  The evolutionary dynamics of a system of cancerous cells in a model of
chronic myeloid leukemia (CML) is investigated by a statistical approach.
Cancer progression is explored by applying a Monte Carlo method to simulate the
stochastic behavior of cell reproduction and death in a population of blood
cells which can experience genetic mutations. In CML front line therapy is
represented by the tyrosine kinase inhibitor imatinib which strongly affects
the reproduction of leukemic cells only. In this work, we analyze the effects
of a targeted therapy on the evolutionary dynamics of normal, first-mutant and
cancerous cell populations. Several scenarios of the evolutionary dynamics of
imatinib-treated leukemic cells are described as a consequence of the efficacy
of the different modeled therapies. We show how the patient response to the
therapy changes when an high value of the mutation rate from healthy to
cancerous cells is present. Our results are in agreement with clinical
observations. Unfortunately, development of resistance to imatinib is observed
in a proportion of patients, whose blood cells are characterized by an
increasing number of genetic alterations. We find that the occurrence of
resistance to the therapy can be related to a progressive increase of
deleterious mutations.
