Determinants Of The Pulmonary Input Impedance Spectrum: Theoretical Considerations Based On A Mathematical Model

Abstract

The determinants of the shape of the pulmonary input impedance spectrum were investigated using a mathematical model based on Womersley’s equations for pulsatile flow in constrained viscoelastic tubes and structural data (morphometry, elasticity, and rheology) provided for the entire cat lung by Zhuang et al. Mean distending pressures and diameters of vessels were determined from the struc-tured data and four independent variables: cardiac output and left atrial, pleural, and alveolar pressures. Studies were performed in a control model and a model whose structure was designed to imitate that of a subject with pulmonary vascular impairment. Model simplifications were investigated. Increasing left atrial pressure or cardiac output caused passive distention of vessels that increased total blood volume and decreased vascular resistance, creating a slight spectral shift downward and to the right. Increasing pleural pressure decreased total blood volume and increased vascular resistance, creating a spectral shift upward and to the right. Increasing levels of alveolar pressure resulted in increased vascular resistance and pressures find a shift in blood volume from the capillaries to the arteries without significant change in total blood volume, creating a spectral shift that was slightly downward and to the right. Model simplification studies demonstrated that (1) all vessels distal to the tenth generation (arteries with zero distending pressure diameters < 50 μM) can be modelled as a simple resistor or (2) all vessels distal to the fourth generation can be modelled as a modified Windkessel. Results obtained from the passive studies were consistent with those obtained from normal lambs and lam be with chronically elevated pulmonary blood flow. To model a hypertensive state created by ifljury to the lung microvasculature, the number and size of small vessels and the compliance constants of all arteries were decreased and the viscoelastic constant was increased, which created the requisite shift to the right and upward. To better match the modulus fluctuation and negative phase angles at higher frequencies in the hypertensive animals, the development of a major reflection site between the main and branch arteries was hypothesized.