Capillary recruitment in a theoretical model for blood flow regulation in heterogeneous microvessel networks

Metabolic blood flow regulation in a hybrid model of the human retinal microcirculation

The retinal vascular network supplies perfusion to vital visual structures, including retinal ganglion cells responsible for vision. Impairments in retinal blood flow and oxygenation are involved in the progression of many ocular diseases, including glaucoma. In this study, an established theoretical hybrid model of a retinal microvascular network is extended to include the effects of local blood flow regulation on oxygenation. A heterogeneous representation of the arterioles based on confocal microscopy images is combined with a compartmental description of the downstream capillaries and venules. A Green's function method is used to simulate oxygen transport in the arterioles, and a Krogh cylinder model is applied to the capillary and venular compartments. Acute blood flow regulation is simulated in response to changes in pressure, shear stress, and metabolism. Model results predict that both increased intraocular pressure and impairment of blood flow regulation can cause decreased tissue oxygenation, indicating that both mechanisms represent factors that could lead to impaired oxygenation characteristic of ocular disease. Results also indicate that the metabolic response mechanism reduces the fraction of poorly oxygenated tissue but that the pressure- and shear stress-dependent response mechanisms may hinder the vascular response to changes in oxygenation. Importantly, the heterogeneity of the vascular network demonstrates that traditionally reported average values of tissue oxygen levels hide significant localized defects in tissue oxygenation that may be involved in disease processes, including glaucoma. Ultimately, the model framework presented in this study will facilitate future comparisons to sectorial-specific clinical data to better assess the role of impaired blood flow regulation in ocular disease.

Modeling the Effect of Hyperoxia on the Spin-Lattice Relaxation Rate R1 of Tissues

PURPOSE

Inducing hyperoxia in tissues is common practice in several areas of research, including oxygen-enhanced MRI (OE-MRI), which attempts to use the resulting signal changes to detect regions of tumor hypoxia or pulmonary disease. The linear relationship between PO₂ and R1 has been reproduced in phantom solutions and body fluids such as vitreous fluid; however, in tissue and blood experiments, factors such as changes in deoxyhemoglobin levels can also affect the ΔR1.

THEORY AND METHODS

This manuscript proposes a three-compartment model for estimating the hyperoxia-induced changes in R1 of tissues depending on B0, SO₂ , blood volume, hematocrit, oxygen extraction fraction, and changes in blood and tissue PO₂ . The model contains two blood compartments (arterial and venous) and a tissue compartment. This model has been designed to be easy for researchers to tailor to their tissue of interest by substituting their preferred model for tissue oxygen diffusion and consumption. A specific application of the model is demonstrated by calculating the resulting ΔR1 expected in healthy, hypoxic and necrotic tumor tissues. In addition, the effect of sex-based hematocrit differences on ΔR1 is assessed.

RESULTS

The ΔR1 values predicted by the model are consistent with reported literature OE-MRI results: with larger positive changes in the vascular periphery than hypoxic and necrotic regions. The observed sex-based differences in ΔR1 agree with findings by Kindvall et al. suggesting that differences in hematocrit levels may sometimes be a confounding factor in ΔR1.

CONCLUSION

This model can be used to estimate the expected tissue ΔR1 in oxygen-enhanced MRI experiments.

Functional implications of microvascular heterogeneity for oxygen uptake and utilization

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

Microvessel Density: Integrating Sex-Based Differences and Elevated Cardiovascular Risks in Metabolic Syndrome

Metabolic syndrome (MetS) is a complex pathological state consisting of metabolic risk factors such as hypertension, insulin resistance, and obesity. The interconnectivity of cellular pathways within various biological systems suggests that each individual component of MetS may share common pathological sources. Additionally, MetS is closely associated with vasculopathy, including a reduction in microvessel density (MVD) (rarefaction) and elevated risk for various cardiovascular diseases. Microvascular impairments may contribute to perfusion-demand mismatch, where local metabolic needs are insufficiently met due to the lack of nutrient and oxygen supply, thus creating pathological positive-feedback loops and furthering the progression of disease. Sexual dimorphism is evident in these underlying cellular mechanisms, which places males and females at different levels of risk for cardiovascular disease and acute ischemic events. Estrogen exhibits protective effects on the endothelium of pre-menopausal women, while androgens may be antagonistic to cardiovascular health. This review examines MetS and its influences on MVD, as well as sex differences relating to the components of MetS and cardiovascular risk profiles. Finally, translational relevance and interventions are discussed in the context of these sex-based differences.

Distinct roles of red-blood-cell-derived and wall-derived mechanisms in metabolic regulation of blood flow

OBJECTIVE

A theoretical model is used to analyze combinations of RBC-derived and wall-derived (RBC-independent) mechanisms for metabolic blood flow regulation, with regard to their oxygen transport properties.

METHODS

Heterogeneous microvascular network structures are derived from observations in rat mesentery and hamster cremaster. The effectiveness of metabolic blood flow regulation using combinations of RBC-dependent and RBC-independent mechanisms is simulated in these networks under conditions of reduced oxygen delivery and increased oxygen demand.

RESULTS

Metabolic regulation by a wall-derived mechanism results in higher predicted total blood flow rate and number of flowing vessels, and lower tissue hypoxic fraction, than regulation by combinations of RBC-derived and wall-derived signals. However, a combination of RBC-derived and wall-derived signals results in a higher predicted median tissue P_O2 than either mechanism acting alone.

CONCLUSIONS

Model results suggest complementary roles for RBC-derived and wall-derived mechanisms of metabolic flow regulation, with the wall-derived mechanism responsible for avoiding hypoxia, and the RBC-derived mechanism responsible for maintaining P_O2 levels high enough for optimal tissue function.

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

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

Role of Regular Physical Exercise in Tumor Vasculature: Favorable Modulator of Tumor Milieu

The tumor vessel network has been investigated as a precursor of an inhospitable tumor microenvironment, including its repercussions in tumor perfusion, oxygenation, interstitial fluid pressure, pH, and immune response. Dysfunctional tumor vasculature leads to the extravasation of blood to the interstitial space, hindering proper perfusion and causing interstitial hypertension. Consequently, the inadequate delivery of oxygen and clearance of by-products of metabolism promote the development of intratumoral hypoxia and acidification, hampering the action of immune cells and resulting in more aggressive tumors. Thus, pharmacological strategies targeting tumor vasculature were developed, but the overall outcome was not satisfactory due to its transient nature and the higher risk of hypoxia and metastasis. Therefore, physical exercise emerged as a potential favorable modulator of tumor vasculature, improving intratumoral vascularization and perfusion. Indeed, it seems that regular exercise practice is associated with lasting tumor vascular maturity, reduced vascular resistance, and increased vascular conductance. Higher vascular conductance reduces intratumoral hypoxia and increases the accessibility of circulating immune cells to the tumor milieu, inhibiting tumor development and improving cancer treatment. The present paper describes the implications of abnormal vasculature on the tumor microenvironment and the underlying mechanisms promoted by regular physical exercise for the re-establishment of more physiological tumor vasculature.

Blood flow regulation and oxygen transport in a heterogeneous model of the mouse retina

Elevated intraocular pressure is the primary risk factor for glaucoma, yet vascular health and ocular hemodynamics have also been established as important risk factors for the disease. The precise physiological mechanisms and processes by which flow impairment and reduced tissue oxygenation relate to retinal ganglion cell death are not fully known. Mathematical modeling has emerged as a useful tool to help decipher the role of hemodynamic alterations in glaucoma. Several previous models of the retinal microvasculature and tissue have investigated the individual impact of spatial heterogeneity, flow regulation, and oxygen transport on the system. This study combines all three of these components into a heterogeneous mathematical model of retinal arterioles that includes oxygen transport and acute flow regulation in response to changes in pressure, shear stress, and oxygen demand. The metabolic signal (S_i) is implemented as a wall-derived signal that reflects the oxygen deficit along the network, and three cases of conduction are considered: no conduction, a constant signal, and a flow-weighted signal. The model shows that the heterogeneity of the downstream signal serves to regulate flow better than a constant conducted response. In fact, the increases in average tissue PO₂ due to a flow-weighted signal are often more significant than if the entire level of signal is increased. Such theoretical work supports the importance of the non-uniform structure of the retinal vasculature when assessing the capability and/or dysfunction of blood flow regulation in the retinal microcirculation.

August Krogh's theory of muscle microvascular control and oxygen delivery: a paradigm shift based on new data

August Krogh twice won the prestigious international Steegen Prize, for nitrogen metabolism (1906) and overturning the concept of active transport of gases across the pulmonary epithelium (1910). Despite this, at the beginning of 1920, the consummate experimentalist was relatively unknown worldwide and even among his own University of Copenhagen faculty. But, in early 1919, he had submitted three papers to Dr Langley, then editor of The Journal of Physiology in England. These papers coalesced anatomical observations of skeletal muscle capillary numbers with O₂ diffusion theory to propose a novel active role for capillaries that explained the prodigious increase in blood-muscle O₂ flux from rest to exercise. Despite his own appraisal of the first two papers as "rather dull" to his friend, the eminent Cambridge respiratory physiologist, Joseph Barcroft, Krogh believed that the third one, dealing with O₂ supply and capillary regulation, was"interesting". These papers, which won Krogh an unopposed Nobel Prize for Physiology or Medicine in 1920, form the foundation for this review. They single-handedly transformed the role of capillaries from passive conduit and exchange vessels, functioning at the mercy of their upstream arterioles, into independent contractile units that were predominantly closed at rest and opened actively during muscle contractions in a process he termed 'capillary recruitment'. Herein we examine Krogh's findings and some of the experimental difficulties he faced. In particular, the boundary conditions selected for his model (e.g. heavily anaesthetized animals, negligible intramyocyte O₂ partial pressure, binary open-closed capillary function) have not withstood the test of time. Subsequently, we update the reader with intervening discoveries that underpin our current understanding of muscle microcirculatory control and place a retrospectroscope on Krogh's discoveries. The perspective is presented that the imprimatur of the Nobel Prize, in this instance, may have led scientists to discount compelling evidence. Much as he and Marie Krogh demonstrated that active transport of gases across the blood-gas barrier was unnecessary in the lung, capillaries in skeletal muscle do not open and close spontaneously or actively, nor is this necessary to account for the increase in blood-muscle O₂ flux during exercise. Thus, a contemporary model of capillary function features most muscle capillaries supporting blood flow at rest, and, rather than capillaries actively vasodilating from rest to exercise, increased blood-myocyte O₂ flux occurs predominantly via elevating red blood cell and plasma flux in already flowing capillaries. Krogh is lauded for his brilliance as an experimentalist and for raising scientific questions that led to fertile avenues of investigation, including the study of microvascular function.

Vascular reactivity of cutaneous circulation to brief compressive stimuli, in the human forearm

PURPOSE

A brief compressive stimulus is known to induce a rapid hyperemia in skeletal muscles, considered to contribute to the initial phase of functional hyperemia. Whether the same mechano-sensitivity characterizes the cutaneous circulation is debated. This study aims to investigate whether a rapid hyperemic response to compressive stimuli is also expressed by skin blood flow in humans.

METHODS

In 12 subjects, brief compressive stimuli were delivered to the forearm at varying pressures/durations (50/2, 100/2, 200/2, 200/1, 200/5 mmHg/s); the sequence was randomized and repeated with the arm above and below heart level. Laser Doppler flowmetry technique was used to monitor skin blood flow. The response was described in terms of peak skin blood flow normalized to baseline (nSBFpeak), time-to-peak from the release of compression, and excess blood volume (EBV, expressed in terms of seconds of basal flow, s-bf) received during the response.

RESULTS

The results consistently evidenced the occurrence of a compression-induced hyperemic response, with nSBFpeak = 2.9 ± 1.1, EBV = 17.0 ± 6.6 s-bf, time-to-peak = 7.0 ± 0.7 s (200 mmHg, 2 s, below heart level). Both nSBFpeak and EBV were significantly reduced (by about 50%) above compared to below heart level (p < 0.01). In addition, EBV slightly increased with increasing pressure (p < 0.05) and duration (p < 0.01) of the stimulus.

CONCLUSIONS

For the first time, the rapid dilatator response to compressive stimuli was demonstrated in human cutaneous circulation. The functional meaning of this response remains to be elucidated.

The immediate effects of kinesiology taping on cutaneous blood flow in healthy humans under resting conditions: A randomised controlled repeated-measures laboratory study

BACKGROUND

Kinesiology taping (KT) is used in musculoskeletal practice for preventive and rehabilitative purposes. It is claimed that KT improves blood flow in the microcirculation by creating skin convolutions and that this reduces swelling and facilitates healing of musculoskeletal injuries. There is a paucity of physiological studies evaluating the effect of KT on cutaneous blood microcirculation.

OBJECTIVES

The purpose of this parallel-group controlled laboratory repeated measures design study was to evaluate the effects of KT on cutaneous blood microcirculation in healthy human adults using a dual wavelength (infrared and visible-red) laser Doppler Imaging (LDI) system. KT was compared with rigid taping and no taping controls to isolate the effects associated with the elasticity of KT.

METHODS

Forty-five healthy male and female human adults were allocated to one of the three interventions using constrained randomisation following the pre-intervention measurement: (i) KT (ii) ST (standard taping) (iii) NT (no taping). Cutaneous blood perfusion was measured using LDI in the ventral surface of forearm at pre-intervention, during-intervention and post-intervention in a normothermic environment at resting conditions.

RESULTS

Mixed ANOVA of both infrared and visible-red datasets revealed no statistically significant interaction between Intervention and Time. There was statistically significant main effect for Time but not Intervention.

CONCLUSION

KT does not increase cutaneous blood microcirculation in healthy human adults under resting physiological conditions in a normothermic environment. On the contrary, evidence suggests that taping, regardless of the elasticity in the tape, is associated with immediate reductions in cutaneous blood flow.

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

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

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

Modeling acute blood flow responses to a major arterial occlusion

OBJECTIVE

The development of earlier and less invasive treatments for peripheral arterial disease requires a more complete understanding of vascular responses following a major arterial occlusion. A mechanistic model of the vasculature of the rat hindlimb is developed to predict acute (immediate) changes in vessel diameters and smooth muscle tone following femoral arterial occlusion.

METHODS

Vascular responses of collateral arteries and distal arterioles to changes in pressure, shear stress, and metabolism are assessed before and after occlusion. The effects of exercise are also simulated and compared with venous flow measurements from WKY rats.

RESULTS

The model identifies collateral arteries as the primary contributors to flow compensation following occlusion. Increasing the number of capillaries has minimal effect on blood flow while increasing the number of collateral arteries significantly increases flow, since the primary site of resistance shifts upstream to the collateral arteries following occlusion. Despite significant collateral dilation, calf flow remains below pre-occlusion levels and the deficit becomes more severe with increased activity.

CONCLUSIONS

Although unable to compensate fully for an occlusion, the model demonstrates the importance of the shear response in collateral arteries and the metabolic response in the distal microcirculation in acute adaptations to a major arterial occlusion.

Uncoupling of Microvascular Blood Flow and Capillary Density in Vascular Cognitive Impairment

Cerebral small vessel disease (cSVD) plays an important role in dementia and is a major cause for vascular cognitive impairment (VCI). Recent studies hypothesized that capillary dysfunction including reduction of capillary patency, rather than a flow-limiting pathology is crucial in cSVD. As cSVD is considered a systemic microvascular disease, we examined sublingual microvascular blood flow and capillary density in patients with VCI and controls. Fifteen patients with VCI due to cSVD and 15 controls underwent intravital microscopy of the sublingual microvessels. Microvascular blood flow and capillary density in high and low flow areas were determined for each participant. Flow-density coupling was examined by determining the ratio of density changes to flow changes, and the ratio of feed vessel red blood cell (RBC) velocity to capillary RBC velocity. These were compared between VCI and controls. In healthy controls, capillary density increased proportionally with feed vessel blood flow increase. In patients with VCI, no increase of capillary density was observed. Moreover, increase of feed vessel RBC velocity led to significant increase of capillary RBC velocity in VCI, whereas in controls, the capillary RBC increased only slightly. Flow-density coupling differed significantly between VCI and controls, also after correcting for age and hypertension. Our findings suggest uncoupling of microvascular blood flow and capillary density in patients with VCI. This uncoupling may impair oxygen and nutrients exchange when blood flow increases in response to increased metabolic demand, ultimately leading to tissue damage.

Quantifying the impact of tissue metabolism on solute transport in feto-placental microvascular networks

The primary exchange units in the human placenta are terminal villi, in which fetal capillary networks are surrounded by a thin layer of villous tissue, separating fetal from maternal blood. To understand how the complex spatial structure of villi influences their function, we use an image-based theoretical model to study the effect of tissue metabolism on the transport of solutes from maternal blood into the fetal circulation. For solute that is taken up under first-order kinetics, we show that the transition between flow-limited and diffusion-limited transport depends on two new dimensionless parameters defined in terms of key geometric quantities, with strong solute uptake promoting flow-limited transport conditions. We present a simple algebraic approximation for solute uptake rate as a function of flow conditions, metabolic rate and villous geometry. For oxygen, accounting for nonlinear kinetics using physiological parameter values, our model predicts that villous metabolism does not significantly impact oxygen transfer to fetal blood, although the partitioning of fluxes between the villous tissue and the capillary network depends strongly on the flow regime.

Edward F. Adolph Distinguished Lecture. Contemporary model of muscle microcirculation: gateway to function and dysfunction

This review strikes at the very heart of how the microcirculation functions to facilitate blood-tissue oxygen, substrate, and metabolite fluxes in skeletal muscle. Contemporary evidence, marshalled from animals and humans using the latest techniques, challenges iconic perspectives that have changed little over the past century. Those perspectives include the following: the presence of contractile or collapsible capillaries in muscle, unitary control by precapillary sphincters, capillary recruitment at the onset of contractions, and the notion of capillary-to-mitochondrial diffusion distances as limiting O₂ delivery. Today a wealth of physiological, morphological, and intravital microscopy evidence presents a completely different picture of microcirculatory control. Specifically, capillary red blood cell (RBC) and plasma flux is controlled primarily at the arteriolar level with most capillaries, in healthy muscle, supporting at least some flow at rest. In healthy skeletal muscle, this permits substrate access (whether carried in RBCs or plasma) to a prodigious total capillary surface area. Pathologies such as heart failure or diabetes decrease access to that exchange surface by reducing the proportion of flowing capillaries at rest and during exercise. Capillary morphology and function vary disparately among tissues. The contemporary model of capillary function explains how, following the onset of exercise, muscle O₂ uptake kinetics can be extremely fast in health but slowed in heart failure and diabetes impairing contractile function and exercise tolerance. It is argued that adoption of this model is fundamental for understanding microvascular function and dysfunction and, as such, to the design and evaluation of effective therapeutic strategies to improve exercise tolerance and decrease morbidity and mortality in disease.

Spatial and Temporal Heterogeneities of Capillary Hemodynamics and Its Functional Coupling During Neural Activation

The cerebral vascular system provides a means to meet the constant metabolic needs of neuronal activities in the brain. Within the cerebral capillary bed, the interactions of spatial and temporal hemodynamics play a deterministic role in oxygen diffusion, however, the progression of which remains unclear. Taking the advantages of high-spatiotemporal resolution of optical coherence tomography capillary velocimetry designed with the eigen-decomposition statistical analysis, we investigated intrinsic red blood cell (RBC) velocities and their spatiotemporal adjustment within the capillaries permeating mouse cerebral cortex during electrical stimulation of contralateral hind paw. We found that the mean capillary transit velocity (mCTV) is increased and its temporal fluctuation bandwidth (TFB) is broadened within hind-paw somatosensory cortex. In addition, the degree to which the mCTV is increased negatively correlates with resting state mCTV, and the degree to which the TFB is increased negatively correlates with both the resting state mCTV and the TFB. In order to confirm the changes are due to hemodynamic regulation, we performed angiographic analyses and found that the vessel density remains almost constant, suggesting the observed functional activation does not involve recruitment of reserved capillaries. To further differentiate the contributions of the mCTV and the TFB to the spatiotemporally coupled hemodynamics, changes in the mCTV and TBF of the capillary flow were modeled and investigated through a Monte Carlo simulation. The results suggest that neural activation evokes the spatial transit time homogenization within the capillary bed, which is regulated via both the heterogeneous acceleration of RBC flow and the heterogeneous increase of temporal RBC fluctuation, ensuring sufficient oxygenation during functional hyperemia.

Physical and geometric determinants of transport in fetoplacental microvascular networks

Across mammalian species, solute exchange takes place in complex microvascular networks. In the human placenta, the primary exchange units are terminal villi that contain disordered networks of fetal capillaries and are surrounded externally by maternal blood. We show how the irregular internal structure of a terminal villus determines its exchange capacity for diverse solutes. Distilling geometric features into three parameters, obtained from image analysis and computational fluid dynamics, we capture archetypal features of the structure-function relationship of terminal villi using a simple algebraic approximation, revealing transitions between flow- and diffusion-limited transport at vessel and network levels. Our theory accommodates countercurrent effects, incorporates nonlinear blood rheology, and offers an efficient method for testing network robustness. Our results show how physical estimates of solute transport, based on carefully defined geometrical statistics, provide a viable method for linking placental structure and function and offer a framework for assessing transport in other microvascular systems.

Arterial Network Geometric Characteristics and Regulation of Capillary Blood Flow in Hamster Skeletal Muscle Microcirculation

This study was aimed to characterize the geometric arrangement of hamster skeletal muscle arteriolar networks and to assess the in vivo rhythmic diameter changes of arterioles to clarify regulatory mechanisms of the capillary perfusion. The experimental study was carried out in male Syrian hamsters implanted with a plastic chamber in the dorsum skin under pentobarbital anesthesia. The skeletal muscle microvessels were visualized by fluorescence microscopy. The vessel diameters, lengths and the rhythmic diameter changes of arterioles were analyzed with computer-assisted techniques. The arterioles were classified according to a centripetal ordering scheme. In hamster skeletal muscle microvasculature the terminal branchings, differentiated in long and short terminal arteriolar trees (TATs), originated from anastomotic vessels, defined "arcading" arterioles. The long TATs presented different frequencies along the branching vessels; order 4 arterioles had frequencies lower than those observed in the order 3, 2, and 1 vessels. The short TAT order 3 arterioles, directly originating from "arcading" parent vessels, showed a frequency dominating all daughter arterioles. The amplitude of diameter variations in larger vessels was in the range 30-40% of mean diameter, while it was 80-100% in order 3, 2, and 1 vessels. Therefore, the complete constriction of arterioles, caused an intermittent capillary blood perfusion. L-arginine or papaverine infusion caused dilation of arterioles and transient disappearing of vasomotion waves and induced perfusion of all capillaries spreading from short and long TAT arrangements. Therefore, the capillary blood flow was modulated by changes in diameter of terminal arterioles penetrating within the skeletal muscle fibers, facilitating redistribution of blood flow according to the metabolic demands of tissues.

Computational fluid dynamics with imaging of cleared tissue and of in vivo perfusion predicts drug uptake and treatment responses in tumours

Understanding the uptake of a drug by diseased tissue, and the drug's subsequent spatiotemporal distribution, are central factors in the development of effective targeted therapies. However, the interaction between the pathophysiology of diseased tissue and individual therapeutic agents can be complex, and can vary across tissue types and across subjects. Here, we show that the combination of mathematical modelling, high-resolution optical imaging of intact and optically cleared tumour tissue from animal models, and in vivo imaging of vascular perfusion predicts the heterogeneous uptake, by large tissue samples, of specific therapeutic agents, as well as their spatiotemporal distribution. In particular, by using murine models of colorectal cancer and glioma, we report and validate predictions of steady-state blood flow and intravascular and interstitial fluid pressure in tumours, of the spatially heterogeneous uptake of chelated gadolinium by tumours, and of the effect of a vascular disrupting agent on tumour vasculature.

Insights into cerebral haemodynamics and oxygenation utilising in vivo mural cell imaging and mathematical modelling

The neurovascular mechanisms underpinning the local regulation of cerebral blood flow (CBF) and oxygen transport remain elusive. In this study we have combined novel in vivo imaging of cortical microvascular and mural cell architecture with mathematical modelling of blood flow and oxygen transport, to provide new insights into CBF regulation that would be inaccessible in a conventional experimental context. Our study indicates that vasoconstriction of smooth muscle actin-covered vessels, rather than pericyte-covered capillaries, induces stable reductions in downstream intravascular capillary and tissue oxygenation. We also propose that seemingly paradoxical observations in the literature around reduced blood velocity in response to arteriolar constrictions might be caused by a propagation of constrictions to upstream penetrating arterioles. We provide support for pericytes acting as signalling conduits for upstream smooth muscle activation, and erythrocyte deformation as a complementary regulatory mechanism. Finally, we caution against the use of blood velocity as a proxy measurement for flow. Our combined imaging-modelling platform complements conventional experimentation allowing cerebrovascular physiology to be probed in unprecedented detail.

* Skeletal Myoblast-Seeded Vascularized Tissue Scaffolds in the Treatment of a Large Volumetric Muscle Defect in the Rat Biceps Femoris Muscle

High velocity impact injuries can often result in loss of large skeletal muscle mass, creating defects devoid of matrix, cells, and vasculature. Functional regeneration within these regions of large volumetric muscle loss (VML) continues to be a significant clinical challenge. Large cell-seeded, space-filling tissue-engineered constructs that may augment regeneration require adequate vascularization to maintain cell viability. However, the long-term effect of improved vascularization and the effect of addition of myoblasts to vascularized constructs have not been determined in large VMLs. Here, our objective was to create a new VML model, consisting of a full-thickness, single muscle defect, in the rat biceps femoris muscle, and evaluate the ability of myoblast-seeded vascularized collagen hydrogel constructs to augment VML regeneration. Adipose-derived microvessels were cultured with or without myoblasts to form vascular networks within collagen constructs. In the animal model, the VML injury was created in the left hind limb, and treated with the harvested autograft itself, constructs with microvessel fragments (MVF) only, constructs with microvessels and myoblasts (MVF+Myoblasts), or left empty. We evaluated the formation of vascular networks in vitro by light microscopy, and the capacity of vascularized constructs to augment early revascularization and muscle regeneration in the VML using perfusion angiography and creatine kinase activity, respectively. Myoblasts (Pax7+) were able to differentiate into myotubes (sarcomeric myosin MF20+) in vitro. The MVF+Myoblast group showed longer and more branched microvascular networks than the MVF group in vitro, but showed similar overall defect site vascular volumes at 2 weeks postimplantation by microcomputed tomography angiography. However, a larger number of small-diameter vessels were observed in the vascularized construct-treated groups. Yet, both vascularized implant groups showed primarily fibrotic tissue with adipose infiltration, poor maintenance of tissue volume within the VML, and little muscle regeneration. These data suggest that while vascularization may play an important supportive role, other factors besides adequate vascularity may determine the fate of regenerating volumetric muscle defects.

Computational micro-scale model of control of extravascular water and capillary perfusion in the air blood barrier

A computational model of a morphologically-based alveolar capillary unit (ACU) in the rabbit is developed to relate lung fluid balance to mechanical forces between capillary surface and interstitium during development of interstitial edema. We hypothesize that positive values of interstitial liquid pressure Pliq impact on capillary transmural pressure and on blood flow. ACU blood flow, capillary recruitment and filtration are computed by modulating vascular and interstitial pressures. Model results are compared with experimental data of Pliq increasing from ~-10 (control) up to ~4cmH2O in two conditions, hypoxia and collagenase injection. For hypoxia exposure, fitting data requires a linear increase in hydraulic conductivity Lp and capillary pressure PC, that fulfils the need of increase in oxygen delivery. For severe fragmentation of capillary endothelial barrier (collagenase injection), fitting requires a rapid increase in both hydraulic and protein permeability, causing ACU de-recruitment, followed by an increase in PC as a late response to restore blood flow. In conclusion, the model allows to describe the lung adaptive response to edemagenic perturbations; the increase in Pliq, related to the low interstitial compliance, provides an efficient control of extravascular water, by limiting microvascular filtration.

Microcirculatory and mitochondrial hypoxia in sepsis, shock, and resuscitation

After shock, persistent oxygen extraction deficit despite the apparent adequate recovery of systemic hemodynamic and oxygen-derived variables has been a source of uncertainty and controversy. Dysfunction of oxygen transport pathways during intensive care underlies the sequelae that lead to organ failure, and the limitations of techniques used to measure tissue oxygenation in vivo have contributed to the lack of progress in this area. Novel techniques have provided detailed quantitative insight into the determinants of microcirculatory and mitochondrial oxygenation. These techniques, which are based on the oxygen-dependent quenching of phosphorescence or delayed luminescence are briefly reviewed. The application of these techniques to animal models of shock and resuscitation revealed the heterogeneous nature of oxygen distributions and the alterations in oxygen distribution in the microcirculation and in mitochondria. These studies identified functional shunting in the microcirculation as an underlying cause of oxygen extraction deficit observed in states of shock and resuscitation. The translation of these concepts to the bedside has been enabled by our development and clinical introduction of hand-held microscopy. This tool facilitates the direct observation of the microcirculation and its alterations at the bedside under the conditions of shock and resuscitation. Studies identified loss of coherence between the macrocirculation and the microcirculation, in which resuscitation successfully restored systemic circulation but did not alleviate microcirculatory perfusion alterations. Various mechanisms responsible for these alterations underlie the loss of hemodynamic coherence during unsuccessful resuscitation procedures. Therapeutic resolution of persistent heterogeneous microcirculatory alterations is expected to improve outcomes in critically ill patients.

A mathematical model for the vessel recruitment in coronary microcirculation in the absence of active autoregulation

This paper proposes a mathematical model for vessel recruitment in the microvascular coronary network. The model is based on microvascular network units (MVNUs), where we define a MVNU as a portion of the microvascular network comprising seven generations of identical, parallel-arranged vessels (upstream arteries, large and small arterioles, capillaries, small and large venules, and downstream veins). The model implements a new mechanism to describe the variation in the number of MVNU in response to sudden variations of the local input pressure. In particular, it describes a recruitment mechanism dependent on distal pressure which operates in the coronary microcirculatory network even in maximally dilated conditions. We apply the model to interpret data from 29 patients who underwent revascularization by percutaneous coronary intervention (PCI). Treated vessels were the left anterior descending coronary artery, the left circumflex and the right coronary artery in 26, 2 and 1 patients, respectively. Following intracoronary adenosine administration, distal coronary pressure and blood flow were 48 ± 18 mmHg and 45 ± 30 ml/min before PCI, respectively, and significantly increased afterwards to 80 ± 17 mmHg and 68 ± 32 ml/min (p<0.001). The model predicts an increase in MVNU number in patients with preserved wall motion in the myocardial region which underwent PCI. On the contrary, a decrease in MVNU number is predicted by the model in patients with regional dysfunction and implies a relatively lower response of maximal flow to revascularization.

Near infrared spectroscopy (NIRS) to assess the effects of local ischemic preconditioning in the muscle of healthy volunteers and critically ill patients

Near-infrared spectroscopy (NIRS) permits non-invasive evaluation of tissue oxygen saturation (StO2). A vascular occlusion test (VOT) produces transient controlled ischemia similar to that used in ischemic preconditioning. We hypothesized that we could evaluate local responses to ischemic preconditioning by performing repeated VOTs and observing the changes in different NIRS VOT-derived variables. In healthy volunteers (n=20), four VOTs were performed at 30-min intervals on one day and, in a second group (n=21), two VOTs with time intervals of 5, 15 or 30min were performed on 3 separate days. Two cohorts of patients, one with circulatory shock (n=23) and a hemodynamically stable group (n=20), were also studied, repeating the VOT twice with a 5-min interval. In the 1-day volunteers, there was a median decrease of 15 (6-21)% in the Desc slope (StO2 decrease during VOT) after the second VOT, but no significant change in the Asc slope (StO2 increase after VOT). In the 3-day volunteers, the Desc slope also decreased, regardless of the time interval between VOTs. There was no overall decrease in the Desc slope in either patient cohort with repeated VOTs but there was marked individual patient variability. Patients in whom the Desc slope decreased had less organ dysfunction at admission, required less norepinephrine (0.00 vs 0.08mcg/kg/min, p=0.02), less frequently had sepsis (12 vs 50%, p=0.02) and had a lower mortality (6 vs 39%, p=0.03) compared to those in whom it did not decrease. Repeated NIRS VOT can non-invasively assess the local effects of ischemic preconditioning in the muscle.

Impact of increased intramuscular perfusion heterogeneity on skeletal muscle microvascular hematocrit in the metabolic syndrome

OBJECTIVE

To determine HMV and PS in skeletal muscle of OZR and evaluate the impact of increased microvascular perfusion heterogeneity on mass transport/exchange.

METHODS

The in situ gastrocnemius muscle from OZR and LZR was examined under control conditions and following pretreatment with TEMPOL (antioxidant)/SQ-29548 (PGH2 /TxA2 receptor antagonist), phentolamine (adrenergic antagonist), or all agents combined. A spike input of a labeled blood tracer cocktail was injected into the perfusing artery. Tracer washout was analyzed using models for HMV and PS. HT was determined in in situ cremaster muscle of OZR and LZR using videomicroscopy.

RESULTS

HMV was decreased in OZR versus LZR. While TEMPOL/SQ-29548 or phentolamine had minor effects, treatment with all three agents improved HMV in OZR. HT was not different between strains, although variability was increased in OZR, and normalized following treatment with all three agents. PS was reduced in OZR and was not impacted by intervention.

CONCLUSIONS

Increased microvascular perfusion heterogeneity in OZR reduces HMV in muscle vascular networks and increases its variability, potentially contributing to premature muscle fatigue. While targeted interventions can ameliorate this, the reduced microvascular surface area is not acutely reversible.

Metabolic control of microvascular networks: oxygen sensing and beyond

The metabolic regulation of blood flow is central to guaranteeing an adequate supply of blood to the tissues and microvascular network stability. It is assumed that vascular reactions to local oxygenation match blood supply to tissue demand via negative-feedback regulation. Low oxygen (O2) levels evoke vasodilatation, and thus an increase of blood flow and oxygen supply, by increasing (decreasing) the release of vasodilatory (vasoconstricting) metabolic signal substances with decreasing partial pressure of O2. This review analyses the principles of metabolic vascular control with a focus on the prevailing feedback regulations. We propose the following hypotheses with respect to vessel diameter adaptation. (1) In addition to O2-dependent signaling, metabolic vascular regulation can be effected by signal substances produced independently of local oxygenation (reflecting the presence of cells) due to the dilution effect. (2) Control of resting vessel tone, and thus perfusion reserve, could be explained by a vascular activity/hypoxia memory. (3) Vasodilator but not vasoconstrictor signaling can prevent shunt perfusion via signal conduction upstream to feeding arterioles. (4) For low perfusion heterogeneity in the steady state, metabolic signaling from the vessel wall or a perivascular tissue sleeve is optimal. (5) For amplification of perfusion during transient increases of tissue demand, red blood cell-derived vasodilators or vasoconstrictors diluted in flowing blood may be relevant.

Normobaric hyperoxia alters the microcirculation in healthy volunteers

The use of high concentrations of inhaled oxygen has been associated with adverse effects but recent data suggest a potential therapeutic role of normobaric hyperoxia (NH) in sepsis and cerebral ischemia. Hyperoxia may induce vasoconstriction and alter endothelial function, so we evaluated its effects on the microcirculation in 40 healthy adult volunteers using side-stream dark field (SDF) video-microscopy on the sublingual area and near-infrared spectroscopy (NIRS) on the thenar eminence. In a first group of volunteers (n=18), measurements were taken every 30 min: at baseline in air, during NH (close to 100% oxygen via a non-rebreathing mask) and during recovery in air. In a second group (n=22), NIRS measurements were taken in NH or ambient air on two separate days to prevent any potential influence of repeated NIRS measurements. NH significantly decreased the proportion of perfused vessels (PPV) from 92% to 66%, perfused vessel density (PVD) from 11.0 to 7.3 vessels/mm, perfused small vessel density (PSVD) from 9.0 to 5.8 vessels/mm and microvascular flow index (MFI) from 2.8 to 2.0, and increased PPV heterogeneity from 7.5% to 30.4%. Thirty minutes after return to air, PPV, PVD, PSVD and MFI remained partially altered. During NH, NIRS descending slope and NIRS muscle oxygen consumption (VO2) decreased from 8.5 to 7.9%/s and 127 to 103 units, respectively, in the first group and from 10.7 to 9.4%/s and 150 to 115 units in the second group. NH, therefore, alters the microcirculation in healthy subjects, decreasing capillary perfusion and VO2 and increasing the heterogeneity of the perfusion.

Oxygen transport in a cross section of the rat inner medulla: impact of heterogeneous distribution of nephrons and vessels

We have developed a highly detailed mathematical model of oxygen transport in a cross section of the upper inner medulla of the rat kidney. The model is used to study the impact of the structured organization of nephrons and vessels revealed in anatomic studies, in which descending vasa recta are found to lie distant from clusters of collecting ducts. Specifically, we formulated a two-dimensional oxygen transport model, in which the positions and physical dimensions of renal tubules and vessels are based on an image obtained by immunochemical techniques (T. Pannabecker and W. Dantzler, Three-dimensional architecture of inner medullary vasa recta, Am. J. Physiol. Renal Physiol. 290 (2006) F1355-F1366). The model represents oxygen diffusion through interstitium and other renal structures, oxygen consumption by the Na(+)/K(+)-ATPase activities of the collecting ducts, and basal metabolic consumption. Model simulations yield marked variations in interstitial PO2, which can be attributed, in large part, to the heterogeneities in the position and physical dimensions of the collecting ducts. Further, results of a sensitivity study suggest that medullary oxygenation is highly sensitive to medullary blood flow, and that, at high active consumption rates, localized patches of tissue may be vulnerable to hypoxic injury.

Functional sympatholysis and sympathetic escape in a theoretical model for blood flow regulation

A mathematical simulation of flow regulation in vascular networks is used to investigate the interaction between arteriolar vasoconstriction due to sympathetic nerve activity (SNA) and vasodilation due to increased oxygen demand. A network with 13 vessel segments in series is used, each segment representing a different size range of arterioles or venules. The network includes five actively regulating arteriolar segments with time-dependent diameters influenced by shear stress, wall tension, metabolic regulation, and SNA. Metabolic signals are assumed to be propagated upstream along vessel walls via a conducted response. The model exhibits functional sympatholysis, in which sympathetic vasoconstriction is partially abrogated by increases in metabolic demand, and sympathetic escape, in which SNA elicits an initial vasoconstriction followed by vasodilation. In accordance with experimental observations, these phenomena are more prominent in small arterioles than in larger arterioles when SNA is assumed to act equally on arterioles of all sizes. The results imply that a mechanism based on the competing effects on arteriolar tone of SNA and conducted metabolic signals can account for several observed characteristics of functional sympatholysis, including the different responses of large and small arterioles.