Cancer modelling
Open Access
Issue
Math. Model. Nat. Phenom.
Volume 15, 2020
Cancer modelling
Article Number 42
Number of page(s) 28
DOI https://doi.org/10.1051/mmnp/2019043
Published online 22 September 2020
  1. R.A. Anderson and M. Chaplain, Continuous and discrete mathematical models of tumor-induced angiogenesis. Bull. Math. Biol. 60 (1998) 857–899. [Google Scholar]
  2. E.-a. D. Amir, L.K. Davis, D.M. Tadmor, F.E. Simonds, H. Levlne, Jacob, C.S. Bendall, K.D. Shenfeld, S. Krishnaswamy, P.G. Nolan and D. Pe’er, viSNE enables visualization of high dimensional single-cell data and reveals phenotypic heterogeneity of leukemia. Nat. Biotechnol. 31 (2013) 545–552. [CrossRef] [PubMed] [Google Scholar]
  3. K. Bacevic, R. Noble, A. Soffar, O. Wael Ammar, B. Boszonyik, S. Prieto, C. Vincent, E.M. Hochberg, L. Krasinska and D. Fisher, Spatial competition constrains resistance to targeted cancer therapy. Nat. Commun. 8 (2017) 1–15. [CrossRef] [PubMed] [Google Scholar]
  4. I. Bozic, T. Antal, H. Ohtsuki, H. Carter, D. Kim, S. Chen, et al., Accumulation of driver and passenger mutations during tumor progression. PNAS 107 (2010) 18545–18550. [CrossRef] [Google Scholar]
  5. G.B. Birkhead, M.E. Rakin, S. Gallivan, L. Dones and D.R. Rubens, A mathematical model of the development of drug resistance to cancer chemotherapy. Eur. J. Cancer Clin. Oncol. 23 (1987) 1421–1427. [CrossRef] [PubMed] [Google Scholar]
  6. R. Biswas, S. Gao, M.C. Cultraro, K.T. Maity, A. Venugopalan, Z. Abdullaev, K.A. Shaytan, A.C. Carter, A. Thomas, A. Rajan, Y. Song, et al., Genomic profiling of multiple sequentially acquired tumor metastatic sites from an “exceptional responder” lung adenocarcinoma patient reveals extensive genomic heterogeneity and novel somatic variants driving treatment response. Cold Spring Harbor molecular case studies 2 (2016) 1–26. [Google Scholar]
  7. D. Bray, Cell Movements: From Molecules to Motility, Garland Science, 2 edition (2000). [CrossRef] [Google Scholar]
  8. A. Brock, H. Chang and S. Huang, Non-genetic heterogeneity – a mutation-independent driving force for the somatic evolution of tumours. Nat. Rev. Genet. 10 (2009) 336–342. [CrossRef] [PubMed] [Google Scholar]
  9. A.H. Burris, S.H. Rugo, J.S. Vukelja, L.C. Vogel, A.R. Borson, S. Limentani, E. Tan-Chiu, E.I. Krop, A.R. Michaelson, et al., Phase II study of the antibody drug conjugate trastuzumab-DM1 for the treatment of human epidermal growth factor receptor 2 (HER2)-positive breast cancer after prior HER2-directed therapy. J. Clin. Oncol. 29 (2011) 398–405. [CrossRef] [PubMed] [Google Scholar]
  10. A.L. Byers, L. Diao, J. Wang, P. Saintigny, L. Girard, M. Peyton, L. Shen, Y. Fan, U. Giri, K.P. Tumula, B.M. Nilsson, J. Gudikote, et al., An epithelial-mesenchymal transition gene signature predicts resistance to EGFR and PI3K inhibitors and identifies Axl as a therapeutic target for overcoming EGFR inhibitor resistance. Clin. Cancer Res. 19 (2013) 279–290. [CrossRef] [PubMed] [Google Scholar]
  11. C. Carrère, Optimization of an in vitro chemotherapy to avoid resistant tumours. J. Theor. Biol. 413 (2017) 24–33. [CrossRef] [PubMed] [Google Scholar]
  12. H.H. Chang, Y.P. Oh, E.D. Ingber and S. Huang, Multistable and multistep dynamics in neutrophil differentiation. BMC Cell Biol. 7 (2006) 1–12. [CrossRef] [PubMed] [Google Scholar]
  13. H. Cho and D. Levy, Modeling the dynamics of heterogeneity of solid tumors in response to chemotherapy. Bull. Math. Biol. 79 (2017) 2986–3012. [Google Scholar]
  14. H. Cho and D. Levy, Modeling the chemotherapy-induced selection of drug-resistant traits during tumor growth. J. Theor. Biol. 436 (2018) 120–134. [CrossRef] [PubMed] [Google Scholar]
  15. H. Cho and D. Levy, Modeling continuous levels of resistance to multidrug therapy in cancer. Appl. Math. Model. 64 (2018) 733–751. [Google Scholar]
  16. H. Cho, D. Venturi, E.G. Karniadakis, Numerical methods for high-dimensional probability density function equations. J. Comput. Phys. 305 (2016) 817–837. [Google Scholar]
  17. H.R. Chisholm, T. Lorenzi, A. Lorz, K.A. Larsen, N.D.L. Almeida, A. Escargueil and J. Clairambault, Emergence of Drug Tolerance in Cancer Cell Populations: An Evolutionary Outcome of Selection, Nongenetic Instability, and Stress-Induced Adaptation. Cancer Res. 75 (2015) 930–940. [Google Scholar]
  18. K. Dorris, C. Liu, D. Li, R.T. Hummel, X. Wang, J. Perentesis, O.M. Kim and M. Fouladi, A comparison of safety and efficacy of cytotoxicversus molecularly targeted drugs in pediatric phase I solid tumor oncology trials. Pediatr. Blood Cancer 64 (2017) 1–11. [Google Scholar]
  19. T. Eichenlaub, S.M. Cohen and H. Herranz, Cell competition drives the formation of metastatic tumors in a Drosophila model of epithelial tumor formation. Curr. Biol. 26 (2016) 419–427. [CrossRef] [PubMed] [Google Scholar]
  20. V. Fodal, M. Pierobon, L. Liotta and E. Petricoin, Mechanisms of cell adaptation: when and how do cancer cells develop chemoresistance? Cancer J. 17 (2011) 89–95. [CrossRef] [PubMed] [Google Scholar]
  21. J. Foo and F. Michor, Evolution of acquired resistance to anti-cancer therapy. J. Theor. Biol. 355 (2014) 10–20. [CrossRef] [PubMed] [Google Scholar]
  22. K. Fosgerau and T. Hoffmann, Peptide therapeutics: current status and future directions. Drug Discov. Today 20 (2015) 122–128. [CrossRef] [PubMed] [Google Scholar]
  23. K. Furugaki, I. Toshiki, S. Masatoshi, K. Kumiko, M. Yoichiro and M. Kazushige, Schedule–dependent antitumor activity of the combination with erlotinib and docetaxel in human non-small cell lung cancer cells with EGFR mutation , KRAS mutation or both wild-type EGFR and KRAS. Oncol. Rep. 24 (2010) 1141–1146. [PubMed] [Google Scholar]
  24. A.R. Gatenby and T.E. Gawlinski, A reaction-diffusion model of cancer invasion. Cancer Res. 56 (1996) 5745–5753. [Google Scholar]
  25. A.R. Gatenby, S.A. Silva, J.R. Gillies and R.B. Frieden, Adaptive therapy. Cancer Res. 69 (2009) 4894–4903. [Google Scholar]
  26. R. Glasspool, M.J. Teodoridis and R. Brown, Epigenetics as a mechanism driving polygenic clinical drug resistance. Br. J. Cancer 94 (2006) 1087–1092. [CrossRef] [PubMed] [Google Scholar]
  27. B.P. Gupta, M.C. Fillmore, G. Jiang, D.S. Shapira, K. Tao, C. Kuperwasser and S.E. Lander, Stochastic state transitions give rise to phenotypic equilibrium in populations of cancer cells. Cell 146 (2011) 633–644. [CrossRef] [PubMed] [Google Scholar]
  28. M.C. Garvey, E. Spiller, D. Lindsay, C.-T. Chiang, C.N. Choi, B.D. Agus, P. Mallick, J. Foo and M.S. Mumenthaler, A high-content image-based method for quantitatively studying context-dependent cell population dynamics. Sci Rep. 6 (2016) 1–12. [CrossRef] [PubMed] [Google Scholar]
  29. R. Gatenby and R. Gillies, A microenvironmental model of carcinogenesis. Nat. Rev. Cancer 8 (2008) 56–61. [Google Scholar]
  30. J. Gil and T. Rodriguez, Cancer: the transforming power of cell competition. Curr. Biol. 26 (2016) R164–R166. [CrossRef] [PubMed] [Google Scholar]
  31. J.-P. Gillet and M.M. Gottesman, Mechanisms of multidrug resistance in cancer. Methods Mol. Biol. 596 (2010) 47–76. [CrossRef] [PubMed] [Google Scholar]
  32. B.S. Goldberg, R.G. Oxnard, S. Digumarthy, A. Muzikansky, M.D. Jackman, T.I. Lennes and V.L. Sequist, Chemotherapy with Erlotinib or chemotherapy alone in advanced non-small cell lung cancer with acquired resistance to EGFR tyrosine kinase inhibitors. Oncologist 18 (2013) 1214–1220. [CrossRef] [PubMed] [Google Scholar]
  33. M.M. Gottesman, Mechanisms of cancer drug resistance. Annu. Rev. Med. 53 (2002) 615–627. [CrossRef] [PubMed] [Google Scholar]
  34. M.M. Gottesman, T. Fojo and S.E. Bates, Multidrug resistance in cancer: role of ATP-dependent transporters. Nat. Rev. Cancer 2 (2002) 48–58. [Google Scholar]
  35. L. Grasedyck, D. Kressner and C. Tobler, A literature survey of low-rank tensor approximation techniques. GAMM Mitteilungen 36 (2013) 53–78. [CrossRef] [MathSciNet] [Google Scholar]
  36. J. Greene, O. Lavi, M.M. Gottesman and D. Levy, The impact of cell density and mutations in a model of multidrug resistance in solid tumors. Bull. Math. Biol. 74 (2014) 627–653. [Google Scholar]
  37. D. Hanahan and R.A. Weinberg, Hallmarks of cancer: the next generation. Cell 144 (2011) 646–674. [CrossRef] [PubMed] [Google Scholar]
  38. G. Housman, S. Byler, S. Heerboth, K. Lapinska, M. Longacre, N. Snyder and S. Sarkar, Drug resistance in cancer : An Overview. Cancers 6 (2014) 1769–1792. [CrossRef] [PubMed] [Google Scholar]
  39. T. Hillen, M. Lewis, Managing Complexity, 2016 Reducing Perplexity – Modeling biological systems. Springer 13–25. [Google Scholar]
  40. Y. Iwasa, A.M. Nowak and F. Michor, Evolution of resistance during clonal expansion. Genetics 172 (2006) 2557–2566. [CrossRef] [PubMed] [Google Scholar]
  41. S. Jones, W. Chen, G. Parmigiani, F. Diehl, N. Beerenwinkel, T. Antal, et al., Comparative lesion sequencing provides insights into tumor evolution. PNAS 105 (2008) 4283–4288. [CrossRef] [Google Scholar]
  42. Y. Jiang, Q. Yuan and Q. Fang, Schedule-dependent synergistic interaction between docetaxel and gefitinib in NSCLC cell lines regardless of the mutation status of EGFR and KRAS and its molecular mechanisms. J. Cancer Res. Clin. Oncol. 140 (2014) 1087–1095. [CrossRef] [PubMed] [Google Scholar]
  43. R. Levayer, Cell competition: How to take over the space left by your neighbours. Curr. Biol. 28 (2018) R741–R744. [CrossRef] [PubMed] [Google Scholar]
  44. D.V. Jonsson, M.C. Blakely, L. Lin, S. Asthana, N. Matni, V. Olivas, E. Pazarentzos, A.M. Gubens, C.B. Bastian, S.B. Taylor, C.J. Doyle and G.T. Bivona, Novel computational method for predicting polytherapy switching strategies to overcome tumor heterogeneity and evolution. Sci. Rep. 7 (2017) 1–14. [CrossRef] [PubMed] [Google Scholar]
  45. G. Kalemkerian, W. Akerley, P. Bogner, H. Borghaei, L. Chow, R. Downey, L. Gandhi, A. Ganti, R. Govindan, et al., Non-small cell lung cancer. J. Natl. Comprehensive Cancer Netw. 10 (2012) 1236–1271. [CrossRef] [Google Scholar]
  46. N. Komarova, Stochastic modeling of drug resistance in cancer. Theor. Popul. Biol. 239 (2006) 351–366. [Google Scholar]
  47. M. Kimmel, A. Swierniaka and A. Polanski, Infinite-dimensional model of evolution of drug resistance of cancer cells. J. Math. Syst. Estim. Control 8 (1998) 1–16. [Google Scholar]
  48. O. Lavi, M.M. Gottesman and D. Levy, The dynamics of drug resistance: a mathematical perspective. Drug Resist. Updates 15 (2012) 90–97. [CrossRef] [Google Scholar]
  49. T. Lorenzi, H.R. Chisholm and J. Clairambault, Tracking the evolution of cancer cell populations through the mathematical lens of phenotype-structured equations. Biol. Dir. 11 (2016) 1–17. [CrossRef] [Google Scholar]
  50. T. Lorenzi, H.R. Chisholm, L. Desvillettes and D.B. Hughes, Dissecting the dynamics of epigenetic changes in phenotype-structured populations exposed to fluctuating environments. J. Theor. Biol. 386 (2015) 166–176. [CrossRef] [PubMed] [Google Scholar]
  51. A. Lorz, T. Lorenzi, E.M. Hochberg, J. Clairambault and B. Perthame, Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies. ESAIM: M2AN 47 (2013) 377–399. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  52. A. Lorz, T. Lorenzi, J. Clairambault, A. Escargueil and B. Perthame, Modeling the effects of space structure and combination therapies on phenotypic heterogeneity and drug resistance in solid tumors. Bull. Math. Biol. 77 (2015) 1–22. [Google Scholar]
  53. C.C. Maley, A. Aktipis, A.T. Graham, A. Sottoriva, M.A. Boddy, M. Janiszewska, S.A. Silva, M. Gerlinger, Y. Yuan, J.K. Pienta, et al., Classifying the evolutionary and ecological features of neoplasms. Nat. Rev. Cancer 17 (2017) 605–619. [Google Scholar]
  54. A. Marusyk, V. Almendro and K. Polyak, Intra-tumour heterogeneity: a looking glass for cancer? Nat. Rev. Cancer 12 (2012) 323–334. [CrossRef] [PubMed] [Google Scholar]
  55. L. Merlo, J. Pepper, B. Reid and C. Maley, Cancer as an evolutionary and ecological process. Nat. Rev. Cancer 6 (2006) 924–935. [Google Scholar]
  56. K. Masui, B. Gini, J. Wykosky, C. Zanca, P.S. Mischel, F.B. Furnari and W.K. Cavenee, A tale of two approaches: Complementary mechanisms of cytotoxic and targeted therapy resistance may inform next-generation cancer treatments. Carcinogenesis 34 (2013) 725–738. [Google Scholar]
  57. J.P. Medema, Cancer stem cells: the challenges ahead. Nat. Cell Biol. 15 (2013) 338–344. [CrossRef] [PubMed] [Google Scholar]
  58. F. Michor, A.M. Nowak and Y. Iwasa, Evolution of Resistance to Cancer Therapy. Curr. Pharm. Des. 12 (2006) 261–271. [CrossRef] [PubMed] [Google Scholar]
  59. S. Misale, I. Bozic, J. Tong, A. Peraza-Penton, A. Lallo, F. Baldi, K. Lin, M. Truini, L. Trusolino, A. Bertotti, F. Di Nicolantonio, M. Nowak, L. Zhang, K. Wood and A. Bardelli, Vertical suppression of the EGFR pathway prevents onset of resistance in colorectal cancers. Nat. Commun. 6 (2015) 1–9. [Google Scholar]
  60. S.T. Mok, Y.-L. Wu, C.-J. Yu, C. Zhou, Y.-M. Chen, L. Zhang, J. Ignacio, M. Liao, V. Srimuninnimit, et al., Randomized, placebo-controlled, phase II study of sequential Erlotinib and chemotherapy as first-line treatment for advanced non-small-cell lung cancer. J. Clin. Oncol. 27 (2009) 5080–5087. [CrossRef] [PubMed] [Google Scholar]
  61. E. Moreno, Iscell competition relevant to cancer? Nat. Rev. Cancer 8 (2008) 141–147. [Google Scholar]
  62. E. Moreno, K. Basler and G. Morata, Cells compete for decapentaplegic survival factor to prevent apoptosis in Drosophila wing development. Nature 416 (2002) 755–759. [Google Scholar]
  63. M.S. Mumenthaler, J. Foo, C.N. Choi, N. Heise, K. Leder, B.D. Agus, W. Pao, F. Michor and P. Mallick, The impact of microenvironmental heterogeneity on the evolution of drug resistance in cancer cells. Cancer Inf . 14 (2015) 19–31. [Google Scholar]
  64. J. Murray, Mathematical Biology. Springer-Verlag (2002). [CrossRef] [Google Scholar]
  65. B. Perthame and G. Barles, Dirac concentrations in Lotka-Volterra parabolic PDEs. Indiana Univ. Math. J. 57 (2008) 3275–3301. [CrossRef] [MathSciNet] [Google Scholar]
  66. E. Piretto, M. Delitala and M. Ferraro, Combination therapies and intra-tumoral competition: Insights from mathematical modeling. J. Theor. Biol. 446 (2018) 149–159. [CrossRef] [PubMed] [Google Scholar]
  67. O.A. Pisco, A. Brock, J. Zhou, A. Moor, M. Mojtahedi, D. Jackson and S. Huang, Non-darwinian dynamics in therapy-induced cancer drug resistance. Nat. Commun. 4 (2013) 2467. [CrossRef] [PubMed] [Google Scholar]
  68. C. Pouchol and E. Trélat, Global stability with selection in integro-differential Lotka-Volterra systems modelling trait-structured populations. J. Biol. Dyn. 12 (2018) 872–893. [CrossRef] [PubMed] [Google Scholar]
  69. C. Pouchol, J. Clairambault, A. Lorz and E. Trélat, Asymptotic analysis and optimal control of an integro-differential system modelling healthy and cancer cells exposed to chemotherapy. J. Math. Pures Appl. 116 (2018) 268–308. [Google Scholar]
  70. B. Perthame, F. Quirós and L.J. Vázquez, The Hele-Shaw asymptotics for mechanical models of tumor growth. Arch. Rational Mech. Anal. 212 (2014) 93–127. [CrossRef] [MathSciNet] [Google Scholar]
  71. L. Peng, D. Trucu, P. Lin, A. Thompson and A.J.M. Chaplain, A multiscale mathematical model of tumour invasive growth. Bull. Math. Biol. 79 (2016) 389–429. [Google Scholar]
  72. J.M. Rowe and B. Löwenberg, Gemtuzumab ozogamicin in acute myeloid leukemia: a remarkable saga about an active drug. Blood 121 (2013) 4838–4841. [CrossRef] [Google Scholar]
  73. T.J. Ribeiro, T.L. Macedo, G. Curigliano, L. Fumagalli, M. Locatelli, M. Dalton, A. Quintela, B.J. Carvalheira, S. Manunta, L. Mazzarella, J. Brollo and A. Goldhirsch, Cytotoxic drugs for patients with breast cancer in the era of targeted treatment: Back to the future? Ann. Oncol. 23 (2012) 547–555. [CrossRef] [PubMed] [Google Scholar]
  74. T. Roose, S.J. Chapman and P.K. Maini, Mathematical models of avascular tumor growth. SIAM Rev. 49 (2007) 179–208. [CrossRef] [MathSciNet] [Google Scholar]
  75. V.S. Sharma, Y.D. Lee, B. Li, P.M. Quinlan, F. Takahashi, S. Maheswaran, U. McDermott, N. Azizian, L. Zou and M.A. Fischbach, A chromatin-mediated reversible drug-tolerant state in cancer cell subpopulations. Cell 141 (2010) 69–80. [CrossRef] [PubMed] [Google Scholar]
  76. S. Singh, K.N. Tank, P. Dwiwedi, J. Charan, R. Kaur, P. Sidhu and K.V. Chugh, Monoclonal antibodies: a review. Curr. Clin. Pharmacol. 13 (2017) 85–99. [Google Scholar]
  77. P. Simpson, Parameters of cell competition in the compartments of the wing disc of Drosophila. Dev. Biol. 69 (1979) 182–193. [CrossRef] [PubMed] [Google Scholar]
  78. M. Slingerland, H. Guchelaar and H. Gelderblom, Liposomal drug formulations in cancer therapy: 15 years along the road. Drug Discov. Today 17 (2012) 160–166. [CrossRef] [PubMed] [Google Scholar]
  79. S. Suijkerbuijk, G. Kolahgar, I. Kucinski and E. Piddini, Cell competition drives the growth of intestinal adenomas in Drosophila. Curr. Biol. 26 (2016) 428–438. [CrossRef] [PubMed] [Google Scholar]
  80. A. Swierniak, M. Kimmel and J. Smieja, Mathematical modeling as a tool for planning anticancer therapy. Eur. J. Pharmacol. 625 (2009) 108–121. [CrossRef] [PubMed] [Google Scholar]
  81. B.A. Teicher, Cancer Drug Resistance. Humana Press, Totowa, N.J. (2006). [CrossRef] [Google Scholar]
  82. A. Tsuboi, S. Ohsawa, D. Umetsu, Y. Sando, E. Kuranaga, T. Igaki and K. Fujimoto, Competition for space is controlled by apoptosis-induced change of local epithelial topology. Curr. Biol. 28 (2018) 2115–2128. [CrossRef] [PubMed] [Google Scholar]
  83. O. Trédan, M.C. Galmarini, K. Patel and I.F. Tannock, Drug resistance and the solid tumor microenvironment. J. Natl. Cancer Inst. 99 (2007) 1441–1454. [CrossRef] [PubMed] [Google Scholar]
  84. S. Vivarelli, L. Wagstaff and E. Piddini, Cell wars: regulation of cell survival and proliferation by cell competition. Essays Biochem. 53 (2012) 69–82. [CrossRef] [PubMed] [Google Scholar]
  85. L. Wagstaff, G. Kolahgar and E. Piddini, Competitive cell interactions in cancer: a cellular tug of war. Trends Cell Biol. 23 (2013) 160–167. [Google Scholar]
  86. K. Wosikowski, A.J. Silverman, P. Bishop, J. Mendelsohn and E.S. Bates, Reduced growth rate accompanied by aberrant epidermal growth factor signaling in drug resistant human breast cancer cells. Biochim. Biophys. Acta 1497 (2000) 215–226. [CrossRef] [PubMed] [Google Scholar]
  87. N. Yoon, R. Velde, A. Marusyk and J. Scott, Optimal therapy scheduling based on a pair of collaterally sensitive drugs. Bull. Math. Biol. (2018) 1–34. [Google Scholar]
  88. Z. Zhang, C.J. Lee, L. Lin, V. Olivas, V. Au, M. Abdel-rahman, X. Wang, D.A. Levine, J. Kyung, J.Y. Choi, C.-M. Choi, S.-W. Kim, J.S. Jang, S.Y. Park, S.W. Kim, H.D. Lee, J.-S. Lee, V. Miller and M. Arcila, Activation of the AXL kinase causes resistance to EGFR-targeted therapy in lung cancer. Nat. Genet. 44 (2012) 852–860. [Google Scholar]

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