A Theory of the Induction of Bone Cancer by Alpha Radiation

A theory of the induction of osteosarcoma by α particles fits the data for radium in man and dog over the entire dose-time-response surface. The theory postulates that an endosteal cell near bone surface is transformed by three events. Two initiation events, each with a probability of $4\times 10^{-8}/\text{rad}$ (an effective target diameter of 100 Å), are produced in a single cell by two α particles. A promotion event then occurs at a rate of $10^{-2}/\text{year}$, not related to radiation, but proportional to the rate of bone remodeling. In competition with these events is the killing of any endosteal cell by an α particle with a probability of $10^{-2}/\text{rad}$. Killed endosteal cells are assumed to be replaced by stem cells at a rate of $10^{-1}/\text{day}$. Postulated tumor growth takes 3-6 years. These values for man are preliminary. The probability per rad per cell of each initiation appears to be ∼10 times larger in dog than in man. A new method of three-dimensional analysis provides a compact way to report more fully the data for internal emitters and eliminates competing risks from comparisons between theory and experiment. The theory provides an explanation for latent period, for the protraction effect for ^{224}{\rm Ra}$ in man, for the scarcity of tumors in compact bone, for the narrow time distribution of tumors in dog, for the wide time distribution of tumors in man, for the plateau in cumulative incidence at 17-31% observed so far for ^{226}{\rm Ra}-{}^{228}{\rm Ra}$ in man, for the much higher plateau in dog (92%), and for the steep decrease of tumor rate with decreasing dose below the plateau. Tumor rate P is shown to be a function of endosteal dose D, and, at less than 1 rad/day, to be independent of endosteal dose rate F. At low doses, P is proportional to D2. At high doses, P plateaus and becomes independent of D. The onset of the plateau occurs at 140 rad and is governed by the mean lethal dose to endosteal cells. If the two initiation events correspond to two targets within the cell nucleus which are each hit once (rather than one target which is hit twice), and if the cell at risk is flattened against bone surface (rather than rounded and somewhat off bone surface), then there is a low-lying linear component of tumor rate (P proportional to D) which predominates at endosteal doses below roughly 40 rad. The theory provides a number of predictions. (i) The mean time of tumor appearance will stop increasing with decreasing intake o