Effect of heterogeneous target dose and radiosensitivity on BED and TCP for different treatment regimens

Purpose. To evaluate how heterogeneity of the target dose and heterogeneity of intra-tumor radiosensitivity affect biologically effective dose (BED) and tumor control probability (TCP) depending on the number of fractions ($N_f$). Methods. The dependences of TCP and BED in the planning target volume on $N_f$ are studied using the linear-quadratic model. In the considered case, the nominal biologically effective dose $\left(BE{D}_{nom}\right)$ is fixed and the variances of the target dose (${\sigma }_D$) and radiosensitivity (${\sigma }_{\alpha }$) are assumed to be small. Results. By using series expansion of the survival probability of malignant cells, it is analytically shown that for small ${\sigma }_D$ and ${\sigma }_{\alpha }$ both BED and TCP increase with increasing $N_f$ under the condition $BE{D}_{nom}=const.$ In addition, the dependences of BED and TCP on $N_f$ for different values of ${\sigma }_D$ and ${\sigma }_{\alpha }$ are studied by using an analytical expression for BED in the case of Gaussian distributions of both target dose and radiosensitivity. Conclusions. Small variations in the absorbed dose and intratumor radiosensitivity can significantly reduce BED and TCP. The decreases in these quantities can be reduced by increasing the number of fractions. The findings of this study indicate that hypofractionated regimens with $N_f=20$ and dose per fraction $d⩽5$ Gy can lead to higher BED and TCP compared to treatment regimens with $N_f⩽5$ and $d⩾10$ Gy commonly used for stereotactic body radiation therapy (SBRT) and stereotactic radiosurgery (SRS). (paper)