The stochastic aspects of alpha-particle traversals through nuclei of
bone-lining cells from nonuniform radioactive labels are worked out. B
oth the residence time of the target and the hit rate are considered r
andom 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 repr
esents the most dangerous situation. A possible negative correlation b
etween residence times and hit rates, observed in some experiments, te
nds 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 Pu-239 in the hu
man body. In the case of 50 years of chronic ingestion of 1 annual lim
it of intake (ALI) per year for class W and chronic inhalation of 1 AL
I/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, respe
ctively.