Combined effect of heterogeneous target dose and heterogeneous radiosensitivity on tumor control probability for different fractionation regimens

Purpose: To evaluate the combined effect of heterogeneous target dose and heterogeneous radiosensitivity on tumor control probability (TCP) for different number of fractions (N-f). Methods: The linear-quadratic (LQ) model is employed to study dependence of TCP on N-f under the condition of fixed nominal biologically effective dose (BEDnom). Results: Formula for the optimum target dose which maximizes TCP under the condition BEDnom = const is analytically derived. It is shown that the dependence of TCP on N-f is non-monotonic. In addition, the dependence of TCP on N-f for different variances of the target dose and radiosensitivity of malignant cells is demonstrated by using numerical computations. Conclusions: It is shown that the optimum mean dose in the target is defined by the standard deviations of the target dose (sigma(D)) and standard deviations of parameters alpha (sigma(alpha)) and beta (sigma(beta)). The findings of this study indicate that hypofractionated regimens for stereotactic body radiation therapy (SBRT) and stereotactic radio surgery (SRS) with N-f <= 3 can be radiobiologically inferior to the regimens with five or more fractions.