FRACTAL VASCULAR GROWTH PATTERNS.

Abstract

Flow distributions in the heart and lung are heterogeneous but not at all random. The apparent degree of heterogeneity increases as one reduces the size of observable elements; the fact that the dispersion of flows shows a logarithmic relation to element size says that the system is statistically fractal. The fractal characterization is a statement that the system is nonrandom and that it shows correlation. The close near neighbor correlation has as the corollary of long tailing or falloff in correlation with distance, so called spatial persistence. Correlation can be expected because flow is delivered via a branching vascular system, and so it appears that the structure of the vasculature itself contributes. Since it is also practical and efficient for growth to occur via recursive rules, such as branch, grow, and repeat the branching and growing, it appears that fractals may be useful in understanding the ontological aspects of growth of tissues and organs, thereby minimizing the requirements for genetic material.