Bulletin of Mathematical Biology

, Volume 70, Issue 3, pp 728–744

Modeling Imatinib-Treated Chronic Myelogenous Leukemia: Reducing the Complexity of Agent-Based Models

Original Article

DOI: 10.1007/s11538-007-9276-z

Cite this article as:
Kim, P.S., Lee, P.P. & Levy, D. Bull. Math. Biol. (2008) 70: 728. doi:10.1007/s11538-007-9276-z

Abstract

We develop a model for describing the dynamics of imatinib-treated chronic myelogenous leukemia. Our model is based on replacing the recent agent-based model of Roeder et al. (Nat. Med. 12(10):1181–1184, 2006) by a system of deterministic difference equations. These difference equations describe the time-evolution of clusters of individual agents that are grouped by discretizing the state space. Hence, unlike standard agent-base models, the complexity of our model is independent of the number of agents, which allows to conduct simulation studies with a realistic number of cells. This approach also allows to directly evaluate the expected steady states of the system. The results of our numerical simulations show that our model replicates the averaged behavior of the original Roeder model with a significantly reduced computational cost. Our general approach can be used to simplify other similar agent-based models. In particular, due to the reduced computational complexity of our technique, one can use it to conduct sensitivity studies of the parameters in large agent-based systems.

Keywords

Chronic myelogenous leukemiaGleevecImatinibAgent-based modelsDifference equationsSteady states

Copyright information

© Society for Mathematical Biology 2007

Authors and Affiliations

  1. 1.Department of MathematicsStanford UniversityStanfordUSA
  2. 2.Division of Hematology, Department of MedicineStanford UniversityStanfordUSA
  3. 3.Department of Mathematics and Center for Scientific Computations and Mathematical Modeling (CSCAMM)University of MarylandCollege ParkUSA