A 2-STAGE MODEL FOR CHILDHOOD ACUTE LYMPHOBLASTIC-LEUKEMIA - APPLICATION TO HEREDITARY AND NONHEREDITARY LEUKEMOGENESIS

A differential equation model is developed to represent a two-stage mu tational process leading to childhood acute lymphoblastic leukemia (AL L). Leukemogenesis is modeled as transformation of target stem cells t hat initially grow rapidly in the embryo but plateau and then decline in postnatal childhood. Inheritance of the first of two leukemogenic m utations is allowed as a possibility in a small minority of leukemic p atients 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 t he two mutations necessary for ALL would be likely to experience ''mul ticlonal leukemogenesis''; that is, the parallel development of severa l leukemic clones arising from multiple independent leukemic events. T he 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 stoc hastic modeling. The existence of multiclonal leukemogenesis is in pri nciple testable by molecular biological methods (clonality analysis) t hat rely on the random inactivation of one of two X-chromosomes in nor mal female subjects. It is expected that the mathematical methods deve loped here will also be useful for more general (N-stage) models of ma lignant transformation of stem cell populations undergoing growth or d ecline. (C) Elsevier Science Inc., 1997