A PDE model for imatinib-treated chronic myelogenous leukemia.
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.
Kim
Peter S
PS
Laboratoire des Signaux et Systèmes, Ecole Supérieure d'Electricité, 91192, Gif-sur-Yvette, France.
Lee
Peter P
PP
Levy
Doron
D
D000465:Algorithms; D000970:Antineoplastic Agents / Q000494:pharmacology / Q000627:therapeutic use; D017209:Apoptosis / Q000187:drug effects; D001549:Benzamides; D002452:Cell Count; D002454:Cell Differentiation / Q000187:drug effects; D049109:Cell Proliferation / Q000187:drug effects; D003198:Computer Simulation; D006412:Hematopoietic Stem Cells / Q000166:cytology / Q000187:drug effects; D006801:Humans; D000068877:Imatinib Mesylate; D007700:Kinetics; D015464:Leukemia, Myelogenous, Chronic, BCR-ABL Positive / Q000188:drug therapy* / Q000473:pathology; D008954:Models, Biological; D014411:Neoplastic Stem Cells / Q000187:drug effects / Q000473:pathology; D010879:Piperazines / Q000494:pharmacology / Q000627:therapeutic use*; D011743:Pyrimidines / Q000494:pharmacology / Q000627:therapeutic use*
D000970:Antineoplastic Agents; D001549:Benzamides; D010879:Piperazines; D011743:Pyrimidines; D000068877:Imatinib Mesylate