Modeling oxygen transport in the brain: An efficient coarse-grid approach to capture perivascular gradients in the parenchyma.

Recent progresses in intravital imaging have enabled highly-resolved measurements of periarteriolar oxygen gradients (POGs) within the brain parenchyma. POGs are increasingly used as proxies to estimate the local baseline oxygen consumption, which is a hallmark of cell activity. However, the oxygen profile around a given arteriole arises from an interplay between oxygen consumption and delivery, not only by this arteriole but also by distant capillaries. Integrating such interactions across scales while accounting for the complex architecture of the microvascular network remains a challenge from a modelling perspective. This limits our ability to interpret the experimental oxygen maps and constitutes a key bottleneck toward the inverse determination of metabolic rates of oxygen. We revisit the problem of parenchymal oxygen transport and metabolism and introduce a simple, conservative, accurate and scalable direct numerical method going beyond canonical Krogh-type models and their associated geometrical simplifications. We focus on a two-dimensional formulation, and introduce the concepts needed to combine an operator-splitting and a Green's function approach. Oxygen concentration is decomposed into a slowly-varying contribution, discretized by Finite Volumes over a coarse cartesian grid, and a rapidly-varying contribution, approximated analytically in grid-cells surrounding each vessel. Starting with simple test cases, we thoroughly analyze the resulting errors by comparison with highly-resolved simulations of the original transport problem, showing considerable improvement of the computational-cost/accuracy balance compared to previous work. We then demonstrate the model ability to flexibly generate synthetic data reproducing the spatial dynamics of oxygen in the brain parenchyma, with sub-grid resolution. Based on these synthetic data, we show that capillaries distant from the arteriole cannot be overlooked when interpreting POGs, thus reconciling recent measurements of POGs across cortical layers with the fundamental idea that variations of vascular density within the depth of the cortex may reveal underlying differences in neuronal organization and metabolic load.

Is CAA a perivascular brain clearance disease? A discussion of the evidence to date and outlook for future studies.

The brain's network of perivascular channels for clearance of excess fluids and waste plays a critical role in the pathogenesis of several neurodegenerative diseases including cerebral amyloid angiopathy (CAA). CAA is the main cause of hemorrhagic stroke in the elderly, the most common vascular comorbidity in Alzheimer's disease and also implicated in adverse events related to anti-amyloid immunotherapy. Remarkably, the mechanisms governing perivascular clearance of soluble amyloid ß-a key culprit in CAA-from the brain to draining lymphatics and systemic circulation remains poorly understood. This knowledge gap is critically important to bridge for understanding the pathophysiology of CAA and accelerate development of targeted therapeutics. The authors of this review recently converged their diverse expertise in the field of perivascular physiology to specifically address this problem within the framework of a Leducq Foundation Transatlantic Network of Excellence on Brain Clearance. This review discusses the overarching goal of the consortium and explores the evidence supporting or refuting the role of impaired perivascular clearance in the pathophysiology of CAA with a focus on translating observations from rodents to humans. We also discuss the anatomical features of perivascular channels as well as the biophysical characteristics of fluid and solute transport.

Intra-tumoral heterogeneity assessment of the extracellular bone matrix and immune microenvironment in osteosarcoma using digital imaging to predict therapeutic response.

The assessment of chemotherapy response in osteosarcoma (OS), based on the average percentage of viable cells, is limited as it overlooks the spatial heterogeneity of tumor cell response (foci of resistant cells), immune microenvironment and bone microarchitecture. Despite the resulting positive classification for response to chemotherapy, some patients experience early metastatic recurrence, demonstrating that our conventional tools for evaluating treatment response are insufficient. We studied the interactions between tumor cells, immune cells (lymphocytes, histiocytes, osteoclasts), and bone extracellular matrix (ECM) in 18 surgical resection samples of osteosarcoma using multiplex and conventional immunohistochemistry (CD8, CD163, CD68, SATB2), combined with multi-scale characterization approaches in territories of good and poor response (GRT/PRT) to treatment. GRT and PRT were defined as subregions with <10% and ≥10% of viable tumor cells, respectively. Local correlations between bone ECM porosity and density of immune cells were assessed in these territories. Immune cell density was then correlated to overall patient survival. Two patterns were identified for histiocytes and osteoclasts. In poor responder (PR) patients, CD68 osteoclast density exceeded that of CD163 histiocytes, but was not related to bone ECM load. Conversely, in good responder (GR) patients, CD163 histiocytes were more numerous than CD68 osteoclasts. For both of them, a significant negative local correlation with bone ECM porosity was found (p<0,01). Moreover, in PRT, multinucleated osteoclasts were rounded and intermingled with tumor cells, whereas in GRT they were elongated and found in close contact with bone trabeculae. CD8 levels were always low in metastatic patients and those initially considered as GR but rapidly died from their disease. The specific recruitment of histiocytes and osteoclasts within the bone ECM, and the level of CD8 represent new features of osteosarcoma response to treatment. The associated prognostic signatures should be integrated into the therapeutic stratification algorithm of patients, after surgery.

Influence of storage and buffer composition on the mechanical behavior of flowing red blood cells.

On-chip study of blood flow has emerged as a powerful tool to assess the contribution of each component of blood to its overall function. Blood has indeed many functions, from gas and nutrient transport to immune response and thermal regulation. Red blood cells play a central role therein, in particular through their specific mechanical properties, which directly influence pressure regulation, oxygen perfusion, or platelet and white cell segregation toward endothelial walls. As the bloom of in-vitro studies has led to the apparition of various storage and sample preparation protocols, we address the question of the robustness of the results involving cell mechanical behavior against this diversity. The effects of three conservation media (EDTA, citrate, and glucose-albumin-sodium-phosphate) and storage time on the red blood cell mechanical behavior are assessed under different flow conditions: cell deformability by ektacytometry, shape recovery of cells flowing out of a microfluidic constriction, and cell-flipping dynamics under shear flow. The impact of buffer solutions (phosphate-buffered saline and density-matched suspension using iodixanol/Optiprep) are also studied by investigating individual cell-flipping dynamics, relative viscosity of cell suspensions, and cell structuration under Poiseuille flow. Our results reveal that storing blood samples up to 7 days after withdrawal and suspending them in adequate density-matched buffer solutions has, in most experiments, a moderate effect on the overall mechanical response, with a possible rapid evolution in the first 3 days after sample collection.

A few upstream bifurcations drive the spatial distribution of red blood cells in model microfluidic networks.

The physics of blood flow in small vessel networks is dominated by the interactions between Red Blood Cells (RBCs), plasma and blood vessel walls. The resulting couplings between the microvessel network architecture and the heterogeneous distribution of RBCs at network-scale are still poorly understood. The main goal of this paper is to elucidate how a local effect, such as RBC partitioning at individual bifurcations, interacts with the global structure of the flow field to induce specific preferential locations of RBCs in model microfluidic networks. First, using experimental results, we demonstrate that persistent perturbations to the established hematocrit profile after diverging bifurcations may bias RBC partitioning at the next bifurcations. By performing a sensitivity analysis based upon network models of RBC flow, we show that these perturbations may propagate from bifurcation to bifurcation, leading to an outsized impact of a few crucial upstream bifurcations on the distribution of RBCs at network-scale. Based on measured hematocrit profiles, we further construct a modified RBC partitioning model that accounts for the incomplete relaxation of RBCs at these bifurcations. This model allows us to explain how the flow field results in a single pattern of RBC preferential location in some networks, while it leads to the emergence of two different patterns of RBC preferential location in others. Our findings have important implications in understanding and modeling blood flow in physiological and pathological conditions.

Nephrocalcinosis in very low birth weight infants: incidence, associated factors, and natural course.

BACKGROUND: Preterm kidney is exposed to various exogenous factors that may impact its function such as nephrotoxic drugs or nephrocalcinosis. We investigated prevalence and risk factors of nephrocalcinosis (NC) in recently born very low birth weight (VLBW) infants submitted to improved biological monitoring. METHODS: Retrospective, case-control study in very preterm infants (< 32 + 6 weeks, ≤ 1500 g) admitted to a tertiary care unit during a 6-year period. Each case (ultrasound-diagnosed NC) was matched with two controls (no NC). Data were collected at days 15 and 30 of life and 35 weeks corrected age, with follow-up at 18 months and 3 years. RESULTS: Of 525 eligible infants, overall prevalence of NC was 17.1% at 35 weeks corrected age. Prevalence was halved between 2012 (26.1%) and 2017 (11.8%). We included 265 infants, more than half being born before 28 weeks. Cases presented with more severe morbidity than controls, but reached statistical significance only in infants born < 28 weeks (88.2% vs. 68.3%, P = 0.01). Protein, energy, calcium, phosphorus, and vitamin D intakes were similar in the two groups and did not change significantly over the study period. Weight gain was similar in the two groups. Exposure to furosemide (OR [IC95%]: 1.26 [1.02; 1.57]) and postnatal growth (1.65 [1.04; 2.67]) were independent risk factors of NC. NC resolved 12-18 months after diagnosis in 61% of infants. CONCLUSION: Prevalence of NC is significant but can be reduced. Furosemide should be cautiously prescribed in VLBW infants, and nutritional support must be well monitored to support postnatal growth and limit risk of nephrocalcinosis. TRIAL REGISTRATION: ClinicalTrials.gov: NCT 04,860,583. A higher resolution version of the Graphical abstract is available as Supplementary information.

Bernoulli's Principle Applied to Brain Fluids: Intracranial Pressure Does Not Drive Cerebral Perfusion or CSF Flow.

In line with the first law of thermodynamics, Bernoulli's principle states that the total energy in a fluid is the same at all points. We applied Bernoulli's principle to understand the relationship between intracranial pressure (ICP) and intracranial fluids. We analyzed simple fluid physics along a tube to describe the interplay between pressure and velocity. Bernoulli's equation demonstrates that a fluid does not flow along a gradient of pressure or velocity; a fluid flows along a gradient of energy from a high-energy region to a low-energy region. A fluid can even flow against a pressure gradient or a velocity gradient. Pressure and velocity represent part of the total energy. Cerebral blood perfusion is not driven by pressure but by energy: the blood flows from high-energy to lower-energy regions. Hydrocephalus is related to increased cerebrospinal fluid (CSF) resistance (i.e., energy transfer) at various points. Identification of the energy transfer within the CSF circuit is important in understanding and treating CSF-related disorders. Bernoulli's principle is not an abstract concept far from clinical practice. We should be aware that pressure is easy to measure, but it does not induce resumption of fluid flow. Even at the bedside, energy is the key to understanding ICP and fluid dynamics.

Tortuosity and other vessel attributes for arterioles and venules of the human cerebral cortex.

Despite its demonstrated potential in the diagnosis and/or staging of disease, especially in oncology, tortuosity has not received a formal and unambiguous clinical definition yet. Using idealized three-dimensional vessel models (wavy helices) with known characteristics, we first demonstrate that, among various possible tortuosity indices, the standard deviation of the curvature Ksd best satisfies i) scale invariance and ii) positive monotonic response with respect to the amplitude and frequency of vessel oscillations. Ksd can thus be considered as a robust measure of tortuosity. On the contrary, indices previously considered as tortuosity metrics, such as the distance factor metrics (DFM), are highly scale dependent and inappropriate for that purpose. The tortuosity and other vessel attributes (curvature, length-to-diameter ratio (LDR),…) of more than 15,000 cortical vessels are subsequently studied, establishing their statistical properties as a function of the vessel nature (arterioles versus venules) or topological order (hierarchical position). In particular, arterioles have a higher LDR than venules, but the two kinds of vessels have the same mean curvature and tortuosity. Moreover, the lower the order of the vessels, i.e. the nearer to the capillary network, the more curved and tortuous they are. These results provide an essential reference both for diagnosis and for a future large reconstruction of the cerebral microvascular network.

Kinetic modeling in the context of cerebral blood flow quantification by H2(15)O positron emission tomography: the meaning of the permeability coefficient in Renkin-Crone׳s model revisited at capillary scale.

One the one hand, capillary permeability to water is a well-defined concept in microvascular physiology, and linearly relates the net convective or diffusive mass fluxes (by unit area) to the differences in pressure or concentration, respectively, that drive them through the vessel wall. On the other hand, the permeability coefficient is a central parameter introduced when modeling diffusible tracers transfer from blood vessels to tissue in the framework of compartmental models, in such a way that it is implicitly considered as being identical to the capillary permeability. Despite their simplifying assumptions, such models are at the basis of blood flow quantification by H2(15)O Positron Emission Tomgraphy. In the present paper, we use fluid dynamic modeling to compute the transfers of H2(15)O between the blood and brain parenchyma at capillary scale. The analysis of the so-obtained kinetic data by the Renkin-Crone model, the archetypal compartmental model, demonstrates that, in this framework, the permeability coefficient is highly dependent on both flow rate and capillary radius, contrarily to the central hypothesis of the model which states that it is a physiological constant. Thus, the permeability coefficient in Renkin-Crone׳s model is not conceptually identical to the physiologic permeability as implicitly stated in the model. If a permeability coefficient is nevertheless arbitrarily chosen in the computed range, the flow rate determined by the Renkin-Crone model can take highly inaccurate quantitative values. The reasons for this failure of compartmental approaches in the framework of brain blood flow quantification are discussed, highlighting the need for a novel approach enabling to fully exploit the wealth of information available from PET data.

Short-term femoral catheter insertion: a promising alternative to consistently allow long-term erythrocytapheresis therapy in children with sickle cell anemia.

Erythrocytapheresis procedures, increasingly used in the management of patients with severe complications of sickle cell disease, are limited by adequate venous access. We have successfully used short-term femoral catheter insertion, during a 6.5-year period for a total of 443 procedures, to perform long-term erythrocytapheresis in 18 consecutive children with sickle cell disease.

Velocimetry of red blood cells in microvessels by the dual-slit method: effect of velocity gradients.

The dual-slit is a photometric technique used for the measurement of red blood cell (RBC) velocity in microvessels. Two photometric windows (slits) are positioned along the vessel. Because the light is modulated by the RBCs flowing through the microvessel, a time dependent signal is captured for each window. A time delay between the two signals is obtained by temporal cross correlation, and is used to deduce a velocity, knowing the distance between the two slits. Despite its wide use in the field of microvascular research, the velocity actually measured by this technique has not yet been unambiguously related to a relevant velocity scale of the flow (e.g. mean or maximal velocity) or to the blood flow rate. This is due to a lack of fundamental understanding of the measurement and also because such a relationship is crucially dependent on the non-uniform velocity distribution of RBCs in the direction parallel to the light beam, which is generally unknown. The aim of the present work is to clarify the physical significance of the velocity measured by the dual-slit technique. For that purpose, dual-slit measurements were performed on computer-generated image sequences of RBCs flowing in microvessels, which allowed all the parameters related to this technique to be precisely controlled. A parametric study determined the range of optimal parameters for the implementation of the dual-slit technique. In this range, it was shown that, whatever the parameters governing the flow, the measured velocity was the maximal RBC velocity found in the direction parallel to the light beam. This finding was then verified by working with image sequences of flowing RBCs acquired in PDMS micro-systems in vitro. Besides confirming the results and physical understanding gained from the study with computer generated images, this in vitro study showed that the profile of RBC maximal velocity across the channel was blunter than a parabolic profile, and exhibited a non-zero sliding velocity at the channel walls. Overall, the present work demonstrates the robustness and high accuracy of the optimized dual-slit technique in various flow conditions, especially at high hematocrit, and discusses its potential for applications in vivo.

Association Between Homocysteine, Frailty and Biomechanical Response of the CNS in NPH-Suspected Patients.

Frailty is a geriatric syndrome that combines physiological decline, disruptions of homeostatic mechanisms across multiple physiologic systems and thus, strong vulnerability to further pathological stress. Previously, we provided the first evidence that increased risk of poor health outcomes, as quantified by a frailty index (FI), is associated with an alteration of the central nervous system (CNS) biomechanical response to blood pulsatility. In this study, we explored correlation between 14 biological parameters, the CNS elastance coefficient and FI. We included 60 adults (52-92 years) suspected of normal pressure hydrocephalus and presenting with markers of multiple coexisting brain pathologies, including Parkinson disease, Alzheimer disease, and vascular dementia. We showed that the homocysteine (Hcy) level was independently and positively associated with both the FI and the CNS elastance coefficient (adjusted R² of 10% and 6%). We also demonstrated that creatinine clearance and folate level were independently associated with Hcy level. Based on previous literature results describing the involvement of Hcy in endothelial dysfunction, glial activation, and neurodegeneration, we discuss how Hcy could contribute to the altered biomechanical response of the CNS and frailty.

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-ß, 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.

Fractal analysis of vascular networks: insights from morphogenesis.

Considering their extremely complicated and hierarchical structure, a long standing question in vascular physio-pathology is how to characterize blood vessels patterns, including which parameters to use. Another question is how to define a pertinent taxonomy, with applications to normal development and to diagnosis and/or staging of diseases. To address these issues, fractal analysis has been applied by previous investigators to a large variety of healthy or pathologic vascular networks whose fractal dimensions have been sought. A review of the results obtained on healthy vascular networks first shows that no consensus has emerged about whether normal networks must be considered as fractals or not. Based on a review of previous theoretical work on vascular morphogenesis, we argue that these divergences are the signature of a two-step morphogenesis process, where vascular networks form via progressive penetration of arterial and venous quasi-fractal arborescences into a pre-existing homogeneous capillary mesh. Adopting this perspective, we study the multi-scale behavior of generic patterns (model structures constructed as the superposition of homogeneous meshes and quasi-fractal trees) and of healthy intracortical networks in order to determine the artifactual and true components of their multi-scale behavior. We demonstrate that, at least in the brain, healthy vascular structures are a superposition of two components: at low scale, a mesh-like capillary component which becomes homogeneous and space-filling over a cut-off length of order of its characteristic length; at larger scale, quasi-fractal branched (tree-like) structures. Such complex structures are consistent with all previous studies on the multi-scale behavior of vascular structures at different scales, resolving the apparent contradiction about their fractal nature. Consequences regarding the way fractal analysis of vascular networks should be conducted to provide meaningful results are presented. Finally, consequences for vascular morphogenesis or hemodynamics are discussed, as well as implications in case of pathological conditions, such as cancer.

Scaling laws for branching vessels of human cerebral cortex.

OBJECTIVE: Vascular architecture, particularly of cerebral microvessels, has profound implications for both health and disease in a variety of areas, such as neuroimaging, angiogenesis and development, Alzheimer's disease, and vascular tumors. We analyzed the architecture of tree-like vessels of the human cerebral cortex. METHODS: Digital three-dimensional images of the microvascular network were obtained from thick sections of India ink-injected human brain by confocal laser microscopy covering a large zone of secondary cortex. A novel segmentation method was used to extract the skeleton and measure the diameter at every vertex. RESULTS: In this paper, we focus on the topology of the cortical tree-like vessels. Using stem-crown decomposition, power-scaling laws were shown to govern the relationships between integrated parameters, such as the distal cumulative length, volume, or normalized flow. This led us toward an experimental confirmation of the allometric equation between mass and metabolic rate. Inversely, the power-law model did not match the relationships between local parameters, such as diameter, and integrated ones. As a consequence, Murray's law did not appropriately model the architecture of cerebrovascular bifurcations. CONCLUSIONS: This study provides a unique, large database and mathematical characterization that may prove valuable for modeling the cerebral.

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.

Neutrophil adhesion in brain capillaries reduces cortical blood flow and impairs memory function in Alzheimer's disease mouse models.

Cerebral blood flow (CBF) reductions in Alzheimer's disease patients and related mouse models have been recognized for decades, but the underlying mechanisms and resulting consequences for Alzheimer's disease pathogenesis remain poorly understood. In APP/PS1 and 5xFAD mice we found that an increased number of cortical capillaries had stalled blood flow as compared to in wild-type animals, largely due to neutrophils that had adhered in capillary segments and blocked blood flow. Administration of antibodies against the neutrophil marker Ly6G reduced the number of stalled capillaries, leading to both an immediate increase in CBF and rapidly improved performance in spatial and working memory tasks. This study identified a previously uncharacterized cellular mechanism that explains the majority of the CBF reduction seen in two mouse models of Alzheimer's disease and demonstrated that improving CBF rapidly enhanced short-term memory function. Restoring cerebral perfusion by preventing neutrophil adhesion may provide a strategy for improving cognition in Alzheimer's disease patients.

During vertebrate development, arteries exert a morphological control over the venous pattern through physical factors.

The adult vasculature is comprised of three distinct compartments: the arteries, which carry blood away from the heart and display a divergent flow pattern; the capillaries, where oxygen and nutrient delivery from blood to tissues, as well as metabolic waste removal, occurs; and the veins, which carry blood back to the heart and are characterized by a convergent flow pattern. These compartments are organized in series as regard to flow, which proceeds from the upstream arteries to the downstream veins through the capillaries. However, the spatial organization is more complex, as veins may often be found paralleling the arteries. The factors that control the morphogenesis of this hierarchically branched vascular network are not well characterized. Here, we explain how arteries exert a morphological control on the venous pattern. Indeed, during vertebrate development, the following transition may be observed in the spatial organization of the vascular system: veins first develop in series with the arteries, the arterial and venous territories being clearly distinct in space (cis-cis configuration). But after some time, new veins grow parallel to the existing arteries, and the arterial and venous territories become overlapped, with extensive and complex intercalation and interdigitation. Using physical arguments, backed up by experimental evidence (biological data from the literature and in situ optical and mechanical measurements of the chick embryo yolk-sac and midbrain developing vasculatures), we explain how such a transition is possible and why it may be expected with generality, as organisms grow. The origin of this transition lies in the remodeling of the capillary tissue in the vicinity of the growing arteries. This remodeling lays down a prepattern for further venous growth, parallel to the existing arterial pattern. Accounting for the influence of tissue growth, we show that this prepatterned path becomes favored as the body extends. As a consequence, a second flow route with veins paralleling the arteries (cis-trans configuration) emerges when the tissue extends. Between the cis-cis and cis-trans configurations, all configurations are in principle possible, and self-organization of the vessels contributes to determining their exact pattern. However, the global aspect depends on the size at which the growth stops and on the growth rate.

Multiscale modelling of blood flow in cerebral microcirculation: Details at capillary scale control accuracy at the level of the cortex.

Aging or cerebral diseases may induce architectural modifications in human brain microvascular networks, such as capillary rarefaction. Such modifications limit blood and oxygen supply to the cortex, possibly resulting in energy failure and neuronal death. Modelling is key in understanding how these architectural modifications affect blood flow and mass transfers in such complex networks. However, the huge number of vessels in the human brain-tens of billions-prevents any modelling approach with an explicit architectural representation down to the scale of the capillaries. Here, we introduce a hybrid approach to model blood flow at larger scale in the brain microcirculation, based on its multiscale architecture. The capillary bed, which is a space-filling network, is treated as a porous medium and modelled using a homogenized continuum approach. The larger arteriolar and venular trees, which cannot be homogenized because of their fractal-like nature, are treated as a network of interconnected tubes with a detailed representation of their spatial organization. The main contribution of this work is to devise a proper coupling model at the interface between these two components. This model is based on analytical approximations of the pressure field that capture the strong pressure gradients building up in the capillaries connected to arterioles or venules. We evaluate the accuracy of this model for both very simple architectures with one arteriole and/or one venule and for more complex ones, with anatomically realistic tree-like vessels displaying a large number of coupling sites. We show that the hybrid model is very accurate in describing blood flow at large scales and further yields a significant computational gain by comparison with a classical network approach. It is therefore an important step towards large scale simulations of cerebral blood flow and lays the groundwork for introducing additional levels of complexity in the future.