Abstract
In an attempt to include the effects of natural porosity of lung parenchyma into the mathematical study of lung diagnostics, a model describing the propagation of low-frequency Rayleigh waves in relation to the porous architecture of the lung parenchyma is presented. The wave motion is analyzed by assuming that the lung parenchyma behaves as an isotropic elastic half-space containing a distribution of vacuous pores with the visceral pleura as a taut elastic membrane in smooth contact with the half-space. The thinness of the pleural membrane in comparison with the large surface area of contact enables it to be modeled as a material surface in contact with the parenchyma. Utilizing the perturbation technique, an approximate formula for the Rayleigh wave velocity in the parenchyma with allowance for surface tension, mass density, and porosity is derived. In addition, the effect of the tension in the pleural membrane and the porosity in the parenchyma on the propagation of the low-frequency Rayleigh waves is brought out through the dispersion spectrum. It is hoped that the results of this paper would enable a better understanding of the porosity and surface-tension effects on lung parenchyma.
Highlights
The mechanical properties of biological tissues are known to provide information about their pathological condition and have been clinically used for diagnostic purposes in numerous organs [1]
Taking into consideration the observations made above, the present work considers the effect of pleural membrane tension on the propagation of Rayleigh waves in inflated porous lungs by modeling the lung parenchyma as a linear elastic material with voids
Using (13), we study the influence of surface tension in the pleural membrane and the porous structure of the lung parenchyma on the propagation of Rayleigh waves in inflated lungs
Summary
The mechanical properties of biological tissues are known to provide information about their pathological condition and have been clinically used for diagnostic purposes in numerous organs [1]. Despite the plethora of models available for lung parenchyma, recent experimental investigations in the application of Rayleigh wave speed to determine the elastic/viscoelastic properties of lung parenchyma have utilized classical/Biot model in their work, and have not considered the effect of pleural membrane tension on Rayleigh waves, except for the work of Man et al in 1991. Taking into consideration the observations made above, the present work considers the effect of pleural membrane tension on the propagation of Rayleigh waves in inflated porous lungs by modeling the lung parenchyma as a linear elastic material with voids. The characteristic equation for low frequency Rayleigh waves in the lung parenchyma modeled by a LEMV and covered by a taut membrane having a certain mass and a constant surface tension is 2 − s2. The formula has earlier been used to obtain a root of the secular equation of Rayleigh waves in isotropic and anisotropic elastic solids [51]
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