Fractal Branching Pattern in the Pial Vasculature in the Cat

Abstract

Arborization pattern was studied in pial vascular networks by treating them as fractals. Rather than applying elaborate taxonomy assembled from measures from individual vessel segments and bifurcations arranged in their branching order, the authors' approach captured the structural details at once in high-resolution digital images processed for the skeleton of the networks. The pial networks appear random and at the same time having structural elements similar to each other when viewed at different scales—a property known as self-similarity revealed by the geometry of fractals. Fractal (capacity) dimension, Dcap, was calculated to evaluate the network's spatial complexity by the box counting method (BCM) and its variant, the extended counting method (XCM). Box counting method and XCM were subject to numerical testing on ideal fractals of known D. The authors found that precision of these fractal methods depends on the fractal character (branching, nonbranching) of the structure they evaluate. Dcap s (group mean ± SD) for the arterial and venous pial networks in the cat (n = 6) are 1.37 ± 0.04, 1.37 ± 0.02 by XCM, and 1.30 ± 0.04, 1.31 ± 0.03 by BCM, respectively. The arterial and venous systems thus appear to be developed according to the same fractal generation rule in the cat.