An Analytical Poroelastic Model of a Nonhomogeneous Medium Under Creep Compression for Ultrasound Poroelastography Applications—Part II
- 22 April 2019
- journal article
- research article
- Published by ASME International in Journal of Biomechanical Engineering
- Vol. 141 (6)
- https://doi.org/10.1115/1.4040604
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.Keywords
This publication has 44 references indexed in Scilit:
- Effect of Vascular Normalization by Antiangiogenic Therapy on Interstitial Hypertension, Peritumor Edema, and Lymphatic Metastasis: Insights from a Mathematical ModelCancer Research, 2007
- Coupling between elastic strain and interstitial fluid flow: ramifications for poroelastic imagingPhysics in Medicine & Biology, 2006
- A Theoretical Analysis of Water Transport Through ChondrocytesBiomechanics and Modeling in Mechanobiology, 2006
- Porothermoelastic analyses of anisotropic hollow cylinders with applicationsInternational Journal for Numerical and Analytical Methods in Geomechanics, 2004
- A poroelastic model for interstitial pressure in tumorsBiorheology, 1995
- Transport of fluid and macromolecules in tumors. IV. A microscopic model of the perivascular distributionMicrovascular Research, 1991
- Transport of fluid and macromolecules in tumors. II. Role of heterogeneous perfusion and lymphaticsMicrovascular Research, 1990
- The Significance of Electromechanical and Osmotic Forces in the Nonequilibrium Swelling Behavior of Articular Cartilage in TensionJournal of Biomechanical Engineering, 1981
- Transient Temperatures and Thermal Stresses in Hollow Cylinders Due to Heat GenerationJournal of Heat Transfer, 1960
- The determination of the elastic field of an ellipsoidal inclusion, and related problemsProceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences, 1957