Insights from numerical simulations of brain blood flow regulation in large anatomical networks

Blood micro-circulation plays a central role in the local adaptation of cerebral blood flow to neural activity (neuro-vascular coupling). A growing body of evidence indicates that neurons, glia, and cerebral blood vessels, acting as an integrated unit, have a crucial role in mediating the activation-induced changes in blood flow. In particular, the smooth muscle cells surrounding the arterioles, and possibly pericytes, at capillary level, convert the bio-chemical signals that originate from this integrated unit into changes in vascular diameter, thus regulating blood flow by modulating vascular resistance [1]. However, the relative role of arterioles and capillaries in the control of cerebral blood flow is still controversial [1]. In particular, it is at present not clear whether the capillary dilatation experimentally observed in vivo by several groups is a passive consequence of upstream arteriolar dilatation via an alteration in perfusion pressure or the result of an active regulation of the capillary diameter via contraction/relaxation of pericytes [1]. Answering this question is of importance in the context of functional neuroimaging. The spatial resolution and specificity of hemodynamically based functional imaging techniques (including fMRI and PET) are indeed bound to the density and localization of the blood flow regulating structures [2]. However, using experimental means for that purpose is extremely challenging. For example, the penetration depth of the most recent intravital two-photon microscopy techniques (typically ~500 μm) does neither allow to investigate the cortical layers of highest capillary density, which are located approximately in the middle third of the cortex [3] nor those where the fastest capillary dilation occurs [4]. By contrast, several authors [1,5] have pointed out that modelling using anatomically accurate representations of the intracortical vascular network allows a better and more quantitative understanding of cerebral blood flow control. In particular, such an approach can be valuable for generating predictions as to the likely impact of pericyte-mediated capillary diameter regulation [1]. Our group has recently performed the first numerical simulations of blood flow in an anatomically accurate large human intra-cortical vascular network (~ 10000 segments), using a 1D non-linear model taking into account the complex rheological properties of blood flow in microcirculation (i.e. Fahraeus, Fahraeus-Lindquist and phase separation effects) [6]. This model predicts blood pressure, blood flow and hematocrit distributions, volumes of functional vascular territories, regional flow at local, voxel and network scales, etc. Using this approach, we have studied the flow re-organizations induced by arteriolar vasodilations, highlighting the hemodynamic component of various functional neuroimaging techniques [7]. In the present paper, the variations in cerebral blood flow induced by global or localized capillary vasodilations are studied and compared to these previous results, demonstrating that pericyte-mediated regulation of blood flow at capillary level would be efficient for neuro-vascular coupling. By contrast to a regulation situated at the level of arterioles [7], the changes in blood volume can be highly localized in space, with the potential to be as close as possible of areas of neuronal activation. However, the changes in blood flow are much more diffuse. This imposes limits on the ultimate spatial resolution of hemodynamically based brain functional imaging techniques, whatever the localization of the blood flow regulating structures

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

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

Modélisation de la microcirculation sanguine cérébrale : Etat de l'art et perspectives

La microcirculation cérébrale joue un rôle central dans le fonctionnement cérébral, non seulement en alimentant les neurones en oxygène et nutriments, mais aussi en régulant le débit sanguin en fonction de l'activité neuronale. Ce couplage entre activité neuronale et hémodynamique est à la base des techniques d'imagerie fonctionnelles cérébrales, dites hémodynamiques, telle que l'Imagerie par Résonance Magnétique fonctionnelle et la Tomographie à Emission de Positons. La compréhension des relations structure/fonction dans la microcirculation sanguine cérébrale est donc un enjeu majeur à la fois pour la prédiction des conséquences d'anomalies vasculaires (occlusions, dégénérescence des vaisseaux…) et le développement d'outils quantitatifs de diagnostic/suivi des pathologies associées à ces anomalies. Dans ce contexte, les approches de modélisation jouent un rôle croissant. Au niveau international, plusieurs équipes ont, dans la dernière décennie, acquis des bases de données anatomiques permettant de segmenter, dans de larges volumes (~ 1 à 10 mm3) et avec une très grande résolution spatiale (<10 μm), l'ensemble des vaisseaux du cortex cérébral. Mais, à notre connaissance, une seule dispose de données acquises chez l'homme (INSERM U825). Ces données nous ont permis de montrer, à l'aide d'outils quantitatifs de caractérisation multi-échelle, que le réseau vasculaire cérébral est la superposition de deux types de structures : une structure capillaire maillée, homogène au-dessus d’une longueur de coupure correspondant à la longueur caractéristique des vaisseaux capillaires (~50 μm), et des structures arborescentes fractales, composées des artères et des veines. Cette organisation duale est compatible avec les fonctions de distribution et d'échange de la microcirculation cérébrale. S'appuyant sur ces résultats, les écoulements sanguins et les transferts sont étudiés à différentes échelles à l'aide d'approches inspirées de méthodologies développées pour l'étude d'écoulements multiphasiques ou réactifs en milieux poreux. Ces travaux ouvrent des perspectives intéressantes pour l'étude des conséquences fonctionnelles des anomalies vasculaires observées dans diverses pathologies et pour l'optimisation des outils de diagnostic et des stratégies thérapeutiques associés

Simulation study of brain blood flow regulation by intra-cortical arterioles in an anatomically accurate large human vascular network. Part II: Flow variations induced by global or localized modifications of arteriolar diameters

In a companion paper (Lorthois et al., Neuroimage, inpress),we perform the first simulations of blood flow in an anatomically accurate large human intra-cortical vascular network (~10000 segments), using a 1D non-linear model taking into account the complex rheological properties of blood flow in microcirculation. This model predicts blood pressure, blood flow and hematocrit distributions, volumes of functional vascular territories, regional flow at voxel and network scales, etc. Using the same approach, we study flow reorganizations induced by global arteriolar vasodilations (an isometabolic global increase in cerebral blood flow). For small to moderate global vasodilations, the relationship between changes in volume and changes in flowis in close agreement with Grubb's law, providing a quantitative tool for studying the variations of its exponent with underlying vascular architecture. A significant correlation between blood flow and vascular structure at the voxel scale, practically unchanged with respect to baseline, is demonstrated. Furthermore, the effects of localized arteriolar vasodilations, representative of a local increase in metabolic demand, are analyzed. In particular, localized vasodilations induce flowchanges, including vascular steal, in the neighboring arteriolar trunks at small distances (< 300 μm), while their influence in the neighboring veins is much larger (about 1 mm), which provides an estimate of the vascular point spread function.More generally, for the first time, the hemodynamic component of various functional neuroimaging techniques has been isolated from metabolic and neuronal components, and a direct relationship with several known characteristics of the BOLD signal has been demonstrated

Simulation study of brain blood flow regulation by intra-cortical arterioles in an anatomically accurate large human vascular network : Part I : Methodology and baseline flow

Hemodynamically based functional neuroimaging techniques, such as BOLD fMRI and PET, provide indirect measures of neuronal activity. The quantitative relationship between neuronal activity and the measured signals is not yet precisely known, with uncertainties remaining about the relative contribution by their metabolic and hemodynamic components. Empirical observations have demonstrated the importance of the latter component and suggested that micro-vascular anatomy has a potential influence. The recent development of a 3D computer-assisted method for micro-vascular cerebral network analysis has produced a large quantitative library on the microcirculation of the human cerebral cortex (Cassot et al., 2006), which can be used to investigate the hemodynamic component of brain activation through fluid dynamic modeling. For this purpose, we perform the first simulations of blood flow in an anatomically accurate large human intra-cortical vascular network (~10000 segments), using a 1D non-linear model taking account of the complex rheological properties of blood flow in microcirculation. This model predicts blood pressure, blood flow and hematocrit distributions, as well as volumes of functional vascular territories, and regional flow at voxel and network scales. First, the influence of the prescribed boundary conditions (BCs) on the baseline flow structure is investigated, highlighting relevant lower- and upper-bound BCs. Independent of these BCs, large heterogeneities of baseline flow from vessel to vessel and from voxel to voxel, are demonstrated. These heterogeneities are controlled by the architecture of the intra-cortical vascular network. In particular, a correlation between the blood flow and the proportion of vascular volume occupied by arterioles or venules, at voxel scale, is highlighted. Then, the extent of venous contamination downstream to the sites of neuronal activation is investigated, demonstrating a linear relationship between the catchment surface of the activated area and the diameter of the intra-cortical draining vein

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

Experimental study of fibrin/fibrin-specific molecular interactions using a sphere/plane adhesion model

Fibrin, the biopolymer produced in the final step of the coagulation cascade, is involved in the resistance of arterial thrombi to fragmentation under shearflow. However, the nature and strength of specific interactions between fibrin monomers are unknown. Thus, the shear-induced detachment of spherical monodispersed fibrincoated latex particles in adhesive contact with a plane fibrin-coated glass surface has been experimentally studied, using an especially designed shear stress flow chamber. A complete series of experiments for measuring the shear stress necessary to release individual particles under various conditions (various number of fibrin layers involved in the adhesive contact, absence or presence of plasmin, the main physiological fibrinolytic enzyme) has been performed. The nonspecific DLVO interactions have been shown to be negligible compared to the interactions between fibrin monomers.Asimple adhesion model based on the balance of forces and torque on particles, assuming an elastic behavior of the fibrin polymer bonds, to analyze the experimental data in terms of elastic force at rupture of an elementary intermonomeric fibrin bond has been used. The results suggested that this force (of order 400 pN) is an intrinsic quantity, independent of the number of fibrin layers involved in the adhesive contact

An optimized technique for red blood cells velocity measurement in microvessels

Oxygen and nutrient delivery to living tissues, as well as metabolic waste removal, are essentially determined by the dynamics of blood flow in microvascular networks. In these vessels, measuring the velocity distribution of red blood cells (RBCs) is still challenging. One of the most popular techniques used for that purpose is the Dual-Slit (DS), a temporal correlation technique, first introduced by Wayland and Johnson (1967):the vessel under study is trans-illuminated and two photo-sensors (slits) are positioned, separated by a known distance, Ls, along the vessel axis. The time modulation of light is recorded at both positions. A cross-correlation velocity, Vds=Ls/Td, is obtained, where Td is the time delay for which the cross-correlation between the two signals is maximum. However, RBCs are positioned at different depths within the channel and thus move at different velocities. Baker and Wayland (1974) suggested that Vds is related to a dynamic averaged velocity,but this has never been proved. The aim of this work is to determine the relationship between the measured velocity Vds and the actual velocity scales of the flow. For that purpose, the DS technique is first optimized using sequences of synthetic images representing RBCs flow. By this way, all the parameters characterizing the RBCs flow, including the shape of their velocity profile in the direction parallel to the incident light beam, which is inaccessible to the observer in real experiments, are controlled. The DS is then applied to in vitro RBCs flows in microchannels

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