✦ LIBER ✦

Fractal Dimensions and Multifractility in Vascular Branching

✍ Scribed by M. ZAMIR

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 254 KB
Volume: 212
Category: Article
ISSN: 0022-5193
DOI: 10.1006/jtbi.2001.2367

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✦ Synopsis

A de"nition for the fractal dimension of a vascular tree is proposed based on the hemodynamic function of the tree and in terms of two key branching parameters: the asymmetry ratio of arterial bifurcations and the power law exponent governing the relation between vessel diameter and #ow. Data from the cardiovascular system, which generally exhibit considerable scatter in the values of these two parameters, are found to produce the same degree of scatter in the value of the fractal dimension. When this scatter is explored for a multifractal pattern, however, it is found that the required collapse onto a single curve is achieved in terms of the coarse HoK lder exponent. Thus, the presence of multifractility is con"rmed, and the legitimacy of the de"ned dimension is a$rmed in the sense of the theoretical Hausdor! limit in as much as this limit can be reached with experimental data.

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