Depth-dependent flow and pressure characteristics in cortical microvascular networks

Long-wavelength traveling waves of vasomotion modulate the perfusion of cortex

Brain arterioles are active, multicellular complexes whose diameters oscillate at ∼ 0.1 Hz. We assess the physiological impact and spatiotemporal dynamics of vaso-oscillations in the awake mouse. First, vaso-oscillations in penetrating arterioles, which source blood from pial arterioles to the capillary bed, profoundly impact perfusion throughout neocortex. The modulation in flux during resting-state activity exceeds that of stimulus-induced activity. Second, the change in perfusion through arterioles relative to the change in their diameter is weak. This implies that the capillary bed dominates the hydrodynamic resistance of brain vasculature. Lastly, the phase of vaso-oscillations evolves slowly along arterioles, with a wavelength that exceeds the span of the cortical mantle and sufficient variability to establish functional cortical areas as parcels of uniform phase. The phase-gradient supports traveling waves in either direction along both pial and penetrating arterioles. This implies that waves along penetrating arterioles can mix, but not directionally transport, interstitial fluids.

An-Gong-Niu-Huang-Wan (AGNHW) regulates cerebral blood flow by improving hypoperfusion, cerebrovascular reactivity and microcirculation disturbances after stroke

BACKGROUND

The restoration of cerebrovascular regulation and improvement of cerebral blood flow in ischaemic regions are crucial for improving the clinical prognosis after stroke. An-Gong-Niu-Huang-Wan (AGNHW) is a famous traditional compound Chinese medicine that has been used for over 220 years to treat acute ischaemic stroke; however, its role in the regulation of cerebral blood flow is still unclear. The aim of the present study was to investigate the regulatory effect of AGNHW on cerebral blood flow and microcirculation after ischaemic stroke and to elucidate the underlying mechanisms involved.

METHODS

Male C57BL/6 mice were subjected to distal middle cerebral artery occlusion (dMCAO) and randomly assigned to the sham, MCAO, or AGNHW groups. AGNHW was administered intragastrically 1 h after dMCAO. The rotarod test was utilized to evaluate behavioural function; TTC was used to determine the infarct volume; and ischaemic injury was assessed by detecting brain levels of SOD, MDA and NO. Then, cortical perfusion and acetazolamide-induced cerebrovascular reactivity were assessed using laser speckle contrast imaging, and the velocity and flux of red blood cells in cortical capillaries were detected using two-photon laser scanning microscopy. In addition, we employed RNA-Seq to identify variations in gene expression profiles and assessed endothelium-dependent changes in microcirculatory dysfunction by measuring vasoactive mediator levels.

RESULTS

AGNHW significantly increased cerebral blood flow, reduced the infarct volume, and promoted functional recovery after cerebral ischaemia. AGNHW increased the velocity and flux of red blood cells in capillaries and improved cerebrovascular reactivity in the ischaemic cortex. Furthermore, AGNHW regulated endothelium-dependent microcirculation, as evidenced by decreases in the expression of endothelins (Edn1, Edn3 and Ednrb) and the ratios of brain and serum TXB2/6-keto-PGF1α and ET-1/CGRP.

CONCLUSIONS

AGNHW improved cerebral hypoperfusion, regulated cerebrovascular reactivity and attenuated microcirculatory dysfunction within the ischaemic cortex after stroke. This outstanding effect was achieved by modulating the expression of genes related to vascular endothelial cell function and regulating endothelium-dependent vasoactive mediators.

Leptomeningeal collaterals regulate reperfusion in ischemic stroke and rescue the brain from futile recanalization

Recanalization is the mainstay of ischemic stroke treatment. However, even with timely clot removal, many stroke patients recover poorly. Leptomeningeal collaterals (LMCs) are pial anastomotic vessels with yet-unknown functions. We applied laser speckle imaging, ultrafast ultrasound, and two-photon microscopy in a thrombin-based mouse model of stroke and fibrinolytic treatment to show that LMCs maintain cerebral autoregulation and allow for gradual reperfusion, resulting in small infarcts. In mice with poor LMCs, distal arterial segments collapse, and deleterious hyperemia causes hemorrhage and mortality after recanalization. In silico analyses confirm the relevance of LMCs for preserving perfusion in the ischemic region. Accordingly, in stroke patients with poor collaterals undergoing thrombectomy, rapid reperfusion resulted in hemorrhagic transformation and unfavorable recovery. Thus, we identify LMCs as key components regulating reperfusion and preventing futile recanalization after stroke. Future therapeutic interventions should aim to enhance collateral function, allowing for beneficial reperfusion after stroke.

A mathematical model for velocity-selective arterial spin labeling

PURPOSE

To present a theoretical framework that rigorously defines and analyzes key concepts and quantities for velocity selective arterial spin labeling (VSASL).

THEORY AND METHODS

An expression for the VSASL arterial delivery function is derived based on (1) labeling and saturation profiles as a function of velocity and (2) physiologically plausible approximations of changes in acceleration and velocity across the vascular system. The dependence of labeling efficiency on the amplitude and effective bolus width of the arterial delivery function is defined. Factors that affect the effective bolus width are examined, and timing requirements to minimize quantitation errors are derived.

RESULTS

The model predicts that a flow-dependent negative bias in the effective bolus width can occur when velocity selective inversion (VSI) is used for the labeling module and velocity selective saturation (VSS) is used for the vascular crushing module. The bias can be minimized by choosing a nominal labeling cutoff velocity that is lower than the nominal cutoff velocity of the vascular crushing module.

CONCLUSION

The elements of the model are specified in a general fashion such that future advances can be readily integrated. The model can facilitate further efforts to understand and characterize the performance of VSASL and provide critical theoretical insights that can be used to design future experiments and develop novel VSASL approaches.

Continued dysfunction of capillary pericytes promotes no-reflow after experimental stroke in vivo

Incomplete reperfusion of the microvasculature ('no-reflow') after ischaemic stroke damages salvageable brain tissue. Previous ex vivo studies suggest pericytes are vulnerable to ischaemia and may exacerbate no-reflow, but the viability of pericytes and their association with no-reflow remains under-explored in vivo. Using longitudinal in vivo two-photon single-cell imaging over 7 days, we showed that 87% of pericytes constrict during cerebral ischaemia and remain constricted post reperfusion, and 50% of the pericyte population are acutely damaged. Moreover, we revealed ischaemic pericytes to be fundamentally implicated in capillary no-reflow by limiting and arresting blood flow within the first 24 h post stroke. Despite sustaining acute membrane damage, we observed that over half of all cortical pericytes survived ischaemia and responded to vasoactive stimuli, upregulated unique transcriptomic profiles and replicated. Finally, we demonstrated the delayed recovery of capillary diameter by ischaemic pericytes after reperfusion predicted vessel reconstriction in the subacute phase of stroke. Cumulatively, these findings demonstrate that surviving cortical pericytes remain both viable and promising therapeutic targets to counteract no-reflow after ischaemic stroke.

Network response of brain microvasculature to neuronal stimulation

Neurovascular coupling (NVC), or the adjustment of blood flow in response to local increases in neuronal activity is a hallmark of healthy brain function, and the physiological foundation for functional magnetic resonance imaging (fMRI). However, it remains only partly understood due to the high complexity of the structure and function of the cerebrovascular network. Here we set out to understand NVC at the network level, i.e. map cerebrovascular network reactivity to activation of neighbouring neurons within a 500×500×500 μm3 cortical volume (∼30 high-resolution 3-nL fMRI voxels). Using 3D two-photon fluorescence microscopy data, we quantified blood volume and flow changes in the brain vessels in response to spatially targeted optogenetic activation of cortical pyramidal neurons. We registered the vessels in a series of image stacks acquired before and after stimulations and applied a deep learning pipeline to segment the microvascular network from each time frame acquired. We then performed image analysis to extract the microvascular graphs, and graph analysis to identify the branch order of each vessel in the network, enabling the stratification of vessels by their branch order, designating branches 1-3 as precapillary arterioles and branches 4+ as capillaries. Forty-five percent of all vessels showed significant calibre changes; with 85 % of responses being dilations. The largest absolute CBV change was in the capillaries; the smallest, in the venules. Capillary CBV change was also the largest fraction of the total CBV change, but normalized to the baseline volume, arterioles and precapillary arterioles showed the biggest relative CBV change. From linescans along arteriole-venule microvascular paths, we measured red blood cell velocities and hematocrit, allowing for estimation of pressure and local resistance along these paths. While diameter changes following neuronal activation gradually declined along the paths; the pressure drops from arterioles to venules increased despite decreasing resistance: blood flow thus increased more than local resistance decreases would predict. By leveraging functional volumetric imaging and high throughput deep learning-based analysis, our study revealed distinct hemodynamic responses across the vessel types comprising the microvascular network. Our findings underscore the need for large, dense sampling of brain vessels for characterization of neurovascular coupling at the network level in health and disease.

Impaired drainage through capillary-venous networks contributes to age-related white matter loss

The gradual loss of cerebral white matter contributes to cognitive decline during aging. However, microvascular networks that support the metabolic demands of white matter remain poorly defined. We used in vivo deep multi-photon imaging to characterize microvascular networks that perfuse cortical layer 6 and corpus callosum, a highly studied region of white matter in the mouse brain. We show that these deep tissues are exclusively drained by sparse and wide-reaching venules, termed principal cortical venules, which mirror vascular architecture at the human cortical-U fiber interface. During aging, capillary networks draining into deep branches of principal cortical venules are selectively constricted, reduced in density, and diminished in pericyte numbers. This causes hypo-perfusion in deep tissues, and correlates with gliosis and demyelination, whereas superficial tissues become relatively hyper-perfused. Thus, age-related impairment of capillary-venular drainage is a key vascular deficit that contributes to the unique vulnerability of cerebral white matter during brain aging.

Predicting capillary vessel network hemodynamics in silico by machine learning

Blood velocity and red blood cell (RBC) distribution profiles in a capillary vessel cross-section in the microcirculation are generally complex and do not follow Poiseuille's parabolic or uniform pattern. Existing imaging techniques used to map large microvascular networks in vivo do not allow a direct measurement of full 3D velocity and RBC concentration profiles, although such information is needed for accurate evaluation of the physiological variables, such as the wall shear stress (WSS) and near-wall cell-free layer (CFL), that play critical roles in blood flow regulation, disease progression, angiogenesis, and hemostasis. Theoretical network flow models, often used for hemodynamic predictions in experimentally acquired images of the microvascular network, cannot provide the full 3D profiles either. In contrast, such information can be readily obtained from high-fidelity computational models that treat blood as a suspension of deformable RBCs. These models, however, are computationally expensive and not feasible for extension to the microvascular network at large spatial scales up to an organ level. To overcome such limitations, here we present machine learning (ML) models that bypass such expensive computations but provide highly accurate and full 3D profiles of the blood velocity, RBC concentration, WSS, and CFL in every vessel in the microvascular network. The ML models, which are based on artificial neural networks and convolution-based U-net models, predict hemodynamic quantities that compare very well against the true data but reduce the prediction time by several orders. This study therefore paves the way for ML to make detailed and accurate hemodynamic predictions in spatially large microvascular networks at an organ-scale.

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.

The Venular Side of Cerebral Amyloid Angiopathy: Proof of Concept of a Neglected Issue

Small vessel diseases (SVD) is an umbrella term including several entities affecting small arteries, arterioles, capillaries, and venules in the brain. One of the most relevant and prevalent SVDs is cerebral amyloid angiopathy (CAA), whose pathological hallmark is the deposition of amyloid fragments in the walls of small cortical and leptomeningeal vessels. CAA frequently coexists with Alzheimer's Disease (AD), and both are associated with cerebrovascular events, cognitive impairment, and dementia. CAA and AD share pathophysiological, histopathological and neuroimaging issues. The venular involvement in both diseases has been neglected, although both animal models and human histopathological studies found a deposition of amyloid beta in cortical venules. This review aimed to summarize the available information about venular involvement in CAA, starting from the biological level with the putative pathomechanisms of cerebral damage, passing through the definition of the peculiar angioarchitecture of the human cortex with the functional organization and consequences of cortical arteriolar and venular occlusion, and ending to the hypothesized links between cortical venular involvement and the main neuroimaging markers of the disease.

Does Perinatal Intermittent Hypoxia Affect Cerebrovascular Network Development?

Perinatal hypoxia is an inadequate delivery of oxygen to the fetus in the period immediately before, during, or after the birth process. The most frequent form of hypoxia occurring in human development is chronic intermittent hypoxia (CIH) due to sleep-disordered breathing (apnea) or bradycardia events. CIH incidence is particularly high with premature infants. During CIH, repetitive cycles of hypoxia and reoxygenation initiate oxidative stress and inflammatory cascades in the brain. A dense microvascular network of arterioles, capillaries, and venules is required to support the constant metabolic demands of the adult brain. The development and refinement of this microvasculature is orchestrated throughout gestation and in the initial weeks after birth, at a critical juncture when CIH can occur. There is little knowledge on how CIH affects the development of the cerebrovasculature. However, since CIH (and its treatments) can cause profound abnormalities in tissue oxygen content and neural activity, there is reason to believe that it can induce lasting abnormalities in vascular structure and function at the microvascular level contributing to neurodevelopmental disorders. This mini-review discusses the hypothesis that CIH induces a positive feedback loop to perpetuate metabolic insufficiency through derailment of normal cerebrovascular development, leading to long-term deficiencies in cerebrovascular function.

Estimates of the permeability of extra-cellular pathways through the astrocyte endfoot sheath

BACKGROUND

Astrocyte endfoot processes are believed to cover all micro-vessels in the brain cortex and may play a significant role in fluid and substance transport into and out of the brain parenchyma. Detailed fluid mechanical models of diffusive and advective transport in the brain are promising tools to investigate theories of transport.

METHODS

We derive theoretical estimates of astrocyte endfoot sheath permeability for advective and diffusive transport and its variation in microvascular networks from mouse brain cortex. The networks are based on recently published experimental data and generated endfoot patterns are based on Voronoi tessellations of the perivascular surface. We estimate corrections for projection errors in previously published data.

RESULTS

We provide structural-functional relationships between vessel radius and resistance that can be directly used in flow and transport simulations. We estimate endfoot sheath filtration coefficients in the range [Formula: see text] to [Formula: see text], diffusion membrane coefficients for small solutes in the range [Formula: see text] to [Formula: see text], and gap area fractions in the range 0.2-0.6%, based on a inter-endfoot gap width of 20 nm.

CONCLUSIONS

The astrocyte endfoot sheath surrounding microvessels forms a secondary barrier to extra-cellular transport, separating the extra-cellular space of the parenchyma and the perivascular space outside the endothelial layer. The filtration and membrane diffusion coefficients of the endfoot sheath are estimated to be an order of magnitude lower than those of the extra-cellular matrix while being two orders of magnitude higher than those of the vessel wall.

Intraluminal pressure elevates intracellular calcium and contracts CNS pericytes: Role of voltage-dependent calcium channels

Arteriolar smooth muscle cells (SMCs) and capillary pericytes dynamically regulate blood flow in the central nervous system in the face of fluctuating perfusion pressures. Pressure-induced depolarization and Ca2+ elevation provide a mechanism for regulation of SMC contraction, but whether pericytes participate in pressure-induced changes in blood flow remains unknown. Here, utilizing a pressurized whole-retina preparation, we found that increases in intraluminal pressure in the physiological range induce contraction of both dynamically contractile pericytes in the arteriole-proximate transition zone and distal pericytes of the capillary bed. We found that the contractile response to pressure elevation was slower in distal pericytes than in transition zone pericytes and arteriolar SMCs. Pressure-evoked elevation of cytosolic Ca2+ and contractile responses in SMCs were dependent on voltage-dependent Ca2+ channel (VDCC) activity. In contrast, Ca2+ elevation and contractile responses were partially dependent on VDCC activity in transition zone pericytes and independent of VDCC activity in distal pericytes. In both transition zone and distal pericytes, membrane potential at low inlet pressure (20 mmHg) was approximately -40 mV and was depolarized to approximately -30 mV by an increase in pressure to 80 mmHg. The magnitude of whole-cell VDCC currents in freshly isolated pericytes was approximately half that measured in isolated SMCs. Collectively, these results indicate a loss of VDCC involvement in pressure-induced constriction along the arteriole-capillary continuum. They further suggest that alternative mechanisms and kinetics of Ca2+ elevation, contractility, and blood flow regulation exist in central nervous system capillary networks, distinguishing them from neighboring arterioles.

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.

Simultaneous dynamic glucose-enhanced (DGE) MRI and fiber photometry measurements of glucose in the healthy mouse brain

Glucose is the main energy source in the brain and its regulated uptake and utilization are important biomarkers of pathological brain function. Glucose Chemical Exchange Saturation Transfer (GlucoCEST) and its time-resolved version Dynamic Glucose-Enhanced MRI (DGE) are promising approaches to monitor glucose and detect tumors, since they are radioactivity-free, do not require ¹³C labeling and are is easily translatable to the clinics. The main principle of DGE is clear. However, what remains to be established is to which extent the signal reflects vascular, extracellular or intracellular glucose. To elucidate the compartmental contributions to the DGE signal, we coupled it with FRET-based fiber photometry of genetically encoded sensors, a technique that combines quantitative glucose readout with cellular specificity. The glucose sensor FLIIP was used with fiber photometry to measure astrocytic and neuronal glucose changes upon injection of D-glucose, 3OMG and L-glucose, in the anaesthetized murine brain. By correlating the kinetic profiles of the techniques, we demonstrate the presence of a vascular contribution to the signal, especially at early time points after injection. Furthermore, we show that, in the case of the commonly used contrast agent 3OMG, the DGE signal actually anticorrelates with the glucose concentration in neurons and astrocytes.

Altered hemodynamics and vascular reactivity in a mouse model with severe pericyte deficiency

Pericytes are the mural cells of the microvascular network that are in close contact with underlying endothelial cells. Endothelial-secreted PDGFB leads to recruitment of pericytes to the vessel wall, but this is disrupted in Pdgfb^ret/ret mice when the PDGFB retention motif is deleted. This results in severely reduced pericyte coverage on blood vessels. In this study, we investigated vascular abnormalities and hemodynamics in Pdgfb^ret/ret mice throughout the cerebrovascular network and in different cortical layers by in vivo two-photon microscopy. We confirmed that Pdgfb^ret/ret mice are severely deficient in pericytes throughout the vascular network, with enlarged brain blood vessels and a reduced number of vessel branches. Red blood cell velocity, linear density, and tube hematocrit were reduced in Pdgfb^ret/ret mice, which may impair oxygen delivery to the tissue. We also measured intravascular PO₂ and found that concentrations were higher in cortical Layer 2/3 in Pdgfb^ret/ret mice, indicative of reduced blood oxygen extraction. Finally, we found that Pdgfb^ret/ret mice had a reduced capacity for vasodilation in response to an acetazolamide challenge during functional MRI imaging. Taken together, these results suggest that severe pericyte deficiency can lead to vascular abnormalities and altered cerebral blood flow, reminiscent of pathologies such as arteriovenous malformations.

Hyperoxia evokes pericyte-mediated capillary constriction

Oxygen supplementation is regularly prescribed to patients to treat or prevent hypoxia. However, excess oxygenation can lead to reduced cerebral blood flow (CBF) in healthy subjects and worsen the neurological outcome of critically ill patients. Most studies on the vascular effects of hyperoxia focus on arteries but there is no research on the effects on cerebral capillary pericytes, which are major regulators of CBF. Here, we used bright-field imaging of cerebral capillaries and modeling of CBF to show that hyperoxia (95% superfused O₂) led to an increase in intracellular calcium level in pericytes and a significant capillary constriction, sufficient to cause an estimated 25% decrease in CBF. Although hyperoxia is reported to cause vascular smooth muscle cell contraction via generation of reactive oxygen species (ROS), endothelin-1 and 20-HETE, we found that increased cytosolic and mitochondrial ROS levels and endothelin release were not involved in the pericyte-mediated capillary constriction. However, a 20-HETE synthesis blocker greatly reduced the hyperoxia-evoked capillary constriction. Our findings establish pericytes as regulators of CBF in hyperoxia and 20-HETE synthesis as an oxygen sensor in CBF regulation. The results also provide a mechanism by which clinically administered oxygen can lead to a worse neurological outcome.

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.

Modeling a 3-D multiscale blood-flow and heat-transfer framework for realistic vascular systems

Modeling of biological domains and simulation of biophysical processes occurring in them can help inform medical procedures. However, when considering complex domains such as large regions of the human body, the complexities of blood vessel branching and variation of blood vessel dimensions present a major modeling challenge. Here, we present a Voxelized Multi-Physics Simulation (VoM-PhyS) framework to simulate coupled heat transfer and fluid flow using a multi-scale voxel mesh on a biological domain obtained. In this framework, flow in larger blood vessels is modeled using the Hagen–Poiseuille equation for a one-dimensional flow coupled with a three-dimensional two-compartment porous media model for capillary circulation in tissue. The Dirac distribution function is used as Sphere of Influence (SoI) parameter to couple the one-dimensional and three-dimensional flow. This blood flow system is coupled with a heat transfer solver to provide a complete thermo-physiological simulation. The framework is demonstrated on a frog tongue and further analysis is conducted to study the effect of convective heat exchange between blood vessels and tissue, and the effect of SoI on simulation results.

Application of machine learning in predicting blood flow and red cell distribution in capillary vessel networks

Capillary blood vessels in the body partake in the exchange of gas and nutrients with tissues. They are interconnected via multiple vascular junctions forming the microvascular network. Distributions of blood flow and red cells (RBCs) in such networks are spatially uneven and vary in time. Since they dictate the pathophysiology of tissues, their knowledge is important. Theoretical models used to obtain flow and RBC distribution in large networks have limitations as they treat each vessel as a one-dimensional segment and do not explicitly consider cell-cell and cell-vessel interactions. High-fidelity computational models that accurately model each individual RBC are computationally too expensive to predict haemodynamics in large vascular networks and over a long time. Here we investigate the applicability of machine learning (ML) techniques to predict blood flow and RBC distributions in physiologically realistic vascular networks. We acquire data from high-fidelity simulations of deformable RBC suspension flowing in the networks. With the flow and haematocrit specified at an inlet of vasculature, the ML models predict the time-averaged flow rate and RBC distributions in the entire network, time-dependent flow rate and haematocrit in each vessel and vascular bifurcation in isolation over a long time, and finally, simultaneous spatially and temporally evolving quantities through the vessel hierarchy in the networks.

Functional ultrasound localization microscopy reveals brain-wide neurovascular activity on a microscopic scale

The advent of neuroimaging has increased our understanding of brain function. While most brain-wide functional imaging modalities exploit neurovascular coupling to map brain activity at millimeter resolutions, the recording of functional responses at microscopic scale in mammals remains the privilege of invasive electrophysiological or optical approaches, but is mostly restricted to either the cortical surface or the vicinity of implanted sensors. Ultrasound localization microscopy (ULM) has achieved transcranial imaging of cerebrovascular flow, up to micrometre scales, by localizing intravenously injected microbubbles; however, the long acquisition time required to detect microbubbles within microscopic vessels has so far restricted ULM application mainly to microvasculature structural imaging. Here we show how ULM can be modified to quantify functional hyperemia dynamically during brain activation reaching a 6.5-µm spatial and 1-s temporal resolution in deep regions of the rat brain.

Functional ultrasound localization microscopy monitors cerebrovascular blood flow by detecting the flow of injected microbubbles, providing access to brain activity at high spatiotemporal resolution.

Quantitative relationship between cerebrovascular network and neuronal cell types in mice

The cerebrovasculature and its mural cells must meet brain regional energy demands, but how their spatial relationship with different neuronal cell types varies across the brain remains largely unknown. Here we apply brain-wide mapping methods to comprehensively define the quantitative relationships between the cerebrovasculature, capillary pericytes, and glutamatergic and GABAergic neurons, including neuronal nitric oxide synthase-positive (nNOS+) neurons and their subtypes in adult mice. Our results show high densities of vasculature with high fluid conductance and capillary pericytes in primary motor sensory cortices compared with association cortices that show significant positive and negative correlations with energy-demanding parvalbumin+ and vasomotor nNOS+ neurons, respectively. Thalamo-striatal areas that are connected to primary motor sensory cortices also show high densities of vasculature and pericytes, suggesting dense energy support for motor sensory processing areas. Our cellular-resolution resource offers opportunities to examine spatial relationships between the cerebrovascular network and neuronal cell composition in largely understudied subcortical areas.

Neurovascular coupling mechanisms in health and neurovascular uncoupling in Alzheimer's disease

To match the metabolic demands of the brain, mechanisms have evolved to couple neuronal activity to vasodilation, thus increasing local cerebral blood flow and delivery of oxygen and glucose to active neurons. Rather than relying on metabolic feedback signals such as the consumption of oxygen or glucose, the main signalling pathways rely on the release of vasoactive molecules by neurons and astrocytes, which act on contractile cells. Vascular smooth muscle cells and pericytes are the contractile cells associated with arterioles and capillaries, respectively, which relax and induce vasodilation.

Much progress has been made in understanding the complex signalling pathways of neurovascular coupling, but issues such as the contributions of capillary pericytes and astrocyte calcium signal remain contentious. Study of neurovascular coupling mechanisms is especially important as cerebral blood flow dysregulation is a prominent feature of Alzheimer’s disease. In this article we will discuss developments and controversies in the understanding of neurovascular coupling and finish by discussing current knowledge concerning neurovascular uncoupling in Alzheimer’s disease.

Mathematical modelling of haemorrhagic transformation within a multi-scale microvasculature network

Objective Haemorrhagic transformation (HT) is one of the most common complications after ischaemic stroke caused by damage to the blood-brain barrier (BBB) that could be the result of stroke progression or a complication of stroke treatment with reperfusion therapy. The aim of this study is to develop further a previous simple HT mathematical model into an enlarged multi-scale microvasculature model in order to investigate the effects of HT on the surrounding tissue and vasculature. In addition, this study investigates the relationship between tissue displacement and vascular geometry. Approach By modelling tissue displacement, capillary compression, hydraulic conductivity in tissue and vascular permeability, we establish a mathematical model to describe the change of intracranial pressure (ICP) surrounding the damaged vascular bed after HT onset applied to a 3D multi-scale microvasculature. The use of a voxel-scale model then enables us to compare our HT simulation with available clinical imaging data for perfusion and cerebral blood volume (CBV) in the multi-scale microvasculature network. Main results We showed that the haematoma diameter and the maximum tissue displacement are approximately proportional to the diameter of the breakdown vessel. Based on the voxel-scale model, we found that perfusion reduces by approximately 13-17 % and CBV reduces by around 20-25 % after HT onset due to the effect of capillary compression caused by increased interstitial pressure. The results are in good agreement with the limited experimental data. Significance This model, by enabling us to bridge the gap between the microvascular scale and clinically measurable parameters, thus provides a foundation for more detailed validation and understanding of HT in patients.

Challenges and opportunities of integrating imaging and mathematical modelling to interrogate biological processes

Advances in biological imaging have accelerated our understanding of human physiology in both health and disease. As these advances have developed, the opportunities gained by integrating with cutting-edge mathematical models have become apparent yet remain challenging. Combined imaging-modelling approaches provide unprecedented opportunity to correlate data on tissue architecture and function, across length and time scales, to better understand the mechanisms that underpin fundamental biology and also to inform clinical decisions. Here we discuss the opportunities and challenges of such approaches, providing literature examples across a range of organ systems. Given the breadth of the field we focus on the intersection of continuum modelling and in vivo imaging applied to the vasculature and blood flow, though our rationale and conclusions extend widely. We propose three key research pillars (image acquisition, image processing, mathematical modelling) and present their respective advances as well as future opportunity via better integration. Multidisciplinary efforts that develop imaging and modelling tools concurrently, and share them open-source with the research community, provide exciting opportunity for advancing these fields.

Public Volume Electron Microscopy Data: An Essential Resource to Study the Brain Microvasculature

Electron microscopy is the primary approach to study ultrastructural features of the cerebrovasculature. However, 2D snapshots of a vascular bed capture only a small fraction of its complexity. Recent efforts to synaptically map neuronal circuitry using volume electron microscopy have also sampled the brain microvasculature in 3D. Here, we perform a meta-analysis of 7 data sets spanning different species and brain regions, including two data sets from the MICrONS consortium that have made efforts to segment vasculature in addition to all parenchymal cell types in mouse visual cortex. Exploration of these data have revealed rich information for detailed investigation of the cerebrovasculature. Neurovascular unit cell types (including, but not limited to, endothelial cells, mural cells, perivascular fibroblasts, microglia, and astrocytes) could be discerned across broad microvascular zones. Image contrast was sufficient to identify subcellular details, including endothelial junctions, caveolae, peg-and-socket interactions, mitochondria, Golgi cisternae, microvilli and other cellular protrusions of potential significance to vascular signaling. Additionally, non-cellular structures including the basement membrane and perivascular spaces were visible and could be traced between arterio-venous zones along the vascular wall. These explorations revealed structural features that may be important for vascular functions, such as blood-brain barrier integrity, blood flow control, brain clearance, and bioenergetics. They also identified limitations where accuracy and consistency of segmentation could be further honed by future efforts. The purpose of this article is to introduce these valuable community resources within the framework of cerebrovascular research. We do so by providing an assessment of their vascular contents, identifying features of significance for further study, and discussing next step ideas for refining vascular segmentation and analysis.

Optical measurement of microvascular oxygenation and blood flow responses in awake mouse cortex during functional activation

The cerebral cortex has a number of conserved morphological and functional characteristics across brain regions and species. Among them, the laminar differences in microvascular density and mitochondrial cytochrome c oxidase staining suggest potential laminar variability in the baseline O₂ metabolism and/or laminar variability in both O₂ demand and hemodynamic response. Here, we investigate the laminar profile of stimulus-induced intravascular partial pressure of O₂ (pO2) transients to stimulus-induced neuronal activation in fully awake mice using two-photon phosphorescence lifetime microscopy. Our results demonstrate that stimulus-induced changes in intravascular pO₂ are conserved across cortical layers I-IV, suggesting a tightly controlled neurovascular response to provide adequate O₂ supply across cortical depth. In addition, we observed a larger change in venular O₂ saturation (ΔsO₂) compared to arterioles, a gradual increase in venular ΔsO₂ response towards the cortical surface, and absence of the intravascular "initial dip" previously reported under anesthesia. This study paves the way for quantification of layer-specific cerebral O₂ metabolic responses, facilitating investigation of brain energetics in health and disease and informed interpretation of laminar blood oxygen level dependent functional magnetic resonance imaging signals.

Gradual Not Sudden Change: Multiple Sites of Functional Transition Across the Microvascular Bed

In understanding the role of the neurovascular unit as both a biomarker and target for disease interventions, it is vital to appreciate how the function of different components of this unit change along the vascular tree. The cells of the neurovascular unit together perform an array of vital functions, protecting the brain from circulating toxins and infection, while providing nutrients and clearing away waste products. To do so, the brain's microvasculature dilates to direct energy substrates to active neurons, regulates access to circulating immune cells, and promotes angiogenesis in response to decreased blood supply, as well as pulsating to help clear waste products and maintain the oxygen supply. Different parts of the cerebrovascular tree contribute differently to various aspects of these functions, and previously, it has been assumed that there are discrete types of vessel along the vascular network that mediate different functions. Another option, however, is that the multiple transitions in function that occur across the vascular network do so at many locations, such that vascular function changes gradually, rather than in sharp steps between clearly distinct vessel types. Here, by reference to new data as well as by reviewing historical and recent literature, we argue that this latter scenario is likely the case and that vascular function gradually changes across the network without clear transition points between arteriole, precapillary arteriole and capillary. This is because classically localized functions are in fact performed by wide swathes of the vasculature, and different functional markers start and stop being expressed at different points along the vascular tree. Furthermore, vascular branch points show alterations in their mural cell morphology that suggest functional specializations irrespective of their position within the network. Together this work emphasizes the need for studies to consider where transitions of different functions occur, and the importance of defining these locations, in order to better understand the vascular network and how to target it to treat disease.

Network-driven anomalous transport is a fundamental component of brain microvascular dysfunction

Blood microcirculation supplies neurons with oxygen and nutrients, and contributes to clearing their neurotoxic waste, through a dense capillary network connected to larger tree-like vessels. This complex microvascular architecture results in highly heterogeneous blood flow and travel time distributions, whose origin and consequences on brain pathophysiology are poorly understood. Here, we analyze highly-resolved intracortical blood flow and transport simulations to establish the physical laws governing the macroscopic transport properties in the brain micro-circulation. We show that network-driven anomalous transport leads to the emergence of critical regions, whether hypoxic or with high concentrations of amyloid-β, a waste product centrally involved in Alzheimer's Disease. We develop a Continuous-Time Random Walk theory capturing these dynamics and predicting that such critical regions appear much earlier than anticipated by current empirical models under mild hypoperfusion. These findings provide a framework for understanding and modelling the impact of microvascular dysfunction in brain diseases, including Alzheimer's Disease.

Luminal flow actuation generates coupled shear and strain in a microvessel-on-chip

In the microvasculature, blood flow-derived forces are key regulators of vascular structure and function. Consequently, the development of hydrogel-based microvessel-on-chip systems that strive to mimic thein vivocellular organization and mechanical environment has received great attention in recent years. However, despite intensive efforts, current microvessel-on-chip systems suffer from several limitations, most notably failure to produce physiologically relevant wall strain levels. In this study, a novel microvessel-on-chip based on the templating technique and using luminal flow actuation to generate physiologically relevant levels of wall shear stress and circumferential stretch is presented. Normal forces induced by the luminal pressure compress the surrounding soft collagen hydrogel, dilate the channel, and create large circumferential strain. The fluid pressure gradient in the system drives flow forward and generates realistic pulsatile wall shear stresses. Rigorous characterization of the system reveals the crucial role played by the poroelastic behavior of the hydrogel in determining the magnitudes of the wall shear stress and strain. The experimental measurements are combined with an analytical model of flow in both the lumen and the porous hydrogel to provide an exceptionally versatile user manual for an application-based choice of parameters in microvessels-on-chip. This unique strategy of flow actuation adds a dimension to the capabilities of microvessel-on-chip systems and provides a more general framework for improving hydrogel-basedin vitroengineered platforms.

Imaging faster neural dynamics with fast fMRI: A need for updated models of the hemodynamic response

Fast fMRI enables the detection of neural dynamics over timescales of hundreds of milliseconds, suggesting it may provide a new avenue for studying subsecond neural processes in the human brain. The magnitudes of these fast fMRI dynamics are far greater than predicted by canonical models of the hemodynamic response. Several studies have established nonlinear properties of the hemodynamic response that have significant implications for fast fMRI. We first review nonlinear properties of the hemodynamic response function that may underlie fast fMRI signals. We then illustrate the breakdown of canonical hemodynamic response models in the context of fast neural dynamics. We will then argue that the canonical hemodynamic response function is not likely to reflect the BOLD response to neuronal activity driven by sparse or naturalistic stimuli or perhaps to spontaneous neuronal fluctuations in the resting state. These properties suggest that fast fMRI is capable of tracking surprisingly fast neuronal dynamics, and we discuss the neuroscientific questions that could be addressed using this approach.

Revisiting the neurovascular unit

The brain is supplied by an elaborate vascular network that originates extracranially and reaches deep into the brain. The concept of the neurovascular unit provides a useful framework to investigate how neuronal signals regulate nearby microvessels to support the metabolic needs of the brain, but it does not consider the role of larger cerebral arteries and systemic vasoactive signals. Furthermore, the recently emerged molecular heterogeneity of cerebrovascular cells indicates that there is no prototypical neurovascular unit replicated at all levels of the vascular network. Here, we examine the cellular and molecular diversity of the cerebrovascular tree and the relative contribution of systemic and brain-intrinsic factors to neurovascular function. Evidence supports the concept of a 'neurovascular complex' composed of segmentally diverse functional modules that implement coordinated vascular responses to central and peripheral signals to maintain homeostasis of the brain. This concept has major implications for neurovascular regulation in health and disease and for brain imaging.

The Ageing Brain: Investigating the Role of Age in Changes to the Human Cerebral Microvasculature With an in silico Model

Ageing causes extensive structural changes to the human cerebral microvasculature, which have a significant effect on capillary bed perfusion and oxygen transport. Current models of brain capillary networks in the literature focus on healthy adult brains and do not capture the effects of ageing, which is critical when studying neurodegenerative diseases. This study builds upon a statistically accurate model of the human cerebral microvasculature based on ex-vivo morphological data. This model is adapted for “healthy” ageing using in-vivo measurements from mice at three distinct age groups—young, middle-aged, and old. From this new model, blood and molecular exchange parameters are calculated such as permeability and surface-area-to-volume ratio, and compared across the three age groups. The ability to alter the model vessel-by-vessel is used to create a continuous gradient of ageing. It was found that surface-area-to-volume ratio reduced in old age by 6% and permeability by 24% from middle-age to old age, and variability within the networks also increased with age. The ageing gradient indicated a threshold in the ageing process around 75 years old, after which small changes have an amplified effect on blood flow properties. This gradient enables comparison of studies measuring cerebral properties at discrete points in time. The response of middle aged and old aged capillary beds to micro-emboli showed a lower robustness of the old age capillary bed to vessel occlusion. As the brain ages, there is thus increased vulnerability of the microvasculature—with a “tipping point” beyond which further remodeling of the microvasculature has exaggerated effects on the brain. When developing in-silico models of the brain, age is a very important consideration to accurately assess risk factors for cognitive decline and isolate early biomarkers of microvascular health.

Pericytes: Intrinsic Transportation Engineers of the CNS Microcirculation

Pericytes in the brain are candidate regulators of microcirculatory blood flow because they are strategically positioned along the microvasculature, contain contractile proteins, respond rapidly to neuronal activation, and synchronize microvascular dynamics and neurovascular coupling within the capillary network. Analyses of mice with defects in pericyte generation demonstrate that pericytes are necessary for the formation of the blood-brain barrier, development of the glymphatic system, immune homeostasis, and white matter function. The development, identity, specialization, and progeny of different subtypes of pericytes, however, remain unclear. Pericytes perform brain-wide 'transportation engineering' functions in the capillary network, instructing, integrating, and coordinating signals within the cellular communicome in the neurovascular unit to efficiently distribute oxygen and nutrients ('goods and services') throughout the microvasculature ('transportation grid'). In this review, we identify emerging challenges in pericyte biology and shed light on potential pericyte-targeted therapeutic strategies.

Simulation of intravoxel incoherent perfusion signal using a realistic capillary network of a mouse brain

PURPOSE

To simulate the intravoxel incoherent perfusion magnetic resonance magnitude signal from the motion of blood particles in three realistic vascular network graphs from a mouse brain.

METHODS

In three networks generated from the cortex of a mouse scanned by two-photon laser microscopy, blood flow in each vessel was simulated using Poiseuille's law. The trajectories, flow speeds and phases acquired by a fixed number of simulated blood particles during a Stejskal-Tanner bipolar pulse gradient scheme were computed. The resulting magnitude signal was obtained by integrating all phases and the pseudo-diffusion coefficient D* was estimated by fitting an exponential signal decay. To better understand the anatomical source of the intravoxel incoherent motion (IVIM) perfusion signal, the above was repeated restricting the simulation to various types of vessel.

RESULTS

The characteristics of the three microvascular networks were respectively vessel lengths (mean ± std. dev.) 67.2 ± 53.6 μm, 59.8 ± 46.2 μm and 64.5 ± 50.9 μm, diameters 6.0 ± 3.5 μm, 5.7 ± 3.6 μm and 6.1 ± 3.7 μm and simulated blood velocity 0.9 ± 1.7 μm/ms, 1.4 ± 2.5 μm/ms and 0.7 ± 2.1 μm/ms. Exponential fitting of the simulated signal decay as a function of b-value resulted in the following D*-values [10-3 mm2 /s]: 31.7, 40.4 and 33.4. The signal decay for low b-values was the largest in the larger vessels, but the smaller vessels and the capillaries accounted for more of the total volume of the networks.

CONCLUSION

This simulation improves the theoretical understanding of the IVIM perfusion estimation method by directly linking the MR IVIM perfusion signal to an ultra-high resolution measurement of the microvascular network and a realistic blood flow simulation.

Imaging the construction of capillary networks in the neonatal mouse brain

The distribution of blood throughout the brain is facilitated by highly interconnected capillary networks. However, the steps involved in the construction of these networks has remained unclear. We used in vivo two-photon imaging through noninvasive cranial windows to study the engineering of capillary networks in the cerebral cortex of mouse neonates. We find that angiogenic activity originates at ascending venules, which undergo a burst of sprouting in the second postnatal week. This sprouting activity first establishes long paths to connect venules to blood input from neighboring arterioles, and then expands capillary interconnectivity with a multitude of short-range connections. Our study provides an experimental foundation to understand how capillary networks are shaped in the living mammalian brain during postnatal development.

Capillary networks are essential for distribution of blood flow through the brain, and numerous other homeostatic functions, including neurovascular signal conduction and blood–brain barrier integrity. Accordingly, the impairment of capillary architecture and function lies at the root of many brain diseases. Visualizing how brain capillary networks develop in vivo can reveal innate programs for cerebrovascular growth and repair. Here, we use longitudinal two-photon imaging through noninvasive thinned skull windows to study a burst of angiogenic activity during cerebrovascular development in mouse neonates. We find that angiogenesis leading to the formation of capillary networks originated exclusively from cortical ascending venules. Two angiogenic sprouting activities were observed: 1) early, long-range sprouts that directly connected venules to upstream arteriolar input, establishing the backbone of the capillary bed, and 2) short-range sprouts that contributed to expansion of anastomotic connectivity within the capillary bed. All nascent sprouts were prefabricated with an intact endothelial lumen and pericyte coverage, ensuring their immediate perfusion and stability upon connection to their target vessels. The bulk of this capillary expansion spanned only 2 to 3 d and contributed to an increase of blood flow during a critical period in cortical development.

On the Sensitivity Analysis of Porous Finite Element Models for Cerebral Perfusion Estimation

Computational physiological models are promising tools to enhance the design of clinical trials and to assist in decision making. Organ-scale haemodynamic models are gaining popularity to evaluate perfusion in a virtual environment both in healthy and diseased patients. Recently, the principles of verification, validation, and uncertainty quantification of such physiological models have been laid down to ensure safe applications of engineering software in the medical device industry. The present study sets out to establish guidelines for the usage of a three-dimensional steady state porous cerebral perfusion model of the human brain following principles detailed in the verification and validation (V&V 40) standard of the American Society of Mechanical Engineers. The model relies on the finite element method and has been developed specifically to estimate how brain perfusion is altered in ischaemic stroke patients before, during, and after treatments. Simulations are compared with exact analytical solutions and a thorough sensitivity analysis is presented covering every numerical and physiological model parameter. The results suggest that such porous models can approximate blood pressure and perfusion distributions reliably even on a coarse grid with first order elements. On the other hand, higher order elements are essential to mitigate errors in volumetric blood flow rate estimation through cortical surface regions. Matching the volumetric flow rate corresponding to major cerebral arteries is identified as a validation milestone. It is found that inlet velocity boundary conditions are hard to obtain and that constant pressure inlet boundary conditions are feasible alternatives. A one-dimensional model is presented which can serve as a computationally inexpensive replacement of the three-dimensional brain model to ease parameter optimisation, sensitivity analyses and uncertainty quantification. The findings of the present study can be generalised to organ-scale porous perfusion models. The results increase the applicability of computational tools regarding treatment development for stroke and other cerebrovascular conditions.

Neurovascular coupling and oxygenation are decreased in hippocampus compared to neocortex because of microvascular differences

The hippocampus is essential for spatial and episodic memory but is damaged early in Alzheimer's disease and is very sensitive to hypoxia. Understanding how it regulates its oxygen supply is therefore key for designing interventions to preserve its function. However, studies of neurovascular function in the hippocampus in vivo have been limited by its relative inaccessibility. Here we compared hippocampal and visual cortical neurovascular function in awake mice, using two photon imaging of individual neurons and vessels and measures of regional blood flow and haemoglobin oxygenation. We show that blood flow, blood oxygenation and neurovascular coupling were decreased in the hippocampus compared to neocortex, because of differences in both the vascular network and pericyte and endothelial cell function. Modelling oxygen diffusion indicates that these features of the hippocampal vasculature may restrict oxygen availability and could explain its sensitivity to damage during neurological conditions, including Alzheimer's disease, where the brain's energy supply is decreased.

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.

Mathematical synthesis of the cortical circulation for the whole mouse brain-part II: Microcirculatory closure

Recent advancements in multiphoton imaging and vascular reconstruction algorithms have increased the amount of data on cerebrovascular circulation for statistical analysis and hemodynamic simulations. Experimental observations offer fundamental insights into capillary network topology but mainly within a narrow field of view typically spanning a small fraction of the cortical surface (less than 2%). In contrast, larger-resolution imaging modalities, such as computed tomography (CT) or magnetic resonance imaging (MRI), have whole-brain coverage but capture only larger blood vessels, overlooking the microscopic capillary bed. To integrate data acquired at multiple length scales with different neuroimaging modalities and to reconcile brain-wide macroscale information with microscale multiphoton data, we developed a method for synthesizing hemodynamically equivalent vascular networks for the entire cerebral circulation. This computational approach is intended to aid in the quantification of patterns of cerebral blood flow and metabolism for the entire brain. In part I, we described the mathematical framework for image-guided generation of synthetic vascular networks covering the large cerebral arteries from the circle of Willis through the pial surface network leading back to the venous sinuses. Here in part II, we introduce novel procedures for creating microcirculatory closure that mimics a realistic capillary bed. We demonstrate our capability to synthesize synthetic vascular networks whose morphometrics match empirical network graphs from three independent state-of-the-art imaging laboratories using different image acquisition and reconstruction protocols. We also successfully synthesized twelve vascular networks of a complete mouse brain hemisphere suitable for performing whole-brain blood flow simulations. Synthetic arterial and venous networks with microvascular closure allow whole-brain hemodynamic predictions. Simulations across all length scales will potentially illuminate organ-wide supply and metabolic functions that are inaccessible to models reconstructed from image data with limited spatial coverage.

Brain microvasculature has a common topology with local differences in geometry that match metabolic load

The microvasculature underlies the supply networks that support neuronal activity within heterogeneous brain regions. What are common versus heterogeneous aspects of the connectivity, density, and orientation of capillary networks? To address this, we imaged, reconstructed, and analyzed the microvasculature connectome in whole adult mice brains with sub-micrometer resolution. Graph analysis revealed common network topology across the brain that leads to a shared structural robustness against the rarefaction of vessels. Geometrical analysis, based on anatomically accurate reconstructions, uncovered a scaling law that links length density, i.e., the length of vessel per volume, with tissue-to-vessel distances. We then derive a formula that connects regional differences in metabolism to differences in length density and, further, predicts a common value of maximum tissue oxygen tension across the brain. Last, the orientation of capillaries is weakly anisotropic with the exception of a few strongly anisotropic regions; this variation can impact the interpretation of fMRI data.

Adaptive constrained constructive optimisation for complex vascularisation processes

Mimicking angiogenetic processes in vascular territories acquires importance in the analysis of the multi-scale circulatory cascade and the coupling between blood flow and cell function. The present work extends, in several aspects, the Constrained Constructive Optimisation (CCO) algorithm to tackle complex automatic vascularisation tasks. The main extensions are based on the integration of adaptive optimisation criteria and multi-staged space-filling strategies which enhance the modelling capabilities of CCO for specific vascular architectures. Moreover, this vascular outgrowth can be performed either from scratch or from an existing network of vessels. Hence, the vascular territory is defined as a partition of vascular, avascular and carriage domains (the last one contains vessels but not terminals) allowing one to model complex vascular domains. In turn, the multi-staged space-filling approach allows one to delineate a sequence of biologically-inspired stages during the vascularisation process by exploiting different constraints, optimisation strategies and domain partitions stage by stage, improving the consistency with the architectural hierarchy observed in anatomical structures. With these features, the aDaptive CCO (DCCO) algorithm proposed here aims at improving the modelled network anatomy. The capabilities of the DCCO algorithm are assessed with a number of anatomically realistic scenarios.

Modelling the impact of clot fragmentation on the microcirculation after thrombectomy

Many ischaemic stroke patients who have a mechanical removal of their clot (thrombectomy) do not get reperfusion of tissue despite the thrombus being removed. One hypothesis for this 'no-reperfusion' phenomenon is micro-emboli fragmenting off the large clot during thrombectomy and occluding smaller blood vessels downstream of the clot location. This is impossible to observe in-vivo and so we here develop an in-silico model based on in-vitro experiments to model the effect of micro-emboli on brain tissue. Through in-vitro experiments we obtain, under a variety of clot consistencies and thrombectomy techniques, micro-emboli distributions post-thrombectomy. Blood flow through the microcirculation is modelled for statistically accurate voxels of brain microvasculature including penetrating arterioles and capillary beds. A novel micro-emboli algorithm, informed by the experimental data, is used to simulate the impact of micro-emboli successively entering the penetrating arterioles and the capillary bed. Scaled-up blood flow parameters-permeability and coupling coefficients-are calculated under various conditions. We find that capillary beds are more susceptible to occlusions than the penetrating arterioles with a 4x greater drop in permeability per volume of vessel occluded. Individual microvascular geometries determine robustness to micro-emboli. Hard clot fragmentation leads to larger micro-emboli and larger drops in blood flow for a given number of micro-emboli. Thrombectomy technique has a large impact on clot fragmentation and hence occlusions in the microvasculature. As such, in-silico modelling of mechanical thrombectomy predicts that clot specific factors, interventional technique, and microvascular geometry strongly influence reperfusion of the brain. Micro-emboli are likely contributory to the phenomenon of no-reperfusion following successful removal of a major clot.

A porous circulation model of the human brain for in silico clinical trials in ischaemic stroke

The advancement of ischaemic stroke treatment relies on resource-intensive experiments and clinical trials. In order to improve ischaemic stroke treatments, such as thrombolysis and thrombectomy, we target the development of computational tools for in silico trials which can partially replace these animal and human experiments with fast simulations. This study proposes a model that will serve as part of a predictive unit within an in silico clinical trial estimating patient outcome as a function of treatment. In particular, the present work aims at the development and evaluation of an organ-scale microcirculation model of the human brain for perfusion prediction. The model relies on a three-compartment porous continuum approach. Firstly, a fast and robust method is established to compute the anisotropic permeability tensors representing arterioles and venules. Secondly, vessel encoded arterial spin labelling magnetic resonance imaging and clustering are employed to create an anatomically accurate mapping between the microcirculation and large arteries by identifying superficial perfusion territories. Thirdly, the parameter space of the problem is reduced by analysing the governing equations and experimental data. Fourthly, a parameter optimization is conducted. Finally, simulations are performed with the tuned model to obtain perfusion maps corresponding to an open and an occluded (ischaemic stroke) scenario. The perfusion map in the occluded vessel scenario shows promising qualitative agreement with computed tomography images of a patient with ischaemic stroke caused by large vessel occlusion. The results highlight that in the case of vessel occlusion (i) identifying perfusion territories is essential to capture the location and extent of underperfused regions and (ii) anisotropic permeability tensors are required to give quantitatively realistic estimation of perfusion change. In the future, the model will be thoroughly validated against experiments.

Voxelized simulation of cerebral oxygen perfusion elucidates hypoxia in aged mouse cortex

Departures of normal blood flow and metabolite distribution from the cerebral microvasculature into neuronal tissue have been implicated with age-related neurodegeneration. Mathematical models informed by spatially and temporally distributed neuroimage data are becoming instrumental for reconstructing a coherent picture of normal and pathological oxygen delivery throughout the brain. Unfortunately, current mathematical models of cerebral blood flow and oxygen exchange become excessively large in size. They further suffer from boundary effects due to incomplete or physiologically inaccurate computational domains, numerical instabilities due to enormous length scale differences, and convergence problems associated with condition number deterioration at fine mesh resolutions. Our proposed simple finite volume discretization scheme for blood and oxygen microperfusion simulations does not require expensive mesh generation leading to the critical benefit that it drastically reduces matrix size and bandwidth of the coupled oxygen transfer problem. The compact problem formulation yields rapid and stable convergence. Moreover, boundary effects can effectively be suppressed by generating very large replica of the cortical microcirculation in silico using an image-based cerebrovascular network synthesis algorithm, so that boundaries of the perfusion simulations are far removed from the regions of interest. Massive simulations over sizeable portions of the cortex with feature resolution down to the micron scale become tractable with even modest computer resources. The feasibility and accuracy of the novel method is demonstrated and validated with in vivo oxygen perfusion data in cohorts of young and aged mice. Our oxygen exchange simulations quantify steep gradients near penetrating blood vessels and point towards pathological changes that might cause neurodegeneration in aged brains. This research aims to explain mechanistic interactions between anatomical structures and how they might change in diseases or with age. Rigorous quantification of age-related changes is of significant interest because it might aide in the search for imaging biomarkers for dementia and Alzheimer’s disease.

Brain function critically depends on the maintenance of physiological blood supply and metabolism in the cortex. Disturbances to adequate perfusion have been linked to age-related neurodegeneration. However, the precise correlation between age-related hemodynamic changes and the resulting decline in oxygen delivery is not well understood and has not been quantified. Therefore, we introduce a new compact, and therefore highly scalable, computational method for predicting the physiological relationship between hemodynamics and cortical oxygen perfusion for large sections of the cortical microcirculation. We demonstrate the novel mesh generation-free (MGF), multi-scale simulation approach through realistic in vivo case studies of cortical microperfusion in the mouse brain. We further validate mechanistic correlations and a quantitative relationship between blood flow and brain oxygenation using experimental data from cohorts of young, middle aged and old mouse brains. Our computational approach overcomes size and performance limitations of previous unstructured meshing techniques to enable the prediction of oxygen tension with a spatial resolution of least two orders of magnitude higher than previously possible. Our simulation results support the hypothesis that structural changes in the microvasculature induce hypoxic pockets in the aged brain that are absent in the healthy, young mouse.

Microvascular Alterations in Alzheimer's Disease

Alzheimer's disease (AD) is a neurodegenerative disorder associated with continual decline in cognition and ability to perform routine functions such as remembering familiar places or understanding speech. For decades, amyloid beta (Aβ) was viewed as the driver of AD, triggering neurodegenerative processes such as inflammation and formation of neurofibrillary tangles (NFTs). This approach has not yielded therapeutics that cure the disease or significant improvements in long-term cognition through removal of plaques and Aβ oligomers. Some researchers propose alternate mechanisms that drive AD or act in conjunction with amyloid to promote neurodegeneration. This review summarizes the status of AD research and examines research directions including and beyond Aβ, such as tau, inflammation, and protein clearance mechanisms. The effect of aging on microvasculature is highlighted, including its contribution to reduced blood flow that impairs cognition. Microvascular alterations observed in AD are outlined, emphasizing imaging studies of capillary malfunction. The review concludes with a discussion of two therapies to protect tissue without directly targeting Aβ for removal: (1) administration of growth factors to promote vascular recovery in AD; (2) inhibiting activity of a calcium-permeable ion channels to reduce microglial activation and restore cerebral vascular function.

On the poro-elastic models for microvascular blood flow resistance: An in vitro validation

Nowadays, adequate and accurate representation of the microvascular flow resistance constitutes one of the major challenges in computational haemodynamic studies. In this work, a theoretical, porous media framework, ultimately designed for representing downstream resistance, is presented and compared against an in vitro experimental results. The resistor consists of a poro-elastic tube, with either a constant or variable porosity profile in space. The underlying physics, characterizing the fluid flow through the porous media, is analysed by considering flow variables at different network locations. Backward reflections, originated in the reservoir of the in vitro model, are accounted for through a reflection coefficient imposed as an outflow network condition. The simulation results are in good agreement with the measurements for both the homogenous and heterogeneous porosity conditions. In addition, the comparison allows identification of the range of values representing experimental reservoir reflection coefficients. The pressure drops across the heterogeneous porous media increases with respect to the simpler configuration, whilst flow remains almost unchanged. The effect of some fluid network features, such as tube Young's modulus and fluid viscosity, on the theoretical results is also elucidated, providing a reference for the invitro and insilico simulation of different microvascular conditions.

Validation of red blood cell flux and velocity estimations based on optical coherence tomography intensity fluctuations

We present a validation of red blood cell flux and speed measurements based on the passage of erythrocytes through the OCT’s focal volume. We compare the performance of the so-called RBC-passage OCT technique to co-localized and simultaneously acquired two-photon excitation fluorescence microscopy (TPEF) measurements. Using concurrent multi-modal imaging, we show that fluctuations in the OCT signal display highly similar features to TPEF time traces. Furthermore, we demonstrate an overall difference in RBC flux and speed of 2.5 ± 3.27 RBC/s and 0.12 ± 0.67 mm/s (mean ± S.D.), compared to TPEF. The analysis also revealed that the OCT RBC flux estimation is most accurate between 20 RBC/s to 60 RBC/s, and is severely underestimated at fluxes beyond 80 RBC/s. Lastly, our analysis shows that the RBC speed estimations increase in accuracy as the speed decreases, reaching a difference of 0.16 ± 0.25 mm/s within the 0–0.5 mm/s speed range.