developing embryo, may deviate from the optimal bump spacing predicted to minimize flow resistance.

Effect of chronic alcohol consumption on brain damage following transient focal ischemia

Chronic alcohol consumption impairs cerebral vasoreactivity, and thus, may result in an increase in ischemic brain damage. The goal of this study is to examine the influence of chronic alcohol consumption on transient focal ischemia-induced brain damage. Sprague-Dawley rats were divided into two groups, a control group and an alcohol group. Eight weeks after being fed a liquid diet with or without alcohol, responses of parietal pial arterioles to systemic hypoxia and hypercapnia were measured using a cranial window technique. In separate experiments, rats were subjected to right middle cerebral artery occlusion (MCAO) for 2 h under ketamine/xylazine or isoflurane anesthesia. Regional cerebral blood flow (rCBF) was monitored through a Laser-Doppler flow probe attached to the lateral aspect of the skull. Neurological evaluation and ischemic lesion were assessed 24 h after reperfusion. Dilation of pial arterioles in response to hypoxia and hypercapnia was significantly reduced in alcohol-fed rats. Alcohol-fed rats had significantly larger infarct volumes and worse neurological outcomes than non-alcohol-fed rats under ketamine/xylazine or isoflurane anesthesia. In addition, rCBF measurement indicated that alcohol-fed rats had less regulatory rebound increase in rCBF after the initial drop in rCBF at the onset of MCAO. Our findings suggest that chronic alcohol consumption exacerbates transient focal ischemia-induced brain damage. Increased ischemic brain damage during alcohol consumption may be related to an impaired cerebral vasoreactivity.

Vascular metabolic dissipation in Murray's law

The metabolic dissipation in Murray's minimum energy hypothesis includes only the blood metabolism. The metabolic dissipation of the vascular tree, however, should also include the metabolism of passive and active components of the vessel wall. In this study, we extend the metabolic dissipation to include blood metabolism, as well as passive and active components of the vessel wall. The analysis is extended to the entire vascular arterial tree rather than a single vessel as in Murray's formulation. The calculations are based on experimentally measured morphological data of coronary artery network and the longitudinal distribution of blood pressure along the tree. Whereas the model includes multiple dissipation sources, the total metabolic consumption of a complex vascular tree is found to remain approximately proportional to the cumulative arterial volume of the unit. This implies that the previously described scaling relations for the various morphological features (volume, length, diameter, and flow) remain unchanged under the generalized condition of metabolic requirements of blood and blood vessel wall.

Structural adaptation increases predicted perfusion capacity after vessel obstruction in arteriolar arcade network of pig skeletal muscle

Arteriolar arcades provide alternate pathways for blood flow after obstruction of arteries or arterioles such as occurs in stroke and coronary and peripheral vascular disease. When obstruction is prolonged, remaining vessels adjust their diameters chronically in response to altered hemodynamic and metabolic conditions. Here, the effectiveness of arcades in maintaining perfusion both immediately following obstruction and after structural adaptation was examined. Morphometric data from a vascular casting of the pig triceps brachii muscle and published data were used to develop a computational model for the hemodynamics and structural adaptation of the arcade network between two feed artery branches, FA1 and FA2. The predicted total flow to capillaries (Q(TA)) in the region initially supplied by FA2 decreased to 26% of the normal value immediately after FA2 obstruction but was restored to 78% of the normal value after adaptation. After obstruction of 1-10 randomly selected arcade segments, Q(TA) was on average 18% higher in the arcade network than in a corresponding two-tree network without arcades. Structural adaptation increased Q(TA) by an additional 16% in the arcade network but had almost no effect in the two-tree network. These results indicate that arcades can partially maintain blood flow after vascular blockage and that this effect is substantially enhanced by structural adaptation.

Matching coronary blood flow to myocardial oxygen consumption

At rest the myocardium extracts approximately 75% of the oxygen delivered by coronary blood flow. Thus there is little extraction reserve when myocardial oxygen consumption is augmented severalfold during exercise. There are local metabolic feedback and sympathetic feedforward control mechanisms that match coronary blood flow to myocardial oxygen consumption. Despite intensive research the local feedback control mechanism remains unknown. Physiological local metabolic control is not due to adenosine, ATP-dependent K(+) channels, nitric oxide, prostaglandins, or inhibition of endothelin. Adenosine and ATP-dependent K(+) channels are involved in pathophysiological ischemic or hypoxic coronary dilation and myocardial protection during ischemia. Sympathetic beta-adrenoceptor-mediated feedforward arteriolar vasodilation contributes approximately 25% of the increase in coronary blood flow during exercise. Sympathetic alpha-adrenoceptor-mediated vasoconstriction in medium and large coronary arteries during exercise helps maintain blood flow to the vulnerable subendocardium when cardiac contractility, heart rate, and myocardial oxygen consumption are high. In conclusion, several potential mediators of local metabolic control of the coronary circulation have been evaluated without success. More research is needed.

Fractal Analysis of the Vascular Tree in the Human Retina

The retinal circulation of the normal human retinal vasculature is statistically self-similar and fractal. Studies from several groups present strong evidence that the fractal dimension of the blood vessels in the normal human retina is approximately 1.7. This is the same fractal dimension that is found for a diffusion-limited growth process, and it may have implications for the embryological development of the retinal vascular system. The methods of determining the fractal dimension for branching trees are reviewed together with proposed models for the optimal formation (Murray Principle) of the branching vascular tree in the human retina and the branching pattern of the human bronchial tree. The limitations of fractal analysis of branching biological structures are evaluated. Understanding the design principles of branching vascular systems and the human bronchial tree may find applications in tissue and organ engineering, i.e., bioartificial organs for both liver and kidney.

Differential structural adaptation to haemodynamics along single rat cremaster arterioles

We tested the hypothesis that under physiological conditions, arterioles match their diameter to the level of shear stress. Haemodynamic and anatomical data were obtained in segments of the first-order arteriole of the rat cremaster muscle. Along this segment of ~10 mm in length, local blood pressure decreased from 68 +/- 4 mmHg upstream to 54 +/- 3 mmHg downstream (n = 5). Pulse pressure decreased from 8.2 +/- 1.3 mmHg upstream to 4.1 +/- 0.6 mmHg downstream. At the same locations, an increase in arteriolar diameter was measured in vivo, from 179 +/- 4 microm upstream to 203 +/- 4 microm downstream (n = 10). In vitro pressure-diameter relations of maximally dilated vessels showed that the passive diameter was larger in downstream than upstream segments over a 15-125 mmHg pressure range (n = 18). The wall stress was similar for the upstream vs. downstream location: 266 +/- 16 vs. 260 +/- 14 mN mm-2. However, shear stress decreased from 30 +/- 5 to 21 +/- 5 dyn cm-2 (3.0 +/- 0.5 to 2.1 +/- 0.5 N m-2; n = 4) along the artery. In conclusion, these results demonstrate that shear stress is not the only factor in determining vascular calibre. We suggest that arteriolar calibre may rather depend on an interplay between shear stress and the local pressure profile.

Quantification of myocardial microcirculatory function with X-ray CT

A mathematical model of the intramyocardial coronary microcirculation is used to explore the validity of a fast CT imaging method for characterizing the myocardial microcirculatory functional status. The fast CT method depends on the demonstrated CT-based estimation of myocardial perfusion (F) and the intramyocardial blood volume (B(v)). The observed curvilinear myocardial blood volume-to-flow relationship, empirically fitted to B(v) = a.F + b.F(0.5), is a signature of the underlying early pathophysiologic processes thought to be involved in systemic disease processes, such as atherosclerosis, hypertension, and diabetes mellitus. The sensitivity and specificity of the CT-based estimate of this characteristic relationship is explored by altering the characteristics of the vascular diameter-to-flow relationship and the variation in the fraction of capillaries perfused at different coronary flows. The simulation results also indicate that if the vascular diameters change so that the vascular resistance corresponds to the change in flow, then the empirically observed myocardial B(v)-to-F relationship holds well.

Arterial branching within the confines of fractal L-system formalism

Parametric Lindenmayer systems (L-systems) are formulated to generate branching tree structures that can incorporate the physiological laws of arterial branching. By construction, the generated trees are de facto fractal structures, and with appropriate choice of parameters, they can be made to exhibit some of the branching patterns of arterial trees, particularly those with a preponderant value of the asymmetry ratio. The question of whether arterial trees in general have these fractal characteristics is examined by comparison of pattern with vasculature from the cardiovascular system. The results suggest that parametric L-systems can be used to produce fractal tree structures but not with the variability in branching parameters observed in arterial trees. These parameters include the asymmetry ratio, the area ratio, branch diameters, and branching angles. The key issue is that the source of variability in these parameters is not known and, hence, it cannot be accurately reproduced in a model. L-systems with a random choice of parameters can be made to mimic some of the observed variability, but the legitimacy of that choice is not clear.

Branching exponent heterogeneity and wall shear stress distribution in vascular trees

A bifurcating arterial system with Poiseuille flow can function at minimum cost and with uniform wall shear stress if the branching exponent (z) = 3 [where z is defined by (D(1))(z) = (D(2))(z) + (D(3))(z); D(1) is the parent vessel diameter and D(2) and D(3) are the two daughter vessel diameters at a bifurcation]. Because wall shear stress is a physiologically transducible force, shear stress-dependent control over vessel diameter would appear to provide a means for preserving this optimal structure through maintenance of uniform shear stress. A mean z of 3 has been considered confirmation of such a control mechanism. The objective of the present study was to evaluate the consequences of a heterogeneous distribution of z values about the mean with regard to this uniform shear stress hypothesis. Simulations were carried out on model structures otherwise conforming to the criteria consistent with uniform shear stress when z = 3 but with varying distributions of z. The result was that when there was significant heterogeneity in z approaching that found in a real arterial tree, the coefficient of variation in shear stress was comparable to the coefficient of variation in z and nearly independent of the mean value of z. A systematic increase in mean shear stress with decreasing vessel diameter was one component of the variation in shear stress even when the mean z = 3. The conclusion is that the influence of shear stress in determining vessel diameters is not, per se, manifested in a mean value of z. In a vascular tree having a heterogeneous distribution in z values, a particular mean value of z (e.g., z = 3) apparently has little bearing on the uniform shear stress hypothesis.

Temporal effect of alcohol consumption on reactivity of pial arterioles: role of oxygen radicals

Chronic alcohol consumption reduces nitric oxide synthase-dependent responses of pial arterioles via mechanisms that remain uncertain. In addition, the temporal effects of alcohol on pial arterioles is unclear. Thus our goals were to examine the role of oxygen-derived free radicals in alcohol-induced impairment of cerebrovascular reactivity and the temporal effect of alcohol on reactivity of pial arterioles. Sprague-Dawley rats were pair-fed a liquid diet with or without alcohol for 2-3 wk, 2-3 mo, or 5-6 mo. We measured the in vivo diameter of pial arterioles in response to nitric oxide synthase-dependent dilators acetylcholine and ADP and the nitric oxide synthase-independent dilator nitroglycerin. In nonalcohol-fed rats, acetylcholine (1.0 and 10 microM) and ADP (10 and 100 microM) produced dose-related dilatation of pial arterioles. Whereas there was no difference in reactivity of arterioles to the agonists in rats fed the nonalcohol and alcohol diets for a period of 2-3 wk, there was a significant impairment in reactivity of arterioles to acetylcholine and ADP, but not nitroglycerin, in rats fed the alcohol diet for longer durations. We then found that treatment with superoxide dismutase did not alter baseline diameter of pial arterioles in nonalcohol-fed or alcohol-fed rats, but significantly improved impaired nitric oxide synthase-dependent dilatation of pial arterioles in alcohol-fed rats. Thus our findings suggest a temporal relationship in the effects of alcohol on reactivity of pial arterioles and that impaired nitric oxide synthase-dependent cerebral vasodilatation during chronic alcohol consumption may be related, in part, to enhanced release of oxygen-derived free radicals.

Quantitative analysis of feedforward sympathetic coronary vasodilation in exercising dogs

Recent experiments demonstrate that feedforward sympathetic beta-adrenoceptor coronary vasodilation occurs during exercise. The present study quantitatively examined the contributions of epinephrine and norepinephrine to exercise coronary hyperemia and tested the hypothesis that circulating epinephrine causes feedforward beta-receptor-mediated coronary dilation. Dogs (n = 10) were chronically instrumented with a circumflex coronary artery flow transducer and catheters in the aorta and coronary sinus. During strenuous treadmill exercise, myocardial oxygen consumption increased by approximately 3.9-fold, coronary blood flow increased by approximately 3.6-fold, and arterial plasma epinephrine concentration increased by approximately 2.4-fold over resting levels. At arterial concentrations matching those during strenuous exercise, epinephrine infused at rest (n = 6) produced modest increases (18%) in flow and myocardial oxygen consumption but no evidence of direct beta-adrenoceptor-mediated coronary vasodilation. Arterial norepinephrine concentration increased by approximately 5. 4-fold during exercise, and coronary venous norepinephrine was always higher than arterial, indicating norepinephrine release from cardiac sympathetic nerves. With the use of a mathematical model of cardiac capillary norepinephrine transport, these norepinephrine concentrations predict an average interstitial norepinephrine concentration of approximately 12 nM during strenuous exercise. Published dose-response data indicate that this norepinephrine concentration increases isolated coronary arteriolar conductance by approximately 67%, which can account for approximately 25% of the increase in flow observed during exercise. It is concluded that a significant portion of coronary exercise hyperemia ( approximately 25%) can be accounted for by direct feedforward beta-adrenoceptor coronary vascular effects of norepinephrine, with little effect from circulating epinephrine.

An optimization principle for vascular radius including the effects of smooth muscle tone

An optimization principle is proposed for the regulation of vascular morphology. This principle, which extends Murray's law, is based on the hypothesis that blood vessel diameter is controlled by a mechanism that minimizes the total energy required to drive the blood flow, to maintain the blood supply, and to support smooth muscle tone. A theoretical analysis reveals that the proposed principle predicts that the optimum shear stress on the vessel wall due to blood flow increases with blood pressure. This result agrees qualitatively with published findings that the fluid shear stress in veins is significantly smaller than it is in arteries.

Control of skeletal muscle blood flow during dynamic exercise: contribution of endothelium-derived nitric oxide

Traditional explanations for the hyperaemia which accompanies exercise have invoked the 'metabolic theory' of vasodilation, whereby contractile activity in the active muscle gives rise to metabolic by-products which dilate vessels bathed in interstitial fluid. Whilst metabolites with vasodilator properties have been identified, this theory does not adequately explain the magnitude of hyperaemia observed in active skeletal muscle, principally because large increases in flow are dependent on dilation of 'feed' arteries which lie outside the tissue parenchyma and are not subjected to changes in the interstitial milieu. Coordinated resistance vessel dilation during exercise is therefore dependent on a signal which 'ascends' from the microvessels to the feed arteries located upstream. Recent studies of ascending vasodilation have concentrated on the possible contribution of the endothelium, a monolayer of flattened squamous cells which lie at the interface between the circulating blood and vascular wall. These cells are uniquely positioned to respond to changes in rheological and humoral conditions within the cardiovascular system, and to transduce these changes into vasoactive signals which regulate blood flow, vascular tone and arterial pressure. Endothelial cells produce nitric oxide (NO), a rapidly diffusing labile substance which relaxes adjacent vascular smooth muscle. NO is released basally and contributes to the regulation of vascular tone by acting as a functional antagonist to sympathetic neural constriction. In addition, NO is spontaneously released in response to deformation of the endothelial cell membrane, indicating that changes in pulsatile flow and wall shear stress are likely physiological stimuli. Since the dilation of microvessels in response to exercise increases blood flow through the upstream feed arteries, which subsequently dilate, one explanation for ascending vasodilation is that NO release is stimulated by flow-induced shear stress. Evidence that NO contributes to ascending vasodilation is reviewed, along with studies which indicate that NO mediates exercise hyperaemia, that physical conditioning upregulates NO production and that NO controls blood flow by modifying other physiological mechanisms.

Distributing and delivering vessels of the human heart

The branching characteristics of the right coronary artery, acute marginal, posterior descending, left anterior descending, circumflex, and obtuse marginal arteries are compared with those of diagonal branches, left and right ventricular branches, septal, and higher-order branches, to test a newly proposed functional classification of the coronary arteries in which the first group rank as distributing vessels and the second as delivering vessels. According to this classification, the function of the first type is merely to convey blood to the borders of myocardial zones, while the function of the second is to implement the actual delivery of blood into these zones. This functional difference is important in the hemodynamic analysis of coronary heart disease, as it provides an assessment of the role of a vessel within the coronary network and hence an assessment of the functional importance of that vessel in a particular heart. Measurements from casts of human coronary arteries are used to examine the relevant characteristics of these vessels and hence to test the basis of this classification.

Relation of branching angles to optimality for four cost principles

The literature has suggested that branching angles depend on some principle of optimality. Most often cited are the minimization of lumen surface, volume, power and drag. The predicted angles depend on the principle applied, chi and alpha. Assuming flow o r chi, chi can be determined from r chi 0 = r chi 1 + r chi 2 when the radii of the parent (r0) major (r1) and minor (r2) daughters are known. The term alpha = r2/r1. Using different values for chi and alpha, we present graphs for the major and minor branching angles theta 1 and theta 2 and psi = theta 1 + theta 2 for each of the four optimization principles. Because psi is almost independent of alpha for values of chi and alpha found in 198 junctions taken from a human pulmonary artery, we are able to produce a plot of psi versus chi for each of the four principles on one graph. A junction can be provisionally classified as optimizing for a given principle if, knowing chi, the psi obs - psi pred is least for that principle. We find that this nomographic classification agrees almost perfectly with a previous classification based on a more exacting measure, the percent cost index I, where I = observed cost/minimum cost. We explain why this is to be expected in most but not all cases. First we generate a contoured percent cost surface of c = I - 100 around the optimally located junction, J, and superimpose a surface of equal angular deviations a = psi pred-psi obs. We find that c increases and a usually increases with distance from J as the actual junction moves along a straight line away from J. We then produce a plot of c versus a for two competing principles. A comparison of the principles demonstrates that, for most cases, a is smaller for the principle which has the smaller c value.