Comparison of Poroviscoelastic Models for Sound and Vibration in the Lungs

Abstract

Noninvasive measurement of mechanical wave motion (sound and vibration) in the lungs may be of diagnostic value, as it can provide information about the mechanical properties of the lungs, which in turn are affected by disease and injury. In this study, two previously derived theoretical models of the vibroacoustic behavior of the lung parenchyma are compared: (1) a Biot theory of poroviscoelasticity and (2) an effective medium theory for compression wave behavior (also known as a "bubble swarm" model). A fractional derivative formulation of shear viscoelasticity is integrated into both models. A measurable "fast" compression wave speed predicted by the Biot theory formulation has a significant frequency dependence that is not predicted by the effective medium theory. Biot theory also predicts a slow compression wave. The experimentally measured fast compression wave speed and attenuation in a pig lung ex vivo model agreed well with the Biot theory. To obtain the parameters for the Biot theory prediction, the following experiments were undertaken: quasistatic mechanical indentation measurements were performed to estimate the lung static shear modulus; surface wave measurements were performed to estimate lung tissue shear viscoelasticity; and flow permeability was measured on dried lung specimens. This study suggests that the Biot theory may provide a more robust and accurate model than the effective medium theory for wave propagation in the lungs over a wider frequency range.

A comprehensive computational model of sound transmission through the porcine lung

“…28 Measurements of compression wave speed and attenuation in freshly exercised pig lung matched theoretical predictions based on Biot theory much more closely than did the effective medium theory. The shear wave propagation in the lung was also well predicted by the Biot theory.…”

“…A partial diagram of the lung airway tree based on this model down to n ¼ 11 can be found in Fredburg et al 23 For the purpose of developing a tractable set of equations for predicting small-amplitude mechanical wave motion in the parenchyma for wavelengths larger than the microscopic heterogeneous features of the lung, macroscopic homogenized representations of the lung's physical properties have been proposed. [24][25][26][27][28] Based on this homogenous or stochastic spatially averaged view, two different models for wave propagation have been put forth. One is sometimes referred to as the "effective medium" or "bubble swarm" theory.…”

“…[24][25][26] More recently, there has been an interest in applying Biot's theory of poroelasticity to the lung parychyma. 27,28 Application of Biot theory leads to a more complex theoretical model that predicts more wave types as compared to the effective medium theory.…”

“…In our frequency range of interest (100-2000 Hz), the slow compression wave cannot propagate as the relative motion between the lung parenchyma and air is impeded by viscous drag. 28 Hence only the fast compression wave can propagate in the parenchyma.…”

Acoustic Characterization of Axial Flow Left Ventricular Assist Device Operation In Vitro and In Vivo

“…The gel elastic modulus was measured using an indentation test as described in references and was noted to be comparable with biological soft tissue. 14 The LVAD was positioned such that the entirety of the pump housing was contained within the gel, and the driveline, inflow cannula, and outflow cannula remained unobstructed and accessible. To the outflow cannula was attached 1.27 cm inner diameter flexible vinyl tubing with length 157 cm.…”