A multiscale analytical model of bronchial airway acoustics

Abstract

Sound transmission and resulting airway wall vibration in a complex multiscale viscoelastic model of the subglottal bronchial tree was calculated using a modified one-dimensional (1D) branching acoustic waveguide approach. This is an extension of previous work to enable use of complex airway trees that are partially derived from subject-specific medical images, without the need for self-similarity in the geometric structure. The approach was validated numerically for simplified airway geometries, as well as experimentally by comparison to previous studies. A comprehensive conducting airway tree with about 60 000 branches was then modified to create fibrotic, bronchoconstrictive, and pulmonary infiltrate conditions. The fibrotic case-systemic increase in soft tissue stiffness-increased the Helmholtz resonance frequency due to the increased acoustic impedance. Bronchoconstriction, with geometric changes in small conducting airways, decreased acoustic energy transmission to the peripheral airways due in part to the increased impedance mismatch between airway orders. Pulmonary infiltrate significantly altered the local acoustic field in the affected lobe. Calculation of acoustic differences between healthy versus pathologic cases can be used to enhance the understanding of vibro-acoustic changes correlated to pathology, and potentially provide improved tools for the diagnosis of pulmonary diseases that uniquely alter the acoustics of the airways.

Simulation of bronchial airway acoustics in healthy and asthmatic subjects

“…The acoustic impedance was higher in the asthmatic subjects at both the respiratory volumes considered. This is particularly relevant for the terminal impedance and is in line to what is expected in [13]. In fact, the reduction of the diameter together with the thickening of the walls due to the pathology lead to a significant increment of the wall impedance, which is reflected in the acoustic impedance of the segment due to the direct proportionality between the two terms as reported in [13].…”

“…The acoustic pressure planar wave could be introduced virtually everywhere in the bronchial tree. However, for the purpose of this work and to allow an easier comparison with [13] the acoustic wave was introduced as a non-homogeneous boundary condition at the inlet of the trachea, simulating an insonification experiment from an external source. The amplitude Table 1.…”

“…of the wave was chosen equal to 1 Pa and the frequencies analyzed were 200 Hz and 600 Hz as they can be considered relevant for respiratory sounds [21]: in particular, abnormal respiratory sounds such as crackles [22,23], wheezes [22], stridor and pleural rub [1] have their frequency content completely or partially included in the chosen range. Additionally, those frequencies belong to the range evaluated in the validation phase of the model [13].…”

“…Reference [13] provides more detailed information on the computation of each parameter and on the definition of the boundary conditions of the model. For each parameter, the median values calculated on all the segments belonging to that generation were reported in absolute value.…”

“…Lulich et al [11,12] focused on the analysis of resonance phenomena and wave propagation velocities in the lower respiratory tract. Henry et al [13] further extended the approach in [8,14] to account for image-based geometries in healthy subjects and proposed a simplified approach to specific pathological conditions. In the present work, we applied the analytical model developed by Henry et al [13] to study the sound propagation in real tracheobronchial trees reconstructed from CT data in healthy and asthmatic subjects.…”