Objective: Severe radiation-induced lymphopenia occurs in 40% of patients treated for primary brain tumors and is an independent risk factor of poor survival outcomes. We developed an in-silico framework that estimates the radiation doses received by lymphocytes during VMAT brain irradiation. 
Approach: We implemented a simulation consisting of two interconnected compartmental models describing the slow recirculation of lymphocytes between lymphoid organs (M_1) and the bloodstream (M_2). We used dosimetry data from 33 patients treated with chemo-radiation for glioblastoma to compare three cases of the model, corresponding to different physical and biological scenarios: H1) lymphocytes circulation only in the bloodstream i.e., circulation in M_2 only; H2) lymphocytes recirculation between lymphoid organs i.e. circulation in M_1 and M_2 interconnected; H3) lymphocytes recirculation between lymphoid organs and deep-leaning computed out-of-field dose to head and neck lymphoid structures. A sensitivity analysis of the model's parameters was also performed. 
Main results: For H1, H2 and H3 cases respectively, the irradiated fraction of lymphocytes was 99.8±0.7%, 40.4±10.2% et 97.6±2.5%, and the average dose to irradiated pool was 309.9±74.7mGy, 52.6±21.1mGy and 265.6±48.5mGy. The recirculation process considered in the H2 case implied that irradiated lymphocytes were irradiated in the field only 1.58±0.91 times on average after treatment. The out-of-field irradiation of head and neck lymphoid structures considered in H3 was an important contribution to lymphocytes dose. In all cases, the estimated doses are low compared with lymphocytes radiosensitivity, and other mechanisms could explain high prevalence of RIL in patients with brain tumors.
Significance: Our framework is the first to take into account out-of-field doses and recirculation in lymphocyte dose assessment during brain irradiation. Our results demonstrate the need to clarify the indirect effects of irradiation on lymphopenia, in order to potentiate the combination of radio-immunotherapy or the abscopal effect.