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

Abstract

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.

Estimation of Mechanical and Transport Parameters in Cancers Using Short Time Poroelastography

“…This assumption is typically valid for cancers [5] , [45] , [50] , [51] as most fluid flow occurs through the capillary walls. Therefore, VP and axial strain TC in cancers should not be spatially variant inside the inclusion [28] , [52] .…”

A Spline Interpolation–based Data Reconstruction Technique for Estimation of Strain Time Constant in Ultrasound Poroelastography

“…The strain time constant (TC) is an important poroelastographic parameter as it carries information on the fluid transport properties of the tissue. [6][7][8] Fluid transport properties of tissues can be clinically very informative, especially in cancer applications.…”

An Analysis of the Error Associated to Single and Double Exponential Approximations of Theoretical Poroelastic Models

“…Our group has recently reported the closed-form solutions of the effective Poisson's ratio (EPR) and fluid pressure inside and outside a poroelastic inclusion embedded inside another poroelastic material under stress relaxation and creep compression. [11][12][13][14] When a poroelastic material is subjected to sustained compression, fluid exudation causes the stress to rise above the equilibrium value during the compression phase, 8,15 while in the relaxation phase, no fluid exudation occurs, and the internal fluid redistributes inside the sample. All aforementioned theoretical works demonstrate that the displacements, strains, and fluid pressure in a poroelastic material under sustained compression are temporally varying and that their theoretical temporal expressions contain an infinite number of exponentials.…”

“…All aforementioned theoretical works demonstrate that the displacements, strains, and fluid pressure in a poroelastic material under sustained compression are temporally varying and that their theoretical temporal expressions contain an infinite number of exponentials. 8,[11][12][13][14][15] The presence of an infinite number of exponentials in the analytic expressions of the displacements and strains creates hardship in the analysis and parameter estimation and is unpractical in clinical imaging settings. Parameter estimation is important for extracting diagnostically important tissue mechanical parameters such as Poisson's ratio, product of aggregate modulus, and interstitial permeability, which have been found to be useful in diagnosis, prognosis, and treatment of diseases like cancer.…”

“…Our group has recently reported the closed-form solutions of the effective Poisson’s ratio (EPR) and fluid pressure inside and outside a poroelastic inclusion embedded inside another poroelastic material under stress relaxation and creep compression. 11-14…”