Role of arterial design on pulse wave reflection in a fractal pulmonary network

Abstract

A novel interpretation of pulmonary arterial input impedance was evaluated for the lung as a fractal vascular network. We hypothesized that local sources of reflection introduce trends of global reflection into the input impedance spectra. These trends are related to the network topology, geometry, and design according to Rb = Rdx, where Rb is the branching ratio, Rd is the diameter ratio, and x is the fractal dimension quantifying design. Simulations using values of Rd and x, which were derived morphometrically, confirmed two patterns of global reflection: a continuous trend attributed to a single effective site of reflection caused by frequency-dependent sources of impedance contrast and a discrete trend arising from a longitudinal distribution of frequency-independent sources of reflection. The continuous trend depended only on the network parameter Rd, whereas the discrete trend depended on Rd and x. Our results indicate that the impedance-matching properties of a deterministic pulmonary fractal network encode arterial geometry and topology via function and that typical values of Rd and x for the pulmonary circulation facilitate shear stress amplification in its peripheral vessels. Thus, inasmuch as shear forces may be involved in the endothelial mechanisms for pathological, or physiological, vascular remodeling, broadband input impedance analysis may reveal interactions between network organization and vascular function.