A mathematical model for the dynamics of cancer hepatocytes under therapeutic actions. (English) Zbl 1336.92037
Summary: This paper deals with the development of a mathematical model for the in vitro dynamics of malignant hepatocytes exposed to anti-cancer therapies. The model consists of a set of integro-differential equations describing the dynamics of tumor cells under the effects of mutation and competition phenomena, interactions with cytokines regulating cell proliferation as well as the action of cytotoxic drugs and targeted therapeutic agents. Asymptotic analysis and simulations, developed with an exploratory aim, are addressed to enlighten the role played by the biological phenomena under consideration in the dynamics of hepatocellular carcinoma, with particular reference to the intra-tumor heterogeneity and the response to therapies. The obtained results suggest that cancer progression selects for highly proliferative clones. Moreover, it seems that intra-tumor heterogeneity makes targeted therapeutic agents to be less effective than cytotoxic drugs and a joint action of these two classes of agents may mutually increase their efficacy. Finally, it is highlighted how targeted therapeutic agents might act as an additional selective pressure leading to the selection for the most fitting, and then most resistant, cancer clones.
MSC:
| 92C50 | Medical applications (general) |
Keywords:
hepatocelular carcinoma; structured populations; cancer modeling and therapy; evolution; concentration phenomenaReferences:
| [1] | Bellomo, N.; Delitala, M., From the mathematical kinetic, and stochastic game theory to modeling mutations, onset, progression and immune competition of cancer cells, Phys. Life Rev., 5, 183-206 (2008) |
| [2] | Bellomo, N.; Li, N. K.; Maini, P. K., On the foundations of cancer modeling, Math. Models Methods Appl. Sci., 18, 593-646 (2008) · Zbl 1151.92014 |
| [3] | Bellouquid, A.; Delitala, M., Modelling Complex Multicellular Systems—A Kinetic Theory Approach (2006), Birkhäuser: Birkhäuser Boston · Zbl 1178.92002 |
| [4] | Castiglione, F.; Piccoli, B., Cancer immunotherapy, mathematical modeling and optimal control, J. Theor. Biol., 247, 723-732 (2007) · Zbl 1455.92068 |
| [5] | Delitala, M.; Lorenzi, T., A mathematical model for progression and heterogeneity in colorectal cancer dynamics, Theor. Pop. Biol., 79, 130-138 (2011) · Zbl 1338.92045 |
| [6] | Desvillettes, L.; Jabin, P. E.; Mischler, S.; Raoul, G., On selection dynamics for continuous structured populations, Commun. Math. Sci., 6, 729-747 (2008) · Zbl 1176.45009 |
| [7] | Diekmann, O.; Jabin, P. E.; Mischler, S.; Perthame, B., The dynamics of adaptation: an illuminating example and a Hamilton-Jacobi approach, Theor. Pop. Biol., 67, 257-271 (2005) · Zbl 1072.92035 |
| [8] | Farazi, P. A.; DePinho, R. A., Hepatocellular carcinoma pathogenesis: from genes to environment, Nat. Rev. Cancer, 6, 674-687 (2006) |
| [9] | Foo, J.; Michor, F., Evolution of resistance to anti-cancer therapy during general dosing schedules, J. Theor. Biol., 263, 179-188 (2010) · Zbl 1406.92294 |
| [10] | Komarova, N. L.; Wodarz, D., Drug resistance in cancer: principles of emergence and prevention, Proc. Natl. Acad. Sci. USA, 102, 9714-9719 (2005) |
| [11] | Maynard Smith, J., Evolution and the Theory of Games (1982), Cambridge University Press · Zbl 0526.90102 |
| [12] | Merlo, L. M.; Pepper, J. W.; Reid, B. J.; Maley, C. C., Cancer as an evolutionary and ecological process, Nat. Rev. Cancer, 6, 924-935 (2006) |
| [13] | Michor, F.; Nowak, M. A.; Iwasa, Y., Evolution of resistance to cancer therapy, Curr. Pharm. Des., 12, 261-271 (2006) |
| [14] | Nowell, P. C., The clonal evolution of tumor cell populations, Science, 194, 23-28 (1976) |
| [15] | Perthame, B., Transport Equations in Biology (2007), Birkhäuser: Birkhäuser Basel · Zbl 1185.92006 |
| [16] | Scianna, M.; Merks, R.; Preziosi, L.; Medico, E., Individual cell-based models of cell scatter of ARO and MLP-29 cells in response to hepatocyte growth factor, J. Theor. Biol., 260, 151-160 (2009) · Zbl 1402.92160 |
| [17] | Szymanska, Z.; Urbanski, J.; Marciniak-Czochra, A., Mathematical modelling of the influence of heat shock proteins on cancer invasion of tissue, J. Math. Biol., 58, 819-840 (2009) · Zbl 1311.92042 |
| [18] | Tarin, D.; Thompson, E. W.; Newgreen, D. F., The fallacy of epithelial mesenchymal transition in neoplasia, Cancer Res., 65, 5996-6000 (2005) |
| [19] | Turner, C.; Kohandel, M., Investigating the link between epithelial to mesenchymal transition and the cancer stem cell phenotype: a mathematical approach, J. Theor. Biol., 265, 329-335 (2010) · Zbl 1460.92059 |
| [20] | Weinberg, R. A., The Biology of Cancer (2007), Garland Science |
| [21] | van Zijl, F.; Mall, S.; Machat, G.; Pirker, C.; Zeillinger, R.; Weinhäusel, A.; Bilban, M.; Berger, W.; Mikulits, W., A human model of epithelial to mesenchymal transition to monitor drug efficacy in hepatocellular carcinoma progression, Mol. Cancer Ther., 10, 850-860 (2011) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
