Determination of the beam quality correction factor k Q msr ${k}_{{Q}_{{\mathrm{msr}}}}$ for the PTW Semiflex 3D ionization chamber for the reference dosimetry at ZAP-X

Purpose

The self-shielding radiosurgery system ZAP-X consists of a 3 MV linear accelerator and eight round collimators. For this system, it is a common practice to perform the reference dosimetry using the largest 25 mm diameter collimator at a source-to-axis distance (SAD) of 45 cm with the PTW Semiflex3D chamber placed at a measurement depth of 7 mm in water. Existing dosimetry protocols do not provide correction for these measurement conditions. Therefore, Monte Carlo simulations were performed to quantify the associated beam quality correction factor $k_{Q_{\mathrm{msr}},Q_{\mathrm{ref}}}^{f_{\mathrm{msr}},f_{\mathrm{ref}}}$.

Methods

The $k_{Q_{\mathrm{msr}},Q_{\mathrm{ref}}}^{f_{\mathrm{msr}},f_{\mathrm{ref}}}$ of the Semiflex3D chamber was computed from the ratio of the absorbed doses in a water voxel and in the sensitive air volume of the chamber simulated using a ⁶⁰Co spectrum as the calibration beam quality (Q_ref) and the spectrum of the ZAP-X 3 MV photon beam (Q_msr). $k_{Q_{\mathrm{msr}},Q_{\mathrm{ref}}}^{f_{\mathrm{msr}},f_{\mathrm{ref}}}$ was computed as a function of measurement depth from 4 to 50 mm. Furthermore, detailed simulations were performed to determine the individual chamber's perturbation correction factors by modifying the chamber's model step-wise.

Results

All perturbation correction factors, except S_w,air ⋅P_fl, show depth-dependent behavior up to a depth of 15 mm. In particular, the volume-averaging P_vol and density P_dens perturbation correction factors and, consequently, the resulting gradient perturbation correction factor P_gr = P_vol∙P_dens increase with decreasing measurement depth. Therefore, $k_{Q_{\mathrm{msr}},Q_{\mathrm{ref}}}^{f_{\mathrm{msr}},f_{\mathrm{ref}}}$ is larger than unity, amounting to $1.0104\pm 0.0072$ at 7 mm measurement depth. At larger depths (> 15 mm), the $k_{Q_{\mathrm{msr}},Q_{\mathrm{ref}}}^{f_{\mathrm{msr}},f_{\mathrm{ref}}}=0.9964\pm 0.0025$ can be considered as constant.

Conclusion

At small measurement depths, $k_{Q_{\mathrm{msr}},Q_{\mathrm{ref}}}^{f_{\mathrm{msr}},f_{\mathrm{ref}}}$ was found to be depth-dependent with values larger than unity due to the gradient-related perturbation factors. Therefore, the uncertainty related to the chamber's positioning can be reduced by performing the reference dosimetry at ZAP-X at depths larger than 15 mm, where $k_{Q_{\mathrm{msr}},Q_{\mathrm{ref}}}^{f_{\mathrm{msr}},f_{\mathrm{ref}}}$ can be regarded as depth independent.