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 6 from the paper (where CML decreases 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.
$\frac{d \mathrm{Tn}}{d \mathrm{time}}=\mathrm{sn}-\mathrm{dn}\mathrm{Tn}+\mathrm{kn}\mathrm{Tn}\frac{C}{C+\mathrm{eta}}$
$\frac{d \mathrm{Te}}{d \mathrm{time}}=\mathrm{alpha\_n}\mathrm{kn}\mathrm{Tn}\frac{C}{C+\mathrm{eta}}+\mathrm{alpha\_e}\mathrm{Te}\frac{C}{C+\mathrm{eta}}-\mathrm{de}\mathrm{Te}+\mathrm{gamma\_e}C\mathrm{Te}$
$\frac{d C}{d \mathrm{time}}=\mathrm{rc}C\ln \left(\frac{\mathrm{Cmax}}{C}\right)-\mathrm{dc}C+\mathrm{gamma\_c}C\mathrm{Te}$
2004-04-21keywordJournal of Theoretical Biology800100000A Mathematical Model for Chronic Myelogenous Leukemia (CML) and T Cell Interaction (Decreasing CML Variant)
The University of Auckland, Bioengineering Institute
Moore and Li's 2004 mathematical model for chronic myelogenous leukemia and T cell interaction.
T lymphocyteThe University of AucklandThe Bioengineering InstituteMayLloydCatherinec.lloyd@auckland.ac.nz15038986Tnnaive T cells
This is the CellML description of Moore and Li's 2004 mathematical model for chronic myelogenous leukemia and T cell interaction.
2004-03-27t cellcancerimmunologyT cellMooreHelenCatherine LloydTeeffector T cells specific to CML
A mathematical model for chronic myelogenous leukemia (CML) and T cell interaction
513523227KLiNatashaCchronic myelogenous leukemia (CML) cancer cells