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Technical Brief

Dynamic Simulation of Viscoelastic Soft Tissue in Acoustic Radiation Force Creep Imaging

[+] Author and Article Information
Xiaodong Zhao

Department of Mechanical and Aerospace Engineering,
Rutgers, the State University of New Jersey,
98 Brett Road,
Piscataway, NJ 08854-8058
e-mail: xiaodong.zhao@rutgers.edu

Assimina A. Pelegri

Fellow ASME
Department of Mechanical and Aerospace Engineering,
Rutgers, the State University of New Jersey,
98 Brett Road,
Piscataway, NJ 08854-8058
e-mail: pelegri@jove.rutgers.edu

1Corresponding author.

Manuscript received October 28, 2013; final manuscript received June 20, 2014; accepted manuscript posted July 1, 2014; published online July 15, 2014. Assoc. Editor: Jeffrey Ruberti.

J Biomech Eng 136(9), 094502 (Jul 15, 2014) (7 pages) Paper No: BIO-13-1510; doi: 10.1115/1.4027934 History: Received October 28, 2013; Revised June 20, 2014; Accepted July 01, 2014

Acoustic radiation force (ARF) creep imaging applies step ARF excitation to induce creep displacement of soft tissue, and the corresponding time-dependent responses are used to estimate soft tissue viscoelasticity or its contrast. Single degree of freedom (SDF) and homogeneous analytical models have been used to characterize soft tissue viscoelasticity in ARF creep imaging. The purpose of this study is to investigate the fundamental limitations of the commonly used SDF and homogeneous assumptions in ARF creep imaging. In this paper, finite element (FE) models are developed to simulate the dynamic behavior of viscoelastic soft tissue subjected to step ARF. Both homogeneous and heterogeneous models are studied with different soft tissue viscoelasticity and ARF configurations. The results indicate that the SDF model can provide good estimations for homogeneous soft tissue with high viscosity, but exhibits poor performance for low viscosity soft tissue. In addition, a smaller focal region of the ARF is desirable to reduce the estimation error with the SDF models. For heterogeneous media, the responses of the focal region are highly affected by the local heterogeneity, which results in deterioration of the effectiveness of the SDF and homogeneous simplifications.

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Figures

Grahic Jump Location
Fig. 1

Model diagram and validation: (a) Diagram of the axisymmetric model with a spherical inclusion in the center of the model and (b) axial displacement induced by ARF for the homogeneous case with μ = 3 kPa. The horizontal axis in (b) is the axial distance from the focal center.

Grahic Jump Location
Fig. 2

Creep displacement responses to step ARF for soft tissue with different viscoelasticity. Three time constants are studied: (a) τ = 0.0003 s, (b) τ = 0.0009 s, and (c) τ = 0.0027 s. The corresponding normalized creep displacement responses are shown in (d), (e), and (f).

Grahic Jump Location
Fig. 3

REE of τ by fitting the SDF models with the FE simulated creep displacement responses. (a) SDF model without considering the inertial effect and (b) SDF model with the inertial component included. Each marker represents cases with the same shear viscosity.

Grahic Jump Location
Fig. 4

Creep displacement responses to different ARF configurations: (a) ARFs with different magnitude, but the same distribution, i.e., Fnumber = 0.83; and (b) ARFs with different distribution, but the same magnitude, i.e., fo. The corresponding normalized creep displacement responses are shown in (c) and (d). The model is homogeneous with μ = 3 kPa, and τ = 0.0009 s.

Grahic Jump Location
Fig. 5

Creep displacement responses at the origin of the heterogeneous models with different inclusion sizes: (a) Sphere with diameter 3 mm and (b) Sphere with diameter 6 mm. The corresponding normalized creep displacement responses are shown in (c) and (d). The solid black line denotes the homogeneous case. τ = 0.0003 s is for both background and inclusion.

Grahic Jump Location
Fig. 6

Axial normal strain field near the region of the 3-mm-diameter spherical inclusion after a 10 ms step ARF excitation. The dimension of the region is h = 6 mm (axial length) and r = 3 mm (radial length). The time constant is 0.0009 s and the shear moduli are: (a) μΒ = 3 kPa, and μΙ = 3 kPa; (b) μΒ = 0.3 kPa, and μΙ = 3 kPa; and (c) μΒ = 30 kPa, and μΙ = 3 kPa.

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