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Frontiers in Mathematical Oncology

Mathematical modeling of heterogeneity and clonal selection in acute leukemias

Anna Marciniak-Czochra

University of Heidelberg


Motivated by clonal selection observed in acute leukemias (AML and ALL), we propose a range of mathematical models describing evolution of a multiclonal and hierarchical cell population. The models are applied to study the role of self-renewal properties, growth kinetics and regulatory feedbacks during disease development and relapse. Effects of different time and space scales are investigated. It is shown how resulting nonlinear and nonlocal terms may lead to a selection process and ultimately to therapy resistance. Model results imply that enhanced self-renewal of cancer stem cells may be the key mechanism in the clonal selection process, while heterogeneity in the progenitor cell population does not play such a role in cancer evolution. The models allow also to study how mutation rates and phenotypic changes induced by mutations influence the genetic interdependence of the leukemic clones.  The results help to understand which phenotypes may be present at different times over the course of disease and how treatment affects the clonal evolution of the disease. Model-based interpretation of clinical data allows estimating parameters that cannot be measured directly. This may have clinical implications for future treatment and follow-up strategies.