A one-dimensional model for the propagation of transient pressure waves through the lung

Abstract

The propagation of pressure waves in the lung has been investigated by many authors concerned with respiratory physiology, ultrasound medical techniques or thoracic impact injuries. In most of the theoretical studies, the lung has been modeled as an isotropic and homogeneous medium, and by using Hooke's constitutive law (see e.g. Ganesan et al. Respir. Physiol. 110 (1997) 19; Jahed et al. J. Appl. Physiol. 66 (1989) 2675; Grimal et al. C.R. Acad. Sci., Paris 329 (IIb) (2001) 655–662), or more elaborated material laws (see, e.g. Bush and Challener (Proceedings of the International Research Council on Biokinetics Impacts (IRCOBI), Bergish-gladbach, 1988); Stuhmiller et al. J. Trauma 28 (1988) S132; Yang and Wang, Finite element modeling of the human thorax. Web page: http://wwwils.nlm.nih.gov/research/visible/vhpconf98/AUTHORS/YANG/YANG.HTM.). The hypothesis of homogeneous medium may be inappropriate for certain problems. Because of its foam-like structure, the behavior of the lung—even if the air and the soft tissue are assumed to behave like linearly elastic materials—is susceptible to be frequency dependent. In the present study, the lung is viewed as a one-dimensional stack of air and soft tissue layers; wave propagation in such a stack can be investigated in an equivalent mass–spring chain (El-Raheb (J. Acoust. Soc. Am. 94 (1993) 172; Int. J. Solids Struct. 34 (1997) 2969), where the masses and springs, respectively, represent the alveolar walls and alveolar gas. Results are presented in the time and frequency domains. The frequency dependence (cutoff frequency, variations in phase velocity) of the lung model is found to be highly dependent on the mean alveolar size. We found that short pulses induced by high velocity impacts (bullet stopped by a bulletproof jacket) can be highly distorted during the propagation. The pressure differential between two alveoli is discussed as a possible injury criterion.