Open Access
Issue |
Math. Model. Nat. Phenom.
Volume 18, 2023
|
|
---|---|---|
Article Number | 18 | |
Number of page(s) | 27 | |
Section | Mathematical physiology and medicine | |
DOI | https://doi.org/10.1051/mmnp/2023023 | |
Published online | 11 August 2023 |
- C. Aktipis, A.M. Boddy, R.A. Gatenby, J.S. Brown and C.C. Maley, Life history trade-offs in cancer evolution. Nat. Rev. Cancer 13 (2013) 883–892. [CrossRef] [PubMed] [Google Scholar]
- L. Almeida, R.H. Chisholm, J. Clairambault, T. Lorenzi, A. Lorz, C. Pouchol and E. Trélat, Why is evolution important in cancer and what mathematics should be used to treat cancer? Focus on drug resistance. Trends Biomath. Model. Optim. Comput. Probl. (2018) 107–120. [Google Scholar]
- D. Ansari, H. Friess, M. Bauden, J. Samnegård and R. Andersson, Pancreatic cancer: disease dynamics, tumor biology and the role of the microenvironment. Oncotarget 9 (2018) 6644. [CrossRef] [PubMed] [Google Scholar]
- A. Ardaševa, R.A. Gatenby, A.R. Anderson, H.M. Byrne, P.K. Maini and T. Lorenzi, A mathematical dissection of the adaptation of cell populations to fluctuating oxygen levels. Bull. Math. Biol. 82 (2020) 1–24. [CrossRef] [Google Scholar]
- S. Astanin and L. Preziosi, Mathematical modelling of the warburg effect in tumour cords. J. Theoret. Biol. 258 (2009) 578–590. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- S. Benzekry, C. Lamont, A. Beheshti, A. Tracz, J.M. Ebos, L. Hlatky and P. Hahnfeldt, Classical mathematical models for description and prediction of experimental tumor growth. PLoS Comput. Biol. 10 (2014) e1003800. [CrossRef] [Google Scholar]
- S. Bhatia, P. Wang, A. Toh and E.W. Thompson, New insights into the role of phenotypic plasticity and emt in driving cancer progression. Front. Mol. Biosci. 7 (2020) 71. [CrossRef] [Google Scholar]
- J.M. Brown and W.R. Wilson, Exploiting tumour hypoxia in cancer treatment. Nat. Rev. Cancer 4 (2004) 437–447. [CrossRef] [PubMed] [Google Scholar]
- E. Bouin, V. Calvez, N. Meunier, S. Mirrahimi, B. Perthame, G. Raoul and R. Voituriez, Invasion fronts with variable motility: phenotype selection, spatial sorting and wave acceleration. Comptes Rendus Math. 350 (2012) 761–766. [CrossRef] [Google Scholar]
- A.M. Boddy, W. Huang and A. Aktipis, Life history trade-offs in tumors. Curr. Pathobiol. Rep. 6 (2018) 201–207. [CrossRef] [Google Scholar]
- R.H. Chisholm, T. Lorenzi and J. Clairambault, Cell population heterogeneity and evolution towards drug resistance in cancer: biological and mathematical assessment, theoretical treatment optimisation. Biochim. Biophys. Acta (BBA) – Gen. Subj. 1860 (2016) 2627–2645. [CrossRef] [Google Scholar]
- J. Clairambault and O. Fercoq, Physiologically structured cell population dynamic models with applications to combined drug delivery optimisation in oncology. Math. Model. Natural Phenomena 11 (2016) 45–70. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- G. Chiari, G. Fiandaca and M.E. Delitala, Hypoxia-related radiotherapy resistance in tumours: treatment efficacy investigation in an eco-evolutionary perspective. Front. Appl. Math. Stat. 9 (2023) 104063. [CrossRef] [Google Scholar]
- G. Chiari, M.E. Delitala, D. Morselli and M. Scianna, A hybrid modeling environment to describe aggregates of cells heterogeneous for genotype and behavior with possible phenotypic transitions. Int. J. Non-Linear Mech. 144 (2022) 104063. [CrossRef] [Google Scholar]
- P. Cumsille, A. Coronel, C. Conca, C. Quiñinao and C. Escudero, Proposal of a hybrid approach for tumor progression and tumor-induced angiogenesis. Theoret. Biol. Med. Model. 12 (2015) 1–22. [CrossRef] [Google Scholar]
- M. Damaghi, J. West, M. Robertson-Tessi, L. Xu, M.C. Ferrall-Fairbanks, P. A. Stewart, E. Persi, B.L. Fridley, P.M. Altrock, R.A. Gatenby et al., The harsh microenvironment in early breast cancer selects for a warburg Phenotype. Proc. Natl. Acad. Sci. U.S.A. 118 (2021) e2011342118. [CrossRef] [PubMed] [Google Scholar]
- A. Daşu, I. Toma-Dasu and M. Karlsson, Theoretical simulation of tumour oxygenation and results from acute and chronic hypoxia. Phys. Med. Biol. 48 (2003) 2829. [CrossRef] [PubMed] [Google Scholar]
- V.M. de Oliveira, A. Amado and P.R. Campos, The interplay of tradeoffs within the framework of a resource-based modelling. Ecol. Model. 384 (2018) 249–260. [CrossRef] [Google Scholar]
- W. Doerfler and P. Böhm, DNA methylation: development, genetic disease and cancer, Vol. 310. Springer Science & Business Media (2006). [CrossRef] [Google Scholar]
- P. Domschke, D. Trucu, A. Gerisch and M.A. Chaplain, Structured models of cell migration incorporating molecular binding processes. J. Math. Biol. 75 (2017) 1517–1561. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- E. Ehrlich, L. Becks and U. Gaedke, Trait–fitness relationships determine how trade-off shapes affect species coexistence. Ecology 98 (2017) 3188–3198. [CrossRef] [PubMed] [Google Scholar]
- R. Fisher, L. Pusztai and C. Swanton, Cancer heterogeneity: implications for targeted therapeutics. Br. J. cancer 108 (2013) 479–485. [CrossRef] [PubMed] [Google Scholar]
- G. Fiandaca, M. Delitala and T. Lorenzi, A mathematical study of the influence of hypoxia and acidity on the evolutionary dynamics of cancer. Bull. Math. Biol. 83 (2021) 83. [CrossRef] [PubMed] [Google Scholar]
- E. Flashner-Abramson, S. Vasudevan, I.A. Adejumobi, A. Sonnenblick and N. Kravchenko-Balasha, Decoding cancer heterogeneity: studying patient-specific signaling signatures towards personalized cancer therapy. Theranostics 9 (2019) 5149. [CrossRef] [PubMed] [Google Scholar]
- J. Folkman and M. Hochberg, Self-regulation of growth in three dimensions, J. Exp. Med. 138 (1973) 745–753. [CrossRef] [PubMed] [Google Scholar]
- R.A. Gatenby, K. Smallbone, P.K. Maini, F. Rose, J. Averill, R.B. Nagle, L. Worrall and R.J. Gillies, Cellular adaptations to hypoxia and acidosis during somatic evolution of breast cancer. Br. J. Cancer 97 (2007) 646–653. [CrossRef] [PubMed] [Google Scholar]
- R.A. Gatenby and J.S. Brown, Integrating evolutionary dynamics into cancer therapy. Nat. Rev. Clin. Oncol. 17 (2020) 675–686. [CrossRef] [PubMed] [Google Scholar]
- A. Ibrahim-Hashim, R.J. Gillies, J.S. Brown and R.A. Gatenby, Coevolution of tumor cells and their microenvironment: “niche construction in cancer”, in Ecology and Evolution of Cancer. Elsevier (2017) 111–117. [CrossRef] [Google Scholar]
- P.-E. Jabin and G. Raoul, On selection dynamics for competitive interactions. J. Math. Biol. 63 (2011) 493–517. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- K.S. Korolev, J.B. Xavier and J. Gore, Turning ecology and evolution against cancer. Nat. Rev. Cancer 14 (2014) 371–380. [Google Scholar]
- H.P. Langtangen and A. Logg, Solving PDEs in Python. Springer (2017). [Google Scholar]
- M. Leszczyński, U. Ledzewicz and H. Schättler, Optimal control for a mathematical model for chemotherapy with pharmacometrics, Math. Model. Natural Phenomena 15 (2020) 69. [CrossRef] [EDP Sciences] [Google Scholar]
- S.Y. Lee, M.K. Ju, H.M. Jeon, E.K. Jeong, Y.J. Lee, C.H. Kim, H.G. Park, S.I. Han and H.S. Kang, Regulation of tumor progression by programmed necrosis. Oxid. Med. Cell. Longev. 2018 (2018) 1–28. [Google Scholar]
- T. Lorenzi, R.H. Chisholm and J. Clairambault, Tracking the evolution of cancer cell populations through the mathematical lens of phenotype-structured equations. Biol. Direct 11 (2016) 1–17. [Google Scholar]
- 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]
- T. Lorenzi, C. Venkataraman, A. Lorz and M.A. Chaplain, The role of spatial variations of abiotic factors in mediating intratumour phenotypic heterogeneity. J. Theor. Biol. 451 (2018) 101–110. [CrossRef] [Google Scholar]
- C. Maley, A. Aktipis, T. Graham, A. Sottoriva et al., Classifying the evolutionary and ecological features of neoplasms. Nat. Rev. Cancer 17 (2017) 605–619. [CrossRef] [PubMed] [Google Scholar]
- A. Martínez-González, G.F. Calvo, L.A. Pérez Romasanta and V.M. Pérez-García, Hypoxic cell waves around necrotic cores in glioblastoma: a biomathematical model and its therapeutic implications. Bull. Math. Biol. 74 (2012) 2875–2896. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- S. Nawaz, N.A. Trahearn, A. Heindl, S. Banerjee, C.C. Maley, A. Sottoriva and Y. Yuan, Analysis of tumour ecological balance reveals resource-dependent adaptive strategies of ovarian cancer. EBioMedicine 48 (2019) 224–235. [CrossRef] [PubMed] [Google Scholar]
- M.-E. Oraiopoulou, E. Tzamali, G. Tzedakis, A. Vakis, J. Papamatheakis and V. Sakkalis, In vitro/in silico study on the role of doubling time heterogeneity among primary glioblastoma cell lines. Biomed. Res. Int. 2017 (2017) 1–12. [CrossRef] [Google Scholar]
- M.J. Pollheimer, P. Kornprat, R.A. Lindtner, L. Harbaum, A. Schlemmer, P. Rehak and C. Langner, Tumor necrosis is a new promising prognostic factor in colorectal cancer. Hum. Pathol. 41 (2010) 1749–1757. [CrossRef] [Google Scholar]
- K. Ruan, G. Song and G. Ouyang, Role of hypoxia in the hallmarks of human cancer. J. Cell. Biochem. 107 (2009) 1053–1062. [CrossRef] [Google Scholar]
- B. Shashni, S. Ariyasu, R. Takeda, T. Suzuki, S. Shiina, K. Akimoto, T. Maeda, N. Aikawa, R. Abe, T. Osaki, N. Itoh and S. Aoki, Size-based differentiation of cancer and normal cells by a particle size analyzer assisted by a cell-recognition PC software. Biol. Pharmaceut. Bull. 41 (2018) 487–503. [CrossRef] [PubMed] [Google Scholar]
- M.A. Strobl, A.L. Krause, M. Damaghi, R. Gillies, A.R. Anderson and P.K. Maini, Mix and match: Phenotypic coexistence as a key facilitator of cancer invasion. Bull. Math. Biol. 82 (2020) 1–26. [CrossRef] [Google Scholar]
- H. Sung, J. Ferlay, R.L. Siegel, M. Laversanne, I. Soerjomataram, A. Jemal and F. Bray, Global cancer statistics 2020: Globocan estimates of incidence and mortality worldwide for 36 cancers in 185 countries. CA 1 (2021) 394–424. [Google Scholar]
- P. Vaupel, O. Thews and M. Hoeckel, Treatment resistance of solid tumors. Med. Oncol. 18 (2001) 243–259. [CrossRef] [PubMed] [Google Scholar]
- C. Villa, M.A. Chaplain and T. Lorenzi, Modeling the emergence of phenotypic heterogeneity in vascularized tumors. SIAM J. Appl. Math. 81 (2021) 434–453. [CrossRef] [MathSciNet] [Google Scholar]
- C. Villa, M.A. Chaplain and T. Lorenzi, Evolutionary dynamics in vascularised tumours under chemotherapy: mathematical modelling, asymptotic analysis and numerical simulations. Vietnam J. Math. 49 (2021) 143–167. [CrossRef] [MathSciNet] [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.