Internal bone marrow dosimetry: the effect of the exposure due to $^{90}$Sr incorporated in the adjacent bone segments

The paper is devoted to dosimetric modelling of the human red bone marrow (RBM) internal exposure due to beta-emitting $^{90}$Sr incorporated in spongiosa bone. The dose factor calculation (absorbed dose rate due to unit specific activity of $^{90}$Sr) is based on the modelling of radiation transport in segments of the skeleton bones with active hematopoiesis. Segmentation considerably simplifies the modelling, but can lead to an underestimation due to electron emission from the neighboring parts of the bone adjacent to the studied segment. The objective of the study is to determine this cross-fire effect on the absorbed dose in RBM. For this purpose, we analyze the results of the numerical experiment on modelling of dose absorption within the bone segments of various shape and size that were parts of the computational phantoms of skeletons of people of different sex and age. We analyze dose factor dependencies on the area of the spongiosa bone surface and the ratio of weights of bone and RBM. It is found that if the area of the spongiosa surface (SS) > 6 cm$^2$, then the effect of neighboring bone parts exposure is negligible. For a smaller $SS$ the extension of the linear dimensions of the spongiosa bone by 2 mean electron path lengths results in dose factor increase proportional to the ratio of the extended spongiosa bone surface area to the original one to the power of 0,28. For human computational phantoms, these values are in the range 1,03 – 1,21 and are used as adjustment coefficients for the dose factors. Relative standard uncertainty of the adjustment coefficient is 5%.