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

SpinFlowSim: A blood flow simulation framework for histology-informed diffusion MRI microvasculature mapping in cancer

Diffusion Magnetic Resonance Imaging (dMRI) sensitises the MRI signal to spin motion. This includes Brownian diffusion, but also flow across intricate networks of capillaries. This effect, the intra-voxel incoherent motion (IVIM), enables microvasculature characterisation with dMRI, through metrics such as the vascular signal fraction fV or the vascular Apparent Diffusion Coefficient (ADC) D∗. The IVIM metrics, while sensitive to perfusion, are protocol-dependent, and their interpretation can change depending on the flow regime spins experience during the dMRI measurements (e.g., diffusive vs ballistic), which is in general not known for a given voxel. These facts hamper their practical clinical utility, and innovative vascular dMRI models are needed to enable the in vivo calculation of biologically meaningful markers of capillary flow. These could have relevant applications in cancer, as in the assessment of the response to anti-angiogenic therapies targeting tumour vessels. This paper tackles this need by introducing SpinFlowSim, an open-source simulator of dMRI signals arising from blood flow within pipe networks. SpinFlowSim, tailored for the laminar flow patterns within capillaries, enables the synthesis of highly-realistic microvascular dMRI signals, given networks reconstructed from histology. We showcase the simulator by generating synthetic signals for 15 networks, reconstructed from liver biopsies, and containing cancerous and non-cancerous tissue. Signals exhibit complex, non-mono-exponential behaviours, consistent with in vivo signal patterns, and pointing towards the co-existence of different flow regimes within the same network, as well as diffusion time dependence. We also demonstrate the potential utility of SpinFlowSim by devising a strategy for microvascular property mapping informed by the synthetic signals, and focussing on the quantification of blood velocity distribution moments and of an apparent network branching index. These were estimated in silico and in vivo, in healthy volunteers scanned at 1.5T and 3T and in 13 cancer patients, scanned at 1.5T. In conclusion, realistic flow simulations, as those enabled by SpinFlowSim, may play a key role in the development of the next-generation of dMRI methods for microvascular mapping, with immediate applications in oncology.

Impaired capillary-venous drainage contributes to gliosis and demyelination in white matter during aging

The progressive loss of cerebral white matter during aging contributes to cognitive decline, but whether reduced blood flow is a cause or consequence remains debated. Using deep multi-photon imaging in mice, we examined microvascular networks perfusing myelinated tissues in cortical layer 6 and corpus callosum. We identified sparse, wide-reaching venules, termed principal cortical venules, that exclusively drain deep tissues and resemble vasculature at the human cortex and U-fiber interface. Aging involved selective constriction and rarefaction of capillaries in deep branches of principal cortical venules. This resulted in mild hypoperfusion that was associated with microgliosis, astrogliosis and demyelination in deep tissues, but not upper cortex. Inducing a comparable hypoperfusion in adult mice using carotid artery stenosis triggered a similar tissue pathology specific to layer 6 and corpus callosum. Thus, impaired capillary-venous drainage is a contributor to hypoperfusion and a potential therapeutic target for preserving blood flow to white matter during aging.

Distal activity patterns shape the spatial specificity of neurovascular coupling

Neurovascular coupling links brain activity to local changes in blood flow, forming the basis for non-invasive brain mapping. Using multiscale imaging, we investigated how vascular activity spatially relates to neuronal activity elicited by single whiskers across different columns and layers of mouse cortex. Here we show that mesoscopic hemodynamic signals quantitatively reflect neuronal activity across space but are composed of a highly heterogeneous pattern of responses across individual vessel segments that is poorly predicted by local neuronal activity. Rather, this heterogeneity is dependent on vessel directionality, specifically in thalamocortical input layer 4, where capillaries respond preferentially to neuronal activity patterns along their downstream perfusion domain. Thus, capillaries fine-tune blood flow based on distant activity and encode laminar-specific activity patterns. These findings imply that vascular anatomy sets a resolution limit on functional imaging signals, where individual blood vessels inaccurately report neuronal activity in their immediate vicinity but, instead, integrate activity patterns along the vascular arbor.

The role of leptomeningeal collaterals in redistributing blood flow during stroke

Leptomeningeal collaterals (LMCs) connect the main cerebral arteries and provide alternative pathways for blood flow during ischaemic stroke. This is beneficial for reducing infarct size and reperfusion success after treatment. However, a better understanding of how LMCs affect blood flow distribution is indispensable to improve therapeutic strategies. Here, we present a novel in silico approach that incorporates case-specific in vivo data into a computational model to simulate blood flow in large semi-realistic microvascular networks from two different mouse strains, characterised by having many and almost no LMCs between middle and anterior cerebral artery (MCA, ACA) territories. This framework is unique because our simulations are directly aligned with in vivo data. Moreover, it allows us to analyse perfusion characteristics quantitatively across all vessel types and for networks with no, few and many LMCs. We show that the occlusion of the MCA directly caused a redistribution of blood that was characterised by increased flow in LMCs. Interestingly, the improved perfusion of MCA-sided microvessels after dilating LMCs came at the cost of a reduced blood supply in other brain areas. This effect was enhanced in regions close to the watershed line and when the number of LMCs was increased. Additional dilations of surface and penetrating arteries after stroke improved perfusion across the entire vasculature and partially recovered flow in the obstructed region, especially in networks with many LMCs, which further underlines the role of LMCs during stroke.

Modeling the response of homogeneous and heterogeneous cerebral capillary networks to local changes in vessel diameters

While microvascular cerebral capillary networks are known to be highly heterogeneous, previous computational models have predicted that heterogeneous cerebral capillary flow patterns result in lower brain tissue partial oxygen pressures. Moreover, as blood flow increases, the flux among capillaries homogenizes. This homogenization of flow is expected to improve the efficiency of oxygenation extraction from the blood. In this work, we use mathematical modeling to explore a possible functional role for the high degree of heterogeneity observed in cerebral capillary networks. Our results suggest that heterogeneity allows for a greater response of tissue oxygen levels to local changes in vessel diameters due to neuronal activation. This result is confirmed for a full 3-dimensional model of capillary networks that includes oxygen diffusion within the tissue region and a reduced model that accounts for changes in capillary blood flow.

Modeling Reactive Hyperemia to Better Understand and Assess Microvascular Function: A Review of Techniques

Reactive hyperemia is a well-established technique for the non-invasive evaluation of the peripheral microcirculatory function, measured as the magnitude of limb re-perfusion after a brief period of ischemia. Despite widespread adoption by researchers and clinicians alike, many uncertainties remain surrounding interpretation, compounded by patient-specific confounding factors (such as blood pressure or the metabolic rate of the ischemic limb). Mathematical modeling can accelerate our understanding of the physiology underlying the reactive hyperemia response and guide in the estimation of quantities which are difficult to measure experimentally. In this work, we aim to provide a comprehensive guide for mathematical modeling techniques that can be used for describing the key phenomena involved in the reactive hyperemia response, alongside their limitations and advantages. The reported methodologies can be used for investigating specific reactive hyperemia aspects alone, or can be combined into a computational framework to be used in (pre-)clinical settings.

Spatiotemporal analysis of blood plasma and blood cell flow fluctuations of cerebral microcirculation in anesthetized rats

Cerebral hemodynamics fluctuates spontaneously over broad frequency ranges. However, its spatiotemporal coherence of flow oscillations in cerebral microcirculation remains incompletely understood. The objective of this study was to characterize the spatiotemporal fluctuations of red blood cells (RBCs) and plasma flow in the rat cerebral microcirculation by simultaneously imaging their dynamic behaviors. Comparisons of changes in cross-section diameters between RBC and plasma flow showed dissociations in penetrating arterioles. The results indicate that vasomotion has the least effect on the lateral movement of circulating RBCs, resulting in variable changes in plasma layer thickness. Parenchymal capillaries exhibited slow fluctuations in RBC velocity (0.1 to 0.3 Hz), regardless of capillary diameter fluctuations (<0.1 Hz). Temporal fluctuations and the velocity of RBCs decreased significantly at divergent capillary bifurcations. The results indicate that a transit of RBCs generates flow resistance in the capillaries and that slow velocity fluctuations of the RBCs are subject to a number of bifurcations. In conclusion, the high-frequency oscillation of the blood flow is filtered at the bifurcation through the capillary networks. Therefore, a number of bifurcations in the cerebral microcirculation may contribute to the power of low-frequency oscillations.

The coronary capillary bed and its role in blood flow and oxygen delivery: A review

The assumption that the coronary capillary blood flow is exclusively regulated by precapillary vessels is not supported by recent data. Rather, the complex coronary capillary bed has unique structural and geometric characteristics that invalidate many assumptions regarding red blood cell (RBC) transport, for example, data based on a single capillary or that increases in flow are the result of capillary recruitment. It is now recognized that all coronary capillaries are open and that their variations in flow are due to structural differences, local O₂ demand and delivery, and variations in hematocrit. Recent data reveal that local mechanisms within the capillary bed regulate flow via signaling mechanisms involving RBC signaling and endothelial-associated pericytes that contract and relax in response to humoral and neural signaling. The discovery that pericytes respond to vasoactive signals (e.g., nitric oxide, phenylephrine, and adenosine) underscores the role of these cells in regulating capillary diameter and consequently RBC flux and oxygen delivery. RBCs also affect blood flow by sensing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>P</mml:mi> <mml:msub><mml:mi>O</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:msub> </mml:math> and releasing nitric oxide to facilitate relaxation of pericytes and a consequential capillary dilation. New data indicate that these signaling mechanisms allow control of blood flow in specific coronary capillaries according to their oxygen requirements. In conclusion, mechanisms in the coronary capillary bed facilitate RBC density and transit time, hematocrit, blood flow and O₂ delivery, factors that decrease capillary heterogeneity. These findings have important clinical implications for myocardial ischemia and infarction, as well as other vascular diseases.

Pericyte remodeling is deficient in the aged brain and contributes to impaired capillary flow and structure

Deterioration of brain capillary flow and architecture is a hallmark of aging and dementia. It remains unclear how loss of brain pericytes in these conditions contributes to capillary dysfunction. Here, we conduct cause-and-effect studies by optically ablating pericytes in adult and aged mice in vivo. Focal pericyte loss induces capillary dilation without blood-brain barrier disruption. These abnormal dilations are exacerbated in the aged brain, and result in increased flow heterogeneity in capillary networks. A subset of affected capillaries experience reduced perfusion due to flow steal. Some capillaries stall in flow and regress, leading to loss of capillary connectivity. Remodeling of neighboring pericytes restores endothelial coverage and vascular tone within days. Pericyte remodeling is slower in the aged brain, resulting in regions of persistent capillary dilation. These findings link pericyte loss to disruption of capillary flow and structure. They also identify pericyte remodeling as a therapeutic target to preserve capillary flow dynamics.

Parallel generation of extensive vascular networks with application to an archetypal human kidney model

Given the relevance of the inextricable coupling between microcirculation and physiology, and the relation to organ function and disease progression, the construction of synthetic vascular networks for mathematical modelling and computer simulation is becoming an increasingly broad field of research. Building vascular networks that mimic in vivo morphometry is feasible through algorithms such as constrained constructive optimization (CCO) and variations. Nevertheless, these methods are limited by the maximum number of vessels to be generated due to the whole network update required at each vessel addition. In this work, we propose a CCO-based approach endowed with a domain decomposition strategy to concurrently create vascular networks. The performance of this approach is evaluated by analysing the agreement with the sequentially generated networks and studying the scalability when building vascular networks up to 200 000 vascular segments. Finally, we apply our method to vascularize a highly complex geometry corresponding to the cortex of a prototypical human kidney. The technique presented in this work enables the automatic generation of extensive vascular networks, removing the limitation from previous works. Thus, we can extend vascular networks (e.g. obtained from medical images) to pre-arteriolar level, yielding patient-specific whole-organ vascular models with an unprecedented level of detail.

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.

The severity of microstrokes depends on local vascular topology and baseline perfusion

Cortical microinfarcts are linked to pathologies like cerebral amyloid angiopathy and dementia. Despite their relevance for disease progression, microinfarcts often remain undetected and the smallest scale of blood flow disturbance has not yet been identified. We employed blood flow simulations in realistic microvascular networks from the mouse cortex to quantify the impact of single-capillary occlusions. Our simulations reveal that the severity of a microstroke is strongly affected by the local vascular topology and the baseline flow rate in the occluded capillary. The largest changes in perfusion are observed in capillaries with two inflows and two outflows. This specific topological configuration only occurs with a frequency of 8%. The majority of capillaries have one inflow and one outflow and is likely designed to efficiently supply oxygen and nutrients. Taken together, microstrokes bear potential to induce a cascade of local disturbances in the surrounding tissue, which might accumulate and impair energy supply locally.

Brain capillary pericytes exert a substantial but slow influence on blood flow

The majority of the brain's vasculature is composed of intricate capillary networks lined by capillary pericytes. However, it remains unclear whether capillary pericytes influence blood flow. Using two-photon microscopy to observe and manipulate brain capillary pericytes in vivo, we find that their optogenetic stimulation decreases lumen diameter and blood flow, but with slower kinetics than similar stimulation of mural cells on upstream pial and precapillary arterioles. This slow vasoconstriction was inhibited by the clinically used vasodilator fasudil, a Rho-kinase inhibitor that blocks contractile machinery. Capillary pericytes were also slower to constrict back to baseline following hypercapnia-induced dilation, and slower to dilate towards baseline following optogenetically induced vasoconstriction. Optical ablation of single capillary pericytes led to sustained local dilation and a doubling of blood cell flux selectively in capillaries lacking pericyte contact. These data indicate that capillary pericytes contribute to basal blood flow resistance and slow modulation of blood flow throughout the brain.

Simulation of a detoxifying organ function: Focus on hemodynamics modeling and convection-reaction numerical simulation in microcirculatory networks

When modeling a detoxifying organ function, an important component is the impact of flow on the metabolism of a compound of interest carried by the blood. We here study the effects of red blood cells (such as the Fahraeus-Lindqvist effect and plasma skimming) on blood flow in typical microcirculatory components such as tubes, bifurcations and entire networks, with particular emphasis on the liver as important representative of detoxifying organs. In one of the plasma skimming models, under certain conditions, oscillations between states are found and analyzed in a methodical study to identify their causes and influencing parameters. The flow solution obtained is then used to define the velocity at which a compound would be transported. A convection-reaction equation is studied to simulate the transport of a compound in blood and its uptake by the surrounding cells. Different types of signal sharpness have to be handled depending on the application to address different temporal compound concentration profiles. To permit executing the studied models numerically stable and accurate, we here extend existing transport schemes to handle converging bifurcations, and more generally multi-furcations. We study the accuracy of different numerical schemes as well as the effect of reactions and of the network itself on the bolus shape. Even though this study is guided by applications in liver micro-architecture, the proposed methodology is general and can readily be applied to other capillary network geometries, hence to other organs or to bioengineered network designs.

Predicting Vessel Diameter Changes to Up-Regulate Biphasic Blood Flow During Activation in Realistic Microvascular Networks

A dense network of blood vessels distributes blood to different regions of the brain. To meet the temporarily and spatially varying energy demand resulting from changes in neuronal activity, the vasculature is able to locally up-regulate the blood supply. However, to which extent diameter changes of different vessel types contribute to the up-regulation, as well as the spatial and temporal characteristics of their changes, are currently unknown. Here, we present a new simulation method, which solves an inverse problem to calculate diameter changes of individual blood vessels needed to achieve predefined blood flow distributions in microvascular networks. This allows us to systematically compare the impact of different vessel types in various regulation scenarios. Moreover, the method offers the advantage that it handles the stochastic nature of blood flow originating from tracking the movement of individual red blood cells. Since the inverse problem is formulated for time-averaged pressures and flow rates, a deterministic approach for calculating the diameter changes is used, which allows us to apply the method for large realistic microvascular networks with high-dimensional parameter spaces. Our results obtained in both artificial and realistic microvascular networks reveal that diameter changes at the level of capillaries enable a very localized regulation of blood flow. In scenarios where only larger vessels, i.e., arterioles, are allowed to adapt, the flow increase cannot be confined to a specific activated region and flow changes spread into neighboring regions. Furthermore, relatively small dilations and constrictions of all vessel types can lead to substantial changes of capillary blood flow distributions. This suggests that small scale regulation is necessary to obtain a localized increase in blood flow.

A 3D-1D coupled blood flow and oxygen transport model to generate microvascular networks

In this work, we introduce an algorithmic approach to generate microvascular networks starting from larger vessels that can be reconstructed without noticeable segmentation errors. Contrary to larger vessels, the reconstruction of fine-scale components of microvascular networks shows significant segmentation errors, and an accurate mapping is time and cost intense. Thus there is a need for fast and reliable reconstruction algorithms yielding surrogate networks having similar stochastic properties as the original ones. The microvascular networks are constructed in a marching way by adding vessels to the outlets of the vascular tree from the previous step. To optimise the structure of the vascular trees, we use Murray's law to determine the radii of the vessels and bifurcation angles. In each step, we compute the local gradient of the partial pressure of oxygen and adapt the orientation of the new vessels to this gradient. At the same time, we use the partial pressure of oxygen to check whether the considered tissue block is supplied sufficiently with oxygen. Computing the partial pressure of oxygen, we use a 3D-1D coupled model for blood flow and oxygen transport. To decrease the complexity of a fully coupled 3D model, we reduce the blood vessel network to a 1D graph structure and use a bi-directional coupling with the tissue which is described by a 3D homogeneous porous medium. The resulting surrogate networks are analysed with respect to morphological and physiological aspects.

COPD is deleterious for pericytes: implications during training-induced angiogenesis in skeletal muscle

Improvements in skeletal muscle endurance and oxygen uptake are blunted in patients with chronic obstructive pulmonary disease (COPD), possibly because of a limitation in the muscle capillary oxygen supply. Pericytes are critical for capillary blood flow adaptation during angiogenesis but may be impaired by COPD systemic effects, which are mediated by circulating factors. This study compared the pericyte coverage of muscle capillaries in response to 10 wk of exercise training in patients with COPD and sedentary healthy subjects (SHS). Fourteen patients with COPD were compared with seven matched SHS. SHS trained at moderate intensity corresponding to an individualized moderate-intensity patient with COPD trained at the same relative (%V̇o₂: COPD-RI) or absolute (mL·min^-1·kg^-1: COPD-AI) intensity as SHS. Capillary-to-fiber ratio (C/F) and NG2⁺ pericyte coverage were assessed from vastus lateralis muscle biopsies, before and after 5 and 10 wk of training. We also tested in vitro the effect of COPD and SHS serum on pericyte morphology and mesenchymal stem cell (MSC) differentiation into pericytes. SHS showed greater improvement in aerobic capacity (V̇o_2VT) than both patients with COPD-RI and patients with COPD-AI (Group × Time: P = 0.004). Despite a preserved increase in the C/F ratio, NG2⁺ pericyte coverage did not increase in patients with COPD in response to training, contrary to SHS (Group × Time: P = 0.011). Conversely to SHS serum, COPD serum altered pericyte morphology (P < 0.001) and drastically reduced MSC differentiation into pericytes (P < 0.001). Both functional capacities and pericyte coverage responses to exercise training are blunted in patients with COPD. We also provide direct evidence of the deleterious effect of COPD circulating factors on pericyte morphology and differentiation.NEW & NOTEWORTHY This work confirms the previously reported impairment in the functional response to exercise training of patients with COPD compared with SHS. Moreover, it shows for the first time that pericyte coverage of the skeletal capillaries is drastically reduced in patients with COPD compared with SHS during training-induced angiogenesis. Finally, it provides experimental evidence that circulating factors are involved in the impaired pericyte coverage of patients with COPD.

Local vs. Global Blood Flow Modulation in Artificial Microvascular Networks: Effects on Red Blood Cell Distribution and Partitioning

Our understanding of cerebral blood flow (CBF) regulation during functional activation is still limited. Alongside with the accepted role of smooth muscle cells in controlling the arteriolar diameter, a new hypothesis has been recently formulated suggesting that CBF may be modulated by capillary diameter changes mediated by pericytes. In this study, we developed in vitro microvascular network models featuring a valve enabling the dilation of a specific micro-channel. This allowed us to investigate the non-uniform red blood cell (RBC) partitioning at microvascular bifurcations (phase separation) and the hematocrit distribution at rest and for two scenarios modeling capillary and arteriolar dilation. RBC partitioning showed similar phase separation behavior during baseline and activation. Results indicated that the RBCs at diverging bifurcations generally enter the high-flow branch (classical partitioning). Inverse behavior (reverse partitioning) was observed for skewed hematocrit profiles in the parent vessel of bifurcations, especially for high RBC velocity (i.e., arteriolar activation). Moreover, results revealed that a local capillary dilation, as it may be mediated in vivo by pericytes, led to a localized increase of RBC flow and a heterogeneous hematocrit redistribution within the whole network. In case of a global increase of the blood flow, as it may be achieved by dilating an arteriole, a homogeneous increase of RBC flow was observed in the whole network and the RBCs were concentrated along preferential pathways. In conclusion, overall increase of RBC flow could be obtained by arteriolar and capillary dilation, but only capillary dilation was found to alter the perfusion locally and heterogeneously.

Precapillary sphincters maintain perfusion in the cerebral cortex

Active nerve cells release vasodilators that increase their energy supply by dilating local blood vessels, a mechanism termed neurovascular coupling and the basis of BOLD functional neuroimaging signals. Here, we reveal a mechanism for cerebral blood flow control, a precapillary sphincter at the transition between the penetrating arteriole and first order capillary, linking blood flow in capillaries to the arteriolar inflow. The sphincters are encircled by contractile mural cells, which are capable of bidirectional control of the length and width of the enclosed vessel segment. The hemodynamic consequence is that precapillary sphincters can generate the largest changes in the cerebrovascular flow resistance of all brain vessel segments, thereby controlling capillary flow while protecting the downstream capillary bed and brain tissue from adverse pressure fluctuations. Cortical spreading depolarization constricts sphincters and causes vascular trapping of blood cells. Thus, precapillary sphincters are bottlenecks for brain capillary blood flow.

Precapillary sphincters are mural cells encircling an indentation of blood vessels where capillaries branch off from penetrating arterioles (PAs), but their existence and role in the brain is not fully understood. Here authors describe these structures at PAs in the cortex and show that they constrict during cortical spreading depolarization in mice.

In vitro investigations of red blood cell phase separation in a complex microchannel network

Microvascular networks feature a complex topology with multiple bifurcating vessels. Nonuniform partitioning (phase separation) of red blood cells (RBCs) occurs at diverging bifurcations, leading to a heterogeneous RBC distribution that ultimately affects the oxygen delivery to living tissues. Our understanding of the mechanisms governing RBC heterogeneity is still limited, especially in large networks where the RBC dynamics can be nonintuitive. In this study, our quantitative data for phase separation were obtained in a complex in vitro network with symmetric bifurcations and 176 microchannels. Our experiments showed that the hematocrit is heterogeneously distributed and confirmed the classical result that the branch with a higher blood fraction received an even higher RBC fraction (classical partitioning). An inversion of this classical phase separation (reverse partitioning) was observed in the case of a skewed hematocrit profile in the parent vessels of bifurcations. In agreement with a recent computational study [P. Balogh and P. Bagchi, Phys. Fluids 30,051902 (2018)], a correlation between the RBC reverse partitioning and the skewness of the hematocrit profile due to sequential converging and diverging bifurcations was reported. A flow threshold below which no RBCs enter a branch was identified. These results highlight the importance of considering the RBC flow history and the local RBC distribution to correctly describe the RBC phase separation in complex networks.

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.

Small Vessels Are a Big Problem in Neurodegeneration and Neuroprotection

The cerebral microcirculation holds a critical position to match the high metabolic demand by neuronal activity. Functionally, microcirculation is virtually inseparable from other nervous system cells under both physiological and pathological conditions. For successful bench-to-bedside translation of neuroprotection research, the role of microcirculation in acute and chronic neurodegenerative disorders appears to be under-recognized, which may have contributed to clinical trial failures with some neuroprotectants. Increasing data over the last decade suggest that microcirculatory impairments such as endothelial or pericyte dysfunction, morphological irregularities in capillaries or frequent dynamic stalls in blood cell flux resulting in excessive heterogeneity in capillary transit may significantly compromise tissue oxygen availability. We now know that ischemia-induced persistent abnormalities in capillary flow negatively impact restoration of reperfusion after recanalization of occluded cerebral arteries. Similarly, microcirculatory impairments can accompany or even precede neural loss in animal models of several neurodegenerative disorders including Alzheimer's disease. Macrovessels are relatively easy to evaluate with radiological or experimental imaging methods but they cannot faithfully reflect the downstream microcirculatory disturbances, which may be quite heterogeneous across the tissue at microscopic scale and/or happen fast and transiently. The complexity and size of the elements of microcirculation, therefore, require utilization of cutting-edge imaging techniques with high spatiotemporal resolution as well as multidisciplinary team effort to disclose microvascular-neurodegenerative connection and to test treatment approaches to advance the field. Developments in two photon microscopy, ultrafast ultrasound, and optical coherence tomography provide valuable experimental tools to reveal those microscopic events with high resolution. Here, we review the up-to-date advances in understanding of the primary microcirculatory abnormalities that can result in neurodegenerative processes and the combined neurovascular protection approaches that can prevent acute as well as chronic neurodegeneration.

Brain Capillary Networks Across Species: A few Simple Organizational Requirements Are Sufficient to Reproduce Both Structure and Function

Despite the key role of the capillaries in neurovascular function, a thorough characterization of cerebral capillary network properties is currently lacking. Here, we define a range of metrics (geometrical, topological, flow, mass transfer, and robustness) for quantification of structural differences between brain areas, organs, species, or patient populations and, in parallel, digitally generate synthetic networks that replicate the key organizational features of anatomical networks (isotropy, connectedness, space-filling nature, convexity of tissue domains, characteristic size). To reach these objectives, we first construct a database of the defined metrics for healthy capillary networks obtained from imaging of mouse and human brains. Results show that anatomical networks are topologically equivalent between the two species and that geometrical metrics only differ in scaling. Based on these results, we then devise a method which employs constrained Voronoi diagrams to generate 3D model synthetic cerebral capillary networks that are locally randomized but homogeneous at the network-scale. With appropriate choice of scaling, these networks have equivalent properties to the anatomical data, demonstrated by comparison of the defined metrics. The ability to synthetically replicate cerebral capillary networks opens a broad range of applications, ranging from systematic computational studies of structure-function relationships in healthy capillary networks to detailed analysis of pathological structural degeneration, or even to the development of templates for fabrication of 3D biomimetic vascular networks embedded in tissue-engineered constructs.

White matter capillaries in vascular and neurodegenerative dementias

Previous studies suggest white matter (WM) integrity is vulnerable to chronic hypoperfusion during brain ageing. We assessed ~ 0.7 million capillary profiles in the frontal lobe WM across several dementias comprising Alzheimer’s disease, dementia with Lewy bodies, Parkinson’s disease with dementia, vascular dementia, mixed dementias, post-stroke dementia as well as post-stroke no dementia and similar age ageing and young controls without significant brain pathology. Standard histopathological methods were used to determine microvascular pathology and capillary width and densities in 153 subjects using markers of the basement membrane (collagen IV; COL4) and endothelium (glucose transporter-1; GLUT-1). Variable microvascular pathology including coiled, tortuous, collapsed and degenerated capillaries as well as occasional microaneurysms was present in all dementias. As expected, WM microvascular densities were 20–49% lower than in the overlying cortex. This differential in density between WM and cortex was clearly demonstrated by COL4, which was highly correlated with GLUT-1 densities (Spearman’s rho = 0.79, P = 0.000). WM COL4 immunopositive microvascular densities were decreased by ~ 18% across the neurodegenerative dementias. However, we found WM COL4 densities were increased by ~ 57% in post-stroke dementia versus ageing and young controls and other dementias. Using three different methods to measure capillary diameters, we found WM capillaries to be significantly wider by 19–45% compared to those in overlying neocortex apparent with both COL4 and GLUT-1. Remarkably, WM capillary widths were increased by ~ 20% across all dementias compared to ageing and young controls (P < 0.01). We also noted mean WM pathology scores incorporating myelin loss, arteriolosclerosis and perivascular spacing were correlated with COL4 immunopositive capillary widths (Pearson’s r = 0.71, P = 0.032). Our key finding indicates that WM capillaries are wider compared to those in the overlying neocortex in controls but they dilate further during dementia pathogenesis. We suggest capillaries undergo restructuring in the deep WM in different dementias. This reflects compensatory changes to retain WM perfusion and integrity during hypoperfusive states in ageing-related dementias.

The Relation Between Capillary Transit Times and Hemoglobin Saturation Heterogeneity. Part 2: Capillary Networks

Brain metabolism is highly dependent on continuous oxygen supply. Cortical microvascular networks exhibit heterogeneous blood flow, leading to non-uniform tissue oxygenation and capillary hemoglobin saturation. We recently proposed capillary outflow saturation heterogeneity (COSH) to represent effects of heterogeneity on oxygen supply to tissue regions most vulnerable to hypoxia, and showed that diffusive oxygen exchange among red blood cells within capillaries and among capillaries (diffusive interaction) significantly reduces COSH in simplified geometrical configurations. Here, numerical simulations of oxygen transport in capillary network geometries derived from mouse somatosensory cortex are presented. Diffusive interaction was found to reduce COSH by 41 to 62% compared to simulations where diffusive interaction was excluded. Hemoglobin saturation drop across the microvascular network is strongly correlated with red blood cell transit time, but the coefficient of variation of saturation drop is approximately one third lower. Unexpectedly, the radius of the tissue cylinder supplied by a capillary correlates weakly with the anatomical tissue cylinder radius, but strongly with hemoglobin saturation. Thus, diffusive interaction contributes greatly to the microcirculation's ability to achieve tissue oxygenation, despite heterogeneous capillary transit time and hematocrit distribution. These findings provide insight into the effects of cerebral small vessel disease on tissue oxygenation and brain function.

Pericyte Structural Remodeling in Cerebrovascular Health and Homeostasis

The biology of brain microvascular pericytes is an active area of research and discovery, as their interaction with the endothelium is critical for multiple aspects of cerebrovascular function. There is growing evidence that pericyte loss or dysfunction is involved in the pathogenesis of Alzheimer’s disease, vascular dementia, ischemic stroke and brain injury. However, strategies to mitigate or compensate for this loss remain limited. In this review, we highlight a novel finding that pericytes in the adult brain are structurally dynamic in vivo, and actively compensate for loss of endothelial coverage by extending their far-reaching processes to maintain contact with regions of exposed endothelium. Structural remodeling of pericytes may present an opportunity to foster pericyte-endothelial communication in the adult brain and should be explored as a potential means to counteract pericyte loss in dementia and cerebrovascular disease. We discuss the pathophysiological consequences of pericyte loss on capillary function, and the biochemical pathways that may control pericyte remodeling. We also offer guidance for observing pericytes in vivo, such that pericyte structural remodeling can be more broadly studied in mouse models of cerebrovascular disease.

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.

Compromised microvascular oxygen delivery increases brain tissue vulnerability with age

Despite the possible role of impaired cerebral tissue oxygenation in age-related cognition decline, much is still unknown about the changes in brain tissue pO₂ with age. Using a detailed investigation of the age-related changes in cerebral tissue oxygenation in the barrel cortex of healthy, awake aged mice, we demonstrate decreased arteriolar and tissue pO₂ with age. These changes are exacerbated after middle-age. We further uncovered evidence of the presence of hypoxic micro-pockets in the cortex of awake old mice. Our data suggests that from young to middle-age, a well-regulated capillary oxygen supply maintains the oxygen availability in cerebral tissue, despite decreased tissue pO₂ next to arterioles. After middle-age, due to decreased hematocrit, reduced capillary density and higher capillary transit time heterogeneity, the capillary network fails to compensate for larger decreases in arterial pO₂. The substantial decrease in brain tissue pO₂, and the presence of hypoxic micro-pockets after middle-age are of significant importance, as these factors may be related to cognitive decline in elderly people.

The relative influence of hematocrit and red blood cell velocity on oxygen transport from capillaries to tissue

OBJECTIVE

Oxygen transport to parenchymal cells occurs mainly at the microvascular level and depends on convective RBC flux, which is proportional in an individual capillary to the product of capillary hematocrit and RBC velocity. This study investigates the relative influence of these two factors on tissue PO₂ .

METHODS

A simple analytical model is used to quantify the respective influences of hematocrit, RBC velocity, and RBC flow on tissue oxygenation around capillaries. Predicted tissue PO₂ levels are compared with a detailed computational model.

RESULTS

Hematocrit is shown to have a larger influence on tissue PO₂ than RBC velocity. The effect of RBC velocity increases with distance from the arterioles. Good agreement between analytical and numerical results is obtained, and the discrepancies are explained. Significant dependence of MTCs on RBC velocity at low hematocrit is demonstrated.

CONCLUSIONS

For a given RBC flux in a capillary, the PO₂ in the surrounding tissue increases with increasing hematocrit, as a consequence of decreasing IVR to diffusive oxygen transport from RBCs to tissue. These results contribute to understanding the effects of blood flow changes on oxygen transport, such as those that occur in functional hyperemia in the brain.

The effects of capillary transit time heterogeneity on the BOLD signal

Neurovascular coupling mechanisms give rise to vasodilation and functional hyperemia upon neural activation, thereby altering blood oxygenation. This blood oxygenation level dependent (BOLD) contrast allows studies of activation patterns in the working human brain by functional MRI (fMRI). The BOLD-weighted fMRI signal shows characteristic transients in relation to functional activation, such as the so-called initial dip, overshoot, and post-stimulus undershoot. These transients are modulated by other physiological stimuli and in disease, but the underlying physiological mechanisms remain incompletely understood. Capillary transit time heterogeneity (CTH) has been shown to affect oxygen extraction, and hence blood oxygenation. Here, we examine how recently reported redistributions of capillary blood flow during functional activation would be expected to affect BOLD signal transients. We developed a three-compartment (hemoglobin, plasma, and tissue) model to predict the BOLD signal, incorporating the effects of dynamic changes in CTH. Our model predicts that the BOLD signal represents the superposition of a positive component resulting from increases in cerebral blood flow (CBF), and a negative component, resulting from elevated tissue metabolism and homogenization of capillary flows (reduced CTH). The model reproduces salient features of BOLD signal dynamics under conditions such as hypercapnia, hyperoxia, and caffeine intake, where both brain physiology and BOLD characteristics are altered. Neuroglial signaling and metabolism could affect CBF and capillary flow patterns differently. Further studies of neurovascular and neuro-capillary coupling mechanisms may help us relate BOLD signals to the firing of certain neuronal populations based on their respective BOLD "fingerprints."

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.

Optimal occlusion uniformly partitions red blood cells fluxes within a microvascular network

In animals, gas exchange between blood and tissues occurs in narrow vessels, whose diameter is comparable to that of a red blood cell. Red blood cells must deform to squeeze through these narrow vessels, transiently blocking or occluding the vessels they pass through. Although the dynamics of vessel occlusion have been studied extensively, it remains an open question why microvessels need to be so narrow. We study occlusive dynamics within a model microvascular network: the embryonic zebrafish trunk. We show that pressure feedbacks created when red blood cells enter the finest vessels of the trunk act together to uniformly partition red blood cells through the microvasculature. Using mathematical models as well as direct observation, we show that these occlusive feedbacks are tuned throughout the trunk network to prevent the vessels closest to the heart from short-circuiting the network. Thus occlusion is linked with another open question of microvascular function: how are red blood cells delivered at the same rate to each micro-vessel? Our analysis shows that tuning of occlusive feedbacks increase the total dissipation within the network by a factor of 11, showing that uniformity of flows rather than minimization of transport costs may be prioritized by the microvascular network.

Arterial trees shuttle red blood cells from the heart to billions of capillaries distributed throughout the body. These trees have long been thought to be organized to minimize transport costs. Yet red blood cells are tightly squeezed within the finest vessels, meaning that these vessels account for as much as half of the total transport costs within the arterial network. It is unclear why vessel diameters and red blood cell diameters are so closely matched in a network that is presumed to optimize transport. Here, we use mathematical modeling and direct observations of red blood cell movements in embryonic zebrafish to show that occlusive feedbacks—the pressure feedbacks that alter the flows into a vessel when it is nearly blocked by a red blood cell—can optimally distribute red blood cells through microvessels. In addition to revealing an adaptive function for the matching of vessel and red blood cell diameters, this work shows that uniformity of red blood cell fluxes can be a unifying principle for understanding the elegant hydraulic organization of microvascular networks.

Disturbances in the control of capillary flow in an aged APPswe/PS1ΔE9 model of Alzheimer's disease

Vascular changes are thought to contribute to the development of Alzheimer's disease, and both cerebral blood flow and its responses during neural activation are reduced before Alzheimer's disease symptoms onset. One hypothetical explanation is that capillary dysfunction reduces oxygen extraction efficacy. This study compares the morphology and hemodynamics of the microvasculature in the somatosensory cortex of 18-month-old APP^SWE/PS1ΔE9 (transgenic [Tg]) mice and wild-type (WT) littermates. In particular, the extent to which their capillary transit times homogenize during functional activation was measured and compared. Capillary length density was similar in both groups but capillary blood flow during rest was lower in the Tg mice, indicating that cortical oxygen availability is reduced. The capillary hemodynamic response to functional activation was larger, and lasted longer in Tg mice than in WT mice. The homogenization of capillary transit times during functional activation, which we previously demonstrated in young mice, was absent in the Tg mice. This study demonstrates that both neurovascular coupling and capillary function are profoundly disturbed in aged Tg and WT mice.

Vascular density and distribution in neocortex

An amazingly wide range of complex behavior emerges from the cerebral cortex. Much of the information processing that leads to these behaviors is performed in neocortical circuits that span throughout the six layers of the cortex. Maintaining this circuit activity requires substantial quantities of oxygen and energy substrates, which are delivered by the complex yet well-organized and tightly-regulated vascular system. In this review, we provide a detailed characterization of the most relevant anatomical and functional features of the cortical vasculature. This includes a compilation of the available data on laminar variation of vascular density and the topological aspects of the microvascular system. We also review the spatio-temporal dynamics of cortical blood flow regulation and oxygenation, many aspects of which remain poorly understood. Finally, we discuss some of the important implications of vascular density, distribution, oxygenation and blood flow regulation for (laminar) fMRI.

Depth-dependent flow and pressure characteristics in cortical microvascular networks

A better knowledge of the flow and pressure distribution in realistic microvascular networks is needed for improving our understanding of neurovascular coupling mechanisms and the related measurement techniques. Here, numerical simulations with discrete tracking of red blood cells (RBCs) are performed in three realistic microvascular networks from the mouse cerebral cortex. Our analysis is based on trajectories of individual RBCs and focuses on layer-specific flow phenomena until a cortical depth of 1 mm. The individual RBC trajectories reveal that in the capillary bed RBCs preferentially move in plane. Hence, the capillary flow field shows laminar patterns and a layer-specific analysis is valid. We demonstrate that for RBCs entering the capillary bed close to the cortical surface (< 400 μm) the largest pressure drop takes place in the capillaries (37%), while for deeper regions arterioles are responsible for 61% of the total pressure drop. Further flow characteristics, such as capillary transit time or RBC velocity, also vary significantly over cortical depth. Comparison of purely topological characteristics with flow-based ones shows that a combined interpretation of topology and flow is indispensable. Our results provide evidence that it is crucial to consider layer-specific differences for all investigations related to the flow and pressure distribution in the cortical vasculature. These findings support the hypothesis that for an efficient oxygen up-regulation at least two regulation mechanisms must be playing hand in hand, namely cerebral blood flow increase and microvascular flow homogenization. However, the contribution of both regulation mechanisms to oxygen up-regulation likely varies over depth.

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.

Going beyond 20 μm-sized channels for studying red blood cell phase separation in microfluidic bifurcations

Despite the development of microfluidics, experimental challenges are considerable for achieving a quantitative study of phase separation, i.e., the non-proportional distribution of Red Blood Cells (RBCs) and suspending fluid, in microfluidic bifurcations with channels smaller than 20 μm. Yet, a basic understanding of phase separation in such small vessels is needed for understanding the coupling between microvascular network architecture and dynamics at larger scale. Here, we present the experimental methodologies and measurement techniques developed for that purpose for RBC concentrations (tube hematocrits) ranging between 2% and 20%. The maximal RBC velocity profile is directly measured by a temporal cross-correlation technique which enables to capture the RBC slip velocity at walls with high resolution, highlighting two different regimes (flat and more blunted ones) as a function of RBC confinement. The tube hematocrit is independently measured by a photometric technique. The RBC and suspending fluid flow rates are then deduced assuming the velocity profile of a Newtonian fluid with no slip at walls for the latter. The accuracy of this combination of techniques is demonstrated by comparison with reference measurements and verification of RBC and suspending fluid mass conservation at individual bifurcations. The present methodologies are much more accurate, with less than 15% relative errors, than the ones used in previous in vivo experiments. Their potential for studying steady state phase separation is demonstrated, highlighting an unexpected decrease of phase separation with increasing hematocrit in symmetrical, but not asymmetrical, bifurcations and providing new reference data in regimes where in vitro results were previously lacking.