Vascular tree structure affects lung blood flow heterogeneity simulated in three dimensions

Abstract

Pulmonary arterial tree structures related to blood flow heterogeneity were simulated by using a symmetrical, bifurcating model in three-dimensional space. The branch angle (Theta), daughter-parent length ratio (rL), branch rotation angle (phi), and branch fraction of parent flow (gamma) for a single bifurcation were defined and repeated sequentially through 11 generations. With phi fixed at 90 degrees , tree structures were generated with Theta between 60 and 90 degrees , rL between 0.65 and 0.85, and an initial segment length of 5.6 cm and sectioned into 1-cm3 samples for analysis. Blood flow relative dispersions (RD%) between 52 and 42% and fractal dimensions (Ds) between 1.20 and 1.15 in 1-cm3 samples were observed even with equal branch flows. When gamma not equal 0.5, RD% increased, but Ds either decreased with gravity bias of higher branch flows or increased with random assignment of higher flows. Blood flow gradients along gravity and centripetal vectors increased with biased flow assignment of higher flows, and blood flows correlated negatively with distance only when gamma not equal 0.5. Thus a recursive branching vascular tree structure simulated Ds and RD% values for blood flow heterogeneity similar to those observed experimentally in the pulmonary circulation due to differences in the number of terminal arterioles per 1-cm3 sample, but blood flow gradients and a negative correlation of flows with distance required unequal partitioning of blood flows at branch points.