Cellular Potts modeling of tumor growth, tumor invasion, and tumor evolution

Frontiers in Oncology

Volumn 3 APR, Issue , 2013, Pages

  Szabó, András ^a,b,c   Merks, Roeland M H ^a,b,c,d  

^a CWI   (Netherlands)

^b Netherlands Consortium for Systems Biology   (Netherlands)

^c Netherlands Institute for Systems Biology   (Netherlands)

^d LEIDEN UNIVERSITY   (Netherlands)

Author keywords

Cell based modeling; Cellular potts model; Evolutionary tumor model; Multiscale modeling; Tumor growth model; Tumor invasion model; Tumor metastasis model

Indexed keywords

ANGIOGENESIS; BIOPHYSICS; CANCER CELL; CELL ADHESION; CELL DEATH; CELL DIVISION; CELL GROWTH; CELL MOTILITY; CELL PROLIFERATION; CELL SELECTION; CELL VOLUME; COMPUTER SIMULATION; ENERGY METABOLISM; EXTRACELLULAR MATRIX; GASTRULATION; GENE MUTATION; GLIOBLASTOMA; HOMEOSTASIS; HUMAN; MOLECULAR INTERACTION; NEOPLASM; NONHUMAN; NUTRIENT SUPPLY; PHENOTYPE; REVIEW; TUMOR GROWTH; TUMOR INVASION; TUMOR SPHEROID; VASCULAR TUMOR;

EID: 84890606259     PISSN: None     EISSN: 2234943X     Source Type: Journal    
DOI: 10.3389/fonc.2013.00087     Document Type: Review

References (103)

1. Alarcón, T., Byrne, H. M., and Maini, P. K. (2003). A cellular automaton model for tumour growth in inhomogeneous environment. J. Theor. Biol. 225, 257-274.
2. Andasari, V., and Chaplain, M. A. J. (2012). Intracellular modelling of cell-matrix adhesion during cancer cell invasion. Math. Model. Nat. Phenom. 7, 29-48.
3. Andasari, V., Gerisch, A., Lolas, G., South, A. P., and Chaplain, M. A. J. (2011). Mathematical modeling of cancer cell invasion of tissue: biological insight from mathematical analysis and computational simulation. J. Math. Biol. 63, 141-171.
4. Anderson, A. R. A., Basanta, D., Gerlee, P., and Rejniak, K. A. (2011). "Evolution, regulation, and disruption of homeostasis, and its role in carcinogenesis," in Multiscale Cancer Modeling, eds T. S. Deisboeck and G. S. Stamatakos (Boca Raton: Taylor & Francis), 1-30.
5. Anderson, A. R. A., Rejniak, K. A., Gerlee, P., and Quaranta, V. (2009). Microenvironment driven invasion: a multiscale multimodel investigation. J. Math. Biol. 58, 579-624.
6. Anderson, A. R. A., Weaver, A. M., Cummings, P. T., and Quaranta, V. (2006). Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment. Cell 127, 905-915.
7. Basanta, D., Gatenby, R. A., and Anderson, A. R. A. (2012). Exploiting evolution to treat drug resistance: combination therapy and the double bind. Mol. Pharm. 9, 914-921.
8. Bauer, A. L., Jackson, T. L., and Jiang, Y. (2007). A cell-based model exhibiting branching and anastomosis during tumor-induced angiogenesis. Biophys. J. 92, 3105-3121.
9. Bauer, A. L., Jackson, T. L., and Jiang, Y. (2009). Topography of extracellular matrix mediates vascular morphogenesis and migration speeds in angiogenesis. PLoS Comput. Biol. 5:e1000445. doi:10.1371/journal.pcbi.1000445
10. Bentley, K., Jones, M., and Cruys, B. (2013). Predicting the future: towards symbiotic computational and experimental angiogenesis research. Exp. Cell Res. doi:10.1016/j.yexcr.2013.02.001
11. Brodland, G. W., Viens, D., and Veldhuis, J. H. (2007). A new cell-based FE model for the mechanics of embryonic epithelia. Comput. Methods Biomech. Biomed. Eng. 10, 121-128.
12. Chaplain, M. A. J., McDougall, S. R., and Anderson, A. R. A. (2006). Mathematical modeling of tumor-induced angiogenesis. Annu. Rev. Biomed. Eng. 8, 233-257.
13. Chen, N., Glazier, J. A., Izaguirre, J. A., and Alber, M. S. (2007). A parallel implementation of the cellular Potts Model for simulation of cell-based morphogenesis. Comput. Phys. Commun. 176, 670-681.
14. Daub, J. T., and Merks, R. M. H. (2013). A cell-based model of extracellular-matrix-guided endothelial cell migration during angiogenesis. Bull. Math. Biol. doi:10.1007/s11538-013-9826-5
15. Drasdo, D., and Höhme, S. (2003). Individual-based approaches to birth and death in avascu1ar tumors. Math. Comput. Model. 37, 1163-1175.
16. Drasdo, D., Kree, R., and McCaskill, J. S. (1995). Monte Carlo approach to tissue-cell populations. Phys. Rev. E 52, 6635-6657.
17. Enderling, H., Anderson, A. R. A., Chaplain, M. A. J., Beheshti, A., Hlatky, L., and Hahnfeldt, P. (2009). Paradoxical dependencies of tumor dormancy and progression on basic cell kinetics. Cancer Res. 69, 8814-8821.
18. Farhadifar, R., Röper, J.-C., Aigouy, B., Eaton, S., and Jülicher, F. (2007). The influence of cell mechanics, cell-cell interactions, and proliferation on epithelial packing. Curr. Biol. 17, 2095-2104.
19. Folkman, J., and Hochberg, M. (1973). Self-regulation of growth in three dimensions. J. Exp. Med. 138, 745-753.
20. Frezza, C., Zheng, L., Folger, O., Rajagopalan, K. N., MacKenzie, E. D., Jerby, L., et al. (2011). Haem oxygenase is synthetically lethal with the tumour suppressor fumarate hydratase. Nature 477, 225-228.
21. Friedl, P., and Wolf, K. (2008). Tube travel: the role of proteases in individual and collective cancer cell invasion. Cancer Res. 68, 7247-7249.
22. Gamba, A., Ambrosi, D., Coniglio, A., de Candia, A., Di Talia, S., Giraudo, E., et al. (2003). Percolation, morphogenesis, and burgers dynamics in blood vessels formation. Phys. Rev. Lett. 90, 118101.
23. Gao, X., McDonald, J. T., Hlatky, L., and Enderling, H. (2013). Acute and fractionated irradiation differentially modulate glioma stem cell division kinetics. Cancer Res. 73, 1481-1490.
24. Gatenby, R. (2012). Perspective: finding cancer's first principles. Nature 491, S55.
25. Gatenby, R. A., and Vincent, T. L. (2003). An evolutionary model of carcinogenesis. Cancer Res. 63, 6212-6220.
26. Gerlinger, M., Rowan, A. J., Horswell, S., Larkin, J., Endesfelder, D., Gronroos, E., et al. (2012). Intratumor heterogeneity and branched evolution revealed by multiregion sequencing. N. Engl. J. Med. 366, 883-892.
27. Gevertz, J. L., and Torquato, S. (2006). Modeling the effects of vasculature evolution on early brain tumor growth. J. Theor. Biol. 243, 517-531.
28. Giverso, C., Scianna, M., Preziosi, L., Lo Buono, N., and Funaro, A. (2010). Individual cell-based model for in-vitro mesothelial invasion of ovarian cancer. Math. Model. Nat. Phenom. 5, 203-223.
29. Glazier, J. A., and Graner, F. (1993). Simulation of the differential adhesion driven rearrangement of biological cells. Phys. Rev. E 47, 2128-2154.
30. Gompertz, B. (1825). On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philos. Trans. R. Soc. Lond. 115, 513-583.
31. Graner, F., and Glazier, J. A. (1992). Simulation of biological cell sorting using a two-dimensional extended Potts model. Phys. Rev. Lett. 69, 2013-2016.
32. Hanahan, D., and Weinberg, R. A. (2000). The hallmarks of cancer. Cell 100, 57-70.
33. Hanahan, D., and Weinberg, R. A. (2011). Hallmarks of cancer: the next generation. Cell 144, 646-674.
34. Hatzikirou, H., Breier, G., and Deutsch, A. (2008). "Cellular automaton models of tumor invasion," in Encyclopedia of Complexity and Systems Science, Chap. 417, ed. R. A. Meyers (Heidelberg: Springer), 1-18.
35. Hatzikirou, H., Deutsch, A., Schaller, C., Simon, M., and Swanson, K. (2005). Mathematical modelling of glioblastoma tumour development: a review. Math. Models Methods Appl. Sci. 15, 1779-1794.
36. Hester, S. D., Belmonte, J. M., Gens, J. S., Clendenon, S. G., and Glazier, J. A. (2011). A multi-cell, multi-scale model of vertebrate segmentation and somite formation. PLoS Comput. Biol. 7:e1002155. doi:10.1371/journal.pcbi.1002155
37. Hirashima, T., Iwasa, Y., and Morishita, Y. (2009). Dynamic modeling of branching morphogenesis of ureteric bud in early kidney development. J. Theor. Biol. 259, 58-66.
38. Huang, S., and Ingber, D. E. (1999). The structural and mechanical complexity of cell-growth control. Nat. Cell Biol. 1, E131-E138.
39. Jiang, Y., Bauer, A. L., and Jackson, T. L. (2012). "Cell-based models of tumor angiogenesis," in Modeling Tumor Vasculature: Molecular, Cellular, and Tissue Level Aspects and Implications, ed. T. L. Jackson (New York: Springer), 135-150.
40. Jiang, Y., Pjesivac-Grbovic, J., Cantrell, C., and Freyer, J. P. (2005). A multiscale model for avascular tumor growth. Biophys. J. 89, 3884-3894.
41. Kabla, A. J. (2012). Collective cell migration: leadership, invasion and segregation. J. R. Soc. Interface 9, 3268-3278.
42. Keller, R., and Davidson, L. (2004). "Cell crawling, cell behaviour and biomechanics during convergence and extension," in Cell Motility: From Molecules to Organisms, Chap. 18, eds A. Ridley, M. Peckham, and P. Clark (Chichester: John Wiley & Sons, Ltd), 277-297.
43. Kim, Y., and Othmer, H. G. (2013). A hybrid model of tumor-stromal interactions in breast cancer. Bull. Math. Biol. doi:10.1007/s11538-012-9787-01-47
44. Kim, Y., Stolarska, M. A., and Othmer, H. G. (2007). A hybrid model for tumor spheroid growth in vitro i: theoretical development and early results. Math. Models Methods Appl. Sci. 17, 1773-1798.
45. Koli, K. M., and Arteaga, C. L. (1996). Complex role of tumor cell transforming growth factor (TGF)-ßs on breast carcinoma progression. J. Mammary Gland Biol. Neoplasia 1, 373-380.
46. Laird, A. K. (1964). Dynamics of tumor growth. Br. J. Cancer 18, 490-502.
47. Levine, A. J., and Puzio-Kuter, A. M. (2010). The control of the metabolic switch in cancers by oncogenes and tumor suppressor genes. Science 330, 1340-1344.
48. Macklin, P., Edgerton, M. E., Thompson, A. M., and Cristini, V. (2012). Patient-calibrated agent-based modelling of ductal carcinoma in situ (dcis): from microscopic measurements to macroscopic predictions of clinical progression. J. Theor. Biol. 301, 122-140.
49. Manoussaki, D., Lubkin, S. R., Vernon, R. B., and Murray, J. D. (1996). A mechanical model for the formation of vascular networks in vitro. Acta Biotheor. 44, 271-282.
50. Marusyk, A., Almendro, V., and Polyak, K. (2012). Intra-tumour heterogeneity: a looking glass for cancer? Nat. Rev. Cancer 12, 323-334.
51. McElwain, D. L. S., and Pettet, G. J. (1993). Cell migration in multicell spheroids: swimming against the tide. Bull. Math. Biol. 55, 655-674.
52. Merks, R. M. H., and Glazier, J. A. (2005). A cell-centered approach to developmental biology. Physica A 352, 113-130.
53. Merks, R. M. H., Brodsky, S. V., Goligorksy, M. S., Newman, S. A., and Glazier, J. A. (2006). Cell elongation is key to in silico replication of in vitro vasculogenesis and subsequent remodeling. Dev. Biol. 289, 44-54.
54. Merks, R. M. H., Guravage, M., Inzé, D., and Beemster, G. T. S. (2011). VirtualLeaf: an open-source framework for cell-based modeling of plant tissue growth and development. Plant Physiol. 155, 656-666.
55. Merks, R. M. H., Perryn, E. D., Shirinifard, A., and Glazier, J. A. (2008). Contact-inhibited chemotaxis in de novo and sprouting blood-vessel growth. PLoS Comput. Biol. 4:e1000163. doi:10.1371/journal.pcbi.1000163
56. Nakata, D., Hamada, J. I., Ba, Y., Matsushita, K., Shibata, T., Hosokawa, M., et al. (2002). Enhancement of tumorigenic, metastatic and in vitro invasive capacity of rat mammary tumor cells by transforming growth factor-ß. Cancer Lett. 175, 95-106.
57. Newman, T. J. (2005). Modeling multicellular systems using subcellular elements. Math. Biosci. Eng. 2, 611-622.
58. Newman, T. J. (2008). "Grid-free models of multicellular systems, with an application to large-scale vortices accompanying primitive streak formation," in Multiscale Modeling of Developmental Systems, Current Topics in Developmental Biology, Vol. 81, eds S. Schnell, P. K. Maini, S. A. Newman, and T. J. Newman (Amsterdam: Academic Press), 157-182.
59. Owen, M. R., Stamper, I. J., Muthana, M., Richardson, G. W., Dobson, J., Lewis, C. E., et al. (2011). Mathematical modeling predicts synergistic antitumor effects of combining a macrophage-based, hypoxia-targeted gene therapy with chemotherapy. Cancer Res. 71, 2826-2837.
60. Palm, M. M., and Merks, R. M. H. (2013). Vascular networks due to dynamically arrested crystalline ordering of elongated cells. Phys. Rev. E 87:012725. doi:10.1103/PhysRevE.87.012725
61. Peirce, S. M., Mac Gabhann, F., and Bautch, V. L. (2012). Integration of experimental and computational approaches to sprouting angiogenesis. Curr. Opin. Hematol. 19, 184-191.
62. Pleasance, E. D., Stephens, P. J., O'Meara, S., McBride, D. J., Meynert, A., Jones, D., et al. (2010). A small-cell lung cancer genome with complex signatures of tobacco exposure. Nature 463, 184-190.
63. Poplawski, N. J., Agero, U., Gens, J. S., Swat, M., Glazier, J. A., and Anderson, A. R. A. (2009). Front instabilities and invasiveness of simulated avascular tumors. Bull. Math. Biol. 71, 1189-1227.
64. Pugh, T. J., Weeraratne, S. D., Archer, T. C., Pomeranz Krummel, D. A., Auclair, D., Bochicchio, J., et al. (2012). Medulloblastoma exome sequencing uncovers subtype-specific somatic mutations. Nature 488, 106-110.
65. Rejniak, K. A. (2007). An immersed boundary framework for modelling the growth of individual cells: an application to the early tumour development. J. Theor. Biol. 247, 186-204.
66. Rejniak, K. A., and Anderson, A. R. A. (2011). Hybrid models of tumor growth. Wiley Interdiscip. Rev. Syst. Biol. Med. 3, 115-125.
67. Reya, T., Morrison, S. J., Clarke, M. F., and Weissman, I. L. (2001). Stem cells, cancer, and cancer stem cells. Nature 414, 105-111.
68. Rubenstein, B. M., and Kaufman, L. J. (2008). The role of extracellular matrix in glioma invasion: a cellular Potts model approach. Biophys. J. 95, 5661-5680.
69. Sandersius, S. A., Chuai, M., Weijer, C. J., and Newman, T. J. (2011a). Correlating cell behavior with tissue topology in embryonic epithelia. PLoS ONE 6:e18081. doi:10.1371/journal.pone.0018081
70. Sandersius, S. A., Weijer, C. J., and Newman, T. J. (2011b). Emergent cell and tissue dynamics from subcellular modeling of active biomechanical processes. Phys. Biol. 8:045007. doi:10.1088/1478-3975/8/4/045007
71. Sandersius, S. A., and Newman, T. J. (2008). Modeling cell rheology with the subcellular element model. Phys. Biol. 5:015002. doi:10.1088/1478-3975/5/1/015002
72. Savill, N. J., and Hogeweg, P. (1997). Modelling morphogenesis: from single cells to crawling slugs. J. Theor. Biol. 184, 229-235.
73. Scianna, M., and Preziosi, L. (2012). A hybrid model describing different morphologies of tumor invasion fronts. Math. Model. Nat. Phenom. 7, 78-104.
74. Scianna, M., Preziosi, L., and Wolf, K. (2013). A Cellular Potts Model simulating cell migration on and in matrix environments. Math. Biosci. Eng. 10, 235-261.
75. Selmeczi, D., Mosler, S., Hagedorn, P. H., Larsen, N. B., and Flyvbjerg, H. (2005). Cell motility as persistent random motion: theories from experiments. Biophys. J. 89, 912-931.
76. Shah, S. P., Morin, R. D., Khattra, J., Prentice, L., Pugh, T., Burleigh, A., et al. (2009). Mutational evolution in a lobular breast tumour profiled at single nucleotide resolution. Nature 461, 809-813.
77. Shirinifard, A., Gens, J. S., Zaitlen, B. L., Poplawski, N. J., Swat, M., and Glazier, J. A. (2009). 3D multi-cell simulation of tumor growth and angiogenesis. PLoS ONE 4:e7190. doi:10.1371/journal.pone.0007190
78. Shirinifard, A., Glazier, J. A., Swat, M., Gens, J. S., Family, F., Jiang, Y., et al. (2012). Adhesion failures determine the pattern of choroidal neovascularization in the eye: a computer simulation study. PLoS Comput. Biol. 8:e1002440. doi:10.1371/journal.pcbi.1002440
79. Sottoriva, A., Verhoeff, J. J. C., Borovski, T., McWeeney, S. K., Naumov, L., Medema, J. P., et al. (2010). Cancer stem cell tumor model reveals invasive morphology and increased phenotypical heterogeneity. Cancer Res. 70, 46-56.
80. Sottoriva, A., Vermeulen, L., and Tavaré, S. (2011). Modeling evolutionary dynamics of epigenetic mutations in hierarchically organized tumors. PLoS Comput. Biol. 7:e1001132. doi:10.1371/journal.pcbi.1001132
81. Stamper, I. J., Byrne, H. M., Owen, M. R., and Maini, P. K. (2007). Modelling the role of angiogenesis and vasculogenesis in solid tumour growth. Bull. Math. Biol. 69, 2737-2772.
82. Starruß, J., Bley, Th., Søgaard Andersen, L., and Deutsch, A. (2007). A new mechanism for collective migration in Myxococcus xanthus. J. Stat. Phys. 128, 269-286.
83. Steinberg, M. S. (1970). 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, 395-433.
84. Stokes, C. L., Lauffenburger, D. A., and Williams, S. K. (1991). Migration of individual microvessel endothelial cells: stochastic model and parameter measurement. J. Cell. Sci. 99, 419-430.
85. Stott, E. L., Britton, N. F., Glazier, J. A., and Zajac, M. (1999). Stochastic simulation of benign avascular tumour growth using the Potts model. Math. Comput. Model 30, 183-198.
86. Swat, M. H., Thomas, G. L., Belmonte, J. M., Shirinifard, A., Hmeljak, D., and Glazier, J. A. (2012). "Multi-scale modeling of tissues using CompuCell3D," in Computational Methods in Cell Biology, Methods in Cell Biology, Vol. 110, Chap. 13, eds A. R. Asthagiri and A. P. Arkin (London: Academic Press), 325-366.
87. Szabó, A., and Czirók, A. (2010). The role of cell-cell adhesion in the formation of multicellular sprouts. Math. Model Nat. Phenom. 5, 106-122.
88. Szabo, A., Mehes, E., Kosa, E., and Czirok, A. (2008). Multicellular sprouting in vitro. Biophys. J. 95, 2702-2710.
89. Szabo, A., Perryn, E. D., and Czirok, A. (2007). Network formation of tissue cells via preferential attraction to elongated structures. Phys. Rev. Lett. 98:038102. doi:10.1103/PhysRevLett.98.038102
90. Szabó, A., Ünnep, R., Méhes, E., Twal, W. O., Argraves, W. S., Cao, Y., et al. (2010). Collective cell motion in endothelial monolayers. Phys. Biol. 7:046007. doi:10.1088/1478-3975/7/4/046007
91. Szabó, A., Varga, K., Garay, T., Hegedus, B., and Czirók, A. (2012). Invasion from a cell aggregate-the roles of active cell motion and mechanical equilibrium. Phys. Biol. 9:016010. doi:10.1088/1478-3975/9/1/016010
92. Thomas, R. K., Baker, A. C., DeBiasi, R. M., Winckler, W., LaFramboise, T., Lin, W. M., et al. (2007). High-throughput oncogene mutation profiling in human cancer. Nat. Genet. 39, 347-351.
93. Tripodi, S., Ballet, P., and Rodin, V. (2010). "Computational energetic model of morphogenesis based on multi-agent cellular Potts model," in Advances in Computational Biology, Advances in Experimental Medicine and Biology, Vol. 680, ed. H. R. Arabnia (New York: Springer), 685-692.
94. Turner, S., and Sherratt, J. A. (2002). Intercellular adhesion and cancer invasion: a discrete simulation using the extended Potts model. J. Theor. Biol. 216, 85-100.
95. Turner, S., Sherratt, J. A., and Cameron, D. (2004). Tamoxifen treatment failure in cancer and the nonlinear dynamics of TGFbeta. J. Theor. Biol. 229, 101-111.
96. Uren, A. G., Kool, J., Matentzoglu, K., de Ridder, J., Mattison, J., van Uitert, M., et al. (2008). Large-scale mutagenesis in p19ARF-and p53-deficient mice identifies cancer genes and their collaborative networks. Cell 133, 727-741.
97. Van Leeuwen, I. M. M., Mirams, G. R., Walter, A., Fletcher, A., Murray, P., Osborne, J., et al. (2009). An integrative computational model for intestinal tissue renewal. Cell Prolif. 42, 617-636.
98. Vazquez, A., Liu, J., Zhou, Y., and Oltvai, Z. N. (2010). Catabolic efficiency of aerobic glycolysis: the warburg effect revisited. BMC Syst. Biol. 4:58. doi:10.1186/1752-0509-4-58
99. Visvader, J. E., and Lindeman, G. J. (2008). Cancer stem cells in solid tumours: accumulating evidence and unresolved questions. Nat. Rev. Cancer 8, 755-768.
100. Voss-Böhme, A. (2012). Multi-scale modeling in morphogenesis: a critical analysis of the cellular Potts model. PLoS ONE 7:e42852. doi:10.1371/journal.pone.0042852
101. Witten, T. A. Jr., and Sander, L. M. (1981). Diffusion-limited aggregation, a kinetic critical phenomenon. Phys. Rev. Lett. 47, 1400-1403.
102. Yachida, S., Jones, S., Bozic, I., Antal, T., Leary, R., Fu, B., et al. (2010). Distant metastasis occurs late during the genetic evolution of pancreatic cancer. Nature 467, 1114-1117.
103. Zajac, M., Jones, G. L., and Glazier, J. A. (2003). Simulating convergent extension by way of anisotropic differential adhesion. J. Theor. Biol. 222, 247-259.