Mathematical modeling of sound propagation through the respiratory tract in a modified gas environment

The aim of the work was to develop a mathematical model of sound propagation through the human respiratory tract when breathing certain respiratory gas mixtures. We based the model on an assembler model of branching of the respiratory tract. For calculations, we presented the human tracheobronchial tree in the form of an equivalent T-shaped cut section diagram, which includes parameters of the walls of the respiratory tract. We carried the simulation out in two main stages. At the first stage, we calculated the impedance of the flow from the small airways to the larger airways. At the second stage, we calculated the sound pressure caused by breathing. As a result, we obtained the curves of the impedance dependence on the frequency spectrum, as well as the sound power from the respiratory flow. We noted that when breathing air, the impedance value remains constant with increasing frequency. Moreover, we also noted that when exposed to a heavier gas than air, the impedance value constantly increases, and when exposed to lighter gases, after reaching a maximum, the impedance value decreases. We found that the highest sound pressure is typical for the oxygen-krypton mixture, and the lowest for the oxygen–helium mixture. We also found that in the case of modeling the laminar flow regime (with a critical Reynolds number equal to 1800), sound affects how many generations of bronchi more than in the case of modeling the transient flow regime (with a critical Reynolds number equal to 2700). Thus, we drew conclusions about the influence of the physical properties of gaseous media on the amount of sound pressure and the propagation of sound through the human respiratory tract.