A mechanistic model for medulloblastoma induction in mice

Medulloblastomas in Patched heterozygous mice (Ptc1^+/- mice) are induced with high probability by ionizing radiation applied in the immediate post-natal period. A mathematical model is described here that accommodates the dependence of the medulloblastoma incidence on dose, age at exposure and age. The model assumes that the first step in the development of the cancer is already present in all cells of the patched mouse due to germ-line inactivation of one allele of the patched tumor suppressor gene. The subsequent rate-limiting step is dependent linearly on dose at least up to 3 Gy. The observed strong decrease in carcinogenic effect of radiation between exposure on day 1 and day 10 is described by a physiological elimination of target cells during post-natal maturation of the brain. A single malignant cell develops into a tumor following a gamma-distribution with mean of about 160 days. The multiplicity of medulloblastomas is predicted.