2016, 13(6): 1185-1206. doi: 10.3934/mbe.2016038

Limiting the development of anti-cancer drug resistance in a spatial model of micrometastases

1. 

Department of Biology, The College of New Jersey, Ewing, NJ, United States

2. 

Integrated Mathematical Oncology Department and Center of Excellence in Cancer Imaging and Technology, H. Lee Mott Cancer Center and Research Institute, Department of Oncologic Sciences, University of South Florida, Tampa, FL, United States

3. 

Department of Mathematics and Statistics, The College of New Jersey, Ewing, NJ, United States

Received  October 2015 Revised  May 2016 Published  August 2016

While chemoresistance in primary tumors is well-studied, much less is known about the influence of systemic chemotherapy on the development of drug resistance at metastatic sites. In this work, we use a hybrid spatial model of tumor response to a DNA damaging drug to study how the development of chemoresistance in micrometastases depends on the drug dosing schedule. We separately consider cell populations that harbor pre-existing resistance to the drug, and those that acquire resistance during the course of treatment. For each of these independent scenarios, we consider one hypothetical cell line that is responsive to metronomic chemotherapy, and another that with high probability cannot be eradicated by a metronomic protocol. Motivated by experimental work on ovarian cancer xenografts, we consider all possible combinations of a one week treatment protocol, repeated for three weeks, and constrained by the total weekly drug dose. Simulations reveal a small number of fractionated-dose protocols that are at least as effective as metronomic therapy in eradicating micrometastases with acquired resistance (weak or strong), while also being at least as effective on those that harbor weakly pre-existing resistant cells. Given the responsiveness of very different theoretical cell lines to these few fractionated-dose protocols, these may represent more effective ways to schedule chemotherapy with the goal of limiting metastatic tumor progression.
Citation: Ami B. Shah, Katarzyna A. Rejniak, Jana L. Gevertz. Limiting the development of anti-cancer drug resistance in a spatial model of micrometastases. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1185-1206. doi: 10.3934/mbe.2016038
References:
[1]

B. Baguley, Multiple drug resistance mechanisms in cancer,, Mol. Biotechnol., 46 (2010), 308.  doi: 10.1007/s12033-010-9321-2.  Google Scholar

[2]

S. Benzekry and P. Hahnfeldt, Maximum tolerated dose versus metronomic scheduling in the treatment of metastatic cancers,, Journal of Theoretical Biology, 335 (2013), 235.  doi: 10.1016/j.jtbi.2013.06.036.  Google Scholar

[3]

I. Bozic, J. Reiter, B. Allen, T. Antal, K. Chatterjee, P. Shah, Y. S. Moon, A. Yaqubie, N. Kelly, D. Le, E. Lipson, P. Chapman, L. Diaz, B. Vogelstein and M. Nowak, Evolutionary dynamics of cancer in response to targeted combination therapy,, eLife, 2 (2013).  doi: 10.7554/eLife.00747.  Google Scholar

[4]

T. Brocato, P. Dogra, E. J. Koay, A. Day, Y.-L. Chuang, Z. Wang and V. Cristini, Understanding drug resistance in breast cancer with mathematical oncology,, Curr. Breast Cancer Rep., 6 (2014), 110.  doi: 10.1007/s12609-014-0143-2.  Google Scholar

[5]

L. Buffoni, D. Dongiovanni, C. Barone, C. Fissore, D. Ottaviani, V. Dongiovanni, R. Grillo, A. Salvadori, N. Birocco, M. Schena and O. Bertetto, Fractionated dose of cisplatin (CDDP) and vinorelbine (VNB) chemotherapy for elderly patients with advanced non-small cell lung cancer: Phase II trial,, Lung Cancer, 54 (2006), 353.  doi: 10.1016/j.lungcan.2006.08.013.  Google Scholar

[6]

J. Casciari, S. Sotirchos and R. Sutherland, Variations in tumor cell growth rates and metabolism with oxygen concentration, glucose concentration and extracellular pH,, J. Cellular Physiol., 151 (1992), 386.  doi: 10.1002/jcp.1041510220.  Google Scholar

[7]

A. Coldman and J. Goldie, A stochastic model for the origin and treatment of tumors containing drug-resistant cells,, Bull. Math. Biol., 48 (1986), 279.  doi: 10.1007/BF02459682.  Google Scholar

[8]

J. Cunningham, J. Brown, T. L. Vincent3 and R. A. Gatenby, Divergent and convergent evolution in metastases suggest treatment strategies based on specific metastatic sites,, Evolution, 2015 (2015), 76.  doi: 10.1093/emph/eov006.  Google Scholar

[9]

J. Cunningham, R. Gatenby and J. Brown, Evolutionary dynamics in cancer therapy,, Mol. Pharm., 8 (2011), 2094.  doi: 10.1021/mp2002279.  Google Scholar

[10]

R. De Souza, P. Zahedi, R. Badame, C. Allen and M. Piquette-Miller, Chemotherapy dosing schedule influences drug resistance development in ovarian cancer,, Mol. Cancer Ther., 10 (2011), 1289.  doi: 10.1158/1535-7163.MCT-11-0058.  Google Scholar

[11]

U. Emmenegger, G. Francia, A. Chow, Y. Shaked, A. Kouri, S. Man and R. Kerbel, Tumor that acquire resistance to low-dose metronomic cyclophosphamide retain sensitivity to maximum tolerated dose cyclophosphamide,, Neoplasia, 13 (2011), 40.  doi: 10.1593/neo.101174.  Google Scholar

[12]

J. Foo, K. Leder and S. Mumenthaler, Cancer as a moving target: Understanding the composition and rebound growth kinetics of recurrent tumors,, Evol. Appl., 6 (2013), 54.  doi: 10.1111/eva.12019.  Google Scholar

[13]

J. Foo and F. Michor, Evolution of resistance to targeted anti-cancer therapies during continuous and pulsed administration strategies,, PLoS Comput. Biol., 5 (2009).  doi: 10.1371/journal.pcbi.1000557.  Google Scholar

[14]

J. Foo and F. Michor, Evolution of resistance to anti-cancer therapy during general dosing schedules,, J. Theor. Biol., 263 (2010), 179.  doi: 10.1016/j.jtbi.2009.11.022.  Google Scholar

[15]

J. Foo and F. Michor, Evolution of acquired resistance to anti-cancer therapy,, J. Theor. Biol., 355 (2014), 10.  doi: 10.1016/j.jtbi.2014.02.025.  Google Scholar

[16]

J. Freyer and R. Sutherland, A reduction in the in situ rates of oxygen and glucose consumption of cells in EMT6/Ro spheroids during growth,, J. Cellular Physiol., 124 (1985), 516.  doi: 10.1002/jcp.1041240323.  Google Scholar

[17]

F. Fu, M. Nowak and S. Bonhoeffer, Spatial heterogeneity in drug concentrations can facilitate the emergence of resistance to cancer therapy,, PLoS Comput. Biol., 11 (2015).  doi: 10.1371/journal.pcbi.1004142.  Google Scholar

[18]

R. Gatenby, A. Silva, R. Gillies and B. Frieden, Adaptive therapy,, Cancer Res., 69 (2009), 4894.  doi: 10.1158/0008-5472.CAN-08-3658.  Google Scholar

[19]

J. Gevertz, Z. Aminzare, K.-A. Norton, J. Perez-Velazquez, A. Volkening and K. Rejniak, Emergence of anti-cancer drug resistance: Exploring the importance of the microenvironmental niche via a spatial model,, in Applications of Dynamical Systems in Biology and Medicine (eds. T. Jackson and A. Radunskaya), (2015), 1.  doi: 10.1007/978-1-4939-2782-1_1.  Google Scholar

[20]

J. Greene, O. Lavi, M. Gottesman and D. Levy, The impact of cell density and mutations in a model of multidrug resistance in solid tumors,, Bull. Math. Biol., 76 (2014), 627.  doi: 10.1007/s11538-014-9936-8.  Google Scholar

[21]

M. Hadjiandreou and G. Mitsis, Mathematical modeling of tumor growth, drug- resistance, toxicity, and optimal therapy design,, IEEE Trans. Biomed. Eng., 61 (2013), 415.   Google Scholar

[22]

D. Hanahan, G. Bergers and E. Bergsland, Less is more, regularly: Metronomic dosing of cytotoxic drugs can target tumor angiogenesis in mice,, The Journal of Clinical Investigations, 105 (2000), 1045.  doi: 10.1172/JCI9872.  Google Scholar

[23]

T. Jackson and H. Byrne, A mathematical model to study the effects of drug resistance and vasculature on the response of solid tumors to chemotherapy,, Math. Biosci., 164 (2000), 17.  doi: 10.1016/S0025-5564(99)00062-0.  Google Scholar

[24]

J. Kim and I. Tannock, Repopulation of cancer cells during therapy: An important cause of treatment failure,, Nat. Rev. Cancer, 5 (2005), 516.  doi: 10.1038/nrc1650.  Google Scholar

[25]

N. Komarova and D. Wodarz, Drug resistance in cancer: Principles of emergence and prevention,, Proc. Natl. Acad. Sci., 102 (2005), 9714.  doi: 10.1073/pnas.0501870102.  Google Scholar

[26]

N. Komarova and D. Wodarz, Stochastic modeling of cellular colonies with quiescence: An application to drug resistance in cancer,, Theor. Popul. Biol., 72 (2007), 523.  doi: 10.1016/j.tpb.2007.08.003.  Google Scholar

[27]

O. Lavi, M. Gottesman and D. Levy, The dynamics of drug resistance: A mathematical perspective,, Drug Resist. Update, 15 (2012), 90.  doi: 10.1016/j.drup.2012.01.003.  Google Scholar

[28]

O. Lavi, J. Greene, D. Levy and M. Gottesman, The role of cell density and intratumoral heterogeneity in multidrug resistance,, Cancer Res., 73 (2013), 7168.  doi: 10.1158/0008-5472.CAN-13-1768.  Google Scholar

[29]

U. Ledzewicz, B. Amni and H. Schattler, Dynamics and control of a mathematical model for metronomic chemotherapy,, Mathematical Biosciences and Engineering, 12 (2015), 1257.  doi: 10.3934/mbe.2015.12.1257.  Google Scholar

[30]

U. Ledzewicz and H. Schattler, Drug resistance in cancer chemotherapy as an optimal control problem,, Discret. Contin. Dyn-B, 6 (2006), 129.   Google Scholar

[31]

U. Ledzewicz, H. Schattler, M. Gahrooi and S. Dehkordi, On the MTD paradigm and optimal control for multi-drug cancer chemotherapy,, Math. Biosci. Eng., 10 (2013), 803.  doi: 10.3934/mbe.2013.10.803.  Google Scholar

[32]

A. Lorz, T. Lorenzi, J. Clairambault, A. Escargueil and B. Perthame, Modeling effects of space structure and combination therapies on phenotypic heterogeneity and drug resistance in solid tumors,, Bull. Math. Biol., 77 (2015), 1.  doi: 10.1007/s11538-014-0046-4.  Google Scholar

[33]

A. Lorz, T. Lorenzi, M. Hochberg, J. Clairambault and B. Perthame, Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies,, ESAIM: Math. Model. Num. Anal., 47 (2013), 377.  doi: 10.1051/m2an/2012031.  Google Scholar

[34]

V. Malik P.S.and Raina and N. Andre, Metronomics as maintenance treatment in oncology: Time for chemo-switch,, Front. Oncol., 4 (2014).   Google Scholar

[35]

F. Meineke, C. Potten and M. Loeffler, Cell migration and organization in the intestinal crypt using a lattice-free model,, Cell Prolif., 34 (2001), 253.  doi: 10.1046/j.0960-7722.2001.00216.x.  Google Scholar

[36]

S. Menchon, The effect of intrinsic and acquired resistances on chemotherapy effectiveness,, Acta Biother., 63 (2015), 113.  doi: 10.1007/s10441-015-9248-x.  Google Scholar

[37]

K. Mross and S. Steinbild, Metronomic anti-cancer therapy - an ongoing treatment option for advanced cancer patients,, Journal of Cancer Therapeutics & Research, 1 (2012), 1.  doi: 10.7243/2049-7962-1-32.  Google Scholar

[38]

S. Mumenthaler, J. Foo, K. Leder, N. Choi, D. Agus, W. Pao, P. Mallick and F. Michor, Evolutionary modeling of combination treatment strategies to overcome resistance to tyrosine kinase inhibitors in non-small cell lung cancer,, Mol. Pharm., 8 (2011), 2069.  doi: 10.1021/mp200270v.  Google Scholar

[39]

O. G. Scharovsky, L. Mainetti and V. Rozados, Metronomic chemotherapy: Changing the paradigm that more is better,, Current Oncology, 16 (2012), 7.   Google Scholar

[40]

P. Orlando, R. Gatenby and J. Brown, Cancer treatment as a game: Integrating evolutionary game theory into the optimal control of chemotherapy,, Phys. Biol., 9 (2012).   Google Scholar

[41]

K. Pietras and D. Hanahan, A multitargeted, metronomic, and maximum-tolerated dose "chemo-switch" regimen is antiangiogenic, producing objective responses and survival benefit in a mouse model of cancer,, J. Clinical Oncology, 23 (2005), 939.  doi: 10.1200/JCO.2005.07.093.  Google Scholar

[42]

A. Pisco and S. Huang, Non-genetic cancer cell plasticity and therapy-induced stemness in tumour relapse: 'What does not kill me strengthens me',, Br. J. Cancer, 112 (2015), 1725.  doi: 10.1038/bjc.2015.146.  Google Scholar

[43]

G. Powathil, M. Chaplain and M. Swat, Investigating the development of chemotherapeutic drug resistance in cancer: A multiscale computational study,, , ().   Google Scholar

[44]

S. Saxena and G. Christofori, Rebuilding cancer metastasis in the mouse,, Molecular Oncology, 7 (2013), 283.  doi: 10.1016/j.molonc.2013.02.009.  Google Scholar

[45]

A. Silva and R. Gatenby, A theoretical quantitative model for evolution of cancer chemotherapy resistance,, Biol. Direct., 5 (2010).  doi: 10.1186/1745-6150-5-25.  Google Scholar

[46]

O. Trédan, C. Galmarini, K. Patel and I. Tannock, Drug resistance and the solid tumor microenvironment,, J. Natl. Cancer Inst., 99 (2007), 1441.   Google Scholar

[47]

R. Turner and S. J. Charlton, Assessing the minimum number of data points required for accurate IC50 determination,, Assay Drug Dev Technol., 3 (2005), 525.   Google Scholar

[48]

M. Vives, M. Ginesta, K. Gracova, M. Graupera, O. Casanovas, G. Capella, T. Serrano, B. Laquente and F. Vinals, Motronomic chemotherapy following the maximum tolerated dose is an effective anti-tumour therapy affecting angiogenesis, tumour dissemination and cancer stem cells,, International Journal of Cancer, 133 (2013), 2464.   Google Scholar

[49]

B. Waclaw, I. Bozic, M. Pittman, R. Hruban, B. Vogelstein and M. Nowak, A spatial model predicts that dispersal and cell turnover limit intratumor heterogeneity,, Nature, 525 (2015), 261.   Google Scholar

[50]

A. Wu, K. Loutherback, G. Lambert, L. Estévez-Salmeron, T. Tlsty, R. Austin and J. Sturma, Cell motility and drug gradients in the emergence of resistance to chemotherapy,, Proc. Natl. Acad. Sci., 110 (2013), 16103.  doi: 10.1073/pnas.1314385110.  Google Scholar

[51]

H. Zahreddine and K. Borden, Mechanisms and insights into drug resistance in cancer,, Front. Pharmacol., 4 (2013).  doi: 10.3389/fphar.2013.00028.  Google Scholar

show all references

References:
[1]

B. Baguley, Multiple drug resistance mechanisms in cancer,, Mol. Biotechnol., 46 (2010), 308.  doi: 10.1007/s12033-010-9321-2.  Google Scholar

[2]

S. Benzekry and P. Hahnfeldt, Maximum tolerated dose versus metronomic scheduling in the treatment of metastatic cancers,, Journal of Theoretical Biology, 335 (2013), 235.  doi: 10.1016/j.jtbi.2013.06.036.  Google Scholar

[3]

I. Bozic, J. Reiter, B. Allen, T. Antal, K. Chatterjee, P. Shah, Y. S. Moon, A. Yaqubie, N. Kelly, D. Le, E. Lipson, P. Chapman, L. Diaz, B. Vogelstein and M. Nowak, Evolutionary dynamics of cancer in response to targeted combination therapy,, eLife, 2 (2013).  doi: 10.7554/eLife.00747.  Google Scholar

[4]

T. Brocato, P. Dogra, E. J. Koay, A. Day, Y.-L. Chuang, Z. Wang and V. Cristini, Understanding drug resistance in breast cancer with mathematical oncology,, Curr. Breast Cancer Rep., 6 (2014), 110.  doi: 10.1007/s12609-014-0143-2.  Google Scholar

[5]

L. Buffoni, D. Dongiovanni, C. Barone, C. Fissore, D. Ottaviani, V. Dongiovanni, R. Grillo, A. Salvadori, N. Birocco, M. Schena and O. Bertetto, Fractionated dose of cisplatin (CDDP) and vinorelbine (VNB) chemotherapy for elderly patients with advanced non-small cell lung cancer: Phase II trial,, Lung Cancer, 54 (2006), 353.  doi: 10.1016/j.lungcan.2006.08.013.  Google Scholar

[6]

J. Casciari, S. Sotirchos and R. Sutherland, Variations in tumor cell growth rates and metabolism with oxygen concentration, glucose concentration and extracellular pH,, J. Cellular Physiol., 151 (1992), 386.  doi: 10.1002/jcp.1041510220.  Google Scholar

[7]

A. Coldman and J. Goldie, A stochastic model for the origin and treatment of tumors containing drug-resistant cells,, Bull. Math. Biol., 48 (1986), 279.  doi: 10.1007/BF02459682.  Google Scholar

[8]

J. Cunningham, J. Brown, T. L. Vincent3 and R. A. Gatenby, Divergent and convergent evolution in metastases suggest treatment strategies based on specific metastatic sites,, Evolution, 2015 (2015), 76.  doi: 10.1093/emph/eov006.  Google Scholar

[9]

J. Cunningham, R. Gatenby and J. Brown, Evolutionary dynamics in cancer therapy,, Mol. Pharm., 8 (2011), 2094.  doi: 10.1021/mp2002279.  Google Scholar

[10]

R. De Souza, P. Zahedi, R. Badame, C. Allen and M. Piquette-Miller, Chemotherapy dosing schedule influences drug resistance development in ovarian cancer,, Mol. Cancer Ther., 10 (2011), 1289.  doi: 10.1158/1535-7163.MCT-11-0058.  Google Scholar

[11]

U. Emmenegger, G. Francia, A. Chow, Y. Shaked, A. Kouri, S. Man and R. Kerbel, Tumor that acquire resistance to low-dose metronomic cyclophosphamide retain sensitivity to maximum tolerated dose cyclophosphamide,, Neoplasia, 13 (2011), 40.  doi: 10.1593/neo.101174.  Google Scholar

[12]

J. Foo, K. Leder and S. Mumenthaler, Cancer as a moving target: Understanding the composition and rebound growth kinetics of recurrent tumors,, Evol. Appl., 6 (2013), 54.  doi: 10.1111/eva.12019.  Google Scholar

[13]

J. Foo and F. Michor, Evolution of resistance to targeted anti-cancer therapies during continuous and pulsed administration strategies,, PLoS Comput. Biol., 5 (2009).  doi: 10.1371/journal.pcbi.1000557.  Google Scholar

[14]

J. Foo and F. Michor, Evolution of resistance to anti-cancer therapy during general dosing schedules,, J. Theor. Biol., 263 (2010), 179.  doi: 10.1016/j.jtbi.2009.11.022.  Google Scholar

[15]

J. Foo and F. Michor, Evolution of acquired resistance to anti-cancer therapy,, J. Theor. Biol., 355 (2014), 10.  doi: 10.1016/j.jtbi.2014.02.025.  Google Scholar

[16]

J. Freyer and R. Sutherland, A reduction in the in situ rates of oxygen and glucose consumption of cells in EMT6/Ro spheroids during growth,, J. Cellular Physiol., 124 (1985), 516.  doi: 10.1002/jcp.1041240323.  Google Scholar

[17]

F. Fu, M. Nowak and S. Bonhoeffer, Spatial heterogeneity in drug concentrations can facilitate the emergence of resistance to cancer therapy,, PLoS Comput. Biol., 11 (2015).  doi: 10.1371/journal.pcbi.1004142.  Google Scholar

[18]

R. Gatenby, A. Silva, R. Gillies and B. Frieden, Adaptive therapy,, Cancer Res., 69 (2009), 4894.  doi: 10.1158/0008-5472.CAN-08-3658.  Google Scholar

[19]

J. Gevertz, Z. Aminzare, K.-A. Norton, J. Perez-Velazquez, A. Volkening and K. Rejniak, Emergence of anti-cancer drug resistance: Exploring the importance of the microenvironmental niche via a spatial model,, in Applications of Dynamical Systems in Biology and Medicine (eds. T. Jackson and A. Radunskaya), (2015), 1.  doi: 10.1007/978-1-4939-2782-1_1.  Google Scholar

[20]

J. Greene, O. Lavi, M. Gottesman and D. Levy, The impact of cell density and mutations in a model of multidrug resistance in solid tumors,, Bull. Math. Biol., 76 (2014), 627.  doi: 10.1007/s11538-014-9936-8.  Google Scholar

[21]

M. Hadjiandreou and G. Mitsis, Mathematical modeling of tumor growth, drug- resistance, toxicity, and optimal therapy design,, IEEE Trans. Biomed. Eng., 61 (2013), 415.   Google Scholar

[22]

D. Hanahan, G. Bergers and E. Bergsland, Less is more, regularly: Metronomic dosing of cytotoxic drugs can target tumor angiogenesis in mice,, The Journal of Clinical Investigations, 105 (2000), 1045.  doi: 10.1172/JCI9872.  Google Scholar

[23]

T. Jackson and H. Byrne, A mathematical model to study the effects of drug resistance and vasculature on the response of solid tumors to chemotherapy,, Math. Biosci., 164 (2000), 17.  doi: 10.1016/S0025-5564(99)00062-0.  Google Scholar

[24]

J. Kim and I. Tannock, Repopulation of cancer cells during therapy: An important cause of treatment failure,, Nat. Rev. Cancer, 5 (2005), 516.  doi: 10.1038/nrc1650.  Google Scholar

[25]

N. Komarova and D. Wodarz, Drug resistance in cancer: Principles of emergence and prevention,, Proc. Natl. Acad. Sci., 102 (2005), 9714.  doi: 10.1073/pnas.0501870102.  Google Scholar

[26]

N. Komarova and D. Wodarz, Stochastic modeling of cellular colonies with quiescence: An application to drug resistance in cancer,, Theor. Popul. Biol., 72 (2007), 523.  doi: 10.1016/j.tpb.2007.08.003.  Google Scholar

[27]

O. Lavi, M. Gottesman and D. Levy, The dynamics of drug resistance: A mathematical perspective,, Drug Resist. Update, 15 (2012), 90.  doi: 10.1016/j.drup.2012.01.003.  Google Scholar

[28]

O. Lavi, J. Greene, D. Levy and M. Gottesman, The role of cell density and intratumoral heterogeneity in multidrug resistance,, Cancer Res., 73 (2013), 7168.  doi: 10.1158/0008-5472.CAN-13-1768.  Google Scholar

[29]

U. Ledzewicz, B. Amni and H. Schattler, Dynamics and control of a mathematical model for metronomic chemotherapy,, Mathematical Biosciences and Engineering, 12 (2015), 1257.  doi: 10.3934/mbe.2015.12.1257.  Google Scholar

[30]

U. Ledzewicz and H. Schattler, Drug resistance in cancer chemotherapy as an optimal control problem,, Discret. Contin. Dyn-B, 6 (2006), 129.   Google Scholar

[31]

U. Ledzewicz, H. Schattler, M. Gahrooi and S. Dehkordi, On the MTD paradigm and optimal control for multi-drug cancer chemotherapy,, Math. Biosci. Eng., 10 (2013), 803.  doi: 10.3934/mbe.2013.10.803.  Google Scholar

[32]

A. Lorz, T. Lorenzi, J. Clairambault, A. Escargueil and B. Perthame, Modeling effects of space structure and combination therapies on phenotypic heterogeneity and drug resistance in solid tumors,, Bull. Math. Biol., 77 (2015), 1.  doi: 10.1007/s11538-014-0046-4.  Google Scholar

[33]

A. Lorz, T. Lorenzi, M. Hochberg, J. Clairambault and B. Perthame, Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies,, ESAIM: Math. Model. Num. Anal., 47 (2013), 377.  doi: 10.1051/m2an/2012031.  Google Scholar

[34]

V. Malik P.S.and Raina and N. Andre, Metronomics as maintenance treatment in oncology: Time for chemo-switch,, Front. Oncol., 4 (2014).   Google Scholar

[35]

F. Meineke, C. Potten and M. Loeffler, Cell migration and organization in the intestinal crypt using a lattice-free model,, Cell Prolif., 34 (2001), 253.  doi: 10.1046/j.0960-7722.2001.00216.x.  Google Scholar

[36]

S. Menchon, The effect of intrinsic and acquired resistances on chemotherapy effectiveness,, Acta Biother., 63 (2015), 113.  doi: 10.1007/s10441-015-9248-x.  Google Scholar

[37]

K. Mross and S. Steinbild, Metronomic anti-cancer therapy - an ongoing treatment option for advanced cancer patients,, Journal of Cancer Therapeutics & Research, 1 (2012), 1.  doi: 10.7243/2049-7962-1-32.  Google Scholar

[38]

S. Mumenthaler, J. Foo, K. Leder, N. Choi, D. Agus, W. Pao, P. Mallick and F. Michor, Evolutionary modeling of combination treatment strategies to overcome resistance to tyrosine kinase inhibitors in non-small cell lung cancer,, Mol. Pharm., 8 (2011), 2069.  doi: 10.1021/mp200270v.  Google Scholar

[39]

O. G. Scharovsky, L. Mainetti and V. Rozados, Metronomic chemotherapy: Changing the paradigm that more is better,, Current Oncology, 16 (2012), 7.   Google Scholar

[40]

P. Orlando, R. Gatenby and J. Brown, Cancer treatment as a game: Integrating evolutionary game theory into the optimal control of chemotherapy,, Phys. Biol., 9 (2012).   Google Scholar

[41]

K. Pietras and D. Hanahan, A multitargeted, metronomic, and maximum-tolerated dose "chemo-switch" regimen is antiangiogenic, producing objective responses and survival benefit in a mouse model of cancer,, J. Clinical Oncology, 23 (2005), 939.  doi: 10.1200/JCO.2005.07.093.  Google Scholar

[42]

A. Pisco and S. Huang, Non-genetic cancer cell plasticity and therapy-induced stemness in tumour relapse: 'What does not kill me strengthens me',, Br. J. Cancer, 112 (2015), 1725.  doi: 10.1038/bjc.2015.146.  Google Scholar

[43]

G. Powathil, M. Chaplain and M. Swat, Investigating the development of chemotherapeutic drug resistance in cancer: A multiscale computational study,, , ().   Google Scholar

[44]

S. Saxena and G. Christofori, Rebuilding cancer metastasis in the mouse,, Molecular Oncology, 7 (2013), 283.  doi: 10.1016/j.molonc.2013.02.009.  Google Scholar

[45]

A. Silva and R. Gatenby, A theoretical quantitative model for evolution of cancer chemotherapy resistance,, Biol. Direct., 5 (2010).  doi: 10.1186/1745-6150-5-25.  Google Scholar

[46]

O. Trédan, C. Galmarini, K. Patel and I. Tannock, Drug resistance and the solid tumor microenvironment,, J. Natl. Cancer Inst., 99 (2007), 1441.   Google Scholar

[47]

R. Turner and S. J. Charlton, Assessing the minimum number of data points required for accurate IC50 determination,, Assay Drug Dev Technol., 3 (2005), 525.   Google Scholar

[48]

M. Vives, M. Ginesta, K. Gracova, M. Graupera, O. Casanovas, G. Capella, T. Serrano, B. Laquente and F. Vinals, Motronomic chemotherapy following the maximum tolerated dose is an effective anti-tumour therapy affecting angiogenesis, tumour dissemination and cancer stem cells,, International Journal of Cancer, 133 (2013), 2464.   Google Scholar

[49]

B. Waclaw, I. Bozic, M. Pittman, R. Hruban, B. Vogelstein and M. Nowak, A spatial model predicts that dispersal and cell turnover limit intratumor heterogeneity,, Nature, 525 (2015), 261.   Google Scholar

[50]

A. Wu, K. Loutherback, G. Lambert, L. Estévez-Salmeron, T. Tlsty, R. Austin and J. Sturma, Cell motility and drug gradients in the emergence of resistance to chemotherapy,, Proc. Natl. Acad. Sci., 110 (2013), 16103.  doi: 10.1073/pnas.1314385110.  Google Scholar

[51]

H. Zahreddine and K. Borden, Mechanisms and insights into drug resistance in cancer,, Front. Pharmacol., 4 (2013).  doi: 10.3389/fphar.2013.00028.  Google Scholar

[1]

Adam Glick, Antonio Mastroberardino. Combined therapy for treating solid tumors with chemotherapy and angiogenic inhibitors. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020343

[2]

Giuseppina Guatteri, Federica Masiero. Stochastic maximum principle for problems with delay with dependence on the past through general measures. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020048

[3]

Hui Lv, Xing'an Wang. Dissipative control for uncertain singular markovian jump systems via hybrid impulsive control. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 127-142. doi: 10.3934/naco.2020020

[4]

Sihem Guerarra. Maximum and minimum ranks and inertias of the Hermitian parts of the least rank solution of the matrix equation AXB = C. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 75-86. doi: 10.3934/naco.2020016

[5]

Laurence Cherfils, Stefania Gatti, Alain Miranville, Rémy Guillevin. Analysis of a model for tumor growth and lactate exchanges in a glioma. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020457

[6]

Laurent Di Menza, Virginie Joanne-Fabre. An age group model for the study of a population of trees. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020464

[7]

Weiwei Liu, Jinliang Wang, Yuming Chen. Threshold dynamics of a delayed nonlocal reaction-diffusion cholera model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020316

[8]

Siyang Cai, Yongmei Cai, Xuerong Mao. A stochastic differential equation SIS epidemic model with regime switching. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020317

[9]

Yining Cao, Chuck Jia, Roger Temam, Joseph Tribbia. Mathematical analysis of a cloud resolving model including the ice microphysics. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 131-167. doi: 10.3934/dcds.2020219

[10]

Zhouchao Wei, Wei Zhang, Irene Moroz, Nikolay V. Kuznetsov. Codimension one and two bifurcations in Cattaneo-Christov heat flux model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020344

[11]

Shuang Chen, Jinqiao Duan, Ji Li. Effective reduction of a three-dimensional circadian oscillator model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020349

[12]

Barbora Benešová, Miroslav Frost, Lukáš Kadeřávek, Tomáš Roubíček, Petr Sedlák. An experimentally-fitted thermodynamical constitutive model for polycrystalline shape memory alloys. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020459

[13]

Cuicui Li, Lin Zhou, Zhidong Teng, Buyu Wen. The threshold dynamics of a discrete-time echinococcosis transmission model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020339

[14]

Yolanda Guerrero–Sánchez, Muhammad Umar, Zulqurnain Sabir, Juan L. G. Guirao, Muhammad Asif Zahoor Raja. Solving a class of biological HIV infection model of latently infected cells using heuristic approach. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020431

[15]

Chao Xing, Jiaojiao Pan, Hong Luo. Stability and dynamic transition of a toxin-producing phytoplankton-zooplankton model with additional food. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020275

[16]

H. M. Srivastava, H. I. Abdel-Gawad, Khaled Mohammed Saad. Oscillatory states and patterns formation in a two-cell cubic autocatalytic reaction-diffusion model subjected to the Dirichlet conditions. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020433

[17]

A. M. Elaiw, N. H. AlShamrani, A. Abdel-Aty, H. Dutta. Stability analysis of a general HIV dynamics model with multi-stages of infected cells and two routes of infection. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020441

[18]

Hai-Feng Huo, Shi-Ke Hu, Hong Xiang. Traveling wave solution for a diffusion SEIR epidemic model with self-protection and treatment. Electronic Research Archive, , () : -. doi: 10.3934/era.2020118

[19]

Youming Guo, Tingting Li. Optimal control strategies for an online game addiction model with low and high risk exposure. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020347

[20]

Omid Nikan, Seyedeh Mahboubeh Molavi-Arabshai, Hossein Jafari. Numerical simulation of the nonlinear fractional regularized long-wave model arising in ion acoustic plasma waves. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020466

2018 Impact Factor: 1.313

Metrics

  • PDF downloads (101)
  • HTML views (0)
  • Cited by (13)

[Back to Top]