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

PurposeEquivalent dose in 2 Gy fractions (EQD2), based on the original biological effective dose (BED) equation, is frequently used to guide treatment in the clinic. This work addresses the limitations of EQD2 in the context of voxelized dosimetry, clarifies potential sources of confusion, and provides an alternative formulation for improved precision. Methods and MaterialsThe EQD2 formula was evaluated by a simple insertion of the EQD2 dose into the BED equation. The mathematically exact form of EQD2, referred to here as equivalent physical dose (EPD), was provided by solving the linear-quadratic model BED equation for dose using the quadratic formula. The EPD derivation was compared in terms of absolute error to the EQD2 derivation, which separates the Relative Effect term from the BED equation. ResultsThe EQD2 expression implicitly assumed a homogenous dose, demonstrating that its use in voxelized dosimetry can mislead. As an alternative formulation, EPD was shown to adhere more closely to the first principles of radiobiological modeling. An error analysis identified absolute errors from EQD2 sometimes in excess of 10%. ConclusionsAssumptions in the standard EQD2 equation are inappropriate in the context of voxelized dosimetry, where voxels within a structure, such as a target volume, may receive a dose that differs from the prescribed dose. Using EPD (or BED) instead of EQD2 would address these areas of confusion. Optimizing therapy according to biological properties in this way could provide enhanced and more reliable radiobiological input to radiotherapy treatment planning.