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Special Section: Spotlight on the Future–Imaging and Biomechanical Engineering

An Analytical Poroelastic Model of a Nonhomogeneous Medium Under Creep Compression for Ultrasound Poroelastography Applications—Part II

[+] Author and Article Information
Md Tauhidul Islam

Ultrasound and Elasticity Imaging Laboratory,
Department of Electrical and
Computer Engineering,
Texas A&M University,
College Station, TX 77840
e-mail: tauhid@tamu.edu

J. N. Reddy

Professor
Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77840
e-mail: jnreddy@tamu.edu

Raffaella Righetti

Department of Electrical and
Computer Engineering,
Texas A&M University,
College Station, TX 77840
e-mail: righetti@ece.tamu.edu

1Corresponding author.

Manuscript received November 27, 2017; final manuscript received June 16, 2018; published online April 22, 2019. Assoc. Editor: Steven D. Abramowitch.

J Biomech Eng 141(6), 060903 (Apr 22, 2019) (12 pages) Paper No: BIO-17-1554; doi: 10.1115/1.4040604 History: Received November 27, 2017; Revised June 16, 2018

An analytical theory for the unconfined creep behavior of a cylindrical inclusion (simulating a soft tissue tumor) embedded in a cylindrical background sample (simulating normal tissue) is presented and analyzed in this paper. Both the inclusion and the background are considered as fluid-filled, porous materials, each of them being characterized by a set of mechanical parameters. Specifically, in this derivation, the inclusion is assumed to have significantly higher interstitial permeability than the background. The formulations of the effective Poisson's ratio (EPR) and fluid pressure in the inclusion and in the background are derived for the case of a sample subjected to a creep compression. The developed analytical expressions are validated using finite element models (FEM). Statistical comparison between the results obtained from the developed model and the results from FEM demonstrates accuracy of the proposed theoretical model higher than 99.4%. The model presented in this paper complements the one reported in the companion paper (Part I), which refers to the case of an inclusion having less interstitial permeability than the background.

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Figures

Grahic Jump Location
Fig. 1

A cylindrical sample of a poroelastic material of radius b with a cylindrical inclusion of radius a. Axial direction is along the z direction, radial direction is along the r direction and the circumferential direction is along the angle θ.

Grahic Jump Location
Fig. 2

Two-dimensional view of the setup of a creep experiment where a poroelastic sample is compressed between two compressor plates

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Fig. 3

Effective Poisson's ratio inside the inclusion at different positions for sample A (a), sample B (b), and sample C (c)

Grahic Jump Location
Fig. 4

Fluid pressure inside the inclusion at different positions for sample A (a), sample B (b), and sample C (c)

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Fig. 5

Effective Poisson's ratios outside the inclusion at different positions for sample A (a), sample B (b), and sample C (c)

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Fig. 6

Fluid pressure outside the inclusion at different positions for sample A (a), sample B (b), and sample C (c)

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Fig. 7

Axial strain (a) and displacement (b) at different positions inside and outside the inclusion for sample A

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Fig. 8

Effective Poisson's ratio at different time points of 1 s, 5 s, 10 s, and 15 s from developed analytical model are shown in (a1), (a2), (a3), (a4) and from FEM in (b1), (b2), (b3), (b4) for sample A

Grahic Jump Location
Fig. 9

Effective Poisson's ratio at different time points of 1 s, 5 s, 10 s, and 15 s from developed analytical model are shown in (a1), (a2), (a3), (a4) from FEM in (b1), (b2), (b3), (b4) for sample B and from developed analytical model in (c1), (c2), (c3), (c4) and from FEM in (d1), (d2), (d3), (d4) for sample C

Grahic Jump Location
Fig. 10

Fluid pressures (in kPa) at different time points of 1 s, 5 s, 10 s, and 15 s from developed analytical model are shown in (a1), (a2), (a3), (a4) and from FEM in (b1), (b2), (b3), (b4) for sample A

Grahic Jump Location
Fig. 11

Fluid pressures (in kPa) at different time points of 1 s, 5 s, 10 s, and 15 s from developed analytical model are shown in (a1), (a2), (a3), (a4) from FEM in (b1), (b2), (b3), (b4) for sample B and from developed analytical model in (c1), (c2), (c3), (c4) and from FEM in (d1), (d2), (d3), (d4) for sample C

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