Equivalent physical dose (EPD) for improved precision in voxelized dosimetry

Abstract

Equivalent dose in 2 Gy fractions (EQD2) has long been considered the more practical alternative to biological effective dose (BED) for the clinic. However, the basic mathematics of EQD2 are debated. In this paper, by a simple proof of plugging the EQD2 dose into the BED equation and getting a different result, it is demonstrated that the standard EQD2 equation is mathematically inconsistent. The mathematically exact derivation, referred to here as equivalent physical dose (EPD), which solves for the roots of the quadratic equation, is provided and compared against the existing derivation, which separates the Relative Effect term from the BED equation. Additionally, the EQD2 expression is applied assuming a heterogeneous dose, which has become inappropriate in the era of voxelized dosimetry where a voxel in the structure, like organs at risk, may have a differing dose from the prescription. The implications of the >10% errors introduced from the existing formulations are explored and could explain the reported failings of EQD2 in the hypofractionation, serial organ irradiation, and dose accumulation contexts. This work provides an explanation to confusing aspects about how to apply radiobiology models, which have limited its development. Optimizing therapy around biological dimensions (as conformal radiotherapy did for spatial dimensions) could provide vital flexibility to radiotherapy treatment planning.