Viscoelasticity determined by measured wave absorption coefficient for modeling waves in soft tissues

This paper reports the construction of viscoelasticity models for simulation of wave propagation in soft tissues. Aided by the Carson transform, Fung’s model and Iatridis’s model are transformed into the frequency domain with the imaginary part of the transformed relaxation function shown to be rela...

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Bibliographic Details
Published in:Wave motion 2013-03, Vol.50 (2), p.334-346
Main Authors: Yang, Lixiang, Chen, Yung-Yu, Yu, Sheng-Tao John
Format: Article
Language:English
Subjects:
Absorption coefficient
Computer simulation
Constitutive relationships
Mathematical analysis
Mathematical models
Soft tissues
Viscoelasticity
Wave absorption
Wave propagation
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Summary:This paper reports the construction of viscoelasticity models for simulation of wave propagation in soft tissues. Aided by the Carson transform, Fung’s model and Iatridis’s model are transformed into the frequency domain with the imaginary part of the transformed relaxation function shown to be related to wave absorption effect. Based on measured wave absorption coefficients, the viscoelasticity models in the time domain are determined. Results show that Fung’s model does not support the frequency-dependent damping effect, but Iatridis’ model does. To validate the approach, numerical simulation of propagating wavelets in a skeletal pig muscle is performed. The constructed relaxation function is discretized by parallelly connected Standard Linear Solid (SLS) models. The hereditary integration is then transformed into a set of partial differential equations by introducing the internal variables. Together, the governing equations include the equation of motion, the constitutive equation, and the equations of internal variables. Velocity, stress, and internal variables are the primary unknowns. The model equations are solved by using the space–time CESE method. The calculated wave absorption effect compares well with the measured data. ► We propose a novel theoretical framework to determine viscoelastic constants from measured wave absorption coefficients. ► We use the results to model wave motion in soft tissues. ► Governing equations are cast into a fully-coupled, first-order system of hyperbolic PDEs. ► The framework provides accurate attenuation effects for propagating waves.
ISSN:0165-2125
1878-433X
DOI:10.1016/j.wavemoti.2012.09.002