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      Geometric Characteristics of Arterial Network of Rat Pial Microcirculation


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          Objective: The aim of the study was to assess the geometric characteristics of rat pial microcirculation and describe the vessel bifurcation patterns by ‘connectivity matrix’. Methods: Male Wistar rats were used to visualize pial microcirculation by a fluorescent microscopy technique through an open cranial window, using fluorescein isothiocyanate bound to dextran (molecular weight 70 kDa). The arteriolar network was mapped by stop-frame images. Diameters and lengths of arterioles were measured with a computer-assisted method. Pial arterioles were classified according to a centripetal ordering scheme (Strahler method modified according to diameter) from the smallest order 1 to the largest order 5 arterioles in the preparation. A distinction between arteriolar segments and elements was used to express the series-parallel features of the pial arteriolar networks. A connectivity matrix was used to describe the connection of blood vessels from one order to another. Results: The arterioles were assigned 5 orders of branching by Strahler’s ordering scheme, from order 1 (diameter: 16.0 ± 2.5 µm) to order 5 (62 ± 5.0 µm). Order 1 arterioles gave origin to capillaries, assigned order 0. The diameter, length and branching of the 5 arteriolar orders grew as a geometric sequence with the order number in accordance with Horton’s law. The segments/elements ratio was the highest in order 4 and 3 arterioles, indicating the greatest asymmetry of ramifications. Finally, the branching vessels in the networks were described in details by the connectivity matrix. Fractal dimensions of arteriolar length and diameter were 1.75 and 1.78, respectively. Conclusions: The geometric characteristics of rat pial microcirculation indicate that distribution of vessels is fractal. The connectivity matrix allowed us to describe the number of daughter vessels spreading from parent vessels. This ordering scheme may be useful to describe vessel function, according to diameter, length and branching.

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            Topological structure of rat mesenteric microvessel networks.

            Microvascular lengths, diameters, and flow directions were determined in all vessel segments (n = 1303) between bifurcations in three complete rat mesenteric microvessel networks (25 mm2 each) using intravital video- and photomicroscopy. The classification of vessel segments as arteriolar, venular, or av-segments (all segments connecting the arteriolar to the venular tree) was based on purely topological criteria. The topological structure of the networks was analyzed using the Horton-Strahler technique and a new generation scheme. Generation numbers were assigned to the vessel segments on the basis of the number of upstream (in the arteriolar tree) and downstream (in the venular tree) bifurcations. The mean generation number of the av-segments, a characteristic parameter of the generation scheme, reflects the topological structure of the network more accurately than Horton's branching ratio Rb. Both the arteriolar and venular tree of the mesenteric networks were found to be dichotomous branching structures which were neither strictly symmetric nor strictly asymmetric. The topological information obtained was compared to network models generated by different random branching algorithms. The result of this comparison suggests that the network structure changes at a certain generation level. Distal to this generation level, the mesenteric networks resemble a model network generated by random branching at any segment, while the proximal portion is similar to a model allowing random branching at terminal segments only.
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              Analysis of pig’s coronary arterial blood flow with detailed anatomical data


                Author and article information

                J Vasc Res
                Journal of Vascular Research
                S. Karger AG
                December 2007
                27 September 2007
                : 45
                : 1
                : 69-77
                aDepartment of Physiology and Biochemistry, University of Pisa, Pisa, and bDepartment of Neuroscience, Federico II University Medical School, Naples, Italy
                109078 J Vasc Res 2008;45:69–77
                © 2007 S. Karger AG, Basel

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                Page count
                Figures: 3, Tables: 6, References: 25, Pages: 9
                Research Paper


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