Experimental and Computational Studies of Sound Transmission in a Branching Airway Network Embedded in a Compliant Viscoelastic Medium

Abstract

Breath sounds are often used to aid in the diagnosis of pulmonary disease. Mechanical and numerical models could be used to enhance our understanding of relevant sound transmission phenomena. Sound transmission in an airway mimicking phantom was investigated using a mechanical model with a branching airway network embedded in a compliant viscoelastic medium. The Horsfield self-consistent model for the bronchial tree was adopted to topologically couple the individual airway segments into the branching airway network. The acoustics of the bifurcating airway segments were measured by microphones and calculated analytically. Airway phantom surface motion was measured using scanning laser Doppler vibrometry. Finite element simulations of sound transmission in the airway phantom were performed. Good agreement was achieved between experiments and simulations. The validated computational approach can provide insight into sound transmission simulations in real lungs.

Fig. 1

Diagram of partial airway model of Horsfield (from 35^th to 23^rd order), adapted from Fredberg et al. [19].

Fig. 2

Airway acoustic model with one bifurcation.

Fig. 3

Airway phantom with branching network inside.

Fig. 4

Schematic diagram of the airway tree in the phantom.

Fig. 5

Schematic representation of a Maxwell, SLS, Generalized Maxwell, Voigt, fractional order spring-pot, and fractional order Voigt model (Taken from [24], with permission).

Fig. 6

Schematic diagram of compression wave speed measurement.

Fig. 7

3D geometry of the left half of the phantom.

Fig. 8

Phase angle θ_xy-frequency curve.

Fig. 9

FRF of Mic 2/Mic 1 (Pa/Pa), fixed boundary condition at all terminal segments, (a) Location A&B (b) Location C&D (c) Location E&F and (d) Location G&H. For locations refer to Fig. 4. Key: simulation, theoretical prediction, and experiment.

Fig. 10

Experimental setup of sound coupling into phantom measurement.

Fig. 11

FRF of phantom top surface at 400 Hz. (Left: Simulation, Right: Experiment, color bar: m/s/Pa in dB scale)

Fig. 12

FRF of phantom top surface at 700 Hz. (Left: Simulation, Right: Experiment, color bar: m/s/Pa in dB scale)

Fig. 13

FRF of phantom top surface at 1000 Hz. (Left: Simulation, Right: Experiment, color bar: m/s/Pa in dB scale)

Fig. 14

FRF of phantom top surface at 1300 Hz. (Left: Simulation, Right: Experiment, color bar: m/s/Pa in dB scale)

Fig. 15

FRF of phantom top surface at 1600 Hz. (Left: Simulation, Right: Experiment, color bar: m/s/Pa in dB scale)

Fig. 16

Selected points on phantom top surface

Fig. 17

FRF of selected points on phantom top surface. (a) Point 1 (b) Point 2 (c) Point 3 (d) Point 4 (e) Point 5 and (f) Point 6. Key: experiment, simulation.