Mathematical Biosciences and Engineering, 2011, 8(2): 289-306. doi: 10.3934/mbe.2011.8.289.

Primary: 92C50; Secondary: 92D25, 60G35.

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Mathematical modeling of cyclic treatments of chronic myeloid leukemia

1. Department of Mathematics, University of California Irvine, Irvine CA 92697

Cyclic treatment strategies in Chronic Myeloid Leukemia (CML) are characterized by alternating applications of two (or more) different drugs, given one at a time. One of the main causes for treatment failure in CML is the generation of drug resistance by mutations of cancerous cells. We use mathematical methods to develop general guidelines on optimal cyclic treatment scheduling, with the aim of minimizing the resistance generation. We define a condition on the drugs' potencies which allows for a relatively successful application of cyclic therapies. We find that the best strategy is to start with the stronger drug, but use longer cycle durations for the weaker drug. We further investigate the situation where a degree of cross-resistance is present, such that certain mutations cause cells to become resistant to both drugs simultaneously.
  Figure/Table
  Supplementary
  Article Metrics

Keywords the worst drug rule; CML; mathematical modeling of cancer; drugs resistance; cross-resistance.

Citation: Natalia L. Komarova. Mathematical modeling of cyclic treatments of chronic myeloid leukemia. Mathematical Biosciences and Engineering, 2011, 8(2): 289-306. doi: 10.3934/mbe.2011.8.289

 

This article has been cited by

  • 1. Benjamin Werner, David Lutz, Tim H. Brümmendorf, Arne Traulsen, Stefan Balabanov, Mikhail V. Blagosklonny, Dynamics of Resistance Development to Imatinib under Increasing Selection Pressure: A Combination of Mathematical Models and In Vitro Data, PLoS ONE, 2011, 6, 12, e28955, 10.1371/journal.pone.0028955
  • 2. Tor Flå, Florian Rupp, Clemens Woywod, Bifurcation patterns in generalized models for the dynamics of normal and leukemic stem cells with signaling, Mathematical Methods in the Applied Sciences, 2015, 38, 16, 3392, 10.1002/mma.3345
  • 3. Helen Moore, How to mathematically optimize drug regimens using optimal control, Journal of Pharmacokinetics and Pharmacodynamics, 2018, 45, 1, 127, 10.1007/s10928-018-9568-y
  • 4. Antonio Fasano, Adélia Sequeira, , Hemomath, 2017, Chapter 8, 295, 10.1007/978-3-319-60513-5_8
  • 5. Helen Moore, Lewis Strauss, Urszula Ledzewicz, Optimization of combination therapy for chronic myeloid leukemia with dosing constraints, Journal of Mathematical Biology, 2018, 10.1007/s00285-018-1262-6
  • 6. Tor Flå, Florian Rupp, Clemens Woywod, , Recent Trends in Dynamical Systems, 2013, Chapter 11, 221, 10.1007/978-3-0348-0451-6_11

Reader Comments

your name: *   your email: *  

Copyright Info: 2011, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved