Fractal modeling of pulmonary blood flow heterogeneity

The heterogeneity of pulmonary blood flow is not adequately described by gravitational forces alone. We investigated the flow distributions predicted by two fractally branching vascular models to determine how well such networks could explain the observed heterogeneity. The distribution of flow was modeled with a dichotomously branching tree in which the fraction of blood flow from the parent to the daughter branches was gamma and 1-gamma repeatedly at each generation. In one model gamma was held constant throughout the network, and in the other model gamma varied about a mean of 0.5 with a standard deviation of sigma. Both gamma and sigma were optimized in each model for the best fit to pulmonary blood flow data from experimental animals. The predicted relative dispersion of flow from the two model fractal networks produced an excellent fit to the observed data. These fractally branching models relate structure and function of the pulmonary vascular tree and provide a mechanism to describe the spatially correlated distribution of flow and the gravity-independent heterogeneity of blood flow.