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Research Papers

An Analytical Model of Tumors With Higher Permeability Than Surrounding Tissues for Ultrasound Elastography Imaging

[+] 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

Anuj Chaudhry

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

Ginu Unnikrishnan

Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77840
e-mail: ginuuk@gmail.com

J. N. Reddy

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 December 27, 2017; final manuscript received April 30, 2018; published online June 5, 2018. Assoc. Editor: Xiaoning Jiang.

ASME J of Medical Diagnostics 1(3), 031006 (Jun 05, 2018) (12 pages) Paper No: JESMDT-17-2058; doi: 10.1115/1.4040145 History: Received December 27, 2017; Revised April 30, 2018

Cancerous tissues are known to possess different poroelastic properties with respect to normal tissues. Interstitial permeability is one of these properties, and it has been shown to be of diagnostic relevance for the detection of soft tissue cancers and for assessment of their treatment. In some cases, interstitial permeability of cancers has been reported to be lower than the surrounding tissue, while in other cases interstitial permeability of cancers has been reported to be higher than the surrounding tissue. We have previously reported an analytical model of a cylindrical tumor embedded in a more permeable background. In this paper, we present and analyze a poroelastic mathematical model of a tumor tissue in cylindrical coordinate system, where the permeability of the tumor tissue is assumed to be higher than the surrounding normal tissue. A full set of analytical expressions are obtained for radial displacement, strain, and fluid pressure under stress relaxation testing conditions. The results obtained with the proposed analytical model are compared with corresponding finite element analysis results for a broad range of mechanical parameters of the tumor. The results indicate that the proposed model is accurate and closely resembles the finite element analysis. The availability of this model and its solutions can be helpful for ultrasound elastography applications such as for extracting the mechanical parameters of the tumor and normal tissue and, in general, to study the impact of poroelastic material properties in the assessment of tumors.

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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 (2D) view of the setup of a stress relaxation experiment where a poroelastic sample is compressed between two compressor plates

Grahic Jump Location
Fig. 3

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

Grahic Jump Location
Fig. 4

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

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Fig. 5

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

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Fig. 6

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

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Fig. 7

Effective Poisson's ratio at 3 s, 34 s, 56 s, 235 s, and 660 s from the developed analytical model (a1–a5) and from FEM of sample A (b1–b5)

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Fig. 8

Effective Poisson's ratio elastograms at 3 s, 34 s, 56 s, 235 s, and 660 s obtained from the developed analytical model (a1–a5) and from FEM of sample B (b1–b5) and from the developed analytical model (c1–c5) and from FEM of sample C (d1–d5)

Grahic Jump Location
Fig. 9

Fluid pressure at 3 s, 34 s, 56 s, 235 s, and 660 s from the developed analytical model (a1–a5) and from FEM of sample A (b1–b5)

Grahic Jump Location
Fig. 10

Fluid pressure at 3 s, 34 s, 56 s, 235 s, and 660 s from the developed analytical model (a1–a5) and from FEM of sample B (b1–b5) and from the developed analytical model (c1–c5) and from FEM of sample C (d1–d5)

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