Free Access
Issue |
ESAIM: M2AN
Volume 47, Number 2, March-April 2013
|
|
---|---|---|
Page(s) | 377 - 399 | |
DOI | https://doi.org/10.1051/m2an/2012031 | |
Published online | 11 January 2013 |
- N. Bacaër and C. Sokhna, A reaction-diffusion system modeling the spread of resistance to an antimalarial drug. Math. Biosci. Eng. 2 (2005) 227–238. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- G. Barles, Solutions de viscosité et équations de Hamilton–Jacobi. Collec. SMAI, Springer-Verlag, Paris (2002). [Google Scholar]
- G. Barles and B. Perthame, Concentrations and constrained Hamilton–Jacobi equations arising in adaptive dynamics, in Recent Developments in Nonlinear Partial Differential Equations, edited by D. Danielli. Contemp. Math. 439 (2007) 57–68. [Google Scholar]
- G. Barles, S. Mirrahimi and B. Perthame, Concentration in Lotka–Volterra parabolic or integral equations : a general convergence result. Methods Appl. Anal. 16 (2009) 321–340. [CrossRef] [MathSciNet] [Google Scholar]
- G. Bell and S. Collins, Adaptation, extinction and global change. Evolutionary Applications 1 (2008) 3-16. [CrossRef] [PubMed] [Google Scholar]
- I. Bozic, T. Antal, H. Ohtsuki, H. Carter, D. Kim, S. Chen, R. Karchin, K.W. Kinzler, B. Vogelstein and M.A. Nowak, Accumulation of driver and passenger mutations during tumor progression. Proc. Natl. Acad. Sci. USA 107 (2010) 18545–18550. [Google Scholar]
- À. Calsina and S. Cuadrado, A model for the adaptive dynamics of the maturation age. Ecol. Model. 133 (2000) 33–43. [CrossRef] [Google Scholar]
- À. Calsina and S. Cuadrado, Small mutation rate and evolutionarily stable strategies in infinite dimensional adaptive dynamics. J. Math. Biol. 48 (2004) 135–159. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- N. Champagnat, R. Ferrière and S. Méléard, Unifying evolutionary dynamics : from individual stochastic processes to macroscopic models. Theor. Popul. Biol. 69 (2006) 297–321. [Google Scholar]
- J. Clairambault, Modelling physiological and pharmacological control on cell proliferation to optimise cancer treatments. Math. Model. Nat. Phenom. 4 (2009) 12–67 [Google Scholar]
- M.G. Crandall, H. Ishii and P.-L. Lions, User’s guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. 27 (1992) 1–67. [Google Scholar]
- E.M.C. D’Agata, M. Dupont-Rouzeyrol, P. Magal, D. Olivier and S. Ruan, The impact of different antibiotic regimens on the emergence of antimicrobial-resistant bacteria. PLoS One 3 (2008) es4036. [CrossRef] [Google Scholar]
- T. Day and R. Bonduriansky, A unified approach to the evolutionary consequences of genetic and nongenetic inheritance. Amer. Nat. 178 (2011) E18–E36. [CrossRef] [Google Scholar]
- O. Diekmann, A beginner’s guide to adaptive dynamics, in Mathematical modeling of population dynamics, edited by R. Rudnicki. Banach Center Publications 63 (2004) 47–86. [Google Scholar]
- O. Diekmann, P.-E. Jabin, S. Mischler and B. Perthame, The dynamics of adaptation : an illuminating example and a Hamilton–Jacobi approach. Theor. Popul. Biol. 67 (2005) 257–271. [CrossRef] [PubMed] [Google Scholar]
- E.R. Fearon and B. Vogelstein, A genetic model for colorectal tumorigenesis. Cell 61 (1990) 759–767. [CrossRef] [PubMed] [Google Scholar]
- W.H. Fleming and H.M. Soner, Controlled markov processes and vicosity solutions. Appl. Math. 25 (1993). [Google Scholar]
- J. Foo and F. Michor, Evolution of resistance to targeted anti-cancer therapy during continuous and pulsed administration strategies. PLoS Comput. Biol. 5 (2009) e1000557. [CrossRef] [PubMed] [Google Scholar]
- J. Foo and F. Michor, Evolution of resistance to anti-cancer therapy during general dosing schedules. J. Theor. Biol. 263 (2010) 179–188. [CrossRef] [PubMed] [Google Scholar]
- E.C. Friedberg, G.C. Walker, W. Siede, R.D. Wood, R.A. Schultz and T. Ellenberger, DNA repair and mutagenesis. ASM Press (2005). [Google Scholar]
- R.A. Gatenby, A change of strategy in the war on cancer. Nature 459 (2009) 508–509. [CrossRef] [PubMed] [Google Scholar]
- R.A. Gatenby, A.S. Silva, R.J. Gillies and B.R. Frieden, Adaptive therapy. Cancer Res. 69 (2009) 4894–4903. [Google Scholar]
- J. Goldie and A. Coldman, Drug resistance in cancer : mechanisms and models. Cambridge University Press (1998). [Google Scholar]
- R. Gomulkiewicz and R.D. Holt, When does evolution by natural selection prevent extinction? Evolution 49 (1995) 201–207. [CrossRef] [PubMed] [Google Scholar]
- 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]
- M. Greaves and C.C. Maley, Clonal evolution in cancer. Nature 481 (2012) 306–313. [CrossRef] [PubMed] [Google Scholar]
- P.-E. Jabin and G. Raoul, Selection dynamics with competition. J. Math. Biol. 63 (2011) 493–517. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- C.A. Jerez, Metal Extraction and Biomining, The Desk Encyclopedia of Microbiology, edited by M. Schaechter. Elsevier, Oxford 762–775. [Google Scholar]
- M. Kimmel and A. Świerniak, Control theory approach to cancer chemotherapy : benefiting from phase dependence and overcoming drug resistance, in Tutorials in Mathematical Biosciences III, edited by A. Friedman. Lect. Notes Math. 1872 (2006) 185–221. [CrossRef] [Google Scholar]
- M. Kivisaar, Stationary phase mutagenesis : mechanisms that accelerate adaptation of microbial populations under environmental stress. Environ. Microbiol. 5 (2003) 814–827. [CrossRef] [PubMed] [Google Scholar]
- N.L. Komarova and D. Wodarz, Drug resistance in cancer : principles of emergence and prevention. Proc. Natl. Amer. Soc. 102 (2005) 9714–9719. [Google Scholar]
- V. Lemesle, L. Mailleret and M. Vaissayre, Role of spatial and temporal refuges in the evolution of pest resistance to toxic crops. Acta Biotheor. 58 (2010) 89–102. [CrossRef] [PubMed] [Google Scholar]
- A. Lorz, S. Mirrahimi and B. Perthame, Dirac mass dynamics in multidimensional nonlocal parabolic equations. CPDE 36 (2011) 1071–1098. [Google Scholar]
- P. Magal and Webb G.F. Mutation, selection and recombination in a model of phenotype evolution. Discrete Contin. Dyn. Syst. 6 (2000) 221–236. [Google Scholar]
- C. Marzac et al., ATP-Binding-Cassette transporters associated with chemoresistance : transcriptional profiling in extreme cohorts and their prognostic impact in a cohort of 281 acute myeloid leukemia patients. Haematologica 96 (2011) 1293–1301. [CrossRef] [PubMed] [Google Scholar]
- F. McCormick, Cancer therapy based on oncogene addiction. J. Surg. Oncol. 103 (2011) 464–467. [CrossRef] [PubMed] [Google Scholar]
- J. Pasquier, P. Magal, C. Boulangé-Lecomte, G.F. Webb and F. Le Foll, Consequences of cell-to-cell P-glycoprotein transfer on acquired multi-drug resistance in breast cancer : a cell population dynamics model. Biol. Direct 6 (2011) 5. [CrossRef] [PubMed] [Google Scholar]
- B. Perthame, Transport equations in biology. Series in Frontiers in Mathematics. Birkhauser (2007). [Google Scholar]
- B. Perthame and G. Barles, Dirac concentrations in Lotka–Volterra parabolic PDEs. Indiana Univ. Math. J. 57 (2008) 3275–3301. [CrossRef] [MathSciNet] [Google Scholar]
- K.J. Pienta, N. McGregor, R. Axelrod and D.E. Axelrod, Ecological therapy for cancer : defining tumors using an ecosystem paradigm suggests new opportunities for novel cancer treatments. Transl. Oncol. 1 (2008) 158–164. [PubMed] [Google Scholar]
- A. Rafii, P. Mirshahi, M. Poupot, A.M. Faussat, A. Simon, E. Ducros, E. Mery, B. Couderc, R. Lis, J. Capdet, J. Bergalet, D. Querleu, F. Dagonnet, J.J. Fournié, J.P. Marie, E. Pujade-Lauraine, G. Favre, J. Soria and M. Mirshahi, Oncologic trogocytosis of an original stromal cells induces chemoresistance of ovarian tumours. PLoS One 3 (2008) e3894. [CrossRef] [PubMed] [Google Scholar]
- K.W. Scotto, Transcriptional regulation of ABC drug transporters. Oncogene 22 (2003) 7496–7511. [CrossRef] [PubMed] [Google Scholar]
- N.P. Shah, C.T. Tran, F.Y. Lee, P. Chan, D. Norris and C.L. Sawyers, Overriding imatinib resistance with a novel ABL kinase inhibitor. Sci. Rep. 305 (2004) 399–401. [Google Scholar]
- A.S. Silva and R.A. Gatenby, A theoretical quantitative model for evolution of cancer chemotherapy resistance. Biol. Direct 5 (2010) 25. [Google Scholar]
- K. Sprouffske, J.W. Pepper and C.C. Maley, Accurate reconstruction of the temporal order of mutations in neoplastic progression. Cancer Prevention Res. 4 (2011) 1135–1144. [CrossRef] [Google Scholar]
- A.G. Terry and S.A. Gourley, Perverse consequences of infrequently culling a pest. Bull. Math. Biol. 72 (2010) 1666–1695. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- Tomasetti C. and Levy D. An elementary approach to modeling drug resistance in cancer. Math. Biosci. Eng. 7 (2010) 905–918. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- C. Tomasetti and D. Levy, Drug resistance always depends on the cancer turnover rate, SBEC, in IFMBE Proc., edited by K.E. Herold, J. Vossoughi and W.E. Bentley. Springer, Berlin 32 (2010) 552–555. [Google Scholar]
- D.C. Zhou, S. Ramond, F. Viguié, A.-M. Faussat, R. Zittoun and J.-P. Marie, Sequential emergence of mrp and mdr-1 gene overexpression as well as mdr1-gene translocation in homoharringtonine selected K562 human leukemia cell lines. Int. J. Cancer 65 (1996) 365–371. [CrossRef] [PubMed] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.