Evaluation of Therapeutic Gain \factor in Neutron Therapy Based on the Linear Quadratic Model

Abstract

Purpose: To study the dependencies of therapeutic gain factor (TGF) on dose of cyclotron-produced fast neutron beams using the linear-quadratic model (LQM) parameters characterizing radiation response in tumor and normal tissues. Material and methods: The TGF in neutron therapy was calculated as the ratio of the relative biological effectiveness of neutrons for tumor (RBE tumor) to relative biological effectiveness for normal tissue (RBE normal tissue). The LQM was used to calculate the dependencies of neutron RBE on the dose and therapeutic gain factor. We considered two cases: 1) neutron therapy for 3 types of tumors with different radiation response, where the same normal tissue was critical; 2) neutron therapy for the same tumor, when 3 types of normal tissues were taken as critical. Results: Based on calculations and analysis of published data, the dependencies of neutron RBE on dose for selected types of tumors and normal tissues were obtained. The following variants were considered: 1) RBE tumor > RBE normal tissue; 2) RBE tumor < RBE normal tissue, in both two variants, the dependen- cies in the therapeutic dose rate were convergent; 3) the dependencies of RBE tumor and RBE normal tissue on dose are crossed. The dependencies of TGF for neutron therapy on single boost doses and quantitative ratios between the LQM parameters characterizing radiation response of tumor and normal tissues were found. A multivariate ratio between the dependencies on dose of RBE tumor and RBE normal tissue was the cause of variety in the dependencies of TGF on dose. In the first case, the TGF increased with increasing (α/β)γ ratio and decreasing single dose, and the maximum value of TGF was equal to ~ 1.4. In the second case, TGF was < 1, i.e. the effectiveness of neutron therapy was lower than the effectiveness of gamma irradiation, but it was increased with higher single dose and lower radiosensitivity of normal tissue. In the third case, the dose at the intersection point (Di) was the boundary, and TGF was > 1 to the left of the boundary, and TPV was <1 to the right of the boundary, provided that D <Di, RBEtumor > OBEnormal tissue. Conclusion: The obtained results with known parameters of the LQM for tumor and normal tissues allowed us to make an appropriate choice between neutron and gamma- ray therapy in order to increase the effectiveness of treatment for cancer patients. It was shown that in the case of neutron therapy, the analysis of dependencies of TGF on dose allowed the optimal dose fractionation regimen to be selected.