Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T18:11:40.698Z Has data issue: false hasContentIssue false
  • English
  • Français

A Hybrid Model Describing Different Morphologies of TumorInvasion Fronts

Published online by Cambridge University Press:  25 January 2012

M. Scianna  and
L. Preziosi
M. Scianna
Affiliation:
Department of Mathematics, Politecnico di Torino Corso Duca degli Abruzzi 24, 10129 Torino, Italy Institute for Cancer Research and Treatment Strada Provinciale 142, 10060 Candiolo, Italy
L. Preziosi*
Affiliation:
Department of Mathematics, Politecnico di Torino Corso Duca degli Abruzzi 24, 10129 Torino, Italy
*
⋆ Corresponding author. E-mail: [email protected]
Get access

Abstract

The invasive capability is fundamental in determining the malignancy of a solid tumor.Revealing biomedical strategies that are able to partially decrease cancer invasiveness istherefore an important approach in the treatment of the disease and has given rise tomultiple in vitro and in silico models. We here developa hybrid computational framework, whose aim is to characterize the effects of thedifferent cellular and subcellular mechanisms involved in the invasion of a malignantmass. In particular, a discrete Cellular Potts Model is used to represent the populationof cancer cells at the mesoscopic scale, while a continuous approach of reaction-diffusionequations is employed to describe the evolution of microscopic variables, as the nutrientsand the proteins present in the microenvironment and the matrix degrading enzymes secretedby the tumor. The behavior of each cell is then determined by a balance of forces, such ashomotypic (cell-cell) and heterotypic (cell-matrix) adhesions and haptotaxis, and ismediated by the internal state of the individual, i.e. its motility. The resultingcomposite model quantifies the influence of changes in the mechanisms involved in tumorinvasion and, more interestingly, puts in evidence possible therapeutic approaches, thatare potentially effective in decreasing the malignancy of the disease, such as thealteration in the adhesive properties of the cells, the inhibition in their ability toremodel and the disruption of the haptotactic movement. We also extend the simulationframework by including cell proliferation which, following experimental evidence, isregulated by the intracellular level of growth factors. Interestingly, in spite of theincrement in cellular density, the depth of invasion is not significantly increased, asone could have expected.

Keywords

cellular potts modeltumor invasion matrixmetalloproteinases
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 1: Cancer modeling , 2012 , pp. 78 - 104
Copyright
© EDP Sciences, 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abercrombie, M.. The crawling movement of cells. Proc. R. Soc. London B., 207 (1980), 129–147. CrossRefGoogle Scholar
Alarcon, T., Byrne, H., Maini, P.. A cellular automaton model for tumour growth in inhomogeneous environment. J. Theor. Biol., 225 (2003), 257–274. CrossRefGoogle ScholarPubMed
B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, P. Walter. Molecular Biology of the Cell, 4th ed. Garland Science, New York, 2002.
Anderson, A., Weaver, A., Commmings, P., Quaranta, V.. Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment. Cell, 127 (2006), 905–915. CrossRefGoogle ScholarPubMed
Anderson, A.. A hybrid mathematical model of solid tumour invasion : the importance of cell adhesion. Math. Med. Biol., 22 (2005), 163–186. CrossRefGoogle ScholarPubMed
Araujo, R., McElwain, D.. A history of the study of solid tumour growth : the contribution of mathematical modelling. Bull. Math. Biol., 66 (2004), 1039–1091. CrossRefGoogle ScholarPubMed
A. Balter, R. M. H. Merks, N. J. Poplawski, M. Swat, J. A. Glazier. The Glazier-Graner-Hogeweg model : extensions, future directions, and opportunities for further study. In A. R. A. Anderson, M. A. J. Chaplain, and K. A. Rejniak editors, Single-Cell-Based Models in Biology and Medicine, Mathematics and Biosciences in Interactions, Birkaüser, 151–167, 2007.
Bellomo, N., Li, N. K., Maini, P. K.. On the foundations of cancer modelling : selected topics, speculations, and perspectives. Math. Models Methods Appl. Sci., 18 (2008), 593–646. CrossRefGoogle Scholar
Bock, J. M., Sinclair, L. L., Bedford, N. S., Jackson, R. E., Lee, J. H., Trask, D. K.. Modulation of cellular invasion by VEGF-C expression in squamous cell carcinoma of the head and neck. Arch. Otolaryngol. Head. Neck. Surg., 134 (2008), No. 4, 355–362. CrossRefGoogle Scholar
Brown, J. M.. Tumor microenvironment and the response to anticancer therapy. Cancer Biol. Ther., 1 (2002), 453–458. CrossRefGoogle Scholar
Bru, A., Albertos, S., Subiza, J. L., García-Asenjo, J. L., Bru, I.. The universal dynamics of tumor growth. Bioph. J., 85 (2003), No. 5, 2948–2961. CrossRefGoogle ScholarPubMed
Cancer modeling and simulation, L. Preziosi editor, Mathematical Biology and Medicine Sciences, Chapman and Hall/CRC, 2003.
Byrne, H., Alarcon, T., Owen, M., Webb, S., Maini, P.. Modeling aspects of cancer dynamics : a review. Philos. Trans. R. Soc. A., 364 (2006), 1563–1578. CrossRefGoogle Scholar
M. A. J. Chaplain, A. R. A. Anderson. Mathematical modelling of tissue invasion. In L. Preziosi editor, Cancer Modelling and Simulation, Chapman Hall/CRC, 269–297, 2003.
Cristini, V., Frieboes, H., Gatenby, R., Caserta, S., Ferrari, M., Sinek, J.. Morphologic instability and cancer invasion. Clin. Cancer Res., 11 (2005), 6772–6779. CrossRefGoogle ScholarPubMed
Cristini, V., Lowengrub, J., Nie, Q.. Nonlinear simulation of tumor growth. J. Math. Biol., 46 (2003), 191–224. CrossRefGoogle Scholar
Cross, S. S.. Fractals in pathology. J. Pathol., 182 (1997), 1–8. 3.0.CO;2-B>CrossRefGoogle ScholarPubMed
De Luca, A., Arena, N., Sena, L. M., Medico, E.. Met overexpression confers HGF-dependent invasive phenotype to human thyroid carcinoma cells in vitro. J. Cell Physiol., 180 (1999), 365 –371. 3.0.CO;2-B>CrossRefGoogle ScholarPubMed
Di Renzo, M. F., Oliviero, M., Narsimhan, R. P., Bretti, S., Giordano, S., Medico, E., Gaglia, P., Zara, P., Comoglio, P. M.. Expression of the Met/HGF receptor in normal and neoplastic human tissues. Oncogene, 6 (1991), 1997–2003. Google Scholar
Engler, A., Bacakova, L., Newman, C., Hategan, A., Griffin, M., Discher, D.. Substrate compliance versus ligand density in cell on gel responses. Biophys. J., 86 (2004), 617–628. CrossRefGoogle Scholar
Gatenby, R., Smallbone, K., Maini, P., Rose, F., Averill, J., Nagle, R., Worrall, L., Gillies, R.. Cellular adaptations to hypoxia and acidosis during somatic evolution of breast cancer. Br. J. Cancer, 97 (2007), 646–653. CrossRefGoogle ScholarPubMed
Gaudet, C., Marganski, W., Kim, S., Brown, C. T., Gunderia, V., Dembo, M., Wong, J.. Influence of type I collagen surface density on fibroblast spreading, motility, and contractility. Biophys. J., 85 (2003), 3329–3335. CrossRefGoogle Scholar
Gerlee, P., Anderson, A.. An evolutionary hybrid cellular automaton model of solid tumor growth. J. Theor. Biol., 246 (2007), 583–603. CrossRefGoogle Scholar
Gerlee, P., Anderson, A.. Stability analysis of a hybrid cellular automaton model of cell colony growth. Phys. Rev. E, 75 (2007), 051911. CrossRefGoogle ScholarPubMed
Giverso, C., Scianna, M., Preziosi, L., Lo Buono, N., Funaro, A.. Individual cell-based model for in-vitro mesothelial invasion of ovarian cancer. Math. Model. Nat. Phenom., 5 (2010), No. 1, 203–223. CrossRefGoogle Scholar
J. A. Glazier, A. Balter, N. J. Poplawski. Magnetization to morphogenesis : A brief history of the Glazier-Graner-Hogeweg model. In A. R. A. Anderson, M. A. J. Chaplain, and K. A. Rejniak editors, Single-Cell-Based Models in Biology and Medicine, Mathematics and Biosciences in Interactions, Birkaüser, 79–106, 2007.
Glazier, J. A., Graner, F.. Simulation of the differential adhesion driven rearrangement of biological cells. Physical. Rev. E, 47 (1993), 2128–2154. CrossRefGoogle Scholar
Graner, F., Glazier, J. A.. Simulation of biological cell sorting using a two dimensional extended Potts model. Phys. Rev. Lett., 69 (1992), 2013–2017. CrossRefGoogle Scholar
Hatzikirou, H., Deutsch, A., Schaller, C., Simon, M., Swanson, K.. Mathematical modeling of glioblastoma tumour development : a review. Math. Models Methods Appl. Sci., 15 (2005), 1779–1794. CrossRefGoogle Scholar
Hegedus, B., Marga, F., Jakab, K., Sharpe-Timms, K. L., Forgacs, G.. The interplay of cell-cell and cell-matrix interactions in the invasive properties of brain tumors. Biophys. J., 91 (2006), 2708–2716. CrossRefGoogle ScholarPubMed
Hogea, C., Murray, B., Sethian, J.. Simulating complex tumor dynamics from avascular to vascular growth using a general level-set method. J. Math. Biol., 53 (2006), 86–134. CrossRefGoogle ScholarPubMed
Huang, S., Ingber, D. E.. The structural and mechanical complexity of cell-growth control. Nat. Cell Biol., 1 (1999), 131–138. Google ScholarPubMed
Ising, E.. Beitrag zur theorie des ferromagnetismus. Z. Physik., 31 (1925), 253. CrossRefGoogle Scholar
Jiang, Y., Pjesivac-Grbovic, J., Cantrell, C., Freyer, J.. A multiscale model for avascular tumor growth. Biophys. J., 89 (2005), 3884–3894. CrossRefGoogle ScholarPubMed
Kenny, H. A., Kaur, S., Coussens, L. M., Lengyel, E.. The initial steps of ovarian cancer cell metastasis are mediated by MMP-2 cleavage of vitronectin and fibronectin. J. Clin. Invest., 118 (2008), 1367–1379. CrossRefGoogle ScholarPubMed
Landini, G., Hirayama, Y., Li, T. J., Kitano, M.. Increased fractal complexity of the epithelialŰ connective tissue interface in the tongue of 4NQ0-treated rats. Pathol. Res. Pract., 196 (2000), 251–258. CrossRefGoogle Scholar
Li, X., Cristini, V., Nie, Q., Lowengrub, J.. Nonlinear three-dimensional simulation of solid tumor growth. Discrete Dyn. Continuous Dyn. Syst. B, 7 (2007), 581–604. Google Scholar
J. Lowengrub, V. Cristini, H. B. Frieboes, X. Li, P. Macklin, S.Sanga, S. M. Wise, X. Zheng. Nonlinear modeling and simulation of tumor growth, In N. Bellomo, M. Chaplain and E. DeAngelis Modeling and Simulation in Science, Birkaüser, in press, 2011.
J. Lowengrub, V. Cristini. Multiscale modeling of cancer : an integrated experimental and mathematical modeling approach. Cambridge University Press, 2010.
Lowengrub, J., Frieboes, H. B., Jin, F., Chuang, Y.-L., Li, X., Macklin, P., Wise, S. M., Cristini, V.. Nonlinear modeling of cancer : bridging the gap between cells and tumors. Nonlinearity, 23 (2010), 1, R1–R91. CrossRefGoogle Scholar
Macklin, P., Lowengrub, J.. An improved geometry-aware curvature discretization for level set methods : application to tumor growth. J. Comput. Phys., 215 (2006), 392–401. CrossRefGoogle Scholar
Macklin, P., Lowengrub, J.. Nonlinear simulation of the effect of microenvironment on tumor growth. J. Theor. Biol., 245 (2007), No. 4, 677–704. CrossRefGoogle Scholar
A. F. M. Marée, V. A. Grieneisen, P. Hogeweg, P. The Cellular Potts Model and biophysical properties of cells, tissues and morphogenesis. In A. R. A. Anderson, M. A. J. Chaplain, and K. A. Rejniak editors, Single-Cell-Based Models in Biology and Medicine, Mathematics and Biosciences in Interactions, Birkaüser, 107–136, 2007.
Merks, R. M. H., Koolwijk, P.. Modeling morphogenesis in silico and in vitro : towards quantitative, predictive, cell-based modeling. Math. Model. Nat. Phenom., 4 (2009), No. 4, 149–171. CrossRefGoogle Scholar
Metropolis, N., Rosenbluth, A. E., Rosenbluth, M. N., Teller, A. H., Teller, E.. Equation of state calculations by fast computing machines. J. Chem. Phys., 21 (1953), 1087–1092. CrossRefGoogle Scholar
Montero, E., Abreu, C., Tonino, P.. Relationship between VEGF and p53 expression and tumor cell proliferation in human gastrointestinal carcinomas. Journal of Cancer Research and Clinical Oncology, 134 (2007), No. 2, 193–201. CrossRefGoogle ScholarPubMed
Mueller-Klieser, W.. Tumor biology and experimental therapeutics. Crit. Rev. Oncol. Hematol., 36 (2002), 123–139. CrossRefGoogle ScholarPubMed
Murphy, G., Gavrilovic, J.. Proteolysis and cell migration : creating a path ? Curr. Opin. Cell Biol., 11 (1999), 614–621. CrossRefGoogle ScholarPubMed
Osada, H., Takahashi, T.. Genetic alterations of multiple tumor suppressors and oncogenes in the carcinogenesis and progression of lung cancer. Oncogene, 21 (2002), 7421–7434. CrossRefGoogle ScholarPubMed
Ouchi, N. B., Glazier, J. A., Rieu, J. P., Upadhyaya, A., Sawada, J.. Improving the realism of the cellular Potts model in simulations of biological cells. Physica A, 329 (2003), 451–458. CrossRefGoogle Scholar
Potts, R. B.. Some generalized order-disorder transformations. Proc. Camb. Phil. Soc., 48 (1952), 106–109. CrossRefGoogle Scholar
Preziosi, L., Tosin, A.. Multiphase modeling of tumor growth and extracellular matrix interaction : mathematical tools and applications, J. Math. Biol., 58 (2007), No. 4-5, 625–656. CrossRefGoogle Scholar
Preziosi, L., Tosin, A.. Multiphase and multiscale trends in cancer modelling. Math. Model. Nat. Phenom., 4 (2009), No. 3, 1–11. CrossRefGoogle Scholar
Quaranta, V., Weaver, A., Cummings, P., Anderson, A.. Mathematical modeling of cancer : The future of prognosis and treatment. Clin. Chim. Acta, 357 (2005), 173–179. CrossRefGoogle ScholarPubMed
Ramis-Conde, I., Drasdo, D., Anderson, A. R. A., Chaplain, M. A. J.. Modeling the influence of E-cadherin-beta-catenin pathway in cancer cell invasion : a multiscale approach. Biophys. J., 95 (2008), 155–165. CrossRefGoogle ScholarPubMed
Rejniak, K. A., Dillon, R. H.. A single cell-based model of the ductal tumor microarchitecture. Comp. Math. Meth. Med., 8 (2007), No. 1, 51–69. CrossRefGoogle Scholar
Ribba, B., Sautb, O., Colinb, T., Breschc, D., Grenierd, E., Boissel, J. P.. A multiscale mathematical model of avascular tumor growth to investigate the therapeutic benefit of anti-invasive agents. J. Theor. Biol., 243 (2006), 532–541. CrossRefGoogle ScholarPubMed
Rolli, C. G., Seufferlein, T., Kemkemer, R., Spatz, J. P.. Impact of Tumor Cell Cytoskeleton Organization on Invasiveness and Migration : A Microchannel-Based Approach. PLoS ONE, 5 (2010), e8726. doi :10.1371/journal.pone.0008726. CrossRefGoogle Scholar
Sanga, S., Sinek, J., Frieboes, H., Ferrari, M., Fruehauf, J., Cristini, V.. Mathematical modeling of cancer progression and response to chemotherapy. Expert. Rev. Anticancer Ther., 6 (2006), 1361–1376. CrossRefGoogle ScholarPubMed
Savill, N. J., Hogeweg, P.. Modelling morphogenesis : from single cells to crawling slugs. J. Theor. Biol., 184 (1997), 118–124. CrossRefGoogle Scholar
M. Scianna. A multiscale hybrid model for pro-angiogenic calcium signals in a vascular endothelial cell. Bull. Math. Biol., doi : 10.1007/s11538-011-9695-8 (2011), in press.
M. Scianna, L. Preziosi. Multiscale Developments of the Cellular Potts Model. (2010). In revision.
Smith, J. A., Martin, L.. Do cells cycle ? Proc. Natl. Acad. Sci. U.S.A., 70 (1973), 1263–1267. CrossRefGoogle ScholarPubMed
Smolle, J.. Fractal tumor stromal border in a nonequilibrium growth model. Anal. Quant. Cytol. Histol., 20 (1998), 7–13. Google Scholar
Steele, I. A., Edmondson, R. J., Leung, H. Y., Davies, B. R.. Ligands to FGF receptor 2-IIIb induce proliferation, motility, protection from cell death and cytoskeletal rearrangements in epithelial ovarian cancer cell lines. Growth Factors, 24 (2006), No. 1, 45–53. CrossRefGoogle ScholarPubMed
Steinberg, M. S.. Reconstruction of tissues by dissociated cells. Some morphogenetic tissue movements and the sorting out of embryonic cells may have a common explanation. Science, 141 (1963), 401–408. CrossRefGoogle ScholarPubMed
Steinberg, M. S.. Does differential adhesion govern self-assembly processes in histogenesis ? Equilibrium configurations and the emergence of a hierarchy among populations of embryonic cells. J. Exp. Zool., 173 (1970), No. 4, 395–433. CrossRefGoogle ScholarPubMed
Stetler-Stevenson, W. G., Aznavoorian, S., Liotta, L. A.. Tumor cell interactions with the extracellular matrix during invasion and metastasis. Ann. Rev. Cell Biol., 9 (1993), 541–573. CrossRefGoogle ScholarPubMed
Su, J. L., Yang, P. C., Shih, J. Y., Yang, C. Y., Wei, L. H., Kuo, M. L., et al.. The VEGF-C/Flt-4 axis promotes invasion and metastasis of cancer cells. Cancer Cell, 9 (2006), 209–223. CrossRefGoogle ScholarPubMed
Tracqui, P.. Biophysical models of tumour growth. Rep. Prog. Phys., 72 (2009), 5, 056701. CrossRefGoogle Scholar
Turner, S., Sherratt, J. A.. Intercellular adhesion and cancer invasion : A discrete simulation using the extended Potts model. J. Theor. Biol., 216 (2002), 85–100. CrossRefGoogle Scholar
Vaupel, P., Hockel, M.. Blood supply, oxygenation status and metabolic micromilieu of breast cancers : characterization and therapeutic relevance (Review). Int. J. Oncol., 17 (2000), 869–879. Google Scholar
Zhang, Y. W., Vande Woude, G. F.. HGF/SF-Met signaling in the control of branching morphogenesis and invasion. J. Cell Biochem., 88 (2003), 408–417. CrossRefGoogle ScholarPubMed