Limitations of EQD2 Accumulation: Why BED Summation Is Essential for Accurate Toxicity Evaluation
Abstract
Purpose
To determine the most radiobiologically consistent method for accumulating dose from differing treatment schedules for both targets and organs-at-risk in reirradiation scenarios.
Methods
We analyzed paired dose distributions from serial plans (66 and 20 Gy) with mixed fractionation schedules (2- and 5-Gy/fraction, respectively) for a central nervous system cancer patient reirradiation. We evaluated accumulated doses in terms of equivalent dose in 2-Gy fractions (EQD2) and biological effective dose (BED). Biological conversion utilized a fixed α/β-ratio of 10 Gy for the planning target volume (PTV) and 2 Gy for the spinal cord, assuming α=0.1 Gy-1 under the linear-quadratic model. We identified the isoeffective 2-Gy/fraction schedule for the 5-Gy/fraction plan. We used the accumulated EQD2 and total number of fractions to derive local dose-per-fraction. The objective biological effect endpoint was negative natural log surviving fraction (E=−lnSF) for the mean PTV dose and the maximum cord dose (for conservative toxicity risk evaluation). Ground truth was the sum of −lnSF between the two plans, with an acceptance criterion of <3% absolute error.
Results
The 5-Gy/fraction plan of 20 Gy was equivalent to a 2-Gy/fraction plan of 25 Gy. For the 2-Gy/fraction and 5-Gy/fraction plans, respectively, the mean PTV dose was 67.1 and 23.7 Gy and the max cord dose was 42.4 and 18.4 Gy. Dose summation using EQD2 was accurate for PTV (1.4% error) but failed for the cord (14.1% error). This failure arises because EQD2 conversion rigidly applies a reference (2-Gy/fraction) plan-level assumption that neglects the local low dose-per-fraction reality in the organs-at-risk. Only BED summation met the acceptance criterion for both PTV and cord (0% error).
Conclusion
BED summation provides the most mathematically robust framework for composite planning. While direct EQD2 summation is clinically common, it requires caution in organs-at-risk where the reference fraction size differs significantly from the local dose-per-fraction.