Poroelastic model of the lungs at low frequencies predicted by Biot's theory

Abstract

Biot's theory of poroelastic wave propagation inherently lends itself to elucidate the characteristics of a biphasic medium comprising solid and fluid components, such as biological tissues. One of the intricately complex biological tissues that remains poorly understood is the lungs since their properties diversify significantly through their pore geometries affected by inspiratory positive airway pressure (IPAP) and applied frequency range. One hypothesizes that the vibroacoustic behaviour of the lungs can be predicted by Biot's theory, as the nature of the lungs aligns with the principles of the theory at low frequencies. This study aims to analytically investigate the vibroacoustic behaviour of the lungs, considering 10 and 20-cm H;2O IPAP. Utilizing a fractional derivative formulation, one predicts the complex-valued shear wave speed, as well as the fast and slow compression wave speeds, for frequencies ranging from 5 to 100 Hz. A 3D digital thorax twin study using these predicted wave speeds, particularly at 28 Hz and 20 cm H;2O IPAP, is validated against experimental data from the literature. Consequently, applying Biot's theory provides a valuable framework for understanding the dynamic vibroacoustic behaviour of the lung tissues in response to varying IPAP and low frequencies.