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Research Papers

Comparison of Poroviscoelastic Models for Sound and Vibration in the Lungs

[+] Author and Article Information
Zoujun Dai, Ying Peng

University of Illinois at Chicago,
Chicago, IL 60607

Hansen A. Mansy

University of Central Florida,
Orlando, FL 32816
Rush University Medical Center,
Chicago, IL 60612

Richard H. Sandler

University of Central Florida,
Orlando, FL 32816
Nemours Children's Hospital,
Orlando, FL 32827

Thomas J. Royston

University of Illinois at Chicago,
Chicago, IL 60607
e-mail: troyston@uic.edu

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 31, 2013; final manuscript received December 18, 2013; published online July 25, 2014. Editor: Noel C. Perkins.

J. Vib. Acoust 136(5), 050905 (Jul 25, 2014) (11 pages) Paper No: VIB-13-1386; doi: 10.1115/1.4026436 History: Received October 31, 2013; Revised December 18, 2013

Noninvasive measurement of mechanical wave motion (sound and vibration) in the lungs may be of diagnostic value, as it can provide information about the mechanical properties of the lungs, which in turn are affected by disease and injury. In this study, two previously derived theoretical models of the vibroacoustic behavior of the lung parenchyma are compared: (1) a Biot theory of poroviscoelasticity and (2) an effective medium theory for compression wave behavior (also known as a “bubble swarm” model). A fractional derivative formulation of shear viscoelasticity is integrated into both models. A measurable “fast” compression wave speed predicted by the Biot theory formulation has a significant frequency dependence that is not predicted by the effective medium theory. Biot theory also predicts a slow compression wave. The experimentally measured fast compression wave speed and attenuation in a pig lung ex vivo model agreed well with the Biot theory. To obtain the parameters for the Biot theory prediction, the following experiments were undertaken: quasistatic mechanical indentation measurements were performed to estimate the lung static shear modulus; surface wave measurements were performed to estimate lung tissue shear viscoelasticity; and flow permeability was measured on dried lung specimens. This study suggests that the Biot theory may provide a more robust and accurate model than the effective medium theory for wave propagation in the lungs over a wider frequency range.

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Topics: Waves , Lung , Compression
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Figures

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Fig. 1

Microscope image showing morphometric parameters h and r for an alveolar duct

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Fig. 5

Schematic diagram of compression wave measurement

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Fig. 3

Compression and shear wave attenuation at 20 cm H2O Ptp, ––– fast compression wave, Biot theory, – – slow compression wave, Biot theory, – - – compression wave, effective medium model, - - - shear wave

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Fig. 2

Compression and shear wave group velocity at 20 cm H2O Ptp, ––– fast compression wave, Biot theory, – – slow compression wave, Biot theory, – - – compression wave, effective medium model, - - - shear wave

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Fig. 4

Experimental setup for surface wave measurement

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Fig. 6

Lung parenchyma permeability measurement (a) experimental setup and (b) schematic diagram

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Fig. 8

Surface wave speed, (a) 20 cm H2O and (b) 10 cm H2O, ○ ○ ○ experiment, line 1, ◻ ◻ ◻ experiment, line 2, ––– Voigt model least square fit, ––– fractional Voigt model least square fit, - - - SLS model least square fit

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Fig. 9

Time history of the acceleration and velocity of a point at 400 Hz with 10 cm H2O as a result of a 20-cycle tone-burst input. The amplitude of the velocity is increased by 2000 times for ease of viewing here.

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Fig. 10

Fast compression wave group velocity, ○ ○ ○ experiment, 20 cm H2O, ––– Biot theory, 20 cm H2O, –.– effective medium model, 20 cm H2O, ◻ ◻ ◻ experiment, 10 cm H2O, – – Biot theory, 10 cm H2O, - - - effective medium model, 10 cm H2O. Bars on the experimental data denote a 95% confidence interval, as described in Sec. 4.

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Fig. 11

Fast compression wave attenuation, ○ ○ ○ experiment, 20 cm H2O, location 1, ◻ ◻ ◻ experiment, 20 cm H2O, location 2, ––– Biot theory, 20 cm H2O, –.– effective medium model, 20 cm H2O, △ △ △ experiment, 10 cm H2O, location 1, + + + experiment, 10 cm H2O, location 2, – – Biot theory, 10 cm H2O, - - - effective medium model, 10 cm H2O

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Fig. 7

Force and indentation depth relation in indentation measurement, ○ ○ ○ experiment, 20 cm H2O, ––– least square fit, 20 cm H2O, ◻ ◻ ◻ experiment, 10 cm H2O, – – least square fit, 10 cm H2O

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