New Computational Tools for Modeling Chronic Myelogenous Leukemia

M. M. Peet; P. S. Kim; S.-I. Niculescu; D. Levy

Mathematical Modelling of Natural Phenomena (2009)

  • Volume: 4, Issue: 2, page 119-139
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Peet, M. M., et al. "New Computational Tools for Modeling Chronic Myelogenous Leukemia." Mathematical Modelling of Natural Phenomena 4.2 (2009): 119-139. <http://eudml.org/doc/222231>.

@article{Peet2009,
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. },
author = {Peet, M. M., Kim, P. S., Niculescu, S.-I., Levy, D.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {delay-differential equations; model verification; optimization; polynomials; sum-ofsquares; stability; Lyapunov-Krasovskii; chronic myelogenous leukemia; imatinib; polynomials; sum-of squares; stability},
language = {eng},
month = {3},
number = {2},
pages = {119-139},
publisher = {EDP Sciences},
title = {New Computational Tools for Modeling Chronic Myelogenous Leukemia},
url = {http://eudml.org/doc/222231},
volume = {4},
year = {2009},
}

TY - JOUR
AU - Peet, M. M.
AU - Kim, P. S.
AU - Niculescu, S.-I.
AU - Levy, D.
TI - New Computational Tools for Modeling Chronic Myelogenous Leukemia
JO - Mathematical Modelling of Natural Phenomena
DA - 2009/3//
PB - EDP Sciences
VL - 4
IS - 2
SP - 119
EP - 139
AB - 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.
LA - eng
KW - delay-differential equations; model verification; optimization; polynomials; sum-ofsquares; stability; Lyapunov-Krasovskii; chronic myelogenous leukemia; imatinib; polynomials; sum-of squares; stability
UR - http://eudml.org/doc/222231
ER -

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