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.

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.

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.

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.

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.

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.

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. METHODS: From thick sections of india ink-injected human brain, using confocal laser microscopy, the authors developed algorithms adapted to very large data sets to automatically extract and analyze center lines together with diameters of thousands of brain microvessels within a large cortex area. RESULTS: Direct comparison between the original data and the processed vascular skeletons demonstrated the high reliability of this method and its capability to manage a large amount of data, from which morphometry and topology of the cerebral microcirculation could be derived. CONCLUSIONS: Among the many parameters that can be analyzed by this method, the capillary size, the frequency distributions of diameters and lengths, the fractal nature of these networks, and the depth-related density of vessels are all vital features for an adequate model of cerebral microcirculation.

Influence of stent properties on the alteration of cerebral intra-aneurysmal haemodynamics: flow quantification in elastic sidewall aneurysm models.

OBJECTIVES: Stent implantation across the neck of cerebral aneurysms may induce intra-aneurysmal flow reduction, and consequently saccular thrombosis and vessel wall repair. To analyse the influence of different stent parameters on such flow reduction, we studied the flow changes in vascular models, induced by a series of stents. METHODS: Two different neck-sized elastic sidewall aneurysm models were connected to a circulatory loop. Twenty different stents were introduced in both models to analyse the effect of their parameters, such as porosity, filament diameter and permeability. Flow patterns were visualized by using glass particles and laser sheet translumination. The digitally recorded data were transferred for computer analysis. The changes of the vortex velocity for each stent model combination were investigated and statistically evaluated. RESULTS: Intra-aneurysmal flow analysis showed dispersion of the vortices of a variable degree, and velocity reduction of 30% mean in model 1 and 49% mean in model 2. By statistical analysis three groups of stents ('best', 'medium', 'worst') were identified, according to their haemodynamic efficacy. No correlations were observed between the haemodynamic performance of the stents and the porosity, filament diameter and permeability values separately. The stent effects were on average more important in the large-necked than in the small-necked aneurysm model. DISCUSSION: Stent implantation induces intra-aneurysmal loss of vortex coherence and flow reduction. The analysed stent parameters show complex interrelationship, including also stent 'design'. The difference in the haemodynamic efficacy of the individual stents between the two models raises the question of 'stent positioning effects'.

Anatomically shaped internal carotid artery aneurysm in vitro model for flow analysis to evaluate stent effect.

BACKGROUND AND PURPOSE: Stent implantation alone might not be sufficient to produce definitive treatment of cerebral aneurysms. Therefore, extended experimental work is needed to improve results. We show the feasibility of using an in vitro anatomically shaped elastic model for flow evaluation before and after stent implantation. METHODS: Based on human vascular casting, an anatomic elastic internal carotid artery model, including an aneurysm on the supraclinoid portion, was manufactured. The model was connected to a circulatory loop to simulate physiological flow. After visualization of the flow by using glass particles and laser sheet translumination, the digitally recorded data were transferred for computer analysis. Intra-saccular flow pattern changes and the vortex velocity reduction induced by the stent were investigated qualitatively and quantitatively. RESULTS: The distal neck of the aneurysm behaved as a flow divider. Therefore, it was directly exposed to the hemodynamic stress. Inside the sac, a well-defined vortex formed and progressed along the wall toward the proximal neck. After stent implantation this pattern changed significantly; the vortex appeared more dispersed and its residence time increased. The velocity reduction was 32%. Velocity peak was observed close to the distal neck in both cases. CONCLUSION: In vitro anatomic elastic models are feasible for flow evaluation with laser sheet translumination. In our model, stent implantation resulted in hemodynamic changes that might favor the exclusion of the aneurysm from the circulation and can prevent regrowth of the aneurysmal sac.