An analytical poroelastic model of a spherical tumor embedded in normal tissue under creep compression.

An analytical model for a spherical poroelastic tumor embedded in normal poroelastic tissues under creep compression is presented in this paper. The tissue is modeled as a cylindrical sample containing a spherical inclusion having different material properties. Analytical expression for the volumetric strain generated inside the inclusion during creep compression is obtained. Error analysis is carried out by comparing the results from the developed analytical model with corresponding results obtained from an established finite element software for a number of samples with different material properties. The error is found to be below 2.5% for the samples with a small inclusion and 7% in the samples with a large inclusion. The analytical solutions reported in this paper can greatly impact elasticity imaging techniques aiming at reconstructing mechanical properties of tumors such as Young's modulus, Poisson's ratio, interstitial permeability and vascular permeability.

[1]  T. Krouskop,et al.  Elastography: Ultrasonic estimation and imaging of the elastic properties of tissues , 1999, Proceedings of the Institution of Mechanical Engineers. Part H, Journal of engineering in medicine.

[2]  M. Biot.  General Theory of Three‐Dimensional Consolidation , 1941 .

[3]  C. Cryer,et al.  A COMPARISON OF THE THREE-DIMENSIONAL CONSOLIDATION THEORIES OF BIOT AND TERZAGHI , 1963 .

[4]  Md Tauhidul Islam,et al.  An Analytical Model of Tumors With Higher Permeability Than Surrounding Tissues for Ultrasound Elastography Imaging , 2018, Journal of Engineering and Science in Medical Diagnostics and Therapy.

[5]  Md Tauhidul Islam,et al.  A New Method for Estimating the Effective Poisson’s Ratio in Ultrasound Poroelastography , 2018, IEEE Transactions on Medical Imaging.

[6]  M. Swartz,et al.  Interstitial flow and its effects in soft tissues. , 2007, Annual review of biomedical engineering.

[7]  Jeffrey C Bamber,et al.  Towards an acoustic model-based poroelastic imaging method: I. Theoretical foundation. , 2006, Ultrasound in medicine & biology.

[8]  W M Lai,et al.  An analysis of the unconfined compression of articular cartilage. , 1984, Journal of biomechanical engineering.

[9]  Deformation of spherical cavities and inclusions in fluid-infiltrated elastic materials , 1978 .

[10]  J. D. Eshelby.  The determination of the elastic field of an ellipsoidal inclusion, and related problems , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[11]  P. Gullino,et al.  Diffusion and convection in normal and neoplastic tissues. , 1974, Cancer research.

[12]  Md Tauhidul Islam,et al.  An analytical poroelastic model of a non-homogeneous medium under creep compression for ultrasound poroelastography applications - Part II. , 2018, Journal of biomechanical engineering.

[13]  R. Skalak,et al.  Macro- and Microscopic Fluid Transport in Living Tissues: Application to Solid Tumors , 1997 .

[14]  R K Jain,et al.  Transport of fluid and macromolecules in tumors. II. Role of heterogeneous perfusion and lymphatics. , 1990, Microvascular research.

[15]  Francis A. Duck,et al.  Physical properties of tissue : a comprehensive reference book , 1990 .

[16]  Van C. Mow,et al.  Recent Developments in Synovial Joint Biomechanics , 1980 .

[17]  Jonathan Ophir,et al.  The feasibility of using poroelastographic techniques for distinguishing between normal and lymphedematous tissues in vivo , 2007, Physics in medicine and biology.

[18]  Malisa Sarntinoranont,et al.  Interstitial Stress and Fluid Pressure Within a Growing Tumor , 2004, Annals of Biomedical Engineering.

[19]  Triantafyllos Stylianopoulos,et al.  Role of vascular normalization in benefit from metronomic chemotherapy , 2017, Proceedings of the National Academy of Sciences.

[20]  V. Mow,et al.  Biphasic creep and stress relaxation of articular cartilage in compression? Theory and experiments. , 1980, Journal of biomechanical engineering.

[21]  M Ferrari,et al.  A tumor growth model with deformable ECM , 2014, Physical biology.

[22]  Bernhard A. Schrefler,et al.  A monolithic multiphase porous medium framework for (a-)vascular tumor growth. , 2018, Computer methods in applied mechanics and engineering.

[23]  M. Biot.  MECHANICS OF DEFORMATION AND ACOUSTIC PROPAGATION IN POROUS MEDIA , 1962 .

[24]  Md Tauhidul Islam,et al.  A model-based approach to investigate the effect of elevated interstitial fluid pressure on strain elastography , 2018, Physics in medicine and biology.

[25]  J. Rudnicki,et al.  Dynamic transverse shear modulus for a heterogeneous fluid-filled porous solid containing cylindrical inclusions , 2016 .

[26]  Y. Fung.  Mechanical Properties and Active Remodeling of Blood Vessels , 1993 .

[27]  M. Chaplain,et al.  Modelling the role of cell-cell adhesion in the growth and development of carcinomas , 1996 .

[28]  Triantafyllos Stylianopoulos,et al.  The role of mechanical forces in tumor growth and therapy. , 2014, Annual review of biomedical engineering.

[29]  Christos Davatzikos,et al.  Nonlinear elastic registration of brain images with tumor pathology using a biomechanical model [MRI] , 1999, IEEE Transactions on Medical Imaging.

[30]  R K Jain,et al.  Transport of fluid and macromolecules in tumors. I. Role of interstitial pressure and convection. , 1989, Microvascular research.

[31]  Ricky T. Tong,et al.  Effect of vascular normalization by antiangiogenic therapy on interstitial hypertension, peritumor edema, and lymphatic metastasis: insights from a mathematical model. , 2007, Cancer research.

[32]  R. Jain,et al.  Delivery of molecular and cellular medicine to solid tumors. , 1998, Journal of controlled release : official journal of the Controlled Release Society.

[33]  D. P. Mason,et al.  Evolution of stress and strain during the consolidation of a fluid‐saturated porous elastic sphere , 1991 .

[34]  Tomasz Opala.  Elastography as a new diagnostic tool to detect breast cancer - evaluation of research and clinical applications Elastografia jako nowe narzêdzie wykrywania raka piersi - ocena badañ i zastosowañ klinicznych , 2011 .

[35]  Xu Yang,et al.  Performance Analysis of a New Real-Time Elastographic Time Constant Estimator , 2011, IEEE Transactions on Medical Imaging.

[36]  Jeffrey C Bamber,et al.  Coupling between elastic strain and interstitial fluid flow: ramifications for poroelastic imaging , 2006, Physics in medicine and biology.

[37]  J. Suh,et al.  Biphasic Poroviscoelastic Behavior of Hydrated Biological Soft Tissue , 1999 .

[38]  D Pflaster,et al.  A poroelastic finite element formulation including transport and swelling in soft tissue structures. , 1996, Journal of biomechanical engineering.

[39]  Hui Zhi,et al.  Comparison of Ultrasound Elastography, Mammography, and Sonography in the Diagnosis of Solid Breast Lesions , 2007, Journal of ultrasound in medicine : official journal of the American Institute of Ultrasound in Medicine.

[40]  Jiajia Zhou,et al.  Application of Tunable-Slip Boundary Conditions in Particle-Based Simulations , 2015, HiPC 2015.

[41]  H M Byrne,et al.  A mathematical model of the stress induced during avascular tumour growth , 2000, Journal of mathematical biology.

[42]  On Cryer's problem with large displacements , 1989 .

[43]  W Ehlers,et al.  A linear viscoelastic biphasic model for soft tissues based on the Theory of Porous Media. , 2001, Journal of biomechanical engineering.

[44]  R. Skalak,et al.  Time-dependent behavior of interstitial fluid pressure in solid tumors: implications for drug delivery. , 1995, Cancer research.

[45]  R K Jain,et al.  Transport of fluid and macromolecules in tumors. IV. A microscopic model of the perivascular distribution. , 1991, Microvascular research.

[46]  Matija Snuderl,et al.  Coevolution of solid stress and interstitial fluid pressure in tumors during progression: implications for vascular collapse. , 2013, Cancer research.

[47]  R. Jain,et al.  Role of extracellular matrix assembly in interstitial transport in solid tumors. , 2000, Cancer research.

[48]  Jonathan Ophir,et al.  The feasibility of using elastography for imaging the Poisson's ratio in porous media. , 2004, Ultrasound in medicine & biology.

[49]  David A. Jaffray,et al.  A Mathematical Model of the Enhanced Permeability and Retention Effect for Liposome Transport in Solid Tumors , 2013, PloS one.

[50]  R K Jain,et al.  Mechanics of interstitial-lymphatic fluid transport: theoretical foundation and experimental validation. , 1999, Journal of biomechanics.

[51]  Md Tauhidul Islam,et al.  An analytical poroelastic model for ultrasound elastography imaging of tumors , 2018, Physics in medicine and biology.

[52]  T. Krouskop,et al.  Poroelastography: imaging the poroelastic properties of tissues. , 2001, Ultrasound in medicine & biology.

[53]  Md Tauhidul Islam,et al.  An analytical poroelastic model of a non-homogeneous medium under creep compression for ultrasound poroelastography applications - Part I. , 2019, Journal of biomechanical engineering.

[54]  P. Rzymski,et al.  Changes in ultrasound shear wave elastography properties of normal breast during menstrual cycle. , 2011, Clinical and experimental obstetrics & gynecology.

[55]  Farshid Guilak,et al.  Stress, Strain, Pressure and Flow Fields in Articular Cartilage and Chondrocytes , 1994 .

[56]  Y. Fung,et al.  Biomechanics: Mechanical Properties of Living Tissues , 1981 .

[57]  Mickael Tanter,et al.  Viscoelastic shear properties of in vivo breast lesions measured by MR elastography. , 2005, Magnetic resonance imaging.

[58]  G A Ateshian,et al.  A Theoretical Analysis of Water Transport Through Chondrocytes , 2007, Biomechanics and modeling in mechanobiology.

[59]  J. Rudnicki,et al.  Shear properties of heterogeneous fluid-filled porous media with spherical inclusions , 2016 .