Francis Cassot

A Novel Three-Dimensional Computer-Assisted Method for a Quantitative Study of Microvascular Networks of the Human Cerebral Cortex

Objective: Detailed information on microvascular network anatomy is a requirement for understanding several aspects of microcirculation, including oxygen transport, distributions of pressure, and wall shear stress in microvessels, regulation of blood flow, and interpretation of hemodynamically based functional imaging methods, but very few quantitative data on the human brain microcirculation are available. The main objective of this study is to propose a new method to analyze this microcirculation.

Morphometry of the human cerebral cortex microcirculation: General characteristics and space-related profiles

Studies on human brain microcirculation have thus far yielded few quantitative data, preventing the closest possible interpretation of functional imaging methods such as fMRI and PET that necessarily rely on robustly delineated morphology of haemodynamic systems. Inadequate data in this area can lead to severe underestimation of the spatial specificity of the BOLD response. We took thick sections of Indian ink injected human brain and, using confocal laser microscopy and a novel three-dimensional computer-assisted method we extracted and analyzed hundreds of thousands of vascular segments within a large area of cortex. From this database the global densities, the statistical distributions of diameters and lengths were analysed, separating the tree-like and the net-like parts of the microcirculation. Furthermore, our analysis included variations in volume density along the cortical depth and along vectors parallel to the cortical surface. These morphometric parameters are all key requirements for a sound model of cerebral microcirculation.

Effects of Anterior Communicating Artery Diameter on Cerebral Hemodynamics in Internal Carotid Artery Disease A Model Study

BACKGROUND Collateral circulatory pathways are considered the primary determinant of cerebral hemodynamics in patients with obstructive lesions of the internal carotid arteries (ICaAs). However, the hemodynamic effects of the diameter of the anterior communicating artery (ACoA) have never been assessed quantitatively in humans. METHODS AND RESULTS Two different mathematical models were used to simulate changes affecting blood pressures and flows in cerebral arteries as a function of ACoA diameter and ICaA stenoses or occlusions. Small changes in ACoA diameter were found to have marked hemodynamic effects when they occurred within the range of 0.4 to 1.6 mm, a situation observed in 80% of the cases. Outside this range, changes in ACoA diameter had no effect. Simulated pressure drops through a stenotic ICaA were consistent with those observed. They were found to depend on the degrees of the stenoses in both ICaAs and on ACoA diameter according to a simple equation. Pressure reserve in the middle and anterior cerebral arteries decreased to below the lower limit of autoregulation, despite a normal mean arterial blood pressure, when the arteries were distal to a unique 70% ICaA stenosis associated with a small-diameter ACoA or to a 50% ICaA stenosis associated with a contralateral ICaA occlusion and a large-diameter ACoA. Above these thresholds, the circle of Willis allowed for an almost complete global cerebral blood flow compensation that involved all the afferent and communicating vessels. CONCLUSIONS ACoA diameter strongly modulates the effects of ICaA lesions on cerebral hemodynamics. Some proposals for endarterectomy indications can be derived from our study.

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.

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.

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, in press), 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 flow is in close agreement with Grubbs 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 flow changes, 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.

Branching patterns for arterioles and venules of the human cerebral cortex

Branching patterns of microvascular networks influence vascular resistance and allow control of peripheral flow distribution. The aim of this paper was to analyze these branching patterns in human cerebral cortex. 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 skeletons of 228 vascular trees (152 arterioles and 76 venules) and measure the diameter at every vertex. The branching patterns (area ratios and angles of bifurcations) of nearly 10,000 bifurcations of cortical vascular trees were analyzed, establishing their statistical properties and structural variations as a function of the vessel nature (arterioles versus venules), the parent vessel topological order or the bifurcation type. We also describe their connectivity and discuss the relevance of the assumed optimal design of vascular branching to account for the complex nature of microvascular architecture. The functional implications of some of these structural variations are considered. The branching patterns established from a large database of a human organ contributes to a better understanding of the bifurcation design and provides an essential reference both for diagnosis and for a future large reconstruction of cerebral microvascular network.

Maximal Wall Shear Stress in Arterial Stenoses: Application to the Internal Carotid Arteries

Maximal wall shear stress (MWSS) in the convergent part of a stenosis is calculated by the interactive boundary-layer theory. A dimensional analysis of the problem shows that MWSS depends only on a few measurable parameters. A simple relationship between MWSS and these parameters is obtained, validated, and used to calculate the magnitude of MWSS in a carotid stenosis, as a function of the patency of the circle of Willis and the stenotic pattern. This demonstrates the huge effect of collateral pathways. Elevated MWSS are observed even in moderate stenoses, provided they are associated with a contralateral occlusion, a large anterior, and narrow posterior communicating arteries, suggesting a potential risk of embolus release in this configuration.

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.

Clinical applicability of a mathematical model in assessing the functional ability of the communicating arteries of the circle of Willis

BACKGROUND The brain collateral blood supply, which is essential in patients suffering from significant stenoses or occlusions of the extracranial arteries, remains difficult to assess accurately in practice. We compared data obtained from transcranial color-coded duplex sonography (TCCD) combined with carotid compression tests to morphometric autopsy data and to results given by a mathematical model of the cerebral macrocirculation. METHODS AND RESULTS In 16 moribund patients, anterior and posterior communicating arteries of the circle of Willis were divided into functional and non-functional based on the results of the TCCD combined with carotid compression tests. After death of the patients diameters and lengths of the main intracranial arteries were measured at autopsy and these values were treated with a mathematical model for calculating blood flow and blood pressure in all the segments of the arterial network. The diameters and the blood flows through the communicating arteries were found to be significantly higher in the group of functional arteries than in that of non-functional ones. However, blood flow was also shown to be dependent on other parameters such as the pressure difference between the two ends of the vessel. CONCLUSION Our data indicate that functional ability of the Willisian collaterals depends on morphological and functional parameters, and is therefore better assessed by a functional method, such as TCCD, than by a solely morphological one, such as cerebral angiography. Mathematically based circulation modeling, when it will be possible, could be a more comprehensive tool for delineating patients at a higher risk for hemodynamic cerebrovascular insufficiency.