Effects of Partial-Body, Continuous/Pulse Irradiation at Dose Rates from Flash to Conventional Rates on The Level of Surviving Blood Lymphocytes: Modeling Approach II. Two- and Multiple-Pulse Irradiation.

Mathematical models, which describe effects of partial-body, two- and multiple-pulse irradiation at high total doses D and at average dose rates N from FLASH to conventional rates on the level of surviving blood lymphocytes in humans and mice, have been developed originating in the previously proposed approach. These models predict that levels of surviving blood lymphocytes in humans and mice increase with increasing the dose rate from N = D / TR (TR is the time of the blood flowing into or out of the irradiated segment of the blood circulatory system) to FLASH rates and approach an upper limiting level equal to (1- vR), where vR is the fraction of blood volume in the irradiated segment of the blood circulatory system. Levels of surviving blood lymphocytes computed at total doses D of 10-40 Gy and at average of dose rates N, which are equal to or exceed 40 Gy/s for humans and 400 Gy/s for mice, are nearly indistinguishable from the upper limiting level. These results can be interpreted as the models reproducing the optimal blood lymphocyte sparing in these mammals after such exposures. With decreasing the dose rate from N = D/ TR to conventional rates, at multiple-pulse irradiation the levels of surviving blood lymphocytes in humans and mice decrease to lower limiting levels, whereas at two-pulse irradiation they change cyclically and do not fall below their values for the delivery time equal to TR. Additionally, effects of two- and multiple-pulse irradiation of the whole abdomen in mice on the level of surviving blood lymphocytes are simulated within the developed models. Regimens of two- and multiple-pulse irradiation are taken the same as those reported in experiments, where effects of such exposures on the level of surviving crypts in mice were studied. Juxtaposing the modeling results with the experimental data reveals that the level of surviving blood lymphocytes in mice after two- and multiple-pulse irradiation of the abdomen at average dose rates N from FLASH to conventional rates modulates the level of surviving crypts in these animals after such exposures. A hypothesis is proposed to explain this phenomenon.