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Sizing Up Allometric Scaling Theory

Figure 1

Schematic vessel architecture and branching.

A vessel at level k branches into two daughter vessels at level k+1. The branching ratio is thus n = 2. The radii, rk+1, and lengths, lk+1, of the two daughter vessels are identical by Assumption 3. The ratios of the radii and lengths at level k+1 to those at level k are defined as γ, β> and β< in Equations 2 and 3. The choice of β> for the radial ratio corresponds to area-preserving branching and of β< to area-increasing branching. In the WBE model, the cardiovascular system is composed of successive generations of these vascular branchings, from level 0 (the heart) to level N (the capillaries).

Figure 1

doi: https://doi.org/10.1371/journal.pcbi.1000171.g001