Hit probability for cellular targets by bone-surface-seeking alpha emitters

Irradiation of cellular targets near bone surfaces with surface-seeking α-emitters is discussed in terms of hit probabilities to spheres. The geometrical factor describing the average number of hits as a function of distance from the surface is shown to be approximately proportional to the dose rate over most of the particle range. The hit probability is calculated for the case of a non-uniform distribution of cell nuclei at the bone surfaces of the thoracic vertebrae of beagles. The effect of a spatial variation of the specific surface activity and burial depth along bone surfaces is evaluated and a general expression derived, relating the hit probability to the dose rate distribution. From this expression numerical results are calculated using measured dose rate distributions in the lumbar vertebrae of rats. The validity of the underlying assumption and the consequences with respect to tumour models are discussed. (author)