Parameterization of electron beam output factor

• We showed a simple equation for quick MU calculation for electron beams.
• The proposed formula only depends on the beam energy and cutout radius.
• The accuracy of MU calculation was within ±3% for beams from two linacs.
• This method will be helpful for double-check with minimal efforts.

Electron beam dose distribution is dependent on the beam energy and complicated trajectory of particles. Recent treatment planning systems using Monte Carlo calculation algorithm provide accurate dose calculation. However, double check of monitor units (MUs) based on an independent algorithm is still required. In this study, we have demonstrated single equation that reproduces the measured relative output factor (ROF) that can be used for MU calculation for electron radiotherapy. Electron beams generated by an iX (Varian Medical Systems) and a PRIMUS (Siemens) accelerator were investigated. For various energies of electron beams, the ROF at respective dmax were measured using diode detector in a water phantom at SSD of 100 cm. Curve fitting was performed with an exponential generalized equation ROF = α(β – e−γR) including three variables (α, β, γ) as a function of field radius and electron energy. The correlation coefficients between the ROF measured and that calculated by the equation were greater than 0.998. For ROF of Varian electron beams, the average values of all fitting formulas were applied for two of the constants; α and β. The parameter γ showed good agreement with the quadratic approximation as a function of mean energy at surface (E0). The differences between measured and calculated ROF values were within ±3% for beams with cutout radius of ≥1.5 cm for electron beams with energies from 6 MeV to 15 MeV. The proposed formula will be helpful for double-check of MUs, as it requires minimal efforts for MU calculation.