Radiation effects in spheroids of cells exposed to alpha emitters

Purpose: To simulate spheroids of cells and use the spheroid models to establish methods of calculating cell survival following exposure to alpha irradiation from decays of At-211 and Bi-213. Methods: Using a Monte Carlo technique, two models of spheroids of cells were generated in which cells either did not or were allowed to overlap. At 40% packing of the volume it is shown that the two models are equivalent for longer-ranged alpha particles. The overlapping model was used to examine the effects of spheroid size and cell packing on cell survival. Cell survival was also calculated for different distributions of alpha decays such as uniform distribution within the spheroid, external to the spheroid and as a shell on the periphery of the spheroid. Results: Three examples of the cell structure of the spheroids are shown. Detailed calculations show that cell survival decreases from 57% to 37% as the spheroid diameter increases from 75 mum to 225 mum for an average of one At-211 decay per cell and 50% packing. Increasing the packing of the cells in the spheroid from 40% to 70% reduces survival from 46% to 26% for 200 mum diameter spheroids for one At-211 or Bi-213 decay per cell. The presence of small regions of unlabelled cells within the spheroids does not significantly change cell survival. Conclusions: Monte Carlo programmes generating spheroids of cells and their subsequent use to score cell survival for alpha irradiation should be useful in the design and interpretation of work on spheroids of cells in vitro and the application of such modelling to the study of very small tumours in vivo. Copies of the programmes are available from the author on request.