General discrete modelling of lung sound production in normal subjects

Lung sound analysis is of a major importance in diagnostic malfunctions of the respiratory system. In normal subjects, it is known that these sounds are caused by the interaction of the respiratory flows with the bronchial tree structure. However, the detailed knowledge of the reasons for the spectral characteristics of such sounds remains to be elucidated. In this paper we propose a model for normal lung sound production based on a discretization of air flow in particle-like elements. Their transport with the involved interactions is implemented using a pseudo-molecular dynamics Monte Carlo procedure. General physical principles were considered for the interaction of these elements with the bronchial tree as well as a two-body interaction potential. The particle-tree interactions and the particle-particle interactions represent the flow-tree and the internal flow interactions, respectively. According to the model, sound is produced in each bronchus with the pitch frequency inversely proportional to its dimensions and with amplitude proportional to the intensity of the interaction, also a function of the bronchus dimensions. The lung sound is then the composition of the sounds produced in each bronchus. The model was successful in approximating the spectral characteristics reported by Gavriely et al (1981, 1995) as a direct consequence of the fractal properties of the bronchial tree and the considered internal fluid interactions. Thus, the reported high-frequency spectrum with its affine property as well as the low-frequency irregularity could be reproduced.