New computational tools for modeling chronic myelogenous leukemia

M. M. Peet, P. S. Kim, S. I. Niculescu, D. Levy

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

In this paper, we consider a system of nonlinear delay-differential equations (DDEs) which models the dynamics of the interaction between chronic myelogenous leukemia (CML), imatinib, and the anti-leukemia immune response. Because of the chaotic nature of the dynamics and the sparse nature of experimental data, we look for ways to use computation to analyze the model without employing direct numerical simulation. In particular, we develop several tools using Lyapunov-Krasovskii analysis that allow us to test the robustness of the model with respect to uncertainty in patient parameters. The methods developed in this paper are applied to understanding which model parameters primarily affect the dynamics of the anti-leukemia immune response during imatinib treatment. The goal of this research is to aid the development of more efficient modeling approaches and more effective treatment strategies in cancer therapy.

Original languageEnglish (US)
Pages (from-to)119-139
Number of pages21
JournalMathematical Modelling of Natural Phenomena
Volume4
Issue number2
DOIs
StatePublished - Jan 1 2009
Externally publishedYes

Keywords

  • Lyapunov-Krasovskii
  • chronic myelogenous leukemia
  • delay-differential equations
  • imatinib
  • model verification
  • optimization
  • polynomials
  • stability
  • sum-ofsquares

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics

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