Hits to bone cell nuclei from nonuniform radioactive labels

The stochastic aspects of alpha-particle traversals through nuclei of bone-lining cells from nonuniform radioactive labels are worked out. Both the residence time of the target and the hit rate are considered random variables. It is shown that with any type of bone remodeling the fraction of cells not hit increases with increasing nonuniformity of the label concentration. Thus, a completely uniform concentration represents the most dangerous situation. A possible negative correlation between residence times and hit rates, observed in some experiments, tends to decrease the probability of alpha-particle hits. As a practical application, the theory is applied to the International Commission on Radiological Protection model of the distribution of 239Pu in the human body. In the case of 50 years of chronic ingestion of 1 annual limit of intake (ALI) per year for class W and chronic inhalation of 1 ALI/year for class Y compounds, more than 19.4 and 8.5% of the nuclei of bone-lining cells are traversed by at least one alpha-particle, respectively.