Purpose: To investigate the effect of variable dose rate on biologically effective dose (BED).

Materials and methods: By using the linear-quadratic (LQ) model with bi-exponential repair, we analytically determine the time-dependent dose rate  which minimizes the effective protraction factor (Geff) and BED under the condition of fixed fraction time and dose per fraction. Because normal tissue complication probability (NTCP) monotonically decreases with decreasing BED, the dose rate  also minimizes NTCP.

Results: The dependences of Geff , BED and NTCP on fraction time were determined for different radiobiological parameters and two different dose rates: constant dose rate R0 and varying dose rate .

Conclusion: The results of this study indicate that under certain conditions the reduction in BED for late-responding tissues due to increased fraction time can be significantly greater than the reduction in BED for tumors. Our analysis also indicates that dose rate optimization can be radiobiologically beneficial because of the resulting decrease in NTCP.