A Mathematical Model for Chronic Myelogenous Leukemia (CML) and T Cell Interaction Catherine Lloyd Auckland Bioengineering Institute, The University of Auckland
Model Status This model runs in OpenCell to recreate the published results. This particular version of the model recreates figure 7 from the paper (where CML increases over a 2 year period). The units have been checked and they are consistent. The CellML model also runs in COR however due to the timescale being in days the model is not ideal for simulation in COR.
Model Structure ABSTRACT: In this paper, we propose and analyse a mathematical model for chronic myelogenous leukemia (CML), a cancer of the blood. We model the interaction between naive T cells, effector T cells, and CML cancer cells in the body, using a system of ordinary differential equations which gives rates of change of the three cell populations. One of the difficulties in modeling CML is the scarcity of experimental data which can be used to estimate parameters values. To compensate for the resulting uncertainties, we use Latin hypercube sampling (LHS) on large ranges of possible parameter values in our analysis. A major goal of this work is the determination of parameters which play a critical role in remission or clearance of the cancer in the model. Our analysis examines 12 parameters, and identifies two of these, the growth and death rates of CML, as critical to the outcome of the system. Our results indicate that the most promising research avenues for treatments of CML should be those that affect these two significant parameters (CML growth and death rates), while altering the other parameters should have little effect on the outcome. The complete original paper reference is cited below: A mathematical model for chronic myelogenous leukemia (CML) and T cell interaction, Helen Moore and Natasha K. Li, 2004, Journal of Theoretical Biology, 11, 369-391. PubMed ID: 15038986 reaction diagram Cell population diagram showing the population dynamics of each cell type and how they interact with each other. These dynamics and interactions are described by the mathematical model equations.
Tn naive T cells $\frac{d \mathrm{Tn}}{d \mathrm{time}}}=\mathrm{sn}-\mathrm{dn}\mathrm{Tn}+\mathrm{kn}\mathrm{Tn}\frac{C}{C+\mathrm{eta}}$ Te effector T cells specific to CML $\frac{d \mathrm{Te}}{d \mathrm{time}}}=\mathrm{alpha_n}\mathrm{kn}\mathrm{Tn}\frac{C}{C+\mathrm{eta}}+\mathrm{alpha_e}\mathrm{Te}\frac{C}{C+\mathrm{eta}}-\mathrm{de}\mathrm{Te}+\mathrm{gamma_e}C\mathrm{Te}$ C chronic myelogenous leukemia (CML) cancer cells $\frac{d C}{d \mathrm{time}}}=\mathrm{rc}C\ln \left(\frac{\mathrm{Cmax}}{C}\right)-\mathrm{dc}C+\mathrm{gamma_c}C\mathrm{Te}$ T cell immunology t cell cancer keyword c.lloyd@auckland.ac.nz Catherine Lloyd May The University of Auckland The Bioengineering Institute Catherine Lloyd Moore and Li's 2004 mathematical model for chronic myelogenous leukemia and T cell interaction. T lymphocyte 15038986 2004-03-27 Helen Moore A Mathematical Model for Chronic Myelogenous Leukemia (CML) and T Cell Interaction (Increasing CML Variant) The University of Auckland, Bioengineering Institute This is the CellML description of Moore and Li's 2004 mathematical model for chronic myelogenous leukemia and T cell interaction. A mathematical model for chronic myelogenous leukemia (CML) and T cell interaction 227 513 523 Natasha Li K 2004-04-21 Journal of Theoretical Biology