A PDE model for imatinib-treated chronic myelogenous leukemia

Authored by Doron Levy, Peter S. Kim, Peter P. Lee

Date Published: 2008-10

DOI: 10.1007/s11538-008-9336-z

Sponsors: American Cancer Society Chateaubriand fellowship United States National Science Foundation (NSF)

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

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.

Tags

Agent-based models mathematical models Difference equations Chronic myelogenous leukemia Gleevec Imatinib partial differential equations