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Computational Cell-Based Modeling and Visualization of Cancer Development and Progression

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New Developments on Computational Methods and Imaging in Biomechanics and Biomedical Engineering

Part of the book series: Lecture Notes in Computational Vision and Biomechanics ((LNCVB,volume 33))

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Abstract

This paper presents a review of the role of mathematical modeling in investigating cancer progression, focusing on five models developed in our group. A brief overview of computational modeling progress is presented, followed by introduction of several mathematical formalisms (e.g., stochastic differential equations), numerical methods (e.g., finite element method, Green’s functions, and combinations of time integration), and Monte Carlo simulations, which are currently used to quantify the underlying biomedical mechanisms, to approximate the results and to evaluate the impact of the input variables. Next, we provide specific examples of the computational models that we developed aimed at predicting the dynamics of the initiation and progression of cancer. Our simulation results show qualitative consistency with references and/or available experimental observations. Finally, perspectives are drawn on the possibilities of mathematical modeling for the prospects of cancer understanding and treatment therapies.

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References

  1. Abbott LH, Michor F (2006) Mathematical models of targeted cancer therapy. Br J Cancer 95(9):1136–1141

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  2. Ahmadzadeh H, Webster MR, Behera R, Jimenez AM, Valencia DW, Weeraratna AT, Shenoy VB (2017) Modeling the two-way feedback between contractility and matrix realignment reveals a nonlinear mode of cancer cell invasion. Proc Natl Acad Sci 114(9):E1617–E1626

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  3. Alvarez-Elizondo MB, Weihs D (2017) Cell-gel mechanical interactions as an approach to rapidly and quantitatively reveal invasive subpopulations of metastatic cancer cells. Tissue Eng Part C Methods 23(3):180–187

    Article  CAS  PubMed  Google Scholar 

  4. Andasari V, Gerisch A, Lolas G, South AP, Chaplain MAJ (2011) Mathematical modeling of cancer cell invasion of tissue: biological insight from mathematical analysis and computational simulation. J Math Biol 63(1):141–171

    Article  PubMed  Google Scholar 

  5. Anderson ARA, Chaplain MAJ, Luke Newman E, Steele RJC, Thompson AM (2000) Mathematical modelling of tumour invasion and metastasis. Comput Math Methods Med 2(2):129–154

    Google Scholar 

  6. Angeli F, Koumakis G, Chen M-C, Kumar S, Delinassios JG (2009) Role of stromal fibroblasts in cancer: promoting or impeding? Tumor Biol 30(3):109–120

    Article  CAS  Google Scholar 

  7. Nicola B, Luidgi P (2000) Modelling and mathematical problems related to tumor evolution and its interaction with the immune system. Math Comput Model 32(3–4):413–452

    Google Scholar 

  8. Fortunato B, Elisa B, Vienna L, Lucio C, Antonella F, Paolo V (2012) Computational model of egfr and igf1r pathways in lung cancer: a systems biology approach for translational oncology. Biotechnol Adv 30(1):142–153

    Article  CAS  Google Scholar 

  9. Block M, Schöll E, Drasdo D (2007) Classifying the expansion kinetics and critical surface dynamics of growing cell populations. Phys Rev Lett 99(24):248101

    Article  CAS  PubMed  Google Scholar 

  10. Bookholt FD, Monsuur HN, Gibbs S, Vermolen FJ (2016) Mathematical modelling of angiogenesis using continuous cell-based models. Biomech Model Mechanobiol 15(6):1577–1600

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  11. Borau C, Polacheck WJ, Kamm RD, García-Aznar JM (2014) Probabilistic voxel-fe model for single cell motility in 3d. Silico Cell Tissue Sci 1(1):1–17

    Article  Google Scholar 

  12. Bougherara H, Mansuet-Lupo A, Alifano M, Ngô C, Damotte D, Le Frère-Belda M-A, Donnadieu E, Peranzoni E (2015) Real-time imaging of resident t cells in human lung and ovarian carcinomas reveals how different tumor microenvironments control t lymphocyte migration. Front Immunol 6:500

    Article  PubMed  PubMed Central  Google Scholar 

  13. Helen B, Dirk D (2009a) Individual-based and continuum models of growing cell populations: a comparison. J Math Biol 58(4):657–687

    Google Scholar 

  14. Helen B, Dirk D (2009b) Individual-based and continuum models of growing cell populations: a comparison. J Math Biol 58(4–5):657–687

    Google Scholar 

  15. Chaffer CL, Weinberg RA (2011) A perspective on cancer cell metastasis. Science 331(6024):1559–1564

    Article  CAS  PubMed  Google Scholar 

  16. Chieh C, Zena W (2001) The many faces of metalloproteases: cell growth, invasion, angiogenesis and metastasis. Trends Cell Biol 11:S37–S43

    Article  Google Scholar 

  17. Chaplain Mark AJ (2000) Mathematical modelling of angiogenesis. J. Neuro-Oncol 50(1):37–51

    Article  Google Scholar 

  18. Chaplain MAJ, McDougall SR, Anderson ARA (2006) Mathematical modeling of tumor-induced angiogenesis. Annu Rev Biomed Eng 8:233–257

    Article  CAS  PubMed  Google Scholar 

  19. Chuanying Chen B, Pettitt M (2011) The binding process of a nonspecific enzyme with dna. Biophys J 101(5):1139–1147

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  20. Chen J, Vermolen FJ (2016) Literature study on cell-based semi-stochastic modelling for the dynamics of growth of cell colonies

    Google Scholar 

  21. Chen J, Weihs D, Van Dijk M, Vermolen FJ (2018a) A phenomenological model for cell and nucleus deformation during cancer metastasis. Biomech Model Mechanobiol 17(5):1429–1450

    Article  PubMed  PubMed Central  Google Scholar 

  22. Chen J, Weihs D, Vermolen FJ (2018b) A model for cell migration in non-isotropic fibrin networks with an application to pancreatic tumor islets. Biomech Model Mechanobiol 17(2):367–386

    Article  PubMed  Google Scholar 

  23. Chen J, Weihs D, Vermolen FJ (2018c) Monte carlo uncertainty quantification in modelling cell deformation during cancer metastasis. In: Proceedings of the CMBBE2018

    Google Scholar 

  24. Chmielecki J, Foo J, Oxnard GR, Hutchinson K, Ohashi K, Somwar R, Wang L, Amato KR, Arcila M, Sos ML et al. (2011) Optimization of dosing for egfr-mutant non–small cell lung cancer with evolutionary cancer modeling. Sci Transl Med 3(90):90ra59–90ra59

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  25. Clarijs R, Ruiter DJ, de Waal RMW (2003) Pathophysiological implications of stroma pattern formation in uveal melanoma. J Cell Physiol 194(3):267–271

    Article  CAS  PubMed  Google Scholar 

  26. European Commission (2016) Animals used for scientific purposes. http://ec.europa.eu/environment/chemicals/lab_animals/3r/alternative_en.htm

  27. Couzin-Frankel J (2013) Cancer immunotherapy. Science 342(6165):1432–1433

    Article  CAS  PubMed  Google Scholar 

  28. Da-Jun T, Tang F, Lee T, Sarda D, Krishnan A, Goryachev A (2004) Parallel computing platform for the agent-based modeling of multicellular biological systems. PDCAT. Springer, Berlin, pp 5–8

    Google Scholar 

  29. Micah D, Yu-Li W (1999) Stresses at the cell-to-substrate interface during locomotion of fibroblasts. Biophys J 76(4):2307–2316

    Article  Google Scholar 

  30. Dirk D, Stefan H (2005) A single-cell-based model of tumor growth in vitro: monolayers and spheroids. Phys Biol 2(3):133

    Article  CAS  Google Scholar 

  31. Dirk D, Stefan H (2005) A single-cell-based model of tumor growth in vitro: monolayers and spheroids. Phys Biol 2(3):133

    Article  CAS  Google Scholar 

  32. Dudaie M, Weihs D, Vermolen FJ, Gefen A (2015) Modeling migration in cell colonies in two and three dimensional substrates with varying stiffnesses. Silico Cell Tissue Sci 2(1):2

    Article  Google Scholar 

  33. DuFort CC, Paszek MJ, Weaver VM (2011) Balancing forces: architectural control of mechanotransduction. Nat Rev Mol Cell Biol 12(5):308–319

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  34. Elliott CM, Stinner B, Venkataraman C (2012) Modelling cell motility and chemotaxis with evolving surface finite elements. J R Soc Interface 9(76):3027–3044

    Article  PubMed  PubMed Central  Google Scholar 

  35. Enderling H, Anderson ARA, Chaplain MAJ (2007a) A model of breast carcinogenesis and recurrence after radiotherapy. PAMM 7(1):1121701–1121702

    Article  Google Scholar 

  36. Enderling H, Anderson ARA, Chaplain MAJ, Munro AJ, Vaidya JS (2006) Mathematical modelling of radiotherapy strategies for early breast cancer. J Theor Biol 241(1):158–171

    Article  PubMed  Google Scholar 

  37. Enderling H, Chaplain MAJ, Anderson ARA, Vaidya JS (2007b) A mathematical model of breast cancer development, local treatment and recurrence. J Theor Biol 246(2):245–259

    Article  CAS  PubMed  Google Scholar 

  38. Fearon ER, Vogelstein B (1990) A genetic model for colorectal tumorigenesis. Cell 61(5):759–767

    Article  CAS  PubMed  Google Scholar 

  39. Ferlay J, Soerjomataram I, Ervik M, Dikshit R, Eser S, Mathers C, Rebelo M, Parkin DM, Forman D, Bray F (2014) Globocan 2012 v1.0, cancer incidence and mortality worldwide: Iarc cancerbase no. 11 [internet]. 2013; Lyon, France: International agency for research on cancer. globocan.iarc.fr/Default.aspx

    Google Scholar 

  40. Folkman J, Haudenschild C (1980) Angiogenesis in vitro

    Article  CAS  PubMed  Google Scholar 

  41. Forkman J (1974) Tumor angiogenesis: Role in regulation of tumor growth. Syrup Soc Dev Biol 30:43–52

    Google Scholar 

  42. Peter F, Katarina W, Jan L (2011) Nuclear mechanics during cell migration. Curr Opin Cell Biol 23(1):55–64

    Article  CAS  Google Scholar 

  43. Friedman R, Boye K, Flatmark K (2013) Molecular modelling and simulations in cancer research. Biochim Biophys Acta (BBA)-Rev Cancer 1836(1):1–14

    Article  CAS  Google Scholar 

  44. Katharine G (2012) Mathematical modelling: forecasting cancer. Nature 491(7425):S66–S67

    Article  Google Scholar 

  45. Gatenby RA (2010) Mathematical modeling in cancer. Biomedical informatics for cancer research. Springer, Berlin, pp 139–147

    Google Scholar 

  46. Gatenby RA, Vincent TL (2003) An evolutionary model of carcinogenesis. Cancer Res 63(19):6212–6220

    CAS  PubMed  Google Scholar 

  47. Glazier JA, Graner F (1993) Simulation of the differential adhesion driven rearrangement of biological cells. Phys Rev E 47(3):2128

    Article  CAS  Google Scholar 

  48. Hanahan D, Weinberg RA (2000) The hallmarks of cancer. Cell 100(1):57–70

    Article  CAS  PubMed  Google Scholar 

  49. Hanahan D, Weinberg RA (2011) Hallmarks of cancer: the next generation. Cell 144(5):646–674

    Article  CAS  PubMed  Google Scholar 

  50. Hatzikirou H, Breier G, Deutsch A (2014) Cellular automaton modeling of tumor invasion. Encyclopedia of complexity and systems science. Springer, Berlin, pp 1–13

    Google Scholar 

  51. Haralambos H, Andreas D (2008) Cellular automata as microscopic models of cell migration in heterogeneous environments. Curr Top Dev Biol 81:401–434

    Article  Google Scholar 

  52. Haralampos H, Andreas D, Carlo S, Matthias S, Kristin S (2005) Mathematical modelling of glioblastoma tumour development: a review. Math Model Methods Appl Sci 15(11):1779–1794

    Article  Google Scholar 

  53. Wonpil I, Stefan S, Benoit R (2000) A grand canonical monte carlo-brownian dynamics algorithm for simulating ion channels. Biophys J 79(2):788–801

    Article  Google Scholar 

  54. Jackson TL (2004) A mathematical model of prostate tumor growth and androgen-independent relapse. Discret Contin Dyn Syst Ser B 4(1):187–202

    Article  Google Scholar 

  55. Jemal A, Bray F, Center MM, Ferlay J, Ward E, Forman D (2011) Global cancer statistics. CA: Cancer J Clin, 61(2):69–90

    Google Scholar 

  56. Jemal A, Murray T, Ward E, Samuels A, Tiwari RC, Ghafoor A, Feuer EJ, Thun MJ (2005) Cancer statistics, 2005. CA: Cancer J Clin 55(1):10–30

    Google Scholar 

  57. Jeon J, Quaranta V, Cummings PT (2010) An off-lattice hybrid discrete-continuum model of tumor growth and invasion. Biophys J 98(1):37–47

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  58. Jolly MK, Boareto M, Debeb BG, Aceto N, Farach-Carson MC, Woodward WA, Levine H (2017) Inflammatory breast cancer: a model for investigating cluster-based dissemination. NPJ Breast Cancer 3(1):21

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  59. Kalebic T, Garbisa S, Glaser B, Liotta LA (1983) Basement membrane collagen: degradation by migrating endothelial cells. Science 221(4607):281–283

    Article  CAS  PubMed  Google Scholar 

  60. Kansal AR, Torquato S, Harsh GR, Chiocca EA, Deisboeck TS (2000) Simulated brain tumor growth dynamics using a three-dimensional cellular automaton. J Theor Biol 203(4):367–382

    Article  CAS  PubMed  Google Scholar 

  61. Kershaw MH, Wang G, Westwood JA, Pachynski RK, Lee Tiffany H, Marincola FM, Wang E, Young HA, Murphy PM, Hwu P (2002) Redirecting migration of t cells to chemokine secreted from tumors by genetic modification with cxcr2. Hum Gene Ther 13(16):1971–1980

    Article  CAS  PubMed  Google Scholar 

  62. Kim Y, Othmer HG (2013) A hybrid model of tumor-stromal interactions in breast cancer. Bull Math Biol 75(8):1304–1350

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  63. Kim Y, Stolarska MA, Othmer HG (2007) A hybrid model for tumor spheroid growth in vitro i: theoretical development and early results. Math Model Methods Appl Sci 17(supp01):1773–1798

    Article  CAS  Google Scholar 

  64. Kirschner D, Panetta JC (1998) Modeling immunotherapy of the tumor-immune interaction. J Math Biol 37(3):235–252

    Article  CAS  PubMed  Google Scholar 

  65. Kristal-Muscal R, Dvir L, Weihs D (2013) Metastatic cancer cells tenaciously indent impenetrable, soft substrates. New J Phys 15(3):035022. https://doi.org/10.1088/1367-2630/15/3/035022/meta

  66. Benoit L, Alice N (2012) Physically based principles of cell adhesion mechanosensitivity in tissues. Rep Prog Phys 75(11):116601

    Article  CAS  Google Scholar 

  67. Lauffenburger DA, Horwitz AF (1996) Cell migration: a physically integrated molecular process. Cell 84(3):359–369

    Article  CAS  PubMed  Google Scholar 

  68. David Logan J, Allman ES, Rhodes JA (2005) Mathematical models in biology. Am Math Mon 112(9):847

    Article  Google Scholar 

  69. Pengfei L, Weaver VM, Werb Z (2012) The extracellular matrix: a dynamic niche in cancer progression. J Cell Biol 196(4):395–406

    Article  CAS  Google Scholar 

  70. Madzvamuse A, George UZ (2013) The moving grid finite element method applied to cell movement and deformation. Finite Elem Anal Des 74:76–92

    Article  Google Scholar 

  71. Mahadevan S (1997) Monte carlo simulation. Mechanical engineering-New York and Basel-Marcel Dekker-, pp 123–146

    Google Scholar 

  72. Massalha S, Weihs D (2016) Metastatic breast cancer cells adhere strongly on varying stiffness substrates, initially without adjusting their morphology. Biomech Model Mechanobiol 16(3):961–970

    Article  PubMed  Google Scholar 

  73. McDougall SR, Anderson ARA, Chaplain MAJ (2006) Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: clinical implications and therapeutic targeting strategies. J Theor Biol 241(3):564–589

    Article  PubMed  Google Scholar 

  74. McDougall SR, Anderson ARA, Chaplain MAJ, Sherratt JA (2002) Mathematical modelling of flow through vascular networks: implications for tumour-induced angiogenesis and chemotherapy strategies. Bull Math Biol 64(4):673–702

    Article  CAS  PubMed  Google Scholar 

  75. Ira M, George C, Glenn D (2011) Cancer immunotherapy comes of age. Nature 480(7378):480–489

    Article  CAS  Google Scholar 

  76. Merkher Y, Weihs D (2017) Proximity of metastatic cells enhances their mechanobiological invasiveness. Ann Biomed Eng 45(6):1399–1406

    Article  PubMed  Google Scholar 

  77. Merks RMH, Koolwijk P (2009) Modeling morphogenesis in silico and in vitro: towards quantitative, predictive, cell-based modeling. Math Model Nat Phenom 4(4):149–171

    Article  Google Scholar 

  78. Florian M, Michael B, Petros K (2008) A hybrid model for three-dimensional simulations of sprouting angiogenesis. Biophys J 95(7):3146–3160

    Article  CAS  Google Scholar 

  79. Mooney CZ (1997) Monte carlo simulation, vol 116. Sage Publications, California

    Book  Google Scholar 

  80. Moreira J, Deutsch A (2002) Cellular automaton models of tumor development: a critical review. Adv Complex Syst 5(02n03):247–267

    Article  Google Scholar 

  81. Murray JD (2003) Mathematical biology ii: spatial models and biomedical applications, 3rd edn. Springer, Berlin

    Book  Google Scholar 

  82. Namazi H, Kulish VV, Wong A (2015) Mathematical modelling and prediction of the effect of chemotherapy on cancer cells. Sci Rep 5:13583

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  83. Ng MR, Brugge JS (2009) A stiff blow from the stroma: collagen crosslinking drives tumor progression. Cancer cell 16(6):455–457

    Article  CAS  PubMed  Google Scholar 

  84. Özdemir BC, Pentcheva-Hoang T, Carstens JL, Zheng X, Chia-Chin W, Simpson TR, Laklai H, Sugimoto H, Kahlert C, Novitskiy SV et al (2014) Depletion of carcinoma-associated fibroblasts and fibrosis induces immunosuppression and accelerates pancreas cancer with reduced survival. Cancer cell 25(6):719–734

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  85. Paszek MJ, Zahir N, Johnson KR, Lakins JN, Rozenberg GI, Gefen A, Reinhart-King CA, Margulies SS, Dembo M, Boettiger D et al (2005) Tensional homeostasis and the malignant phenotype. Cancer cell 8(3):241–254

    Article  CAS  PubMed  Google Scholar 

  86. Powathil G, Kohandel M, Sivaloganathan S, Oza A, Milosevic M (2007) Mathematical modeling of brain tumors: effects of radiotherapy and chemotherapy. Phys Med Biol 52(11):3291

    Article  CAS  PubMed  Google Scholar 

  87. Throm Quinlan AM, Sierad LN, Capulli AK, Firstenberg LE, Billiar KL (2011) Combining dynamic stretch and tunable stiffness to probe cell mechanobiology in vitro. PloS one 6(8):e23272

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  88. Radszuweit M, Block M, Hengstler JG, Schöll E, Drasdo D (2009) Comparing the growth kinetics of cell populations in two and three dimensions. Phys Rev E 79(5):051907

    Article  CAS  Google Scholar 

  89. Ramis-Conde I, Chaplain MAJ, Anderson ARA (2008) Mathematical modelling of cancer cell invasion of tissue. Math Comput Model 47(5):533–545

    Article  Google Scholar 

  90. Reinhardt CA (1994) Alternatives to animal testing: new ways in the biomedical sciences, trends and progress. https://www.cabdirect.org/cabdirect/abstract/19952217321

  91. Reinhart-King CA, Dembo M, Hammer DA (2008a) Cell-cell mechanical communication through compliant substrates. Biophys J 95(12):6044–6051

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  92. Reinhart-King CA, Dembo M, Hammer DA (2008b) Cell-cell mechanical communication through compliant substrates. Biophys J 95(12):6044–6051

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  93. Rejniak KA (2007) An immersed boundary framework for modelling the growth of individual cells: an application to the early tumour development. J Theor Biol 247(1):186–204

    Article  CAS  PubMed  Google Scholar 

  94. Rejniak KA, Anderson ARA (2011) Hybrid models of tumor growth. Wiley Interdiscip Rev Syst Biol Med 3(1):115–125

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  95. Rejniak KA, Dillon RH (2007) A single cell-based model of the ductal tumour microarchitecture. Comput Math Methods Med 8(1):51–69

    Article  Google Scholar 

  96. Lisanne R, Sonja B, Roeland M (2016) Modelling the growth of blood vessels in health and disease. ERCIM News 104:36–37

    Google Scholar 

  97. Rhim AD, Oberstein PE, Thomas DH, Mirek ET, Palermo CF, Sastra SA, Dekleva EN, Saunders T, Becerra CP, Tattersall IW et al (2014) Stromal elements act to restrain, rather than support, pancreatic ductal adenocarcinoma. Cancer cell 25(6):735–747

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  98. Rothman DH, Zaleski S (2004) Lattice-gas cellular automata: simple models of complex hydrodynamics, vol 5. Cambridge University Press, Cambridge

    Google Scholar 

  99. Marc D Ryser, Svetlana V Komarova (2015) Mathematical modeling of cancer metastases. Comput Bioeng 211–230

    Google Scholar 

  100. Hélène S, Emmanuel D (2012) Within tumors, interactions between t cells and tumor cells are impeded by the extracellular matrix. OncoImmunology 1(6):992–994

    Article  Google Scholar 

  101. Neil S (2012) Modelling: computing cancer. Nature 491(7425):S62–S63

    Article  Google Scholar 

  102. Gernot S, Michael M-H (2005) Multicellular tumor spheroid in an off-lattice voronoi-delaunay cell model. Phys Rev E 71(5):051910

    Article  CAS  Google Scholar 

  103. Shirinifard A, Gens JS, Zaitlen BL, Popławski NJ, Swat M, Glazier JA (2009) 3D multi-cell simulation of tumor growth and angiogenesis. PloS one 4(10):e7190

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  104. Siemann DW (2002) Vascular targeting agents. Horizons in cancer therapeutics: from bench to bedside cancer 3:4–15

    Google Scholar 

  105. Simmons A, Burrage PM, Nicolau DV, Lakhani SR, Burrage K (2017) Environmental factors in breast cancer invasion: a mathematical modelling review. Pathology 49(2):172–180

    Article  PubMed  Google Scholar 

  106. Katrin S, Alessandra M (2006) Modeling anticancer drug-dna interactions via mixed qm/mm molecular dynamics simulations. Org Biomol Chem 4(13):2507–2517

    Article  Google Scholar 

  107. Stephanou A, McDougall SR, Anderson ARA, Chaplain MAJ (2005) Mathematical modelling of flow in 2d and 3d vascular networks: applications to anti-angiogenic and chemotherapeutic drug strategies. Math Comput Model 41(10):1137–1156

    Article  Google Scholar 

  108. András S, Merks Roeland MH (2013) Cellular potts modeling of tumor growth, tumor invasion, and tumor evolution. Front Oncol 3:87

    Google Scholar 

  109. Tanaka G, Yoshito Hirata S, Goldenberg L, Bruchovsky N, Aihara K (2010) Mathematical modelling of prostate cancer growth and its application to hormone therapy. Philos Trans R Soc Lond A Math Phys Eng Sci 368(1930):5029–5044

    Google Scholar 

  110. Thompson DW et al. (1942) On growth and form. On growth and form

    Google Scholar 

  111. Tlsty TD, Coussens LM (2006) Tumor stroma and regulation of cancer development. Annu Rev Pathol Mech Dis 1:119–150

    Article  CAS  Google Scholar 

  112. Turjanski AG, Gerhard Hummer J, Gutkind S (2009) How mitogen-activated protein kinases recognize and phosphorylate their targets: a qm/mm study. J Am Chem Soc 131(17):6141–6148

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  113. Turner S, Sherratt JA (2002) Intercellular adhesion and cancer invasion: a discrete simulation using the extended potts model. J Theor Biol 216(1):85–100

    Article  PubMed  Google Scholar 

  114. Jozef VD, Paul P, Jean-Pierre L, Ghislain O (1992) Structural and functional identification of two human, tumor-derived monocyte chemotactic proteins (mcp-2 and mcp-3) belonging to the chemokine family. J Exp Med 176(1):59–65

    Article  Google Scholar 

  115. Paul Van Liedekerke MM, Palm NJ, Drasdo D (2015) Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results. Comput Part Mech 2(4):401–444

    Article  Google Scholar 

  116. van Oers RFM, Rens EG, LaValley DJ, Reinhart-King CA, Merks RMH (2014) Mechanical cell-matrix feedback explains pairwise and collective endothelial cell behavior in vitro. PLoS Comput Biol 10(8):e1003774

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  117. Vermolen FJ (2015) Particle methods to solve modelling problems in wound healing and tumor growth. Comput Part Mech 2(4):381–399

    Article  Google Scholar 

  118. Vermolen FJ, Gefen A (2012a) A semi-stochastic cell-based formalism to model the dynamics of migration of cells in colonies. Biomech Model Mechanobiol 11(1):183–195

    Article  CAS  PubMed  Google Scholar 

  119. Vermolen FJ, Gefen A (2012b) A semi-stochastic cell-based formalism to model the dynamics of migration of cells in colonies. Biomech Model Mechanobiol 11(1–2):183–195

    Article  CAS  PubMed  Google Scholar 

  120. Vermolen FJ, Gefen A (2013a) A phenomenological model for chemico-mechanically induced cell shape changes during migration and cell-cell contacts. Biomech Model Mechanobiol 12(2):301–323

    Article  CAS  PubMed  Google Scholar 

  121. Vermolen FJ, Gefen A (2013b) A semi-stochastic cell-based model for in vitro infected ‘wound’healing through motility reduction: a simulation study. J Theor Biol 318:68–80

    Article  CAS  PubMed  Google Scholar 

  122. Vermolen FJ, Mul MM, Gefen A (2014) Semi-stochastic cell-level computational modeling of the immune system response to bacterial infections and the effects of antibiotics. Biomech Model Mechanobiol 13(4):713–734

    Article  CAS  PubMed  Google Scholar 

  123. Vermolen FJ, Van der Meijden RP, Van Es M, Gefen A, Weihs D (2015) Towards a mathematical formalism for semi-stochastic cell-level computational modeling of tumor initiation. Ann Biomed Eng 43(7):1680–1694

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  124. Vincent TL, Gatenby RA (2008) An evolutionary model for initiation, promotion, and progression in carcinogenesis. Int J Oncol 32(4):729–737

    CAS  PubMed  Google Scholar 

  125. Wang James HC, Jeen-Shang L (2007) Cell traction force and measurement methods. Biomech Model Mechanobiol 6(6):361–371

    Article  PubMed  Google Scholar 

  126. Wang Z, Zhang L, Sagotsky J, Deisboeck TS (2007) Simulating non-small cell lung cancer with a multiscale agent-based model. Theor Biol Med Model 4(1):50

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  127. Ward JP, King JR (1997) Mathematical modelling of avascular-tumour growth. Theor Math Med Biol J IMAand Med Model 14(1):39–69

    Article  CAS  Google Scholar 

  128. Weens W (2012) Mathematical modeling of liver tumor. PhD thesis, Université Pierre et Marie Curie-Paris VI

    Google Scholar 

  129. Winer JP, Chopra A, Kresh JY, Janmey PA (2011) Mechanobiology of cell–cell and cell–matrix interactions. Chapter 2

    Google Scholar 

  130. Wolf K, Wu YI, Liu Y, Geiger J, Tam E, Christopher Overall M, Stack S, Friedl P (2007) Multi-step pericellular proteolysis controls the transition from individual to collective cancer cell invasion. Nat Cell Biol 9(8):893

    Article  CAS  PubMed  Google Scholar 

  131. Yang L, Witten TM, Pidaparti RM (2013) A biomechanical model of wound contraction and scar formation. J Theor Biol 332:228–248

    Article  PubMed  Google Scholar 

Download references

Acknowledgements

This study is financially supported by the China Scholarship Council and the authors are very grateful for this funding. The authors declare that they do not have any conflicts of interest.

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Authors and Affiliations

  1. Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands

    Jiao Chen & Fred J. Vermolen

  2. Faculty of Biomedical Engineering, Technion-Israel Institute of Technology, Haifa, Israel

    Daphne Weihs

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  2. Daphne Weihs
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  3. Fred J. Vermolen
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Correspondence to Jiao Chen .

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Editors and Affiliations

  1. Departamento de Engenharia Mecânica, Faculdade de Engenharia, Universidade do Porto, Porto, Portugal

    João Manuel R. S. Tavares

  2. Department of Mechanical Engineering, IDMEC-IST, Lisbon, Portugal

    Paulo Rui Fernandes

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Chen, J., Weihs, D., Vermolen, F.J. (2019). Computational Cell-Based Modeling and Visualization of Cancer Development and Progression. In: Tavares, J., Fernandes, P. (eds) New Developments on Computational Methods and Imaging in Biomechanics and Biomedical Engineering. Lecture Notes in Computational Vision and Biomechanics, vol 33. Springer, Cham. https://doi.org/10.1007/978-3-030-23073-9_7

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