Effect of Pleural Membrane on the Propagation of Rayleigh Waves in Inflated Porous Lungs–A Study

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.