Growth of confined cancer spheroids: a combined experimental and mathematical modelling approach.

A critical step in the dissemination of ovarian cancer is the formation of multicellular spheroids from cells shed from the primary tumour. The objectives of this study were to apply bioengineered three-dimensional (3D) microenvironments for culturing ovarian cancer spheroids in vitro and simultaneously to build on a mathematical model describing the growth of multicellular spheroids in these biomimetic matrices. Cancer cells derived from human epithelial ovarian carcinoma were embedded within biomimetic hydrogels of varying stiffness and grown for up to 4 weeks. Immunohistochemistry, imaging and growth analyses were used to quantify the dependence of cell proliferation and apoptosis on matrix stiffness, long-term culture and treatment with the anti-cancer drug paclitaxel. The mathematical model was formulated as a free boundary problem in which each spheroid was treated as an incompressible porous medium. The functional forms used to describe the rates of cell proliferation and apoptosis were motivated by the experimental work and predictions of the mathematical model compared with the experimental output. This work aimed to establish whether it is possible to simulate solid tumour growth on the basis of data on spheroid size, cell proliferation and cell death within these spheroids. The mathematical model predictions were in agreement with the experimental data set and simulated how the growth of cancer spheroids was influenced by mechanical and biochemical stimuli including matrix stiffness, culture duration and administration of a chemotherapeutic drug. Our computational model provides new perspectives on experimental results and has informed the design of new 3D studies of chemoresistance of multicellular cancer spheroids.

[1]  Martin A. Schwartz,et al.  Networks and crosstalk: integrin signalling spreads , 2002, Nature Cell Biology.

[2]  David J Mooney,et al.  Can tissue engineering concepts advance tumor biology research? , 2010, Trends in biotechnology.

[3]  R. Kreienberg,et al.  Morphological, immunohistochemical and biochemical characterization of 6 newly established human ovarian carcinoma cell lines , 1992, International journal of cancer.

[4]  L. Moro,et al.  Integrin regulation of epidermal growth factor (EGF) receptor and of EGF-dependent responses. , 2004, Biochemical Society transactions.

[5]  D L S McElwain,et al.  A history of the study of solid tumour growth: The contribution of mathematical modelling , 2004, Bulletin of mathematical biology.

[6]  R. Jain,et al.  Micro-Environmental Mechanical Stress Controls Tumor Spheroid Size and Morphology by Suppressing Proliferation and Inducing Apoptosis in Cancer Cells , 2009, PloS one.

[7]  Dirk Drasdo,et al.  Individual-based and continuum models of growing cell populations: a comparison , 2009, Journal of mathematical biology.

[8]  Dietmar W. Hutmacher,et al.  Long-term effects of hydrogel properties on human chondrocyte behavior , 2010 .

[9]  Mina J Bissell,et al.  Unraveling the microenvironmental influences on the normal mammary gland and breast cancer. , 2008, Seminars in cancer biology.

[10]  H M Byrne,et al.  The influence of growth-induced stress from the surrounding medium on the development of multicell spheroids , 2001, Journal of mathematical biology.

[11]  Matthias P Lutolf,et al.  Biomolecular hydrogels formed and degraded via site-specific enzymatic reactions. , 2007, Biomacromolecules.

[12]  A C Burton,et al.  Rate of growth of solid tumours as a problem of diffusion. , 1966, Growth.

[13]  V. Georgoulias,et al.  Taxol affects nuclear lamina and pore complex organization and inhibits import of karyophilic proteins into the cell nucleus. , 1999, Cancer research.

[14]  K. Anseth,et al.  A synthetic strategy for mimicking the extracellular matrix provides new insight about tumor cell migration. , 2010, Integrative biology : quantitative biosciences from nano to macro.

[15]  Paul S. Freemont,et al.  Computational design approaches and tools for synthetic biology. , 2011, Integrative biology : quantitative biosciences from nano to macro.

[16]  F. Miller,et al.  Factors affecting growth and drug sensitivity of mouse mammary tumor lines in collagen gel cultures. , 1985, Cancer research.

[17]  H. G. Landau,et al.  Heat conduction in a melting solid , 1950 .

[18]  Luigi Preziosi,et al.  Mechanics in Tumor Growth , 2007 .

[19]  S. Cory,et al.  The Bcl2 family: regulators of the cellular life-or-death switch , 2002, Nature Reviews Cancer.

[20]  Ben D MacArthur,et al.  Residual stress generation and necrosis formation in multi-cell tumour spheroids , 2004, Journal of mathematical biology.

[21]  H. Greenspan.  On the growth and stability of cell cultures and solid tumors. , 1976, Journal of theoretical biology.

[22]  Anirikh Chakrabarti,et al.  Multiscale Models of Breast Cancer Progression , 2012, Annals of Biomedical Engineering.

[23]  Thomas A Sellers,et al.  Epidemiology of ovarian cancer. , 2009, Methods in molecular biology.

[24]  H. Dvorak.  Tumors: wounds that do not heal. Similarities between tumor stroma generation and wound healing. , 1986, The New England journal of medicine.

[25]  M. Bogyo,et al.  Caspase-8 association with the focal adhesion complex promotes tumor cell migration and metastasis. , 2009, Cancer research.

[26]  Anna V. Taubenberger,et al.  Phenotypic Characterization of Prostate Cancer LNCaP Cells Cultured within a Bioengineered Microenvironment , 2012, PloS one.

[27]  C. Dumontet,et al.  Microtubule-binding agents: a dynamic field of cancer therapeutics , 2010, Nature Reviews Drug Discovery.

[28]  Paolo A. Netti,et al.  Solid stress inhibits the growth of multicellular tumor spheroids , 1997, Nature Biotechnology.

[29]  H. Ogata,et al.  Annexin V inhibits the 12-O-tetradecanoylphorbol-13-acetate-induced activation of Ras/extracellular signal-regulated kinase (ERK) signaling pathway upstream of Shc in MCF-7 cells , 2000, Oncogene.

[30]  Pamela K. Kreeger,et al.  Cancer systems biology: a network modeling perspective , 2009, Carcinogenesis.

[31]  P. Mendes,et al.  Multi-scale modelling and simulation in systems biology. , 2011, Integrative biology : quantitative biosciences from nano to macro.

[32]  R. Ozols,et al.  Focus on epithelial ovarian cancer. , 2004, Cancer cell.

[33]  David A. Cheresh,et al.  Integrins in cancer: biological implications and therapeutic opportunities , 2010, Nature Reviews Cancer.

[34]  G. Rice,et al.  Role of Integrin Receptors for Fibronectin, Collagen and Laminin in the Regulation of Ovarian Carcinoma Functions in Response to a Matrix Microenvironment , 2005, Clinical & Experimental Metastasis.

[35]  H. Byrne.  Dissecting cancer through mathematics: from the cell to the animal model , 2010, Nature Reviews Cancer.

[36]  R. Sutherland.  Cell and environment interactions in tumor microregions: the multicell spheroid model. , 1988, Science.

[37]  Dietmar W. Hutmacher,et al.  Bioengineered 3D platform to explore cell-ECM interactions and drug resistance of epithelial ovarian cancer cells. , 2010, Biomaterials.

[38]  N. Hacker,et al.  Epidermal growth factor receptor signaling and the invasive phenotype of ovarian carcinoma cells. , 2001, Journal of the National Cancer Institute.

[39]  D L McElwain,et al.  A model of vascular compression in solid tumours. , 1979, Journal of theoretical biology.

[40]  J. Ferlay,et al.  Worldwide burden of gynaecological cancer: the size of the problem. , 2006, Best practice & research. Clinical obstetrics & gynaecology.

[41]  G. Rice,et al.  Multicellular spheroids in ovarian cancer metastases: Biology and pathology. , 2009, Gynecologic oncology.

[42]  Juergen Friedrich,et al.  Experimental anti-tumor therapy in 3-D: Spheroids – old hat or new challenge? , 2007, International journal of radiation biology.

[43]  Matthias P Lutolf,et al.  Enzymatic formation of modular cell-instructive fibrin analogs for tissue engineering. , 2007, Biomaterials.

[44]  Kenneth M. Yamada,et al.  Modeling Tissue Morphogenesis and Cancer in 3D , 2007, Cell.

[45]  W. Kung,et al.  Paclitaxel (Taxol) upregulates expression of functional interleukin-6 in human ovarian cancer cells through multiple signaling pathways , 2006, Oncogene.

[46]  Nils Cordes,et al.  Signalling via integrins: implications for cell survival and anticancer strategies. , 2007, Biochimica et biophysica acta.

[47]  R. Jain,et al.  Solid stress generated by spheroid growth estimated using a linear poroelasticity model. , 2003, Microvascular research.

[48]  R E Durand,et al.  Resistance of tumor cells to chemo- and radiotherapy modulated by the three-dimensional architecture of solid tumors and spheroids. , 2001, Methods in cell biology.

[49]  H. Greenspan.  Models for the Growth of a Solid Tumor by Diffusion , 1972 .

[50]  D. McElwain,et al.  A linear-elastic model of anisotropic tumour growth , 2004, European Journal of Applied Mathematics.

[51]  F. Pampaloni,et al.  The third dimension bridges the gap between cell culture and live tissue , 2007, Nature Reviews Molecular Cell Biology.