×

Do mechanisms matter? Comparing cancer treatment strategies across mathematical models and outcome objectives. (English) Zbl 1501.92042

MSC:

92C50 Medical applications (general)
34C60 Qualitative investigation and simulation of ordinary differential equation models
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] R, A change of strategy in the war on cancer, Nature, 459, 508-509 (2009) · doi:10.1038/459508a
[2] R, Lessons from applied ecology: Cancer control using an evolutionary double bind, Cancer Res., 69, 7499-7502 (2009) · doi:10.1158/0008-5472.CAN-09-1354
[3] R. A. Gatenby, A. S. Silva, R. J. Gillies, B. R. Frieden, Adaptive therapy, Cancer Res., 69 (2009), 4894-4903.
[4] K, Harnessing tumor evolution to circumvent resistance, Trends Genet., 34, 639-651 (2018) · doi:10.1016/j.tig.2018.05.007
[5] J, Integrating evolutionary dynamics into treatment of metastatic castrate-resistant prostate cancer, Nat. Commun., 8, 1816 (2017) · doi:10.1038/s41467-017-01968-5
[6] S, Metronomic reloaded: Theoretical models bringing chemotherapy into the era of precision medicine, Semin. Cancer Biol., 35, 53-61 (2015) · doi:10.1016/j.semcancer.2015.09.002
[7] E, Modifying adaptive therapy to enhance competitive suppression, Cancers, 12, 3556 (2020) · doi:10.3390/cancers12123556
[8] K, Effects of intermittent androgen suppression on androgen-dependent tumors. apoptosis and serum prostate-specific antigen, Cancer, 71, 2782-2790 (1993) · doi:10.1002/1097-0142(19930501)71:9<2782::AID-CNCR2820710916>3.0.CO;2-Z
[9] C, Metronomic chemotherapy: A systematic review of the literature and clinical experience, J. Oncol., 2019, 1-31 (2019)
[10] A, Feedback regulation in a cancer stem cell model can cause an allee effect, Bull. Math. Biol., 78, 754-785 (2016) · Zbl 1341.92029 · doi:10.1007/s11538-016-0161-5
[11] J, Capitalizing on competition: An evolutionary model of competitive release in metastatic castration resistant prostate cancer treatment, J. Theor. Biol., 455, 249-260 (2018) · Zbl 1406.92329 · doi:10.1016/j.jtbi.2018.07.028
[12] R, Predation, apparent competition and the structure of prey communities, Theor. Popul. Biol., 12, 197-229 (1977) · doi:10.1016/0040-5809(77)90042-9
[13] E, Combination therapies and intra-tumoral competition: Insights from mathematical modeling, J. Theor. Biol., 446, 149-159 (2018) · Zbl 1397.92353 · doi:10.1016/j.jtbi.2018.03.014
[14] H, Dynamical properties of a minimally parameterized mathematical model for metronomic chemotherapy, J. Math. Biol., 72, 1255-1280 (2016) · Zbl 1337.92117 · doi:10.1007/s00285-015-0907-y
[15] A, A mathematical model of intermittent androgen suppression for prostate cancer, J. Nonlinear Sci., 18, 593 (2008) · Zbl 1172.92021 · doi:10.1007/s00332-008-9031-0
[16] E, Global dynamics of a model of joint hormone treatment with dendritic cell vaccine for prostate cancer, Discrete Contin. Dyn. Syst. B, 22, 1001-1021 (2017) · Zbl 1360.92060 · doi:10.3934/dcdsb.2017050
[17] A, Analysis of mathematical model of prostate cancer with androgen deprivation therapy, Commun. Nonlinear Sci. Numer. Simul., 66, 41-60 (2019) · Zbl 1508.92113 · doi:10.1016/j.cnsns.2018.06.004
[18] J, Mathematical models of androgen resistance in prostate cancer patients under intermittent androgen suppression therapy, Appl. Sci., 6, 352 (2016) · doi:10.3390/app6110352
[19] H, Mathematical modeling of prostate cancer progression in response to androgen ablation therapy, Proc. Natl. Acad. Sci. USA, 108, 19701-19706 (2011) · doi:10.1073/pnas.1115750108
[20] T, A clinical data validated mathematical model of prostate cancer growth under intermittent androgen suppression therapy, AIP Adv., 2, 011002 (2012) · doi:10.1063/1.3697848
[21] J, Optimal control to develop therapeutic strategies for metastatic castrate resistant prostate cancer, J. Theor. Biol., 459, 67-78 (2018) · Zbl 1406.92288 · doi:10.1016/j.jtbi.2018.09.022
[22] P, Maintenance of high diversity in coral reef fish communities, Am. Nat., 111, 337-359 (1977) · doi:10.1086/283164
[23] R, Competitive exclusion, Am. Nat., 115, 151-170 (1980) · doi:10.1086/283553
[24] L, Intracrine androgen biosynthesis, metabolism and action revisited, Mol. Cell. Endocrinol., 465, 4-26 (2018) · doi:10.1016/j.mce.2017.08.016
[25] Z, Loss of dihydrotestosterone-inactivation activity promotes prostate cancer castration resistance detectable by functional imaging, J. Biol. Chem., 293, 17829-17837 (2018) · doi:10.1074/jbc.RA118.004846
[26] W, Androgen deprivation therapy: progress in understanding mechanisms of resistance and optimizing androgen depletion, Nat. Clin. Pract. Urol., 6, 76-85 (2009) · doi:10.1038/ncpuro1296
[27] D, Does degree of androgen suppression matter in hormone-sensitive prostate cancer?, J. Clin. Oncol., 33, 1098-1100 (2015) · doi:10.1200/JCO.2014.60.1419
[28] K, Solving differential equations in R: package deSolve, J. Stat. Softw., 33, 1-25 (2010)
[29] K, Spatial competition constrains resistance to targeted cancer therapy, Nat. Commun., 8, 1995 (2017) · doi:10.1038/s41467-017-01516-1
[30] J, Spatial heterogeneity and evolutionary dynamics modulate time to recurrence in continuous and adaptive cancer therapies, Cancer Res., 78, 2127-2139 (2018) · doi:10.1158/0008-5472.CAN-17-2649
[31] A, Limiting the development of anti-cancer drug resistance in a spatial model of micrometastases, Math. Biosci. Eng., 13, 1185-1206 (2016) · Zbl 1352.92085 · doi:10.3934/mbe.2016038
[32] M, Modeling multi-mutation and drug resistance: analysis of some case studies, Theor. Biol. Med. Mod., 14, 6 (2017) · doi:10.1186/s12976-017-0052-y
[33] Y, Development of a mathematical model that predicts the outcome of hormone therapy for prostate cancer, J. Theor. Biol., 264, 517-527 (2010) · Zbl 1406.92304 · doi:10.1016/j.jtbi.2010.02.027
[34] R, The genetic/non-genetic duality of drug ’resistance’in cancer, Trends Cancer, 4, 110-118 (2018) · doi:10.1016/j.trecan.2018.01.001
[35] J, Cellular interactions constrain tumor growth, Proc. Natl. Acad. Sci. USA, 116, 1918-1923 (2019) · Zbl 1416.92079 · doi:10.1073/pnas.1804150116
[36] A, Physiologically based mathematical models to optimize therapies against metastatic colorectal cancer: a mini-review, Curr. Pharm. Design, 20, 37-48 (2014) · doi:10.2174/13816128113199990553
[37] G, Adaptive dynamics of unstable cancer populations: The canonical equation, Evol. Appl., 11, 1283-1292 (2018) · doi:10.1111/eva.12625
[38] A, A structural methodology for modeling immune-tumor interactions including pro-and anti-tumor factors for clinical applications, Math. Biosci., 304, 48-61 (2018) · Zbl 1409.92111 · doi:10.1016/j.mbs.2018.07.006
[39] M, A mathematical model of tumor-immune interactions, J. Theor. Biol., 294, 56-73 (2012) · Zbl 1397.92358 · doi:10.1016/j.jtbi.2011.10.027
[40] A, Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies, ESAIM: Math. Model. Num., 47, 377-399 (2013) · Zbl 1274.92025 · doi:10.1051/m2an/2012031
[41] A, A theoretical quantitative model for evolution of cancer chemotherapy resistance, Biol. Direct, 5, 25 (2010) · doi:10.1186/1745-6150-5-25
[42] J, Towards multi-drug adaptive therapy, Cancer Res., 80, 1578-1589 (2020) · doi:10.1158/0008-5472.CAN-19-2669
[43] J, Multidrug cancer therapy in metastatic castrate-resistant prostate cancer: An evolution-based strategy, Clin. Cancer Res., 25, 4413-4421 (2019) · doi:10.1158/1078-0432.CCR-19-0006
[44] J, Developing a minimally structured mathematical model of cancer treatment with oncolytic viruses and dendritic cell injections, Comput. Math. Methods Med., 2018, 8760371 (2018) · Zbl 1431.92053
[45] A, Fibroblasts and Alectinib switch the evolutionary games played by non-small cell lung cancer, Nat. Ecol. Evol., 3, 450-456 (2019) · doi:10.1038/s41559-018-0768-z
[46] M. Gluzman, J. G. Scott, A. Vladimirsky, Optimizing adaptive cancer therapy: dynamic programming and evolutionary game theory, arXiv preprint arXiv: 1812.01805.
[47] Y, Personalizing androgen suppression for prostate cancer using mathematical modeling, Sci. Rep., 8, 2673 (2018) · doi:10.1038/s41598-018-20788-1
[48] Y, A theoretical analysis of tumour containment, Nat. Ecol. Evol., 5, 826-835 (2021) · doi:10.1038/s41559-021-01428-w
[49] F, Cancer therapy optimization based on multiple model adaptive control, Biomed. Signal Process. Control, 48, 255-264 (2019) · doi:10.1016/j.bspc.2018.09.016
[50] U, On drug resistance and metronomic chemotherapy: A mathematical modeling and optimal control approach, Math. Biosci. Eng., 14, 217-235 (2017) · Zbl 1351.49049 · doi:10.3934/mbe.2017014
[51] A, Ultimate dynamics and optimal control of a multi-compartment model of tumor resistance to chemotherapy, Discrete Contin. Dyn. Syst. B, 24, 2017-2038 (2019) · Zbl 1420.92047 · doi:10.3934/dcdsb.2019082
[52] C, Optimization of dose schedules for chemotherapy of early colon cancer determined by high-performance computer simulations, Cancer Inform., 18, 1176935118822804 (2019)
[53] K. Normilio-Silva, A. C. de Figueiredo, A. C. Pedroso-de Lima, G. Tunes-da Silva, A. Nunes da Silva, A. Delgado Dias Levites, A. T. de Simone, P. Lopes Safra, R. Zancani, P. C. Tonini et al., Long-term survival, quality of life, and quality-adjusted survival in critically ill patients with cancer, Crit. Care Med., 44 (2016), 1327-1337.
[54] T, Comparison between mathematical models of intermittent androgen suppression for prostate cancer, J. Theor. Biol., 366, 33-45 (2015) · Zbl 1412.92146 · doi:10.1016/j.jtbi.2014.10.034
[55] J. I. Griffiths, P. Wallet, L. T. Pflieger, D. Stenehjem, X. Liu, P. A. Cosgrove, N. A. Leggett, J. A. McQuerry, G. Shrestha, M. Rosetti, G. Sunga, P. J. Moos, F. R. Adler, J. T. Chang, S. Sharma, A. Bild, Circulating immune cell phenotype dynamics reflect the strength of tumor-immune cell interactions in patients during immunotherapy, Proc. Natl. Acad. Sci. USA, in press.
[56] R, Impact of genetic dynamics and single-cell heterogeneity on development of nonstandard personalized medicine strategies for cancer, Proc. Natl. Acad. Sci. USA, 109, 14586-14591 (2012) · doi:10.1073/pnas.1203559109
[57] K, Optimizing cancer treatment using game theory: A review, JAMA Oncol., 5, 96-103 (2019) · doi:10.1001/jamaoncol.2018.3395
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.