A two-stage model for childhood acute lymphoblastic leukemia: application to hereditary and nonhereditary...

A differential equation model is developed to represent a two-stage mutational process leading to childhood acute lymphoblastic leukemia (ALL). Leukemogenesis is modeled as transformation of target stem cells that initially grow rapidly in the embryo but plateau and then decline in postnatal childhood. Inheritance of the first of two leukemogenic mutations is allowed as a possibility in a small minority of leukemic patients who would characteristically develop leukemia at an early age. The model is shown to be capable of providing good fits to incidence data for childhood ALL; these fits allow estimation of some parameters of the model. The analysis shows that individuals inheriting one of the two mutations necessary for ALL would be likely to experience "multiclonal leukemogenesis"; that is, the parallel development of several leukemic clones arising from multiple independent leukemic events. The model suggests that between two and ten such clones would typically have developed in such individuals by the time of diagnosis. The main conclusions of the deterministic investigation were confirmed by stochastic modeling. The existence of multiclonal leukemogenesis is in principle testable by molecular biological methods (clonality analysis) that rely on the random inactivation of one of two X-chromosomes in normal female subjects. It is expected that the mathematical methods developed here will also be useful for more general (N-stage) models of malignant transformation of stem cell populations undergoing growth or decline.