Mathematical model of breath sound propagation in respiratory tract

Understanding the physical processes of breath sounds formation and propagation in respiratory tract, the difference in these processes in healthy and asthmatic patients can facilitate the determination of criteria for computer diagnostics based on the analysis of respiratory noises. Mathematical modelling of the emergence and propagation of breath sounds in the lungs can be divided into two parts: modelling the anatomical structure of airways and modelling their functioning, physical processes that occur in airways and are associated with air flow. The results of analog modelling of changes in the amplitude-frequency characteristic of breath sounds caused by bronchial asthma syndrome are presented. To overcome a number of difficulties in the analysis of breath sounds, we used analog simulation, in which the consideration of air currents in the airways of the lung is replaced by the consideration of electrical processes. The proposed analog simulation showed that the enhancement of respiratory noise in the characteristic frequency range for bronchial asthma is associated with a narrowing of the airways. This enhancement, using an electrotechnical analogy, has a resonant character. Using the proposed model, the frequency dependence of the ratio of the outlet pressure (pressure at the mouth) to the pressure at the entrance (alveolar pressure) of the healthy and the patient with bronchial obstructive syndrome in bronchial asthma was calculated. This approach makes it possible to relatively easily take into account a large number of elements of the respiratory tract and simulate changes in these sounds caused by various pulmonary diseases. The suggested mathematical model can help in the development of more accurate computer diagnostics in the analysis of breath sounds, and its joint application with other models will allow a better understanding of the processes in the lung.