Research ReportBranching patterns for arterioles and venules of the human cerebral cortex
Introduction
Vascular architecture, particularly of cerebral microvessels, has profound implications for both health and disease. Indeed, providing accurate and comprehensive measurements of vascular morphology is an essential step in the analysis of vascular formation as well as of the structural adaptation of microcirculation under physiological (development, growth and exercise) or pathophysiological conditions (inflammation, hypertension, diabetes, obesity and metabolic syndrome) (Jonk et al., 2007, Levy et al., 2008, Murfee and Schmid-Schonbein, 2008, Patton et al., 2005, Pries et al., 2005, Wiernsperger et al., 2007). More generally, “almost every disease from cancer to the common cold affects blood vessel attributes (vessel number, radius, tortuosity, and branching pattern)” (Bullitt et al., 2005a).Vascular alterations associated with pathology have gained increased attention (Lu et al., 2004) and pathological angiogenesis is now recognized as a hallmark of disease (Carmeliet and Jain, 2000, Carmeliet, 2005, Fukumura and Jain, 2008). Furthermore, the cerebral microcirculation is linked to a number of areas in neuropathology including neurological disease such as Alzheimer's (Meyer et al., 2008), vascular occlusions in cerebro-vascular disease (Nishimura et al., 2007), blood vessel morphologic changes during development and treatment of brain tumors (Baish et al., 1996, Baish and Jain, 2000, Bullitt et al., 2005b, Bullitt et al., 2007, Jain, 2005).
The analysis of these states using functional neuroimaging clearly also requires a sound, underpinning knowledge of both the macro- and microcirculations. In functional magnetic resonance imaging (fMRI), the usefulness of the blood oxygen level dependent (BOLD) technique as a surrogate signal strongly depends on an understanding of neurovascular coupling and the underlying vascular architecture (Goense et al., 2007, Vanzetta, 2006). One established group in this field concluded recently that “tomographic assessments of the vasculature in large cortical fields of view are necessary to obtain the three-dimensional topology of the vascular network, using the currently available methods” (Weber et al., 2008).
Thus, the morphological, topological and functional study of cerebral microcirculation is a topic of growing interest to both vascular physiologists and neuroradiologists (Cassot et al., 2006, Heinzer et al., 2008, Lauwers et al., 2008, Risser et al., 2007, Weber et al., 2008).
Our group recently developed a 3D computer-assisted method for microvascular cerebral network analysis and gathered a quantitative data library on the architecture of the microcirculation of the human cerebral cortex (Cassot et al., 2006). In particular, this large database was analyzed statistically to assess the general morphometric and topological characteristics of the arteriolar, venular and capillary cortical networks, as well as the variations of microvascular density as a function of cortical depth (Lauwers et al., 2008). Moreover, an analysis of the branching vessels of these networks showed that there were scaling laws governing the relationships between cumulative length, cumulative volume and the flow through these vessels(Cassot et al., 2009), giving further evidence of their fractal nature and experimental support for allometric equations (West and Brown, 2005).
In this paper, we subject the data to further analysis with emphasis on properties of bifurcations, specifically area ratios, branching angles and junction exponents. Indeed, anatomists or clinicians focused on the local geometrical properties either of bifurcations, such as optimality deviance (Tapp et al., 2007, Witt et al., 2006), or of the vascular segments themselves, such as tortuosity, and showed their clinical interest. However, most of these previous studies have been rather qualitative, or even subjective, and based on a relatively small number of measurements of the vessel attributes under consideration. Moreover, many of these analyses were derived from 2D measurements, the inadequacy of which has been demonstrated by subsequent 3D data (O'Flynn et al., 2007). Ultimately, little is known about the statistical properties of vessel attributes or branching patterns. In particular, it is unclear whether vessel attributes fit a Gaussian distribution and how dependent upon anatomical location these values might be (Bullitt et al., 2005a). In spite of recent attempts to define better indices to represent the attribute values of a vessel population, which could be quantified automatically and lead to robust characterization, and advances in our understanding of vascular architecture (Heinzer et al., 2008), work is still necessary to reach these goals providing answers to key clinical questions. Revealing “signatures” of normal vascular trees would provide a rationale for diagnosis purpose and would therefore be of value.
Besides this clinical interest, the study of these local properties has also important functional implications as demonstrated in a recent paper of Kassab's group (Kaimovitz et al., 2008), for coronary network, and that we will discuss further in this paper, for brain microvascular network. Actually, phase separation effect, a local phenomena governed by the branching pattern, induces a first coupling between architecture and hemodynamics. Moreover, structural adaptation of the microcirculation as well as the vessels growth process are governed, among other things, by the spatial distribution of pressure throughout the whole microvascular network, which is inherently nonlocal; i.e., the pressure at a given point in space is influenced not only by the pressure distribution in its immediate neighborhood but more globally by the pressure distribution in the entire network. Thus, all the details of the vascular geometry, including the capillary net, the arterial, and venous trees, need to be considered in order to analyze the flow field, particularly the wall shear-stress distribution, in the organ. Finally, this local characterization is important for the future construction of a realistic hemodynamic network model.
Thus, in this paper, we focus on the branching patterns (area ratios and angles of bifurcations) of cortical vascular trees, establishing their statistical properties as a function of the vessel nature (arterioles versus venules), of their taxonomy (based on the parent vessel hierarchical position) or of their type. We also describe their connectivity and discuss whether the assumed optimal design of vascular branching can account for the complex reality of microvascular architecture.
Section snippets
General data on extracted vascular trees
In this first section of the results, we present the global statistics for the morphometric data under consideration. Two hundred twenty-eight vascular arborescences were extracted from 10 mosaics covering a surface of approximately 1.5 cm2 and encompassing a cerebral tissue volume of 28.6 mm3. They were divided into 152 arterial and 76 venous trees according to their morphological features. Fig. 1 displays some examples of these arborescences. These vessels were segmented in 7604 arterial
Discussion
Areas where knowledge of microvascular architecture plays an important role are numerous and varied, with burgeoning interest in morphometric and topological parameters such as microvascular density, fractal dimension and extravascular distance. In a previous paper (Lauwers et al., 2008), we have outlined the implications for neuroimaging techniques of the varying microvascular density along the cortical layers. Among the many fields where our methods and the results obtained from them might
Creation of a microvascular network database of the human cerebral cortex
The procedures used for image acquisition, mosaic construction and vessels segmentation have been described in detail elsewhere (Cassot et al., 2006) and are outlined briefly below.
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