title: Long-term treatment effects in chronic myeloid leukemia.
abstract: We propose and analyze a simplified version of a partial differential equation (PDE) model for chronic myeloid leukemia (CML) derived from an agent-based model proposed by Roeder et al. This model describes the proliferation and differentiation of leukemic stem cells in the bone marrow and the effect of the drug Imatinib on these cells. We first simplify the PDE model by noting that most of the dynamics occurs in a subspace of the original 2D state space. Then we determine the dominant eigenvalue of the corresponding linearized system that controls the long-term behavior of solutions. We mathematically show a non-monotonous dependence of the dominant eigenvalue with respect to treatment dose, with the existence of a unique minimal negative eigenvalue. In terms of CML treatment, this shows that there is a unique dose that maximizes the decay rate of the CML tumor load over long time scales. Moreover this unique dose is lower than the dose that maximizes the initial tumor load decay. Numerical simulations of the full model confirm that this phenomenon is not an artifact of the simplification. Therefore, while optimal asymptotic dosage might not be the best one at short time scales, our results raise interesting perspectives in terms of strategies for achieving and improving long-term deep response.
authors.affiliation: Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, F-69622, Villeurbanne cedex, France. apollos.besse@inria.fr.|INRIA, Villeurbanne, France. apollos.besse@inria.fr.
authors.forename: Apollos
authors.identifier: 0000-0002-3143-304X
authors.initials: A
authors.lastname: Besse
authors.affiliation: Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, F-69622, Villeurbanne cedex, France.|INRIA, Villeurbanne, France.
authors.forename: Thomas
authors.initials: T
authors.lastname: Lepoutre
authors.affiliation: Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, F-69622, Villeurbanne cedex, France.|INRIA, Villeurbanne, France.
authors.forename: Samuel
authors.initials: S
authors.lastname: Bernard
mesh_terms: D000970:Antineoplastic Agents / Q000627:therapeutic use; D006801:Humans; D000068877:Imatinib Mesylate / Q000627:therapeutic use; D015464:Leukemia, Myelogenous, Chronic, BCR-ABL Positive / Q000628:therapy*; D008954:Models, Biological; D013995:Time
chemical_list: D000970:Antineoplastic Agents; D000068877:Imatinib Mesylate
keywords: Chronic myeloid leukemia; Dominant eigenvalue; Renewal model; Structured population dynamic