Volume Ordering for Analysis and Modeling of Vascular Systems

Morphological characteristics of vascular systems are commonly presented in terms of Strahler order because the logarithms of quantities such as vessel diameter and length are often linearly related to Strahler order. However, the ability to interpret Strahler order geometrically or physiologically is compromised because the precision of the order number is limited to integer values. This limitation is overcome by the volume ordering scheme, in which volume order number is defined as the logarithm of the estimated perfused tissue volume for each vascular segment. While Strahler and volume order numbers are equivalent for completely symmetrical branching trees, they deviate in the presence of asymmetries. The physiology-based definition of volume ordering offers benefits in the analysis of vascular design, fractal characterization of vascular systems, and blood flow modeling. These benefits are illustrated based on arterial kidney data that show a linear relationship of logarithmic vessel diameter and conductance as a function of both Strahler order and volume order with differing proportionality constants, which are expected to depend on the branching characteristics of the particular organ investigated.