Comparison of different approaches for the computation of biologically effective dose in a non-uniformly irradiated treatment target in stereotactic body radiation therapy

The biologically effective dose (BED) for a non-uniformly irradiated treatment target can be determined using two approaches: averaging BEDs for different voxels in the target and averaging the probability of tumor cell survival in the target. This study compared these approaches for the computation of BED by examining their general properties and comparing BEDs for different treatment plans. The mean BED (BEDmean) determined by averaging BEDs in different parts of the target and BED (BEDnud) determined by averaging the probability of survival were computed for 51 cases of stereotactic body radiation therapy. For each case, two treatment plans were created using dynamic conformal arcs (DCAs) and volumetric modulated arc therapy (VMAT). For the plans with DCAs, the sample mean of BEDmean was 18% > that of BEDnud (for α = 0.35 Gy−1 and α/β =10 Gy). Conversely, for the VMAT plans and the same values of radiobiological parameters, the sample mean of BEDmean was only 5%> that of BEDnud. Theoretically, BEDmean is always ≥BEDnud. When the mean dose in the target is fixed, BEDmean increases with increasing variance of the target dose (σ2). In contrast, BEDnud decreased with increasing σ2. Although BEDnud depends on both alpha and beta parameters for the irradiated malignant cells, BEDmean depends only on the alpha/beta ratio. Thus, the use of BEDmean instead of BEDnud can cause incorrect ranking of treatment plans.