A model-based approach to investigate the effect of elevated interstitial fluid pressure on strain elastography

Finite element (FE) modeling provides a useful tool to understand the mechanical behavior of complex tissues, such as cancers, in a variety of testing conditions. Although a number of numerical and analytical models for cancerous tumors are retrievable in the literature, none of these models is capable of completely describing the behavior of a cancer embedded in a normal tissue in the conditions typical for an ultrasound elastography experiment. In this paper, we first design and implement a realistic FE model of the mechanical behavior of a cancer embedded in a normal tissue under ultrasound elastography testing conditions. In addition to the commonly used tissue mechanical properties, for the cancer, elevated interstitial fluid pressure (IFP) is incorporated in the model. IFP is a parameter of great clinical significance, but it is not typically considered in elastographic models of tumors. The developed model is then used to thoroughly study the effect of IFP on the axial, lateral and volumetric strains inside the tumor. The results of this study demonstrate that the presence of the IFP affects both the temporal and spatial distributions of the axial, lateral, volumetric strains and related elastographic parameters. Thus, these results lead to two important considerations: (1) that a correct interpretation of experimental elastographic data need a clear understanding of the effect of the IFP on the obtained elastograms and (2) that this IFP-dependent alteration of the elastographic parameters may provide an opportunity to non-invasively gain localized information about this clinically relevant parameter.

[1]  J. Li,et al.  The delivery of BCNU to brain tumors. , 1999, Journal of controlled release : official journal of the Controlled Release Society.

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

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

[4]  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.

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

[6]  John M. L. Ebos,et al.  Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth , 2014, PLoS Comput. Biol..

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

[8]  Namhee Kim,et al.  Effect of Interstitial Fluid Pressure on Ultrasound Axial Strain and Axial Shear Strain Elastography , 2017, Ultrasonic imaging.

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

[10]  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.

[11]  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.

[12]  V. Gkretsi,et al.  Hyaluronan-Derived Swelling of Solid Tumors, the Contribution of Collagen and Cancer Cells, and Implications for Cancer Therapy12 , 2016, Neoplasia.

[13]  Triantafyllos Stylianopoulos,et al.  Causes, consequences, and remedies for growth-induced solid stress in murine and human tumors , 2012, Proceedings of the National Academy of Sciences.

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

[15]  J. Ophir,et al.  Elastography: A Quantitative Method for Imaging the Elasticity of Biological Tissues , 1991, Ultrasonic imaging.

[16]  J. M. Kennedy,et al.  Hourglass control in linear and nonlinear problems , 1983 .

[17]  Malisa Sarntinoranont,et al.  Effect of heterogeneous vasculature on interstitial transport within a solid tumor. , 2007, Microvascular research.

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

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

[20]  Madjid Soltani,et al.  Interstitial Flow in Cancerous Tissue: Effect of Considering RemodeledCapillary Network , 2014 .

[21]  A. Fyles,et al.  Interstitial fluid pressure in cervical carcinoma , 1998, Cancer.

[22]  M. Nazari,et al.  Finite Element Modeling of Avascular Tumor Growth Using a Stress-Driven Model. , 2017, Journal of biomechanical engineering.

[23]  D. Longo,et al.  Interstitial pressure of subcutaneous nodules in melanoma and lymphoma patients: changes during treatment. , 1993, Cancer research.

[24]  R K Jain,et al.  Direct measurement of interstitial convection and diffusion of albumin in normal and neoplastic tissues by fluorescence photobleaching. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

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

[26]  R K Jain,et al.  Interstitial pressure gradients in tissue-isolated and subcutaneous tumors: implications for therapy. , 1990, Cancer research.

[27]  R K Jain,et al.  Microvascular pressure is the principal driving force for interstitial hypertension in solid tumors: implications for vascular collapse. , 1992, Cancer research.

[28]  K Messmer,et al.  Interstitial hypertension in head and neck tumors in patients: correlation with tumor size. , 1992, Cancer research.

[29]  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.

[30]  Jelena Pjesivac-Grbovic,et al.  A multiscale model for avascular tumor growth. , 2005, Biophysical journal.

[31]  Jian Li,et al.  Three-dimensional simulation of IgG delivery to tumors , 1998 .

[32]  Michael F Insana,et al.  Ultrasonic viscoelasticity imaging of nonpalpable breast tumors: preliminary results. , 2008, Academic radiology.

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

[34]  S. Nathanson,et al.  Interstitial fluid pressure in breast cancer, benign breast conditions, and breast parenchyma , 1994, Annals of Surgical Oncology.

[35]  E. Rofstad,et al.  Radiocurability is associated with interstitial fluid pressure in human tumor xenografts. , 2009, Neoplasia.

[36]  Pu Chen,et al.  Effect of tumor shape and size on drug delivery to solid tumors , 2012, Journal of biological engineering.

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

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

[39]  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.

[40]  Anthony Fyles,et al.  Interstitial fluid pressure in tumors: therapeutic barrier and biomarker of angiogenesis. , 2008, Future oncology.

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

[42]  Laura Cattaneo,et al.  Computational models for fluid exchange between microcirculation and tissue interstitium , 2014, Networks Heterog. Media.

[43]  M. Sefidgar,et al.  Numerical modeling of drug delivery in a dynamic solid tumor microvasculature. , 2015, Microvascular research.

[44]  R K Jain,et al.  Interstitial hypertension in human breast and colorectal tumors. , 1992, Cancer research.

[45]  S M Larson,et al.  Characterization of neuroblastoma xenograft in rat flank. I. Growth, interstitial fluid pressure, and interstitial fluid velocity distribution profiles. , 1993, Microvascular research.

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

[47]  J P Laible,et al.  A dynamic material parameter estimation procedure for soft tissue using a poroelastic finite element model. , 1994, Journal of biomechanical engineering.

[48]  Kaamran Raahemifar,et al.  Effect of tumor shape, size, and tissue transport properties on drug delivery to solid tumors , 2014, Journal of biological engineering.

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

[50]  E. Rofstad,et al.  Tumor Interstitial Fluid Pressure—A Link between Tumor Hypoxia, Microvascular Density, and Lymph Node Metastasis , 2014, Neoplasia.

[51]  E. Rofstad,et al.  Associations between Radiocurability and Interstitial Fluid Pressure in Human Tumor Xenografts without Hypoxic Tissue , 2010, Clinical Cancer Research.

[52]  R K Jain,et al.  Delivery of Molecular Medicine to Solid Tumors , 1996, Science.

[53]  Pu Chen,et al.  Numerical Modeling of Fluid Flow in Solid Tumors , 2011, PloS one.

[54]  Paolo A. Netti,et al.  A poroelastic model for interstitial pressure in tumors , 1995 .

[55]  E. Rofstad,et al.  Pulmonary and lymph node metastasis is associated with primary tumor interstitial fluid pressure in human melanoma xenografts. , 2002, Cancer research.

[56]  Pu Chen,et al.  Numerical Modeling of Interstitial Fluid Flow Coupled with Blood Flow through a Remodeled Solid Tumor Microvascular Network , 2013, PloS one.