Research
Modeling Chronic Myelogenous Leukemia

The ModLMC collaborative research initiative is one of the first research projects in France devoted to mathematical modeling of medical conditions related to blood cell production. The initiative unites mathematicians, physicians and biologists to explore different approaches to better understanding the phenomena at work in leukemia.

© N.Bessonov-V.Volpert-L.Pujo-Menjoue t/ université de Lyon Exemple d'utilisation du logiciel Multi-Agent de prolifération cellulaire dans la moelle osseuse Ce logiciel a été développé pour partie dans l’Arc ModLMC.

Chronic myelogenous leukemia is one of the best-known forms of leukemia, making it a good model to use in addressing the mechanisms at the root of blood cell proliferation within bone marrow and in facilitating the development of new anti-tumor medications. Developing mathematical models of this cancer is an important objective for physicians and cancer specialists, and it is the subject of the research that has been underway for two years within the ModLMC collaborative research initiative. Under the initiative, mathematicians from INRIA and the Institut Camille Jordan in Lyon, along with physicians from Inserm, the Hôpital Edouard Herriot (Lyon) and the Institut Bergonié (Bordeaux) confront various models of the evolution of normal and pathological blood cells. One model uses the multi-agent approach to base the behavior of a population of cells on that of its members. Another model uses a spatial approach to study accelerating migration of malignant cells into the bone marrow using models of diffusion in porous environments. Yet a third model describes the development of blood cells based on population dynamics.

The third approach is the one adopted by INRIA teams ANUBIS and BANG in cooperation with hematologists in Bordeaux and Paris, who are modeling the evolution of the number of healthy and leukemic blood cells. It is no simple exercise, however, because the stem cells in bone marrow that produce all types of blood cells (red and white corpuscles and platelets) have a complex life cycle. The cycle lasts several days and can be broken down into four phases during which the cells divide (self-reproduction) or die through apoptosis (programmed cell death) before entering into a resting phase of variable, indeterminate length. Some of the resting cells rejoin the reproduction cycle after an unpredictable period of time, some die through apoptosis and others give birth to differentiated cells that will in turn generate all types of blood cells throughout a series of transformations (differentiation and maturation). In this cycle, a cell's age and maturity are important parameters to describe the evolution of blood cells, and they were the first parameters used. To better represent the biological realities, the researchers added several complications to the existing models; these treat the length of the cellular cycle as random (rather than fixed) and account for interactions between healthy and malignant cells.

The experimental research carried out by hematologists from Inserm, the University of Bordeaux 2 and the Hôpital Edouard Herriot in Lyon specify several parameters for the model, such as the number of cells that are undifferentiated, in apoptosis, in the various phases of reproduction, resting, etc. Similarly, data obtained from chronic myelogenous leukemia patients are valuable in estimating the parameters used in the equations. One of the characteristics of this form of leukemia is that the proportion of leukemic cells in the blood circulation can oscillate among some patients, with a period of up to 80 days. Changes in these proportions can be used to estimate the duration of cellular cycles.

Currently, new observations are being made based on the medicinal treatment of patients with Imatinib, an anti-cancer drug that stabilizes production of cancer cells, although resistance can develop over time. Inhibition of the growth of leukemic cells using this medication can thus be analyzed as a control.
Current results are encouraging, suggesting that proliferation more probably results from increasing rates of reintroduction of dormant cells into the division cycle than from a weakened apoptosis process. These results were presented at the French Society of Hematology's conference on modeling held on March 20 and 21, and there is little doubt that they persuaded many specialists in the field of the usefulness of a mathematical approach to these biological processes.

Contact:

Mostafa Adimy
ANUBIS team, INRIA Bordeaux - Sud-Ouest
Tel.: + 33 5 57 57 11 13