Fluctuations in microvascular blood flow parameters caused by hemodynamic mechanisms

Glomerular microcirculation: Implications for diabetes, preeclampsia, and kidney injury

This review outlines the features of tandem regulation of glomerular microcirculation by autoregulatory mechanisms and intraglomerular redistribution of blood flow. Multiple points of cooperation exist between autoregulatory and distributional mechanisms. Mutual interactions between myogenic and tubuloglomerular feedback (TGF) mechanisms regulating the inflow are briefly discussed. In addition to this, TGF operation involving purinergic, autocoid, and NO signaling affects, however, not only afferent arteriolar tone, but mesangial cell tone as well. The latter reversibly reconfigures the distribution of blood flow between the shorter and longer pathways in the glomerular tuft. I advance a hypothesis that blood flow in these pathways spontaneously alternates, and mesangial cell tonicity serves as a rheostatic shift between them. Furthermore, humoral messengers from macula densa cells, themselves dependent on myogenic mechanisms, fine-tune the secretion of renin and, subsequently, the local, intrarenal generation of angiotensin II, which, in turn, provides additional vasomotor signaling to glomerular capillaries through changing the tone of mesangial cells. This complex regulatory network may partially explain the phenomenon of renal functional reserve, as well as suggest implications for changes in renal function during pregnancy, early diabetes mellitus, and acute kidney injury.

Angiogenic Microvascular Wall Shear Stress Patterns Revealed Through Three-dimensional Red Blood Cell Resolved Modeling

The wall shear stress (WSS) exerted by blood flowing through microvascular capillaries is an established driver of new blood vessel growth, or angiogenesis. Such adaptations are central to many physiological processes in both health and disease, yet three-dimensional (3D) WSS characteristics in real angiogenic microvascular networks are largely unknown. This marks a major knowledge gap because angiogenesis, naturally, is a 3D process. To advance current understanding, we model 3D red blood cells (RBCs) flowing through rat angiogenic microvascular networks using state-of-the-art simulation. The high-resolution fluid dynamics reveal 3D WSS patterns occurring at sub-endothelial cell (EC) scales that derive from distinct angiogenic morphologies, including microvascular loops and vessel tortuosity. We identify the existence of WSS hot and cold spots caused by angiogenic surface shapes and RBCs, and notably enhancement of low WSS regions by RBCs. Spatiotemporal characteristics further reveal how fluctuations follow timescales of RBC "footprints." Altogether, this work provides a new conceptual framework for understanding how shear stress might regulate EC dynamics in vivo.

Hematocrit skewness along sequential bifurcations within a microfluidic network induces significant changes in downstream red blood cell partitioning

There has been a wealth of research conducted regarding the partitioning of red blood cells (RBCs) at bifurcations within the microvasculature. In previous studies, partitioning has been characterized as either regular partitioning, in which the higher flow rate daughter channel receives a proportionally larger percentage of RBCs, or reverse partitioning, in which the opposite occurs. While there are many examples of network studies in silico, most in vitro work has been conducted using single bifurcation. When microfluidic networks have been used, the channel dimensions are typically greater than 20 μm, ignoring conditions where RBCs are highly confined. This paper presents a study of RBC partitioning in a network of sequential bifurcations with channel dimensions less than 8 μm in hydraulic diameter. The study investigated the effect of the volumetric flow rate ratio (Q*) at each bifurcation, solution hematocrit, and channel length on the erythrocyte flux ratio (N*), a measure of RBC partitioning. We report significant differences in partitioning between upstream and downstream bifurcations even when the flow rate ratio remains the same. Skewness analysis, a measure of cell distribution across the width of a vessel, strongly suggests that immediately following the first bifurcation most RBCs are skewed toward the inner channel wall, leading to preferential RBC perfusion into one daughter channel at the subsequent bifurcation even at higher downstream flow rate ratios. The skewness of RBC distribution following the first bifurcation can either manifest as enhanced regular partitioning or reverse partitioning at the succeeding branch.

Structural Features of Microvascular Networks Trigger Blood Flow Oscillations

We analyse mathematical models in order to understand how microstructural features of vascular networks may affect blood flow dynamics, and to identify particular characteristics that promote the onset of self-sustained oscillations. By focusing on a simple three-node motif, we predict that network “redundancy”, in the form of a redundant vessel connecting two main flow-branches, together with differences in haemodynamic resistance in the branches, can promote the emergence of oscillatory dynamics. We use existing mathematical descriptions for blood rheology and haematocrit splitting at vessel branch-points to construct our flow model; we combine numerical simulations and stability analysis to study the dynamics of the three-node network and its relation to the system’s multiple steady-state solutions. While, for the case of equal inlet-pressure conditions, a “trivial” equilibrium solution with no flow in the redundant vessel always exists, we find that it is not stable when other, stable, steady-state attractors exist. In turn, these “nontrivial” steady-state solutions may undergo a Hopf bifurcation into an oscillatory state. We use the branch diameter ratio, together with the inlet haematocrit rate, to construct a two-parameter stability diagram that delineates regimes in which such oscillatory dynamics exist. We show that flow oscillations in this network geometry are only possible when the branch diameters are sufficiently different to allow for a sufficiently large flow in the redundant vessel, which acts as the driving force of the oscillations. These microstructural properties, which were found to promote oscillatory dynamics, could be used to explore sources of flow instability in biological microvascular networks.

Nonlinear Phenomena in Microfluidics

This review focuses on experimental work on nonlinear phenomena in microfluidics, which for the most part are phenomena for which the velocity of a fluid flowing through a microfluidic channel does not scale proportionately with the pressure drop. Examples include oscillations, flow-switching behaviors, and bifurcations. These phenomena are qualitatively distinct from laminar, diffusion-limited flows that are often associated with microfluidics. We explore the nonlinear behaviors of bubbles or droplets when they travel alone or in trains through a microfluidic network or when they assemble into either one- or two-dimensional crystals. We consider the nonlinearities that can be induced by the geometry of channels, such as their curvature or the bas-relief patterning of their base. By casting posts, barriers, or membranes─situated inside channels─from stimuli-responsive or flexible materials, the shape, size, or configuration of these elements can be altered by flowing fluids, which may enable autonomous flow control. We also highlight some of the nonlinearities that arise from operating devices at intermediate Reynolds numbers or from using non-Newtonian fluids or liquid metals. We include a brief discussion of relevant practical applications, including flow gating, mixing, and particle separations.

Origins of 1/f-like tissue oxygenation fluctuations in the murine cortex

The concentration of oxygen in the brain spontaneously fluctuates, and the distribution of power in these fluctuations has a 1/f-like spectra, where the power present at low frequencies of the power spectrum is orders of magnitude higher than at higher frequencies. Though these oscillations have been interpreted as being driven by neural activity, the origin of these 1/f-like oscillations is not well understood. Here, to gain insight of the origin of the 1/f-like oxygen fluctuations, we investigated the dynamics of tissue oxygenation and neural activity in awake behaving mice. We found that oxygen signal recorded from the cortex of mice had 1/f-like spectra. However, band-limited power in the local field potential did not show corresponding 1/f-like fluctuations. When local neural activity was suppressed, the 1/f-like fluctuations in oxygen concentration persisted. Two-photon measurements of erythrocyte spacing fluctuations and mathematical modeling show that stochastic fluctuations in erythrocyte flow could underlie 1/f-like dynamics in oxygenation. These results suggest that the discrete nature of erythrocytes and their irregular flow, rather than fluctuations in neural activity, could drive 1/f-like fluctuations in tissue oxygenation.

Investigation of red blood cell partitioning in an in vitro microvascular bifurcation

There is a long history of research examining red blood cell (RBC) partitioning in microvasculature bifurcations. These studies commonly report results describing partitioning that exists as either regular partitioning, which occurs when the RBC flux ratio is greater than the bulk fluid flowrate ratio, or reverse partitioning when the RBC flux ratio is less than or equal to that of the bulk fluid flowrate. This paper presents a study of RBC partitioning in a single bifurcating microchannel with dimensions of 6 to 16 μm, investigating the effects of hematocrit, channel width, daughter channel flowrate ratio, and bifurcation angle. The erythrocyte flux ratio, N*, manifests itself as either regular or reverse partitioning, and time-dependent partitioning is much more dynamic, occurring as both regular and reverse partitioning. We report a significant reduction in the well-known sigmoidal variation of the erythrocyte flux ratio (N*) versus the volumetric flowrate ratio (Q*), partitioning behavior with increasing hematocrit in microchannels when the channel dimensions are comparable with cell size. RBCs "lingering" or jamming at the bifurcation were also observed and quantified in vitro. Results from trajectory analyses suggest that the RBC position in the feeder channel strongly affects both partitioning and lingering frequency of RBCs, with both being significantly reduced when RBCs flow on streamlines near the edge of the channel as opposed to the center of the channel. Furthermore, our experiments suggest that even at low Reynolds number, partitioning is affected by the bifurcation angle by increasing cell-cell interactions. The presented results provide further insight into RBC partitioning as well as perfusion throughout the microvasculature.

Red blood cells stabilize flow in brain microvascular networks

Capillaries are the prime location for oxygen and nutrient exchange in all tissues. Despite their fundamental role, our knowledge of perfusion and flow regulation in cortical capillary beds is still limited. Here, we use in vivo measurements and blood flow simulations in anatomically accurate microvascular network to investigate the impact of red blood cells (RBCs) on microvascular flow. Based on these in vivo and in silico experiments, we show that the impact of RBCs leads to a bias toward equating the values of the outflow velocities at divergent capillary bifurcations, for which we coin the term “well-balanced bifurcations”. Our simulation results further reveal that hematocrit heterogeneity is directly caused by the RBC dynamics, i.e. by their unequal partitioning at bifurcations and their effect on vessel resistance. These results provide the first in vivo evidence of the impact of RBC dynamics on the flow field in the cortical microvasculature. By structural and functional analyses of our blood flow simulations we show that capillary diameter changes locally alter flow and RBC distribution. A dilation of 10% along a vessel length of 100 μm increases the flow on average by 21% in the dilated vessel downstream a well-balanced bifurcation. The number of RBCs rises on average by 27%. Importantly, RBC up-regulation proves to be more effective the more balanced the outflow velocities at the upstream bifurcation are. Taken together, we conclude that diameter changes at capillary level bear potential to locally change the flow field and the RBC distribution. Moreover, our results suggest that the balancing of outflow velocities contributes to the robustness of perfusion. Based on our in silico results, we anticipate that the bi-phasic nature of blood and small-scale regulations are essential for a well-adjusted oxygen and energy substrate supply.

Glucose and oxygen are key energy sources of the brain. As energy storage capabilities are limited in the brain, a continuous supply of oxygen and glucose via the bloodstream is crucial for the brain’s functioning. The bulk of discharge occurs at the level of capillaries, which are the smallest and most frequent vessels of the cortical vasculature. Nonetheless, our understanding of perfusion and topology of the capillary bed is still limited. Here, we use in vivo two-photon based blood flow measurements and numerical simulations in large realistic microvascular networks to study the flow in the cortical microvasculature. Our results reveal that the impact of red blood cells enhances the robustness of microvascular perfusion and increases the heterogeneity in red blood cell distribution. It is well established that higher neuronal activity leads to an increase in blood flow. However, the precise regulation mechanisms and their spatial extent remain largely unknown. We show that small-scale regulations locally alter flow and red blood cell distribution. We suggest that these mechanisms are key for an efficient and flexible circulatory system. Moreover, our results reveal a novel role of the bi-phasic nature of blood.

A perpetual switching system in pulmonary capillaries

Of the 300 billion capillaries in the human lung, a small fraction meet normal oxygen requirements at rest, with the remainder forming a large reserve. The maximum oxygen demands of the acute stress response require that the reserve capillaries are rapidly recruited. To remain primed for emergencies, the normal cardiac output must be parceled throughout the capillary bed to maintain low opening pressures. The flow-distributing system requires complex switching. Because the pulmonary microcirculation contains contractile machinery, one hypothesis posits an active switching system. The opposing hypothesis is based on passive switching that requires no regulation. Both hypotheses were tested ex vivo in canine lung lobes. The lobes were perfused first with autologous blood, and capillary switching patterns were recorded by videomicroscopy. Next, the vasculature of the lobes was saline flushed, fixed by glutaraldehyde perfusion, flushed again, and then reperfused with the original, unfixed blood. Flow patterns through the same capillaries were recorded again. The 16-min-long videos were divided into 4-s increments. Each capillary segment was recorded as being perfused if at least one red blood cell crossed the entire segment. Otherwise it was recorded as unperfused. These binary measurements were made manually for each segment during every 4 s throughout the 16-min recordings of the fresh and fixed capillaries (>60,000 measurements). Unexpectedly, the switching patterns did not change after fixation. We conclude that the pulmonary capillaries can remain primed for emergencies without requiring regulation: no detectors, no feedback loops, and no effectors-a rare system in biology. NEW & NOTEWORTHY The fluctuating flow patterns of red blood cells within the pulmonary capillary networks have been assumed to be actively controlled within the pulmonary microcirculation. Here we show that the capillary flow switching patterns in the same network are the same whether the lungs are fresh or fixed. This unexpected observation can be successfully explained by a new model of pulmonary capillary flow based on chaos theory and fractal mathematics.

Blood flow and transport in the human placenta

The placenta is a multi-functional organ that exchanges blood gases and nutrients between a mother and her developing fetus. In humans, fetal blood flows through intricate networks of vessels confined within villous trees, the branches of which are bathed in pools of maternal blood. Fluid mechanics and transport processes play a central role in understanding how these elaborate structures contribute to the function of the placenta, and how their disorganization may lead to disease. Recent advances in imaging and computation have spurred significant advances in simulations of fetal and maternal flows within the placenta, across a range of lengthscales. Models describe jets of maternal blood emerging from spiral arteries into a disordered and deformable porous medium, and solute uptake by fetal blood flowing through elaborate three-dimensional capillary networks. We survey recent developments and emerging challenges in modeling flow and transport in this complex organ.

Automated quantification of microvascular perfusion

OBJECTIVE

Changes in microvascular perfusion have been reported in many diseases, yet the functional significance of altered perfusion is often difficult to determine. This is partly because commonly used techniques for perfusion measurement often rely on either indirect or by-hand approaches.

METHODS

We developed and validated a fully automated software technique to measure microvascular perfusion in videos acquired by fluorescence microscopy in the mouse gastrocnemius. Acute perfusion responses were recorded following intravenous injections with phenylephrine, SNP, or saline.

RESULTS

Software-measured capillary flow velocity closely correlated with by-hand measured flow velocity (R²  = 0.91, P < 0.0001). Software estimates of capillary hematocrit also generally agreed with by-hand measurements (R²  = 0.64, P < 0.0001). Detection limits range from 0 to 2000 μm/s, as compared to an average flow velocity of 326 ± 102 μm/s (mean ± SD) at rest. SNP injection transiently increased capillary flow velocity and hematocrit and made capillary perfusion more steady and homogenous. Phenylephrine injection had the opposite effect in all metrics. Saline injection transiently decreased capillary flow velocity and hematocrit without influencing flow distribution or stability. All perfusion metrics were temporally stable without intervention.

CONCLUSIONS

These results demonstrate a novel and sensitive technique for reproducible, user-independent quantification of microvascular perfusion.

Influence of feeding hematocrit and perfusion pressure on hematocrit reduction (Fåhraeus effect) in an artificial microvascular network

OBJECTIVE

Hct in narrow vessels is reduced due to concentration of fast-flowing RBCs in the center, and of slower flowing plasma along the wall of the vessel, which in combination with plasma skimming at bifurcations leads to the striking heterogeneity of local Hct in branching capillary networks known as the network Fåhraeus effect. We analyzed the influence of feeding Hct and perfusion pressure on the Fåhraeus effect in an AMVN.

METHODS

RBC suspensions in plasma with Hcts between 20% and 70% were perfused at pressures of 5-60 cm H₂ O through the AMVN. A microscope and high-speed camera were used to measure RBC velocity and Hct in microchannels of height of 5 μm and widths of 5-19 μm.

RESULTS

Channel Hcts were reduced compared with Hct_feeding in 5 and 7 μm microchannels, but not in larger microchannels. The magnitude of Hct reduction increased with decreasing Hct_feeding and decreasing ΔP (flow velocity), showing an about sevenfold higher effect for 40% Hct_feeding and low pressure/flow velocity than for 60% Hct_feeding and high pressure/flow velocity.

CONCLUSIONS

The magnitude of the network Fåhraeus effect in an AMVN is inversely related to Hct_feeding and ΔP.

Direct Numerical Simulation of Cellular-Scale Blood Flow in 3D Microvascular Networks

We present, to our knowledge, the first direct numerical simulation of 3D cellular-scale blood flow in physiologically realistic microvascular networks. The vascular networks are designed following in vivo images and data, and are comprised of bifurcating, merging, and winding vessels. Our model resolves the large deformation and dynamics of each individual red blood cell flowing through the networks with high fidelity, while simultaneously retaining the highly complex geometric details of the vascular architecture. To our knowledge, our simulations predict several novel and unexpected phenomena. We show that heterogeneity in hemodynamic quantities, which is a hallmark of microvascular blood flow, appears both in space and time, and that the temporal heterogeneity is more severe than its spatial counterpart. The cells are observed to frequently jam at vascular bifurcations resulting in reductions in hematocrit and flow rate in the daughter and mother vessels. We find that red blood cell jamming at vascular bifurcations results in several orders-of-magnitude increase in hemodynamic resistance, and thus provides an additional mechanism of increased in vivo blood viscosity as compared to that determined in vitro. A striking result from our simulations is negative pressure-flow correlations observed in several vessels, implying a significant deviation from Poiseuille's law. Furthermore, negative correlations between vascular resistance and hematocrit are observed in various vessels, also defying a major principle of particulate suspension flow. To our knowledge, these novel findings are absent in blood flow in straight tubes, and they underscore the importance of considering realistic physiological geometry and resolved cellular interactions in modeling microvascular hemodynamics.

Noninvasive Imaging of Cycling Hypoxia in Head and Neck Cancer Using Intrinsic Susceptibility MRI

Purpose: To evaluate intrinsic susceptibility (IS) MRI for the identification of cycling hypoxia, and the assessment of its extent and spatial distribution, in head and neck squamous cell carcinoma (HNSCC) xenografts and patients.Experimental Design: Quantitation of the transverse relaxation rate, R2*, which is sensitive to paramagnetic deoxyhemoglobin, using serial IS-MRI acquisitions, was used to monitor temporal oscillations in levels of paramagnetic deoxyhemoglobin in human CALR xenografts and patients with HNSCC at 3T. Autocovariance and power spectrum analysis of variations in R2* was performed for each imaged voxel, to assess statistical significance and frequencies of cycling changes in tumor blood oxygenation. Pathologic correlates with tumor perfusion (Hoechst 33342), hypoxia (pimonidazole), and vascular density (CD31) were sought in the xenografts, and dynamic contrast-enhanced (DCE) MRI was used to assess patient tumor vascularization. The prevalence of fluctuations within patient tumors, DCE parameters, and treatment outcome were reported.Results: Spontaneous R2* fluctuations with a median periodicity of 15 minutes were detected in both xenografts and patient tumors. Spatially, these fluctuations were predominantly associated with regions of heterogeneous perfusion and hypoxia in the CALR xenografts. In patients, R2* fluctuations spatially correlated with regions of lymph nodes with low Ktrans values, typically in the vicinity of necrotic cores.Conclusions: IS-MRI can be used to monitor variations in levels of paramagnetic deoxyhemoglobin, associated with cycling hypoxia. The presence of such fluctuations may be linked with impaired tumor vasculature, the presence of which may impact treatment outcome. Clin Cancer Res; 23(15); 4233-41. ©2017 AACR.

Optimal hematocrit in an artificial microvascular network

BACKGROUND

Higher hematocrit increases the oxygen-carrying capacity of blood but also increases blood viscosity, thus decreasing blood flow through the microvasculature and reducing the oxygen delivery to tissues. Therefore, an optimal value of hematocrit that maximizes tissue oxygenation must exist.

STUDY DESIGN AND METHODS

We used viscometry and an artificial microvascular network device to determine the optimal hematocrit in vitro. Suspensions of fresh red blood cells (RBCs) in plasma, normal saline, or a protein-containing buffer and suspensions of stored red blood cells (at Week 6 of standard hypothermic storage) in plasma with hematocrits ranging from 10 to 80% were evaluated.

RESULTS

For viscometry, optimal hematocrits were 10, 25.2, 31.9, 37.1, and 37.5% for fresh RBCs in plasma at shear rates of 3.2 or less, 11.0, 27.7, 69.5, and 128.5 inverse seconds. For the artificial microvascular network, optimal hematocrits were 51.1, 55.6, 59.2, 60.9, 62.3, and 64.6% for fresh RBCs in plasma and 46.4, 48.1, 54.8, 61.4, 65.7, and 66.5% for stored RBCs in plasma at pressures of 2.5, 5, 10, 20, 40, and 60 cm H₂ O.

CONCLUSION

Although exact optimal hematocrit values may depend on specific microvascular architecture, our results suggest that the optimal hematocrit for oxygen delivery in the microvasculature depends on perfusion pressure. Therefore, anemia in chronic disorders may represent a beneficial physiological response to reduced perfusion pressure resulting from decreased heart function and/or vascular stenosis. Our results may help explain why a therapeutically increasing hematocrit in such conditions with RBC transfusion frequently leads to worse clinical outcomes.

Red blood cell phase separation in symmetric and asymmetric microchannel networks: effect of capillary dilation and inflow velocity

The non-uniform partitioning or phase separation of red blood cells (RBCs) at a diverging bifurcation of a microvascular network is responsible for RBC heterogeneity within the network. The mechanisms controlling RBC heterogeneity are not yet fully understood and there is a need to improve the basic understanding of the phase separation phenomenon. In this context, in vitro experiments can fill the gap between existing in vivo and in silico models as they provide better controllability than in vivo experiments without mathematical idealizations or simplifications inherent to in silico models. In this study, we fabricated simple models of symmetric/asymmetric microvascular networks; we provided quantitative data on the RBC velocity, line density and flux in the daughter branches. In general our results confirmed the tendency of RBCs to enter the daughter branch with higher flow rate (Zweifach-Fung effect); in some cases even inversion of the Zweifach-Fung effect was observed. We showed for the first time a reduction of the Zweifach-Fung effect with increasing flow rate. Moreover capillary dilation was shown to cause an increase of RBC line density and RBC residence time within the dilated capillary underlining the possible role of pericytes in regulating the oxygen supply.

A novel microfluidic assay reveals a key role for protein kinase C δ in regulating human neutrophil-endothelium interaction

A key step in neutrophil-mediated tissue damage is the migration of activated neutrophils across the vascular endothelium. Previously, we identified protein kinase C δ as a critical regulator of neutrophil migration in sepsis but did not identify specific steps in migration. In this study, we used our novel biomimetic microfluidic assay to delineate systematically the mechanism by which protein kinase C δ regulates individual steps in human neutrophil-endothelial interaction during inflammation. The biomimetic microfluidic assay includes a network of vascular channels, produced from in vivo images connected to a tissue compartment through a porous barrier. HUVECs cultured in vascular channels formed a complete lumen under physiologic shear flow. HUVECs were pretreated with TNF-α ± a protein kinase C δ inhibitor, and the tissue compartment was filled with a chemoattractant (fMLP or IL-8). Under physiologic shear flow, the role of protein kinase C δ on spatial and temporal neutrophil adherence/migration was quantified. Protein kinase C δ inhibition significantly reduced neutrophil adhesion in response to fMLP and IL-8 only under low shear rate and near bifurcations. Protein kinase C δ inhibition also decreased adherence to nonactivated HUVECs in response to fMLP or IL-8. Protein kinase C δ inhibition reduced neutrophil migration into the tissue compartment in response to fMLP and to a lesser degree, to IL-8. Antibody-coated microparticles demonstrated that protein kinase C δ inhibition down-regulated E-selectin and ICAM-1 but not VCAM-1 expression. With the use of a physiologically relevant in vitro model system, we demonstrate that protein kinase C δ plays an important role in the regulation of neutrophil adherence/migration during inflammation and identifies key steps regulated by protein kinase C δ in neutrophil-endothelial interactions.

Computational Network Model Prediction of Hemodynamic Alterations Due to Arteriolar Rarefaction and Estimation of Skeletal Muscle Perfusion in Peripheral Arterial Disease

OBJECTIVE

To estimate the relative influence of input pressure and arteriole rarefaction on gastrocnemius muscle perfusion in patients with PAD after exercise and/or percutaneous interventions.

METHODS

A computational network model of the gastrocnemius muscle microcirculation was adapted to reflect rarefaction based on arteriolar density measurements from PAD patients, with and without exercise. A normalized input pressure was applied at the feeder artery to simulate both reduced and restored ABI in the PAD condition.

RESULTS

In simulations of arteriolar rarefaction, resistance increased non-linearly with rarefaction, leading to a disproportionally large drop in perfusion. In addition, perfusion was less sensitive to changes in input pressure as the degree of rarefaction increased. Reduced arteriolar density was observed in PAD patients and improved 33.8% after three months of exercise. In model simulations of PAD, ABI restoration yielded perfusion recovery to only 66% of baseline. When exercise training was simulated by reducing rarefaction, ABI restoration increased perfusion to 80% of baseline.

CONCLUSION

Microvascular resistance increases non-linearly with increasing arteriole rarefaction. Therefore, muscle perfusion becomes disproportionally less sensitive to ABI restoration as arteriole rarefaction increases. These results highlight the importance of restoring both microvascular structure and upstream input pressure in PAD therapy.

Modeling microcirculatory blood flow: current state and future perspectives

Microvascular blood flow determines a number of important physiological processes of an organism in health and disease. Therefore, a detailed understanding of microvascular blood flow would significantly advance biophysical and biomedical research and its applications. Current developments in modeling of microcirculatory blood flow already allow to go beyond available experimental measurements and have a large potential to elucidate blood flow behavior in normal and diseased microvascular networks. There exist detailed models of blood flow on a single cell level as well as simplified models of the flow through microcirculatory networks, which are reviewed and discussed here. The combination of these models provides promising prospects for better understanding of blood flow behavior and transport properties locally as well as globally within large microvascular networks.

The relationship between red blood cell deformability metrics and perfusion of an artificial microvascular network

The ability of red blood cells (RBC) to undergo a wide range of deformations while traversing the microvasculature is crucial for adequate perfusion. Interpretation of RBC deformability measurements performed in vitro in the context of microvascular perfusion has been notoriously difficult. This study compares the measurements of RBC deformability performed using micropore filtration and ektacytometry with the RBC ability to perfuse an artificial microvascular network (AMVN). Human RBCs were collected from healthy consenting volunteers, leukoreduced, washed and exposed to graded concentrations (0-0.08%) of glutaraldehyde (a non-specific protein cross-linker) and diamide (a spectrin-specific protein cross-linker) to impair the deformability of RBCs. Samples comprising cells with two different levels of deformability were created by adding non-deformable RBCs (hardened by exposure to 0.08% glutaraldehyde) to the sample of normal healthy RBCs. Ektacytometry indicated a nearly linear decline in RBC deformability with increasing glutaraldehyde concentration. Micropore filtration showed a significant reduction only for concentrations of glutaraldehyde higher than 0.04%. Neither micropore filtration nor ektacytometry measurements could accurately predict the AMVN perfusion. Treatment with diamide reduced RBC deformability as indicated by ektacytometry, but had no significant effect on either micropore filtration or the AMVN perfusion. Both micropore filtration and ektacytometry showed a linear decline in effective RBC deformability with increasing fraction of non-deformable RBCs in the sample. The corresponding decline in the AMVN perfusion plateaued above 50%, reflecting the innate ability of blood flow in the microvasculature to bypass occluded capillaries. Our results suggest that in vitro measurements of RBC deformability performed using either micropore filtration or ektacytometry may not represent the ability of same RBCs to perfuse microvascular networks. Further development of biomimetic tools for measuring RBC deformability (e.g. the AMVN) could enable a more functionally relevant testing of RBC mechanical properties.

The impact of capillary dilation on the distribution of red blood cells in artificial networks

Recent studies suggest that pericytes around capillaries are contractile and able to alter the diameter of capillaries. To investigate the effects of capillary dilation on network dynamics, we performed simulations in artificial capillary networks of different sizes and complexities. The unequal partition of hematocrit at diverging bifurcations was modeled by assuming that each red blood cell (RBC) enters the branch with the faster instantaneous flow. Network simulations with and without RBCs were performed to investigate the effect of local dilations. The results showed that the increase in flow rate due to capillary dilation was less when the effects of RBCs are included. For bifurcations with sufficient RBCs in the parent vessel and nearly equal flows in the branches, the flow rate in the dilated branch did not increase. Instead, a self-regulation of flow was observed due to accumulation of RBCs in the dilated capillary. A parametric study was performed to examine the dependence on initial capillary diameter, dilation factor, and tube hematocrit. Furthermore, the conditions needed for an efficient self-regulation mechanism are discussed. The results support the hypothesis that RBCs play a significant role for the fluid dynamics in capillary networks and that it is crucial to consider the blood flow rate and the distribution of RBCs to understand the supply of oxygen in the vasculature. Furthermore, our results suggest that capillary dilation/constriction offers the potential of being an efficient mechanism to alter the distribution of RBCs locally and hence could be important for the local regulation of oxygen delivery.

Imaging tumor hypoxia to advance radiation oncology

SIGNIFICANCE

Most solid tumors contain regions of low oxygenation or hypoxia. Tumor hypoxia has been associated with a poor clinical outcome and plays a critical role in tumor radioresistance.

RECENT ADVANCES

Two main types of hypoxia exist in the tumor microenvironment: chronic and cycling hypoxia. Chronic hypoxia results from the limited diffusion distance of oxygen, and cycling hypoxia primarily results from the variation in microvessel red blood cell flux and temporary disturbances in perfusion. Chronic hypoxia may cause either tumor progression or regressive effects depending on the tumor model. However, there is a general trend toward the development of a more aggressive phenotype after cycling hypoxia. With advanced hypoxia imaging techniques, spatiotemporal characteristics of tumor hypoxia and the changes to the tumor microenvironment can be analyzed.

CRITICAL ISSUES

In this review, we focus on the biological and clinical consequences of chronic and cycling hypoxia on radiation treatment. We also discuss the advanced non-invasive imaging techniques that have been developed to detect and monitor tumor hypoxia in preclinical and clinical studies.

FUTURE DIRECTIONS

A better understanding of the mechanisms of tumor hypoxia with non-invasive imaging will provide a basis for improved radiation therapeutic practices.

A mathematical and numerical investigation of the hemodynamical origins of oscillations in microvascular networks

Evidence is presented to show that self-sustained oscillations of purely hemodynamical origin are possible in some arcade-type microvascular networks supplied with steady boundary conditions, but that in others the oscillations disappear with sufficient reduction of the time step Δt, showing them to be numerical artefacts. In an attempt to elucidate the mechanisms involved in the onset of fluctuations, we proceed to perform a linear stability analysis for the convective model of Kiani et al. (Microvasc. Res. 45:219-232, 1993; Am. J. Physiol. 266(35):H1822-H1828, 1994), and show that this leads via a system of delay differential equations to a nonlinear eigenvalue problem. This result generalises the characteristic equation obtained by Carr et al. (Ann. Biomed. Eng. 33:764-771, 2005) and Geddes et al. (SIAM J. Appl. Dyn. Syst. 6(4):694-727, 2007) who solved a special case in a two node network. An implicit numerical method is proposed for the computation of blood flows in networks using the convective model. In a moderate size subnetwork of one of the networks chosen by Kiani et al. (Am. J. Physiol. 266(35):H1822-H1828, 1994), the topology, vessel lengths, and diameters of which were based on microvascular networks in the rat mesentery, we compare results generated using the original explicit numerical method of Kiani et al. (Am. J. Physiol. 266(35):H1822-H1828, 1994) with those from our implicit scheme. From the linear stability theory, a critical value D RBC,crit of a red blood cell diameter parameter D RBC in the plasma skimming model of Fenton et al. (Pflügers Arch. 403:396-401, 1985b) is identified for the onset of oscillations about steady state and both the explicit and implicit methods are used to calculate the inflow hematocrit solutions in all vessels of the subnetwork at the critical parameter value, subject to perturbed initial conditions. The results of the implicit method are demonstrated to be in excellent and superior agreement with the predictions of the linear analysis in this case. For values of D RBC slightly larger than D RBC,crit the bifurcating periodic solutions calculated using either the explicit or implicit schemes are characteristic of those of a supercritical Hopf bifurcation and the graphs of D RBC vs. oscillation amplitude would seem to converge as Δt→0.

Blunted temporal activity of microvascular perfusion heterogeneity in metabolic syndrome: a new attractor for peripheral vascular disease?

A key clinical outcome for peripheral vascular disease (PVD) in patients is a progressive decay in skeletal muscle performance and its ability to resist fatigue with elevated metabolic demand. We have demonstrated that PVD in obese Zucker rats (OZR) is partially due to increased perfusion distribution heterogeneity at successive microvascular bifurcations within skeletal muscle. As this increased heterogeneity (γ) is longitudinally present in the network, its cumulative impact is a more heterogeneous distribution of perfusion between terminal arterioles than normal, causing greater regional tissue ischemia. To minimize this negative outcome, a likely compensatory mechanism against an increased γ should be an increased temporal switching at arteriolar bifurcations to minimize downstream perfusion deficits. Using in situ cremaster muscle, we determined that temporal activity (the cumulative sum of absolute differences between successive values of γ, taken every 20 s) was lower in OZR than in control animals, and this difference was present in both proximal (1A-2A) and distal (3A-4A) arteriolar bifurcations. Although adrenoreceptor blockade (phentolamine) improved temporal activity in 1A-2A arteriolar bifurcations in OZR, this was without impact in the distal microcirculation, where only interventions against oxidant stress (Tempol) and thromboxane A(2) activity (SQ-29548) were effective. Analysis of the attractor for γ indicated that it was not only elevated in OZR but also exhibited severe reductions in range, suggesting that the ability of the microcirculation to respond to any challenge is highly restricted and may represent the major contributor to the manifestation of poor muscle performance at this age in OZR.

Tumor blood flow differs between mouse strains: consequences for vasoresponse to photodynamic therapy

Fluctuations in tumor blood flow are common and attributed to factors such as vasomotion or local vascular structure, yet, because vessel structure and physiology are host-derived, animal strain of tumor propagation may further determine blood flow characteristics. In the present report, baseline and stress-altered tumor hemodynamics as a function of murine strain were studied using radiation-induced fibrosacomas (RIF) grown in C3H or nude mice. Fluctuations in tumor blood flow during one hour of baseline monitoring or during vascular stress induced by photodynamic therapy (PDT) were measured by diffuse correlation spectroscopy. Baseline monitoring revealed fluctuating tumor blood flow highly correlated with heart rate and with similar median periods (i.e., ∼9 and 14 min in C3H and nudes, respectively). However, tumor blood flow in C3H animals was more sensitive to physiologic or stress-induced perturbations. Specifically, PDT-induced vascular insults produced greater decreases in blood flow in the tumors of C3H versus nude mice; similarly, during baseline monitoring, fluctuations in blood flow were more regular and more prevalent within the tumors of C3H mice versus nude mice; finally, the vasoconstrictor L-NNA reduced tumor blood flow in C3H mice but did not affect tumor blood flow in nudes. Underlying differences in vascular structure, such as smaller tumor blood vessels in C3H versus nude animals, may contribute to strain-dependent variation in vascular function. These data thus identify clear effects of mouse strain on tumor hemodynamics with consequences to PDT and potentially other vascular-mediated therapies.

Relationships between cycling hypoxia, HIF-1, angiogenesis and oxidative stress

This Failla Lecture focused on the inter-relationships between tumor angiogenesis, HIF-1 expression and radiotherapy responses. A common thread that bonds all of these factors together is microenvironmental stress caused by reactive oxygen and nitrogen species formed during tumor growth and angiogenesis or in response to cytotoxic treatment. In this review we focus on one aspect of the crossroad between oxidative stress and angiogenesis, namely cycling hypoxia. Understanding of the relative importance of this feature of the tumor microenvironment has recently expanded; it influences tumor biology in ways that are separate from chronic hypoxia. Cycling hypoxia can influence angiogenesis, treatment responses and metastatic behavior. It represents an important and relatively less well understood feature of tumor biology that requires additional research.

Cycling hypoxia and free radicals regulate angiogenesis and radiotherapy response

Hypoxia and free radicals, such as reactive oxygen and nitrogen species, can alter the function and/or activity of the transcription factor hypoxia-inducible factor 1 (HIF1). Interplay between free radicals, hypoxia and HIF1 activity is complex and can influence the earliest stages of tumour development. The hypoxic environment of tumours is heterogeneous, both spatially and temporally, and can change in response to cytotoxic therapy. Free radicals created by hypoxia, hypoxia-reoxygenation cycling and immune cell infiltration after cytotoxic therapy strongly influence HIF1 activity. HIF1 can then promote endothelial and tumour cell survival. As discussed here, a constant theme emerges: inhibition of HIF1 activity will have therapeutic benefit.

Quiescence as a mechanism for cyclical hypoxia and acidosis

Tumour tissue characteristically experiences fluctuations in substrate supply. This unstable microenvironment drives constitutive metabolic changes within cellular populations and, ultimately, leads to a more aggressive phenotype. Previously, variations in substrate levels were assumed to occur through oscillations in the haemodynamics of nearby and distant blood vessels. In this paper we examine an alternative hypothesis, that cycles of metabolite concentrations are also driven by cycles of cellular quiescence and proliferation. Using a mathematical modelling approach, we show that the interdependence between cell cycle and the microenvironment will induce typical cycles with the period of order hours in tumour acidity and oxygenation. As a corollary, this means that the standard assumption of metabolites entering diffusive equilibrium around the tumour is not valid; instead temporal dynamics must be considered.

Preconditioning of the Tumor Vasculature and Tumor Cells by Intermittent Hypoxia: Implications for Anticancer Therapies

Hypoxia is a common feature in tumors associated with an increased resistance of tumor cells to therapies. In addition to O(2) diffusion-limited hypoxia, another form of tumor hypoxia characterized by fluctuating changes in pO(2) within the disorganized tumor vascular network is described. Here, we postulated that this form of intermittent hypoxia promotes endothelial cell survival, thereby extending the concept of hypoxia-driven resistance to the tumor vasculature. We found that endothelial cell exposure to cycles of hypoxia reoxygenation not only rendered them resistant to proapoptotic stresses, including serum deprivation and radiotherapy, but also increased their capacity to migrate and organize in tubes. By contrast, prolonged hypoxia failed to exert protective effects and even seemed deleterious when combined with radiotherapy. The use of hypoxia-inducible factor-1alpha (HIF-1alpha)-targeting small interfering RNA led us to document that the accumulation of HIF-1alpha during intermittent hypoxia accounted for the higher resistance of endothelial cells. We also used an in vivo approach to enforce intermittent hypoxia in tumor-bearing mice and found that it was associated with less radiation-induced apoptosis within both the vascular and the tumor cell compartments (versus normoxia or prolonged hypoxia). Radioresistance was further ascertained by an increased rate of tumor regrowth in irradiated mice preexposed to intermittent hypoxia and confirmed in vitro using distinctly radiosensitive tumor cell lines. In conclusion, we have documented that intermittent hypoxia may condition endothelial cells and tumor cells in such a way that they are more resistant to apoptosis and more prone to participate in tumor progression. Our observations also underscore the potential of drugs targeting HIF-1alpha to resensitize the tumor vasculature to anticancer treatments.

Tumor-dependent kinetics of partial pressure of oxygen fluctuations during air and oxygen breathing

The primary purpose of this study was to examine the kinetics of partial pressure of oxygen (pO2) fluctuations in fibrosarcoma (FSA) and 9L tumors under air and O2 breathing conditions. The overall hypothesis was that key factors relating to oxygen tension fluctuations would vary between the two tumor types and as a function of the oxygen content of the breathing gas. To assist in the interpretation of the temporal data, spatial pO2 distributions were measured in 10 FSA and 8 9L tumors transplanted into the subcutis of the hind leg of Nembutal-anesthetized (50 mg/kg) Fischer 344 rats. Recessed-tip oxygen microelectrodes were inserted into the tumor, and linear pO2 measurements were recorded in 50-microm steps along a 3-mm path, and blood pressure was simultaneously measured via femoral arterial access. Additionally, pO2 was measured at a single location for 90 to 120 minutes in FSA (n=11) or 9L tumors (n=12). Rats were switched from air to 100% O2 breathing after 45 minutes. Temporal pO2 records were evaluated for their potential radiobiological significance by assessing the number of times they crossed a 10-mm-Hg threshold. In addition, the data were subjected to Fourier analysis for air and O2 breathing. FSA and 9L tumors had spatial median pO2 measurements of 4 and 1 mm Hg, respectively. 9L had more low pO2 measurements < or =2.5 mm Hg than did FSA, whereas between 2.5 and 10 mm Hg this pattern was reversed. Pimonidazole staining patterns in FSA and 9L tumors supported these results. Temporal pO2 instability was observed in all experiments during air and O2 breathing. Threshold analyses indicated that the 10 mm Hg threshold was crossed 2 to 5 times per hour, independent of tumor type. However, the magnitude of 9L pO2 fluctuations was approximately eight times greater than FSA fluctuations, as assessed with Fourier transform analysis (Wilcoxon, P < 0.005). O2 breathing significantly increased median pO2 in FSA from 3 to 8 mm Hg (P < 0.005) and caused a significant increase in frequency and magnitude of pO2 fluctuations. One hundred percent O2 breathing had no effect on 9L tumor pO2, and it decreased the magnitude of pO2 fluctuations with borderline significance. These results show that these two tumors differ significantly with respect to spatial and temporal oxygenation conditions under air and O2 breathing. Fluctuations of pO2 of the type reported herein are predicted to significantly affect radiotherapy response and could be a source for genetic instability, increased angiogenesis, and metastases.

Blood flow switching among pulmonary capillaries is decreased during high hematocrit

Pulmonary capillary perfusion within a single alveolar wall continually switches among segments, even when large-vessel hemodynamics are constant. The mechanism is unknown. We hypothesize that the continually varying size of plasma gaps between individual red blood cells affects the likelihood of capillary segment closure and the probability of cells changing directions at the next capillary junction. We assumed that an increase in hematocrit would decrease the average distance between red blood cells, thereby decreasing the switching at each capillary junction. To test this idea, we observed 26 individual alveolar capillary networks by using videomicroscopy of excised canine lung lobes that were perfused first at normal hematocrit (31–43%) and then at increased hematocrit (51–62%). The number of switches decreased by 38% during increased hematocrit ( P < 0.01). These results support the idea that a substantial part of flow switching among pulmonary capillaries is caused by the particulate nature of blood passing through a complex network of tubes with continuously varying hematocrit.

Biomechanics of microcirculatory blood perfusion

The microcirculation represents a region of the circulation in which blood vessels are directly surrounded by the tissue and cells to which they supply nutrients and from which they collect metabolites. The cellular elements that make up the microcirculation have now been identified, and a large body of evidence has become available that provides molecular definitions of these elements. The blood flow is in a domain in which viscous stresses dominate, but the viscoelastic and active properties of cells lead to nonlinear problems. The ability of cells to actively control cytoplasmic mechanical properties and shape, as well as their membrane adhesion, leads to unique cell behavior in microvessels that has a direct influence on organ transport and function. There is also increasing evidence that the properties of the cells are in turn influenced by fluid shear stresses. These issues have greatly expanded the scope of microvascular analysis. The microcirculation is one of the sites in which diseases manifest themselves at an early stage. The application of biomechanical analysis of the microcirculation is starting to focus on diseases. The field is rich with problems of high significance.

Late effects of ionizing radiation on the microvascular networks in normal tissue

Damage to the microvascular networks constitutes one of the most important components of ionizing radiation damage to normal tissue. Previously, we have reported the early (3, 7 and 30 days postirradiation) effects of ionizing radiation on the structure and function of normal tissue microvascular networks. Here we report on the late effects of ionizing radiation on the structural and functional changes in microvascular networks in locally irradiated (single 10-Gy dose) hamster cremaster muscles observed 60, 120 and 180 days postirradiation; age-matched animals were used as controls. As in the previous study, intravital microscopy was used to measure structural and functional parameters in complete microvascular networks in vivo. A factorial design was used to examine the effects of radiation status, time postirradiation, and network vessel type on the structure and function of microvascular networks. Our results indicate that the progression of radiation-induced microvascular damage continues during the late times but that there is partial recovery from radiation damage within 6 months postirradiation. Red blood cell flux, red blood cell velocity, and capillary blood flow in irradiated networks at 180 days postirradiation were significantly greater than control levels. As at the early times, all vessel types were not damaged equally by radiation at every time.

Causes and effects of heterogeneous perfusion in tumors

A characteristic of solid tumors is their heterogeneous distribution of blood flow, with significant hypoxia and acidity in low-flow regions. We review effects of heterogeneous tumor perfusion are reviewed and propose a conceptual model for its cause. Hypoxic-acidic regions are resistant to chemo- and radiotherapy and may stimulate progression to a more metastatic phenotype. In normal tissues, hypoxia and acidity induce angiogenesis, which is expected to improve perfusion. However, aggressive tumors can have high local microvessel density simultaneously with significant regions of hypoxia and acidosis. A possible explanation for this apparent contradiction is that the mechanisms regulating growth and adaptation of vascular networks are impaired. According to a recent theory for structural adaptation of vascular networks, four interrelated adaptive responses can work as a self-regulating system to produce a mature and efficient blood distribution system in normal tissues. It is proposed that heterogeneous perfusion in tumors may result from perturbation of this system. Angiogenesis may increase perfusion heterogeneity in tumors by increasing the disparity between parallel low- and high-resistance flow pathways. This conceptual model provides a basis for future rational therapies. For example, it indicates that selective destruction of tumor vasculature may increase perfusion efficiency and improve therapeutic efficacy.