A mathematical model, which describes the level of surviving lymphocytes in the blood after ultra-high (FLASH) and lower dose rates of partial-body irradiation, is developed. The model is represented by simple analytic formulae that involve a few parameters, namely, physiologic parameters (characteristics of the blood flow through the blood circulatory system and its irradiated part), a biophysical parameter (a characteristic of the blood lymphocytes radiosensitivity), and the physical parameters (characteristics of irradiation). The model predicts that the level of surviving blood lymphocytes increases as the dose rate increases and approaches the limiting level of (1 - vR), where vR is the fraction of the blood volume in the irradiated part of the blood circulatory system. The model also predicts that the level of surviving blood lymphocytes after the same exposure is higher for lower vR. It is found that FLASH irradiation in humans with doses of 10 to 40 Gy and with exposure times significantly less (<1 s) than the blood circulation time (∼60 s) leads to the maximal blood lymphocyte sparing. Simple formula, which determines effective dose rates for optimal blood lymphocyte sparing, is derived in the framework of the developed model. For the dose range specified above, the obtained modeling prediction of the range of effective dose rates for optimal blood lymphocyte sparing in humans (namely, N ≥40 Gy/s) coincides with the dose rate range in FLASH radiation therapy. It is revealed that the respective effective dose rates for mice are higher than those for humans (for the same dose range) due to the shorter blood circulation time in mice than in humans. Proceeding from the findings obtained in this paper, a hypothesis elucidating the mechanisms of the abscopal effect of FLASH radiation therapy (namely, an antitumor response on metastases located outside of irradiated part of a body) is proposed.
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