For the calculation, we adapted the AAPM guideline AAPM task group 224: Comprehensive proton therapy machine quality assurance (wiley.com) and the Electron Beam Quality Parameters and Absorbed Dose Distributions from Therapy Accelerators (https://doi.org/10.1007/978-3-642-67727-4_4). The data were extracted manually from the figures in the papers with WebPlotDigitizer (Ankit Rohatgi, Version 4.7. 2024). The parameters analysed are:

Lateral profile

• The lateral uniformity, defined about the centre of the beam profile, at 80% of the dose distribution. It is calculated as $F_{lp} = \left( \frac{d_{lp, max}-d_{lp, min}}{d_{lp, max}+d_{lp, min}} \right)$ where $d_{lp, max}$ and $d_{lp, min}$ are the maximum and minimum absorbed dose values in the lateral beam profile measured within the 80% dose profile.

Distal profile

• The depth dose (distal) uniformity: defined as $F_{lp} = \left( \frac{d_{lp, max}-d_{lp, min}}{d_{lp, max}+d_{lp, min}} \right)$ where $d_{lp, max}$ and $d_{lp, min}$ are the maximum and minimum absorbed dose values in the depth dose profile within a defined region.

  For PBS, in particular:

  • The SOBP width or layer stacking consistency (e.g.,the distance in water between the proximal and distal 90% dose or simply $d_d90-d_p90$.)

  For electrons in particular:

  • The therapeutic Range (R80) is defined as the depth interval within which the absorbed dose exceeds 80% of its maximum value. For electrons, the depth dose uniformity is not given (as it is usually (1 - 0.8)/(1 + 0.8) = 11%)