A Class of Flow Bifurcation Models with Lognormal Distribution and Fractal Dispersion

✍ Scribed by HONG QIAN; JAMES B BASSINGTHWAIGHTE

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 150 KB
• Volume: 205
• Category: Article
• ISSN: 0022-5193
• DOI: 10.1006/jtbi.2000.2060

✦ Synopsis

We report a quantitative analysis of a simple dichotomous branching tree model for blood #ow in vascular networks. Using the method of moment-generating function and geometric Brownian motion from stochastic mathematics, our analysis shows that a vascular network with asymmetric branching and random variation at each bifurcating point gives rise to an asymptotic lognormal #ow distribution with a positive skewness. The model exhibits a fractal scaling in the dispersion of the regional #ow in the branches. Experimentally measurable fractal dimension of the relative dispersion in regional #ow is analytically calculated in terms of the asymmetry and the variance at local bifurcation; hence the model suggests a powerful method to obtain the physiological information on local #ow bifurcation in terms of #ow dispersion analysis. Both the fractal behavior and the lognormal distribution are intimately related to the fact that it is the logarithm of #ow, rather than #ow itself, which is the natural variable in the tree models. The kinetics of tracer washout is also discussed in terms of the lognormal distribution.