Fractal branching pattern in the pial vasculature in the cat

Arborization pattern was studied in pial vascular networks by treating them as fractals. Rather than applying elaborate taxonomy assembled from measur es from individual vessel segments and bifurcations arranged in their branc hing order, the authors' approach captured the structural details at once i n high-resolution digital images processed for the skeleton of the networks . The pial networks appear random and at the same time having structural el ements similar to each other when viewed at different scales-a property kno wn as selfsimilarity revealed by the geometry of fractals. Fractal (capacit y) dimension, D-cap, was calculated to evaluate the networks spatial comple xity by the box counting method (BCM) and its variant. the extended countin g method (XCM). Box counting method and XCM were subject to numerical testi ng 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. D(cap)s (group mean +/- SD) for the arteria l 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 arte rial and venous systems thus appear to be developed according to the same f ractal generation rule in the cat.