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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 I

[+] Author and Article Information
Md Tauhidul Islam

Ultrasound and Elasticity Imaging Laboratory,
Department of Electrical &
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 &
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), 060902 (Apr 22, 2019) (16 pages) Paper No: BIO-17-1553; doi: 10.1115/1.4040603 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 properties. Specifically, in this paper, the inclusion is considered to be less permeable than the background. The cylindrical sample is compressed using a constant pressure within two frictionless plates and is allowed to expand in an unconfined way along the radial direction. Analytical expressions for the effective Poisson's ratio (EPR) and fluid pressure inside and outside the inclusion are derived and analyzed. The theoretical results are validated using finite element models (FEMs). Statistical analysis shows excellent agreement between the results obtained from the developed model and the results from FEM. Thus, the developed theoretical model can be used in medical imaging modalities such as ultrasound poroelastography to extract the mechanical parameters of tissues and/or to better understand the impact of different mechanical parameters on the estimated displacements, strains, stresses, and fluid pressure inside a tumor and in the surrounding tissue.

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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. The axial direction is along the z direction, the radial direction is along the r direction, and the circumferential direction is along the angle θ.

Grahic Jump Location
Fig. 2

Two-dimensional (2D) view of the setup of a creep experiment where a poroelastic sample is compressed between two compressor plates

Grahic Jump Location
Fig. 3

Mesh in selected portion of the 2D rectangular sample plane in Abaqus

Grahic Jump Location
Fig. 4

EPR at different positions inside the inclusion for sample A (a) and sample B (b)

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Fig. 5

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

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Fig. 6

EPRs at different positions outside the inclusion for sample A (a) and sample B (b)

Grahic Jump Location
Fig. 7

Axial strains at different positions inside and outside the inclusion for sample A (a1) and sample B (b1). Axial displacements at different positions inside and outside the inclusion for sample A (a2) and sample B (b2).

Grahic Jump Location
Fig. 8

EPR at different positions inside the inclusion for sample C (a) and sample D (b)

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Fig. 9

Fluid pressure at different positions inside the inclusion for sample C (a) and sample D (b)

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Fig. 10

EPR at different positions outside the inclusion for sample C (a) and sample D (b)

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Fig. 11

Fluid pressure at different positions outside the inclusion for sample C (a) and sample D (b)

Grahic Jump Location
Fig. 12

Sample A: (a1), (a2), (a3), (a4), and (a5) show the EPR images at different time points (1 s, 2 s, 5 s, 10 s, and 15s) as obtained from the developed analytical model; (b1), (b2), (b3), (b4), and (b5) show the corresponding EPR images obtained from the FEM. Sample B: (c1), (c2), (c3), (c4), and (c5) show the EPR images at different time points (1 s, 2 s, 5 s, 10 s, and 15s) as obtained from the developed analytical model; (d1), (d2), (d3), (d4), and (d5) show the corresponding EPR images obtained from the FEM.

Grahic Jump Location
Fig. 13

Sample A: (a1), (a2), (a3), (a4), and (a5) show the fluid pressure (kPa) at different time points (1 s, 2 s, 5 s, 10 s, and 15s) as obtained from the developed analytical model; (b1), (b2), (b3), (b4), and (b5) show the corresponding the fluid pressure (kPa) obtained from the FEM. Sample B: (c1), (c2), (c3), (c4), and (c5) show the fluid pressure (kPa) at different time points (1 s, 2 s, 5 s, 10 s, and 15s) as obtained from the developed analytical model; (d1), (d2), (d3), (d4), and (d5) show the corresponding fluid pressure (kPa) obtained from the FEM.

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