
Previous Article
Spatially heterogeneous invasion of toxic plant mediated by herbivory
 MBE Home
 This Issue

Next Article
For Carlos CastilloChavez
Data and implication based comparison of two chronic myeloid leukemia models
1.  School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, United States, United States 
2.  Department of Mathematics, North Carolina State University, Raleigh, NC 27695, United States 
3.  School of Mathematics and Statistical Sciences, Arizona State University, Tempe, AZ 85281 
References:
[1] 
L. H. Abbott and F. Michor, Mathematical models of targeted cancer therapy, British Journal of Cancer, 95 (2006), 11361141. 
[2] 
S. Brandford, Z. Rudzki, A. Grigg, J. F. Seymour, K. Taylor, R. Herrmann, C. Arthur, J. Szer and K. Lynch, The incidence of BCRABL kinase mutations in chronic myeloid leukemia patients is as high in the second year of imatinib therapy as the first but survival after mutation detection is significantly longer for patients with mutations detected in the second year of therapy, BLOOD, 102 (2003), 414A. 
[3] 
M. D. Charles and L. Sawyers, Chronic myeloid leukemia, The New England Journal of Medicine, 340 (1999), 13301340. 
[4] 
J. Foo, M. W. Drummond, B. Clarkson, T. Holyoake and F. Michor, Eradication of chronic myeloid leukemia stem cells: A novel mathematical model predicts no therapeutic benefit of adding GCSF to imatinib, PLoS Computational Biology, 5 (2009), 111. 
[5] 
D. Frame, Chronic myeloid leukemia: Standard treatment options, American Journal of HealthSystem Pharmacy, 63 (2006), S10S14. 
[6] 
M. E. Gorre, M. Mohammed, K. Ellwood, N. Hsu, R. Paquette, P. Nagesh Rao and C. L. Sawyers, Clinical resistance to STI571 cancer therapy caused by BCRABL gene mutation or amplification, Science, 293 (2001), 876880. 
[7] 
I. J. Griswold, M. MacPartline, T. Bumm, V. L. Goss, T. O'Hare, K. A. Lee, A. S. Corbin, E. P. Stoffregen, C. Smith, K. Johnson, E. M. Moseson, L. J. Wood, R. D. Polakiewicz, B. J. Druker and M. W. Deininger, Kinase domain mutants of bcrabl exhibit altered transformation potency, kinase activity, and substrate utilization, irrespective of sensitivity to imatinib, Molecular and Cellular Biology, 26 (2006), 60826093. 
[8] 
J. Jelinek, V. Gharibyan, M. Estecio, K. Kondo, R. He, W. Chung, Y. Lu, N. Zhang, S. Liang, H. Kantarjian, J. Cortes and JP. Issa, Aberrant DNA methylation is associated with disease progression, resistance to imatinib and shortened survival in chronic myelogenous leukemia, PLoS ONE, 6 (2011), e22110. 
[9] 
I. Kareva, F. Berezovskaya and C. CastilloChavez, Myeloid cells in tumourimmune interactions, Journal of Biological Dynamics, 4 (2010), 315327. doi: 10.1080/17513750903261281. 
[10] 
N. L. Komarova and D. Wodarz, Effect of cellular quiescence on the success of targeted CML therapy, PLoS ONE, 2 (2007), e990. 
[11] 
F. Michor, Reply: The longterm response to imatinib treatment of CML, Biritish Journal of Cancer, 96 (2007), 697680. 
[12] 
F. Michor, Quantitative approaches to analyzing imatinibtreated chronic myeloid leukemia, TRENDS in Pharmacological Sciences, 28 (2007), 197199. 
[13] 
F. Michor, T. P. Hughes, Y. Iwasa, S. Branford, N. P. Shah, C. L. Sawyers and M. A. Nowak, Dynamics of chronic myeloid leukemia, Nature, 435 (2005), 12671270. 
[14] 
M. C. Muller, N. Gattermann, T. Lahaye, M. W. N. Deininger, A. Berndt, S. Fruehauf, A. Neubauer, T. Fischer, D. K. Hossfeld, F. Schneller, S. W. Krause, C. Nerl, H. G. Sayer, O. G. Ottmann, C. Waller, W. Aulitzky, P. le Coutre, M. Freund, K. Merx, P. Paschka, H. Konig, S. Kreil, U. Berger, H. Gschaidmeier, R. Hehlmann and A. Hochhaus, Dynamics of BCRABL mRNA expression in firstline therapy of chronic myelogenous leukemia patients with imatinib or interferon a/araC, Leukemia, 17 (2003), 23922400. 
[15] 
C. Nishioka, T. Ikezoe, K. Udaka and A. Yokoyama, Imatinib causes epigenetic alterations of PTEN gene via upregulation of DNA methyltransferases and polycomb group proteins, Blood Cancer Journal, 1 (2011), e48. 
[16] 
T. Portz, Y. Kuang and J. D. Nagy, A clinical data validated mathematical model of prostate cancer growth under intermittent androgen suppression therapy, AIP Advances, 2 (2012), 011002. 
[17] 
I. Roeder, M. Horn, I. Glauche, A. Hochhaus, M. C Mueller and M. Loeffler, Dynamic modeling of imatinibtreated chronic myeloid leukemia: Functional insights and clinical implications, Nature Medicine, 12 (2006), 11811184. 
[18] 
A. M. Stein, D. Bottino, V. Modur, S. Branford, J. Kaeda, J. M. Goldman, T. P. Hughes, J. P. Radich and A. Hochhaus, BCRABL transcript dynamics support the hypothesis that leukemic stem cells are reduced during imatinib treatment, Clinical Cancer Research, 17 (2011), 68126821. 
show all references
References:
[1] 
L. H. Abbott and F. Michor, Mathematical models of targeted cancer therapy, British Journal of Cancer, 95 (2006), 11361141. 
[2] 
S. Brandford, Z. Rudzki, A. Grigg, J. F. Seymour, K. Taylor, R. Herrmann, C. Arthur, J. Szer and K. Lynch, The incidence of BCRABL kinase mutations in chronic myeloid leukemia patients is as high in the second year of imatinib therapy as the first but survival after mutation detection is significantly longer for patients with mutations detected in the second year of therapy, BLOOD, 102 (2003), 414A. 
[3] 
M. D. Charles and L. Sawyers, Chronic myeloid leukemia, The New England Journal of Medicine, 340 (1999), 13301340. 
[4] 
J. Foo, M. W. Drummond, B. Clarkson, T. Holyoake and F. Michor, Eradication of chronic myeloid leukemia stem cells: A novel mathematical model predicts no therapeutic benefit of adding GCSF to imatinib, PLoS Computational Biology, 5 (2009), 111. 
[5] 
D. Frame, Chronic myeloid leukemia: Standard treatment options, American Journal of HealthSystem Pharmacy, 63 (2006), S10S14. 
[6] 
M. E. Gorre, M. Mohammed, K. Ellwood, N. Hsu, R. Paquette, P. Nagesh Rao and C. L. Sawyers, Clinical resistance to STI571 cancer therapy caused by BCRABL gene mutation or amplification, Science, 293 (2001), 876880. 
[7] 
I. J. Griswold, M. MacPartline, T. Bumm, V. L. Goss, T. O'Hare, K. A. Lee, A. S. Corbin, E. P. Stoffregen, C. Smith, K. Johnson, E. M. Moseson, L. J. Wood, R. D. Polakiewicz, B. J. Druker and M. W. Deininger, Kinase domain mutants of bcrabl exhibit altered transformation potency, kinase activity, and substrate utilization, irrespective of sensitivity to imatinib, Molecular and Cellular Biology, 26 (2006), 60826093. 
[8] 
J. Jelinek, V. Gharibyan, M. Estecio, K. Kondo, R. He, W. Chung, Y. Lu, N. Zhang, S. Liang, H. Kantarjian, J. Cortes and JP. Issa, Aberrant DNA methylation is associated with disease progression, resistance to imatinib and shortened survival in chronic myelogenous leukemia, PLoS ONE, 6 (2011), e22110. 
[9] 
I. Kareva, F. Berezovskaya and C. CastilloChavez, Myeloid cells in tumourimmune interactions, Journal of Biological Dynamics, 4 (2010), 315327. doi: 10.1080/17513750903261281. 
[10] 
N. L. Komarova and D. Wodarz, Effect of cellular quiescence on the success of targeted CML therapy, PLoS ONE, 2 (2007), e990. 
[11] 
F. Michor, Reply: The longterm response to imatinib treatment of CML, Biritish Journal of Cancer, 96 (2007), 697680. 
[12] 
F. Michor, Quantitative approaches to analyzing imatinibtreated chronic myeloid leukemia, TRENDS in Pharmacological Sciences, 28 (2007), 197199. 
[13] 
F. Michor, T. P. Hughes, Y. Iwasa, S. Branford, N. P. Shah, C. L. Sawyers and M. A. Nowak, Dynamics of chronic myeloid leukemia, Nature, 435 (2005), 12671270. 
[14] 
M. C. Muller, N. Gattermann, T. Lahaye, M. W. N. Deininger, A. Berndt, S. Fruehauf, A. Neubauer, T. Fischer, D. K. Hossfeld, F. Schneller, S. W. Krause, C. Nerl, H. G. Sayer, O. G. Ottmann, C. Waller, W. Aulitzky, P. le Coutre, M. Freund, K. Merx, P. Paschka, H. Konig, S. Kreil, U. Berger, H. Gschaidmeier, R. Hehlmann and A. Hochhaus, Dynamics of BCRABL mRNA expression in firstline therapy of chronic myelogenous leukemia patients with imatinib or interferon a/araC, Leukemia, 17 (2003), 23922400. 
[15] 
C. Nishioka, T. Ikezoe, K. Udaka and A. Yokoyama, Imatinib causes epigenetic alterations of PTEN gene via upregulation of DNA methyltransferases and polycomb group proteins, Blood Cancer Journal, 1 (2011), e48. 
[16] 
T. Portz, Y. Kuang and J. D. Nagy, A clinical data validated mathematical model of prostate cancer growth under intermittent androgen suppression therapy, AIP Advances, 2 (2012), 011002. 
[17] 
I. Roeder, M. Horn, I. Glauche, A. Hochhaus, M. C Mueller and M. Loeffler, Dynamic modeling of imatinibtreated chronic myeloid leukemia: Functional insights and clinical implications, Nature Medicine, 12 (2006), 11811184. 
[18] 
A. M. Stein, D. Bottino, V. Modur, S. Branford, J. Kaeda, J. M. Goldman, T. P. Hughes, J. P. Radich and A. Hochhaus, BCRABL transcript dynamics support the hypothesis that leukemic stem cells are reduced during imatinib treatment, Clinical Cancer Research, 17 (2011), 68126821. 
[1] 
Natalia L. Komarova. Mathematical modeling of cyclic treatments of chronic myeloid leukemia. Mathematical Biosciences & Engineering, 2011, 8 (2) : 289306. doi: 10.3934/mbe.2011.8.289 
[2] 
Cristian Tomasetti, Doron Levy. An elementary approach to modeling drug resistance in cancer. Mathematical Biosciences & Engineering, 2010, 7 (4) : 905918. doi: 10.3934/mbe.2010.7.905 
[3] 
Pep Charusanti, Xiao Hu, Luonan Chen, Daniel Neuhauser, Joseph J. DiStefano III. A mathematical model of BCRABL autophosphorylation, signaling through the CRKL pathway, and Gleevec dynamics in chronic myeloid leukemia. Discrete and Continuous Dynamical Systems  B, 2004, 4 (1) : 99114. doi: 10.3934/dcdsb.2004.4.99 
[4] 
Urszula Ledzewicz, Heinz Schättler. Drug resistance in cancer chemotherapy as an optimal control problem. Discrete and Continuous Dynamical Systems  B, 2006, 6 (1) : 129150. doi: 10.3934/dcdsb.2006.6.129 
[5] 
Ami B. Shah, Katarzyna A. Rejniak, Jana L. Gevertz. Limiting the development of anticancer drug resistance in a spatial model of micrometastases. Mathematical Biosciences & Engineering, 2016, 13 (6) : 11851206. doi: 10.3934/mbe.2016038 
[6] 
Nicolas Bacaër, Cheikh Sokhna. A reactiondiffusion system modeling the spread of resistance to an antimalarial drug. Mathematical Biosciences & Engineering, 2005, 2 (2) : 227238. doi: 10.3934/mbe.2005.2.227 
[7] 
Urszula Ledzewicz, Shuo Wang, Heinz Schättler, Nicolas André, Marie Amélie Heng, Eddy Pasquier. On drug resistance and metronomic chemotherapy: A mathematical modeling and optimal control approach. Mathematical Biosciences & Engineering, 2017, 14 (1) : 217235. doi: 10.3934/mbe.2017014 
[8] 
Qi Deng, Zhipeng Qiu, Ting Guo, Libin Rong. Modeling withinhost viral dynamics: The role of CTL immune responses in the evolution of drug resistance. Discrete and Continuous Dynamical Systems  B, 2021, 26 (7) : 35433562. doi: 10.3934/dcdsb.2020245 
[9] 
Seema Nanda, Lisette dePillis, Ami Radunskaya. B cell chronic lymphocytic leukemia  A model with immune response. Discrete and Continuous Dynamical Systems  B, 2013, 18 (4) : 10531076. doi: 10.3934/dcdsb.2013.18.1053 
[10] 
Evans K. Afenya. Using Mathematical Modeling as a Resource in Clinical Trials. Mathematical Biosciences & Engineering, 2005, 2 (3) : 421436. doi: 10.3934/mbe.2005.2.421 
[11] 
Avner Friedman, Najat Ziyadi, Khalid Boushaba. A model of drug resistance with infection by health care workers. Mathematical Biosciences & Engineering, 2010, 7 (4) : 779792. doi: 10.3934/mbe.2010.7.779 
[12] 
Zhenzhen Chen, SzeBi Hsu, YaTang Yang. The continuous morbidostat: A chemostat with controlled drug application to select for drug resistance mutants. Communications on Pure and Applied Analysis, 2020, 19 (1) : 203220. doi: 10.3934/cpaa.2020011 
[13] 
Lambertus A. Peletier. Modeling drugprotein dynamics. Discrete and Continuous Dynamical Systems  S, 2012, 5 (1) : 191207. doi: 10.3934/dcdss.2012.5.191 
[14] 
SilviuIulian Niculescu, Peter S. Kim, Keqin Gu, Peter P. Lee, Doron Levy. Stability crossing boundaries of delay systems modeling immune dynamics in leukemia. Discrete and Continuous Dynamical Systems  B, 2010, 13 (1) : 129156. doi: 10.3934/dcdsb.2010.13.129 
[15] 
Urszula Ledzewicz, Heinz Schättler, Mostafa Reisi Gahrooi, Siamak Mahmoudian Dehkordi. On the MTD paradigm and optimal control for multidrug cancer chemotherapy. Mathematical Biosciences & Engineering, 2013, 10 (3) : 803819. doi: 10.3934/mbe.2013.10.803 
[16] 
Andrzej Swierniak, Jaroslaw Smieja. Analysis and Optimization of Drug Resistant an PhaseSpecific Cancer. Mathematical Biosciences & Engineering, 2005, 2 (3) : 657670. doi: 10.3934/mbe.2005.2.657 
[17] 
Amina Eladdadi, Noura Yousfi, Abdessamad Tridane. Preface: Special issue on cancer modeling, analysis and control. Discrete and Continuous Dynamical Systems  B, 2013, 18 (4) : iiii. doi: 10.3934/dcdsb.2013.18.4i 
[18] 
Alacia M. Voth, John G. Alford, Edward W. Swim. Mathematical modeling of continuous and intermittent androgen suppression for the treatment of advanced prostate cancer. Mathematical Biosciences & Engineering, 2017, 14 (3) : 777804. doi: 10.3934/mbe.2017043 
[19] 
Harsh Vardhan Jain, Avner Friedman. Modeling prostate cancer response to continuous versus intermittent androgen ablation therapy. Discrete and Continuous Dynamical Systems  B, 2013, 18 (4) : 945967. doi: 10.3934/dcdsb.2013.18.945 
[20] 
Tianfa Xie, ZhongZhan Zhang. Identifiability of models for clinical trials with noncompliance. Discrete and Continuous Dynamical Systems  B, 2004, 4 (3) : 805811. doi: 10.3934/dcdsb.2004.4.805 
2018 Impact Factor: 1.313
Tools
Metrics
Other articles
by authors
[Back to Top]