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Research Papers

A Novel Finite Element Model to Assess the Effect of Solid Stress Inside Tumors on Elastographic Normal Strains and Fluid Pressure

[+] 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

Raffaella Righetti

Department of Electrical and
Computer Engineering,
Texas A&M University,
College Station, TX 77840
e-mail: righetti@ece.tamu.edu

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING AND SCIENCE IN MEDICAL DIAGNOSTICS AND THERAPY Manuscript received March 9, 2019; final manuscript received May 30, 2019; published online July 3, 2019. Assoc. Editor: Osama Mukdadi.

ASME J of Medical Diagnostics 2(3), 031006 (Jul 03, 2019) (11 pages) Paper No: JESMDT-19-1015; doi: 10.1115/1.4044048 History: Received March 09, 2019; Revised May 30, 2019

Ultrasound elastography is a noninvasive imaging modality used to assess the mechanical behavior of tissues, including cancers. Analytical and finite element (FE) models are useful and effective tools to understand the mechanical behavior of cancers and predict elastographic parameters under different testing conditions. A number of analytical and FE models to describe the mechanical behavior of cancers in elastography have been reported in the literature. However, none of these models consider the presence of solid stress (SS) inside the cancer, a clinically significant mechanical parameter with an influential role in cancer initiation, progression, and metastasis. In this paper, we develop an FE model applicable to cancers, which include both SS and elevated interstitial fluid pressure (IFP). This model is then used to assess the effects of these mechanical parameters on the normal strains and the fluid pressure, estimated using ultrasound poroelastography. Our results indicate that SS creates space-dependent changes in the strains and fluid pressure inside the tumor. This is in contrast to the effects produced by IFP on the strains and fluid pressure, which are uniformly distributed across the cancer. The developed model can help elucidating the role of SS on elastographic parameters and images. It may also provide a means to indirectly obtain information about the SS from the observed changes in the experimental elastographic images.

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References

Stylianopoulos, T. , Martin, J. D. , Snuderl, M. , Mpekris, F. , Jain, S. R. , and Jain, R. K. , 2013, “ Coevolution of Solid Stress and Interstitial Fluid Pressure in Tumors During Progression: Implications for Vascular Collapse,” Cancer Res., 73(13), pp. 3833–3841. [CrossRef] [PubMed]
Stylianopoulos, T. , 2017, “ The Solid Mechanics of Cancer and Strategies for Improved Therapy,” ASME J. Biomech. Eng., 139(2), p. 021004. [CrossRef]
Sarntinoranont, M. , Rooney, F. , and Ferrari, M. , 2003, “ Interstitial Stress and Fluid Pressure Within a Growing Tumor,” Ann. Biomed. Eng., 31(3), pp. 327–335. [CrossRef] [PubMed]
Fernández-Sánchez, M. E. , Barbier, S. , Whitehead, J. , Béalle, G. , Michel, A. , Latorre-Ossa, H. , Rey, C. , Fouassier, L. , Claperon, A. , Brullé, L. , Girard, E. , Servant, N. , Rio-Frio, T. , Marie, H. , Lesieur, S. , Housset, C. , Gennisson, J.-L. , Tanter, M. , Ménager, C. , Fre, S. , Robine, S. , and Farge, E. , 2015, “ Mechanical Induction of the Tumorigenic [Bgr]-Catenin Pathway by Tumour Growth Pressure,” Nature, 523(7558), pp. 92–95. [CrossRef] [PubMed]
Stylianopoulos, T. , Martin, J. D. , Chauhan, V. P. , Jain, S. R. , Diop-Frimpong, B. , Bardeesy, N. , Smith, B. L. , Ferrone, C. R. , Hornicek, F. J. , Boucher, Y. , Munn, L. L. , and Jain, R. K. , 2012, “ Causes, Consequences, and Remedies for Growth-Induced Solid Stress in Murine and Human Tumors,” Proc. Natl. Acad. Sci. U. S. A., 109(38), pp. 15101–15108. [CrossRef] [PubMed]
Rofstad, E. K. , Galappathi, K. , and Mathiesen, B. S. , 2014, “ Tumor Interstitial Fluid Pressure a Link Between Tumor Hypoxia, Microvascular Density, and Lymph Node Metastasis,” Neoplasia, 16(7), pp. 586–594. [CrossRef] [PubMed]
Griffon-Etienne, G. , Boucher, Y. , Brekken, C. , Suit, H. D. , and Jain, R. K. , 1999, “ Taxane-Induced Apoptosis Decompresses Blood Vessels and Lowers Interstitial Fluid Pressure in Solid Tumors,” Cancer Res., 59(15), pp. 3776–3782. http://cancerres.aacrjournals.org/content/59/15/3776.long [PubMed]
Padera, T. P. , Kadambi, A. , di Tomaso, E. , Carreira, C. M. , Brown, E. B. , Boucher, Y. , Choi, N. C. , Mathisen, D. , Wain, J. , Mark, E. J. , and Munn, L. L. , 2002, “ Lymphatic Metastasis in the Absence of Functional Intratumor Lymphatics,” Science, 296(5574), pp. 1883–1886. [CrossRef] [PubMed]
Padera, T. P. , Stoll, B. R. , Tooredman, J. B. , Capen, D. , di Tomaso, E. , and Jain, R. K. , 2004, “ Pathology: Cancer Cells Compress Intratumour Vessels,” Nature, 427(6976), pp. 695–695. [CrossRef] [PubMed]
Facciabene, A. , Peng, X. , Hagemann, I. S. , Balint, K. , Barchetti, A. , Wang, L.-P. , Gimotty, P. A. , Gilks, C. B. , Lal, P. , Zhang, L. , and Coukos, G. , 2011, “ Tumour Hypoxia Promotes Tolerance and Angiogenesis Via ccl28 and Treg Cells,” Nature, 475(7355), pp. 226–230. [CrossRef] [PubMed]
Jain, R. K. , 1988, “ Determinants of Tumor Blood Flow: A Review,” Cancer Res., 48(10), pp. 2641–2658. http://cancerres.aacrjournals.org/content/48/10/2641 [PubMed]
Helmlinger, G. , Netti, P. A. , Lichtenbeld, H. C. , Melder, R. J. , and Jain, R. K. , 1997, “ Solid Stress Inhibits the Growth of Multicellular Tumor Spheroids,” Nat. Biotechnol., 15(8), pp. 778–783. [CrossRef] [PubMed]
Janet, M. T. , Cheng, G. , Tyrrell, J. A. , Wilcox-Adelman, S. A. , Boucher, Y. , Jain, R. K. , and Munn, L. L. , 2012, “ Mechanical Compression Drives Cancer Cells Toward Invasive Phenotype,” Proc. Natl. Acad. Sci. U. S. A., 109(3), pp. 911–916. https://www.pnas.org/content/109/3/911 [PubMed]
Jain, R. K. , 1997, “ Delivery of Molecular and Cellular Medicine to Solid Tumors,” Adv. Drug Delivery Rev., 26(2–3), pp. 71–90. [CrossRef]
Burton , J. K., III , 2016, Theoretical Models for Drug Delivery to Solid Tumors, The University of Arizona, Tucson, AZ.
Iranmanesh, F. , and Nazari, M. A. , 2017, “ Finite Element Modeling of Avascular Tumor Growth Using a Stress-Driven Model,” ASME J. Biomech. Eng., 139(8), p. 081009. [CrossRef]
Jiang, Y. , Pjesivac-Grbovic, J. , Cantrell, C. , and Freyer, J. P. , 2005, “ A Multiscale Model for Avascular Tumor Growth,” Biophys. J., 89(6), pp. 3884–3894. [CrossRef] [PubMed]
Ambrosi, D. , and Mollica, F. , 2002, “ On the Mechanics of a Growing Tumor,” Int. J. Eng. Sci., 40(12), pp. 1297–1316. [CrossRef]
Araujo, R. P. , and McElwain, D. , 2004, “ A Linear-Elastic Model of Anisotropic Tumour Growth,” Eur. J. Appl. Math., 15(3), pp. 365–384. [CrossRef]
MacLaurin, J. , Chapman, J. , Jones, G. W. , and Roose, T. , 2012, “ The Buckling of Capillaries in Solid Tumours,” Proc. R. Soc. A, 468(2148), pp. 4123–4145. [CrossRef]
Kim, Y. , Stolarska, M. A. , and Othmer, H. G. , 2007, “ A Hybrid Model for Tumor Spheroid Growth In Vitro—Part I: Theoretical Development and Early Results,” Math. Models Methods Appl. Sci., 17(Suppl. 1), pp. 1773–1798. [CrossRef]
Baxter, L. T. , and Jain, R. K. , 1989, “ Transport of Fluid and Macromolecules in Tumors—Part I: Role of Interstitial Pressure and Convection,” Microvasc. Res., 37(1), pp. 77–104. [CrossRef] [PubMed]
Baxter, L. T. , and Jain, R. K. , 1990, “ Transport of Fluid and Macromolecules in Tumors—Part II: Role of Heterogeneous Perfusion and Lymphatics,” Microvasc. Res., 40(2), pp. 246–263. [CrossRef] [PubMed]
Baxter, L. T. , and Jain, R. K. , 1991, “ Transport of Fluid and Macromolecules in Tumors—Part IV: A Microscopic Model of the Perivascular Distribution,” Microvasc. Res., 41(2), pp. 252–272. [CrossRef] [PubMed]
Wang, C.-H. , and Li, J. , 1998, “ Three-Dimensional Simulation of Igg Delivery to Tumors,” Chem. Eng. Sci., 53(20), pp. 3579–3600. [CrossRef]
Wang, C.-H. , Li, J. , Teo, C. S. , and Lee, T. , 1999, “ The Delivery of Bcnu to Brain Tumors,” J. Controlled Release, 61(1–2), pp. 21–41. [CrossRef]
Zhao, J. , Salmon, H. , and Sarntinoranont, M. , 2007, “ Effect of Heterogeneous Vasculature on Interstitial Transport Within a Solid Tumor,” Microvasc. Res., 73(3), pp. 224–236. [CrossRef] [PubMed]
Netti, P. , Baxter, L. , Coucher, Y. , Skalak, R. , and Jain, R. , 1995, “ A Poroelastic Model for Interstitial Pressure in Tumors,” Biorheology, 32(2–3), pp. 346–346. [CrossRef]
Soltani, M. , and Chen, P. , 2011, “ Numerical Modeling of Fluid Flow in Solid Tumors,” PLoS One, 6(6), p. e20344. [CrossRef] [PubMed]
Soltani, M. , and Chen, P. , 2013, “ Numerical Modeling of Interstitial Fluid Flow Coupled With Blood Flow Through a Remodeled Solid Tumor Microvascular Network,” PLoS One, 8(6), p. e67025. [CrossRef] [PubMed]
Cattaneo, L. , and Zunino, P. , 2014, “ Computational Models for Fluid Exchange Between Microcirculation and Tissue Interstitium,” Networks Heterogeneous Media, 9(1), pp. 135–159. [CrossRef]
Ambrosi, D. , and Preziosi, L. , 2008, “ Cell Adhesion Mechanisms and Stress Relaxation in the Mechanics of Tumours,” Biomech. Model. Mechanobiol., 8(5), p. 397413. https://link.springer.com/article/10.1007/s10237-008-0145-y
Preziosi, L. , Ambrosi, D. , and Verdier, C. , 2010, “ An Elasto-Visco-Plastic Model of Cell Aggregates,” J. Theor. Biol., 262(1), pp. 35–47. [CrossRef] [PubMed]
Mpekris, F. , Angeli, S. , Pirentis, A. P. , and Stylianopoulos, T. , 2015, “ Stress-Mediated Progression of Solid Tumors: Effect of Mechanical Stress on Tissue Oxygenation, Cancer Cell Proliferation, and Drug Delivery,” Biomech. Model. Mechanobiol., 14(6), pp. 1391–1402. [CrossRef] [PubMed]
Ophir, J. , Cespedes, I. , Ponnekanti, H. , Yazdi, Y. , and Li, X. , 1991, “ Elastography: A Quantitative Method for Imaging the Elasticity of Biological Tissues,” Ultrason. Imaging, 13(2), pp. 111–134. [CrossRef] [PubMed]
Ophir, J. , Alam, S. , Garra, B. , Kallel, F. , Konofagou, E. , Krouskop, T. , and Varghese, T. , 1999, “ Elastography: Ultrasonic Estimation and Imaging of the Elastic Properties of Tissues,” Proc. Inst. Mech. Eng., Part H, 213(3), pp. 203–233. [CrossRef]
Righetti, R. , Garra, B. S. , Mobbs, L. M. , Kraemer-Chant, C. M. , Ophir, J. , and Krouskop, T. A. , 2007, “ The Feasibility of Using Poroelastographic Techniques for Distinguishing Between Normal and Lymphedematous Tissues In Vivo,” Phys. Med. Biol., 52(21), p. 6525. [CrossRef] [PubMed]
Righetti, R. , Ophir, J. , Srinivasan, S. , and Krouskop, T. A. , 2004, “ The Feasibility of Using Elastography for Imaging the Poisson's Ratio in Porous Media,” Ultrasound Med. Biol., 30(2), pp. 215–228. [CrossRef] [PubMed]
Islam, M. T. , Chaudhry, A. , Unnikrishnan, G. , Reddy, J. , and Righetti, R. , 2018, “ An Analytical Model of Tumors With Higher Permeability Than Surrounding Tissues for Ultrasound Elastography Imaging,” J. Eng. Sci. Med. Diagn. Ther., 1(3), p. 031006. [CrossRef]
Islam, M. T. , Chaudhry, A. , Unnikrishnan, G. , Reddy, J. , and Righetti, R. , 2018, “ An Analytical Poroelastic Model for Ultrasound Elastography Imaging of Tumors,” Phys. Med. Biol., 63(2), p. 025031. [CrossRef] [PubMed]
Islam, M. T. , Reddy, J. , and Righetti, R. , 2019, “ An Analytical Poroelastic Model of a Nonhomogeneous Medium Under Creep Compression for Ultrasound Poroelastography Applications—Part I,” ASME J. Biomech. Eng., 141(6), p. 060902. [CrossRef]
Islam, M. T. , Reddy, J. , and Righetti, R. , 2019, “ An Analytical Poroelastic Model of a Nonhomogeneous Medium Under Creep Compression for Ultrasound Poroelastography Applications—Part II,” ASME J. Biomech. Eng., 141(6), p. 060903. [CrossRef]
Islam, M. T. , Reddy, J. , and Righetti, R. , 2018, “ A Model-Based Approach to Investigate the Effect of Elevated Interstitial Fluid Pressure on Strain Elastography,” Phys. Med. Biol., 63(21), p. 215011. [CrossRef] [PubMed]
Leiderman, R. , Barbone, P. E. , Oberai, A. A. , and Bamber, J. C. , 2006, “ Coupling Between Elastic Strain and Interstitial Fluid Flow: Ramifications for Poroelastic Imaging,” Phys. Med. Biol., 51(24), pp. 6291–6313. [CrossRef] [PubMed]
Karlsson, S. , 2006, “Version 6.6, ABAQUS,” ABAQUS, Providence, RI.
Berry, G. P. , Bamber, J. C. , Armstrong, C. G. , Miller, N. R. , and Barbone, P. E. , 2006, “ Towards an Acoustic Model-Based Poroelastic Imaging Method—Part I: Theoretical Foundation,” Ultrasound Med. Biol., 32(4), pp. 547–567. [CrossRef] [PubMed]
Netti, P. A. , Baxter, L. T. , Boucher, Y. , Skalak, R. , and Jain, R. K. , 1997, “ Macro-and Microscopic Fluid Transport in Living Tissues: Application to Solid Tumors,” AIChE J., 43(3), pp. 818–834. [CrossRef]
Zhi, H. , Ou, B. , Luo, B.-M. , Feng, X. , Wen, Y.-L. , and Yang, H.-Y. , 2007, “ Comparison of Ultrasound Elastography, Mammography, and Sonography in the Diagnosis of Solid Breast Lesions,” J. Ultrasound Med., 26(6), pp. 807–815. [CrossRef] [PubMed]
Rzymski, P. , and Opala, T. , 2011, “ Elastography as a New Diagnostic Tool to Detect Breast Cancer–Evaluation of Research and Clinical Applications,” Przegl. Menopauzalny, 10, pp. 357–362. https://www.termedia.pl/Elastography-as-a-new-diagnostic-tool-to-detect-breast-cancer-r-n-evaluation-of-research-and-clinical-applications,4,17580,0,1.html
Mpekris, F. , Baish, J. W. , Stylianopoulos, T. , and Jain, R. K. , 2017, “ Role of Vascular Normalization in Benefit From Metronomic Chemotherapy,” Proc. Natl. Acad. Sci. U. S. A., 114(8), pp. 1994–1999. [CrossRef] [PubMed]
Fung, Y.-C. , 1993, “ Mechanical Properties and Active Remodeling of Blood Vessels,” Biomechanics, Springer, New York, pp. 321–391.
Netti, P. A. , Berk, D. A. , Swartz, M. A. , Grodzinsky, A. J. , and Jain, R. K. , 2000, “ Role of Extracellular Matrix Assembly in Interstitial Transport in Solid Tumors,” Cancer Res., 60(9), pp. 2497–2503. http://cancerres.aacrjournals.org/content/60/9/2497.long [PubMed]
Less, J. R. , Posner, M. C. , Boucher, Y. , Borochovitz, D. , Wolmark, N. , and Jain, R. K. , 1992, “ Interstitial Hypertension in Human Breast and Colorectal Tumors,” Cancer Res., 52(22), pp. 6371–6374. http://cancerres.aacrjournals.org/content/52/22/6371.long [PubMed]
Milosevic, M. F. , Fyles, A. W. , Wong, R. , Pintilie, M. , Kavanagh, M.-C. , Levin, W. , Manchul, L. A. , Keane, T. J. , and Hill, R. P. , 1998, “ Interstitial Fluid Pressure in Cervical Carcinoma,” Cancer, 82(12), pp. 2418–2426. [CrossRef] [PubMed]
Nia, H. T. , Liu, H. , Seano, G. , Datta, M. , Jones, D. , Rahbari, N. , Incio, J. , Chauhan, V. P. , Jung, K. , Martin, J. D. , and Askoxylakis, V. , 2016, “ Solid Stress and Elastic Energy as Measures of Tumour Mechanopathology,” Nat. Biomed. Eng., 1, p. 0004. [CrossRef] [PubMed]
Varghese, T. , and Ophir, J. , 1997, “ A Theoretical Framework for Performance Characterization of Elastography: The Strain Filter,” IEEE Trans. Ultrason., Ferroelectr., Freq. Control, 44(1), pp. 164–172. [CrossRef]
Nieskoski, M. D. , Marra, K. , Gunn, J. R. , Hoopes, P. J. , Doyley, M. M. , Hasan, T. , Trembly, B. S. , and Pogue, B. W. , 2017, “ Collagen Complexity Spatially Defines Microregions of Total Tissue Pressure in Pancreatic Cancer,” Sci. Rep., 7(1), p. 10093. https://www.nature.com/articles/s41598-017-10671-w [PubMed]
Sayed, A. , Layne, G. , Abraham, J. , and Mukdadi, O. , 2012, “ 3D Ultrasound Elastographic Imaging and Characterization of Breast Cancer In Vivo,” ASME Paper No. IMECE2012-89624.
Ma, S. , Zhu, M. , Xia, X. , Guo, L. , Genin, G. M. , Sacks, M. S. , Gao, M. , Mutic, S. , Hu, Y. , Hu, C.-H. , and Feng, Y. , 2019, “ A Preliminary Study of the Local Biomechanical Environment of Liver Tumors In Vivo,” Med. Phys., 46(4), pp. 1728–1739.
Islam, M. T. , Tang, S. , Liverani, C. , Tasciotti, E. , and Righetti, R. , 2018, “ Non-Invasive Imaging of the Young's Modulus and Poisson's Ratio of Cancer Tumor In Vivo,” preprint arXiv:1809.02929.
Islam, M. T. , Tasciotti, E. , and Righetti, R. , 2018, “ Estimation of Vascular Permeability in Irregularly Shaped Cancers Using Ultrasound Poroelastography,” IEEE Trans. Biomed. Eng., (under review).
Locke, S. , 2014, “ The Effect of Interstitial Pressure on Tumour Stiffness,” Ph.D. thesis, University of Toronto, Toronto, ON, Canada. https://tspace.library.utoronto.ca/bitstream/1807/67892/1/Locke_Stuart_201411_MSc_thesis.pdf

Figures

Grahic Jump Location
Fig. 1

(a) A schematic of a cylindrical sample of a poroelastic material with a spherical inclusion of radius a. The axial direction is along the z-axis. Inside the inclusion, R indicates the radial direction. (b) The 2D solution plane for the three dimensional sample.

Grahic Jump Location
Fig. 2

Axial strains at time points of 0.6 s (0+ s), 4.8 s, 9 s, 18 s, and 57.6 s for samples A–D are shown in (A1–A5), (B1–B5), (C1–C5), and (D1–D5), respectively

Grahic Jump Location
Fig. 3

Radial strains at time points of 0.6 s (0+ s), 4.8 s, 9 s, 18 s, and 57.6 s for samples A–D are shown in (A1–A5), (B1–B5), (C1–C5), and (D1–D5), respectively

Grahic Jump Location
Fig. 4

EPRs at time points of 0.6 s (0+ s), 4.8 s, 9 s, 18 s, and 57.6 s for samples A–D are shown in (A1–A5), (B1–B5), (C1–C5), and (D1–D5), respectively

Grahic Jump Location
Fig. 5

Volumetric strains at time points of 0.6 s (0+ s), 4.8 s, 9 s, 18 s, and 57.6 s for samples A–D are shown in (A1–A5), (B1–B5), (C1–C5), and (D1–D5), respectively

Grahic Jump Location
Fig. 6

Fluid pressures at time points of 0.6 s (0+ s), 4.8 s, 9 s, 18 s, and 57.6 s for samples A–D are shown in (A1–A5), (B1–B5), (C1–C5), and (D1–D5), respectively

Grahic Jump Location
Fig. 7

Time profiles of the axial strain (AS) at different radii inside the tumor of samples A–D are shown in (A1), (B1), (C1), and (D1), respectively. Time profiles of the radial strain (RS) at different radii inside the tumor of samples A–D are illustrated in (A2), (B2), (C2), and (D2), respectively. Time profiles of the EPR at different radii inside the tumor of samples A–D are shown in (A3–D3).

Grahic Jump Location
Fig. 8

Time profiles of the volumetric strain (VS) at different radii inside the tumor of samples A–D are shown in (A1), (B1), (C1), and (D1), respectively. Time profiles of the fluid pressure (FP) in Pa at different radii inside the tumor of samples A–D are illustrated in (A2–D2).

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