Statistics of hits to bone cell nuclei

Abstract

The statistics of hits to the nuclei of bone cells irradiated from alpha sources labeling bone tissue is described. It is shown that the law of remodeling of a bone structural unit (BSU), which describes the distribution of quiescence periods of this unit, affects the statistics of hits. It the irradiation of bone cells occurs during the whole cell cycle, the mean number of hits is independent of the law of remodeling. In this case the variance of hits has the minimum value for constant quiescence periods of BSUs (deterministic remodeling) and the maximum value for exponentially distributed quiescence periods (random remodeling). For the first generation of bone cells, i.e. for the cells which existed at the moment of the uptake of the nuclide, the mean number of hits depends on the law of remodeling. For random remodeling the mean number is equal to the mean value for the complete remodeling cycle. For deterministic remodeling the mean is only half this value. For the first generation of bone cells, changing the law of remodeling from random to deterministic increases the probability of no hits to the nuclei of bone cells. For the same mean value of hits, the difference does not exceed 13.3 % of the total number of cells. For the subsequent generations of bone cells, such a change of the law of remodeling decreases the probability of no hits by 20.4%.