Search Advanced

Mathematical Biosciences and Engineering

2016, Volume 13, Issue 6: 1185-1206. doi: 10.3934/mbe.2016038
Previous Article Next Article

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
  • 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
  • 3.
    Department of Mathematics and Statistics, The College of New Jersey, Ewing, NJ
  • Received: 01 October 2015 Accepted: 29 June 2018 Published: 01 August 2016

  • MSC : Primary: 92C50; Secondary: 37N25.

  • 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[J]. Mathematical Biosciences and Engineering, 2016, 13(6): 1185-1206. doi: 10.3934/mbe.2016038

    Related Papers:

    [1] Urszula Ledzewicz, Heinz Schättler, Mostafa Reisi Gahrooi, Siamak Mahmoudian Dehkordi . On the MTD paradigm and optimal control for multi-drug cancer chemotherapy. Mathematical Biosciences and Engineering, 2013, 10(3): 803-819. doi: 10.3934/mbe.2013.10.803
    [2] Hongli Yang, Jinzhi Lei . A mathematical model of chromosome recombination-induced drug resistance in cancer therapy. Mathematical Biosciences and Engineering, 2019, 16(6): 7098-7111. doi: 10.3934/mbe.2019356
    [3] Urszula Ledzewicz, Behrooz Amini, Heinz Schättler . Dynamics and control of a mathematical model for metronomic chemotherapy. Mathematical Biosciences and Engineering, 2015, 12(6): 1257-1275. doi: 10.3934/mbe.2015.12.1257
    [4] Rujing Zhao, Xiulan Lai . Evolutionary analysis of replicator dynamics about anti-cancer combination therapy. Mathematical Biosciences and Engineering, 2023, 20(1): 656-682. doi: 10.3934/mbe.2023030
    [5] Joseph Malinzi, Rachid Ouifki, Amina Eladdadi, Delfim F. M. Torres, K. A. Jane White . Enhancement of chemotherapy using oncolytic virotherapy: Mathematical and optimal control analysis. Mathematical Biosciences and Engineering, 2018, 15(6): 1435-1463. doi: 10.3934/mbe.2018066
    [6] Haifeng Zhang, Jinzhi Lei . Optimal treatment strategy of cancers with intratumor heterogeneity. Mathematical Biosciences and Engineering, 2022, 19(12): 13337-13373. doi: 10.3934/mbe.2022625
    [7] Alexis B. Cook, Daniel R. Ziazadeh, Jianfeng Lu, Trachette L. Jackson . An integrated cellular and sub-cellular model of cancer chemotherapy and therapies that target cell survival. Mathematical Biosciences and Engineering, 2015, 12(6): 1219-1235. doi: 10.3934/mbe.2015.12.1219
    [8] 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 and Engineering, 2017, 14(1): 217-235. doi: 10.3934/mbe.2017014
    [9] Shuo Wang, Heinz Schättler . Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity. Mathematical Biosciences and Engineering, 2016, 13(6): 1223-1240. doi: 10.3934/mbe.2016040
    [10] Alexander S. Bratus, Svetlana Yu. Kovalenko, Elena Fimmel . On viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells. Mathematical Biosciences and Engineering, 2015, 12(1): 163-183. doi: 10.3934/mbe.2015.12.163
  • 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.


    [1] Mol. Biotechnol., 46 (2010), 308-316.
    [2] Journal of Theoretical Biology, 335 (2013), 235-244.
    [3] eLife, 2 (2013), e00747.
    [4] Curr. Breast Cancer Rep., 6 (2014), 110-120.
    [5] Lung Cancer, 54 (2006), 353-357.
    [6] J. Cellular Physiol., 151 (1992), 386-394.
    [7] Bull. Math. Biol., 48 (1986), 279-292.
    [8] Evolution, Medicine, and Public Health, 2015 (2015), 76-87.
    [9] Mol. Pharm., 8 (2011), 2094-2100.
    [10] Mol. Cancer Ther., 10 (2011), 1289-1299.
    [11] Neoplasia, 13 (2011), 40-48.
    [12] Evol. Appl., 6 (2013), 54-69.
    [13] PLoS Comput. Biol., 5 (2009), e1000557, 17pp.
    [14] J. Theor. Biol., 263 (2010), 179-188.
    [15] J. Theor. Biol., 355 (2014), 10-20.
    [16] J. Cellular Physiol., 124 (1985), 516-524.
    [17] PLoS Comput. Biol., 11 (2015), e1004142.
    [18] Cancer Res., 69 (2009), 4894-4903.
    [19] in Applications of Dynamical Systems in Biology and Medicine (eds. T. Jackson and A. Radunskaya), vol. 158 of The IMA Volumes in Mathematics and its Applications, Springer-Verlag, 2015, 1-34.
    [20] Bull. Math. Biol., 76 (2014), 627-653.
    [21] IEEE Trans. Biomed. Eng., 61 (2013), 415-425.
    [22] The Journal of Clinical Investigations, 105 (2000), 1045-1047.
    [23] Math. Biosci., 164 (2000), 17-38.
    [24] Nat. Rev. Cancer, 5 (2005), 516-525.
    [25] Proc. Natl. Acad. Sci., 102 (2005), 9714-9719.
    [26] Theor. Popul. Biol., 72 (2007), 523-538.
    [27] Drug Resist. Update, 15 (2012), 90-97.
    [28] Cancer Res., 73 (2013), 7168-7175.
    [29] Mathematical Biosciences and Engineering, 12 (2015), 1257-1275.
    [30] Discret. Contin. Dyn-B, 6 (2006), 129-150.
    [31] Math. Biosci. Eng., 10 (2013), 803-819.
    [32] Bull. Math. Biol., 77 (2015), 1-22.
    [33] ESAIM: Math. Model. Num. Anal., 47 (2013), 377-399.
    [34] Front. Oncol., 4 (2014), article 76.
    [35] Cell Prolif., 34 (2001), 253-266.
    [36] Acta Biother., 63 (2015), 113-127.
    [37] Journal of Cancer Therapeutics & Research, 1 (2012), 1-32.
    [38] Mol. Pharm., 8 (2011), 2069-2079.
    [39] Current Oncology, 16 (2012), 7-15.
    [40] Phys. Biol., 9 (2012), 065007.
    [41] J. Clinical Oncology, 23 (2005), 939-952.
    [42] Br. J. Cancer, 112 (2015), 1725-1732.
    [43] arXiv:1407.0865.
    [44] Molecular Oncology, 7 (2013), 283-296.
    [45] Biol. Direct., 5 (2010), p25.
    [46] J. Natl. Cancer Inst., 99 (2007), 1441-1454.
    [47] Assay Drug Dev Technol., 3 (2005), 525-531.
    [48] International Journal of Cancer, 133 (2013), 2464-2472.
    [49] Nature, 525 (2015), 261-264.
    [50] Proc. Natl. Acad. Sci., 110 (2013), 16103-16108.
    [51] Front. Pharmacol., 4 (2013), e28.<br/

  • This article has been cited by:

    1. Jill A. Gallaher, Pedro M. Enriquez-Navas, Kimberly A. Luddy, Robert A. Gatenby, Alexander R.A. Anderson, Spatial Heterogeneity and Evolutionary Dynamics Modulate Time to Recurrence in Continuous and Adaptive Cancer Therapies, 2018, 78, 0008-5472, 2127, 10.1158/0008-5472.CAN-17-2649
    2. Baohua Fan, Cunfang Shen, Milu Wu, Junhui Zhao, Qijing Guo, Yushuang Luo, miR-17–92 cluster is connected with disease progression and oxaliplatin/capecitabine chemotherapy efficacy in advanced gastric cancer patients, 2018, 97, 0025-7974, e12007, 10.1097/MD.0000000000012007
    3. Angela M Jarrett, David A Hormuth, Stephanie L Barnes, Xinzeng Feng, Wei Huang, Thomas E Yankeelov, Incorporating drug delivery into an imaging-driven, mechanics-coupled reaction diffusion model for predicting the response of breast cancer to neoadjuvant chemotherapy: theory and preliminary clinical results, 2018, 63, 1361-6560, 105015, 10.1088/1361-6560/aac040
    4. Morgan Craig, Adrianne L. Jenner, Bumseok Namgung, Luke P. Lee, Aaron Goldman, Engineering in Medicine To Address the Challenge of Cancer Drug Resistance: From Micro- and Nanotechnologies to Computational and Mathematical Modeling, 2021, 121, 0009-2665, 3352, 10.1021/acs.chemrev.0c00356
    5. Angela M. Jarrett, David A. Hormuth, Vikram Adhikarla, Prativa Sahoo, Daniel Abler, Lusine Tumyan, Daniel Schmolze, Joanne Mortimer, Russell C. Rockne, Thomas E. Yankeelov, Towards integration of 64Cu-DOTA-trastuzumab PET-CT and MRI with mathematical modeling to predict response to neoadjuvant therapy in HER2 + breast cancer, 2020, 10, 2045-2322, 10.1038/s41598-020-77397-0
    6. Elie Hembe Mukaya, Xavier Yangkou Mbianda, Macromolecular Prodrugs Containing Organoiron-Based Compounds in Cancer Research: A Review, 2020, 20, 13895575, 726, 10.2174/1389557519666191107142926
    7. Li You, Maximilian Knobloch, Teresa Lopez, Vanessa Peschen, Sidney Radcliffe, Praveen Koshy Sam, Frank Thuijsman, Kateřina Staňková, Joel Brown, Including Blood Vasculature into a Game-Theoretic Model of Cancer Dynamics, 2019, 10, 2073-4336, 13, 10.3390/g10010013
    8. Judith Pérez-Velázquez, Katarzyna A. Rejniak, Drug-Induced Resistance in Micrometastases: Analysis of Spatio-Temporal Cell Lineages, 2020, 11, 1664-042X, 10.3389/fphys.2020.00319
    9. Namid R. Stillman, Marina Kovacevic, Igor Balaz, Sabine Hauert, In silico modelling of cancer nanomedicine, across scales and transport barriers, 2020, 6, 2057-3960, 10.1038/s41524-020-00366-8
    10. Hang Xie, Yang Jiao, Qihui Fan, Miaomiao Hai, Jiaen Yang, Zhijian Hu, Yue Yang, Jianwei Shuai, Guo Chen, Ruchuan Liu, Liyu Liu, Nils Cordes, Modeling three-dimensional invasive solid tumor growth in heterogeneous microenvironment under chemotherapy, 2018, 13, 1932-6203, e0206292, 10.1371/journal.pone.0206292
    11. James M. Greene, Jana L. Gevertz, Eduardo D. Sontag, Mathematical Approach to Differentiate Spontaneous and Induced Evolution to Drug Resistance During Cancer Treatment, 2019, 2473-4276, 1, 10.1200/CCI.18.00087
    12. Urszula Ledzewicz, Heinz Schättler, Application of mathematical models to metronomic chemotherapy: What can be inferred from minimal parameterized models?, 2017, 401, 03043835, 74, 10.1016/j.canlet.2017.03.021
    13. Catherine Berrouet, Naika Dorilas, Katarzyna A. Rejniak, Necibe Tuncer, Comparison of Drug Inhibitory Effects (
    IC50
    ) in Monolayer and Spheroid Cultures, 2020, 82, 0092-8240, 10.1007/s11538-020-00746-7
    14. Anh Phong Tran, M. Ali Al-Radhawi, Irina Kareva, Junjie Wu, David J. Waxman, Eduardo D. Sontag, Delicate Balances in Cancer Chemotherapy: Modeling Immune Recruitment and Emergence of Systemic Drug Resistance, 2020, 11, 1664-3224, 10.3389/fimmu.2020.01376
    15. Aleksandra Karolak, Saharsh Agrawal, Samantha Lee, Katarzyna A. Rejniak, 2019, 9780128051443, 130, 10.1016/B978-0-12-801238-3.64117-X
    16. Angela M. Jarrett, Anum S. Kazerouni, Chengyue Wu, John Virostko, Anna G. Sorace, Julie C. DiCarlo, David A. Hormuth, David A. Ekrut, Debra Patt, Boone Goodgame, Sarah Avery, Thomas E. Yankeelov, Quantitative magnetic resonance imaging and tumor forecasting of breast cancer patients in the community setting, 2021, 16, 1754-2189, 5309, 10.1038/s41596-021-00617-y
    17. Cassidy K. Buhler, Rebecca S. Terry, Kathryn G. Link, Frederick R. Adler, Do mechanisms matter? Comparing cancer treatment strategies across mathematical models and outcome objectives, 2021, 18, 1551-0018, 6305, 10.3934/mbe.2021315
  • Reader Comments
  • © 2016 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
3.9

Metrics

Article views(2502) PDF downloads(472) Cited by(17)

Preview PDF
Download XML
Export Citation
Article outline
Abstract
References

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog