Effects of Partial-Body, Continuous/Pulse Irradiation at Dose Rates from Flash to Conventional Rates on the Level of Surviving Blood Lymphocytes: Modeling Approach. I. Continuous Irradiation

A mathematical model developed by Cucinotta and Smirnova is extended to describe effects of continuous, partial-body irradiation at high doses D and at dose N rates from FLASH to conventional rates on the level of surviving blood lymphocytes in humans and small laboratory animals (mice). Specifically, whereas the applicability of the model is limited to the exposure times shorter than a single cardiac cycle T0, the extended model is capable of describing such effects for the aforementioned and longer exposure times. The extended model is implemented as the algebraic equations. It predicts that the level of surviving blood lymphocytes in humans and mice increases with increasing the dose rate from N = D / T0 to FLASH rates and approaches the upper limiting level of 1 – v R where v R is the fraction of blood volume in the irradiated part of the blood circulatory system. Levels of surviving blood lymphocytes computed at doses from 10 Gy to 40 Gy and at dose rates N, which equal or exceed 40 Gy/s for humans and 400 Gy/s for mice, are nearly indistinguishable from the upper limiting level. In turn, the level of surviving blood lymphocytes in humans and mice decreases with decreasing the dose rate from N = D / T0 to conventional rates and approaches a lower limiting level. This level strongly depends on the dose D (it is smaller at larger values of D) with a slight dependence on the dose rate N. The model with the parameters specified for mice (together with the model of the dynamics of lymphopoietic system in mice after partial-body irradiation) reproduce, on a quantitative level, the experimental data, according to which the concentration of blood lymphocytes measured in mice in one day after continuous, partial-body irradiation at a high dose and conventional dose rate is smaller at the larger value of vR. Additionally, the model predicts at the same high dose (>10 Gy) a faster restoration of the blood lymphocyte population in humans exposed to continuous, partial-body irradiation at a FLASH dose rate compared to a conventional dose rate.