A PDE Model for Imatinib-Treated Chronic Myelogenous Leukemia

Original Article

Abstract

We derive a model for describing the dynamics of imatinib-treated chronic myelogenous leukemia (CML). This model is a continuous extension of the agent-based CML model of Roeder et al. (Nat. Med. 12(10), 1181–1184, 2006) and of its recent formulation as a system of difference equations (Kim et al. in Bull. Math. Biol. 70(3), 728–744, 2008). The new model is formulated as a system of partial differential equations that describe various stages of differentiation and maturation of normal hematopoietic cells and of leukemic cells.

An imatinib treatment is also incorporated into the model. The simulations of the new PDE model are shown to qualitatively agree with the results that were obtained with the discrete-time (difference equation and agent-based) models. At the same time, for a quantitative agreement, it is necessary to adjust the values of certain parameters, such as the rates of imatinib-induced inhibition and degradation.

Keywords

Chronic myelogenous leukemia Gleevec Imatinib Mathematical models Agent-based models Difference equations Partial differential equations 

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Copyright information

© Society for Mathematical Biology 2008

Authors and Affiliations

  1. 1.Laboratoire des Signaux et SystèmesÉcole Supérieure d’ÉlectricitéGif-sur-YvetteFrance
  2. 2.Division of Hematology, Department of MedicineStanford UniversityStanfordUSA
  3. 3.Department of Mathematics and Center for Scientific Computation and Mathematical Modeling (CSCAMM)University of MarylandCollege ParkUSA

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