A mathematical approach to beam matching

This report provides the mathematical commissioning instructions for the evaluation of beam matching between two different linear accelerators.

Test packages were first obtained including an open beam profile, a wedge beam profile and a depth-dose curve, each from a 10×10 cm(2) beam. From these plots, a spatial error (SE) and a percentage dose error were introduced to form new plots. These three test package curves and the associated error curves were then differentiated in space with respect to dose for a first and second derivative to determine the slope and curvature of each data set. The derivatives, also known as bandwidths, were analysed to determine the level of acceptability for the beam matching test described in this study.

The open and wedged beam profiles and depth-dose curve in the build-up region were determined to match within 1% dose error and 1-mm SE at 71.4% and 70.8% for of all points, respectively. For the depth-dose analysis specifically, beam matching was achieved for 96.8% of all points at 1%/1 mm beyond the depth of maximum dose.

To quantify the beam matching procedure in any clinic, the user needs to merely generate test packages from their reference linear accelerator. It then follows that if the bandwidths are smooth and continuous across the profile and depth, there is greater likelihood of beam matching. Differentiated spatial and percentage variation analysis is appropriate, ideal and accurate for this commissioning process.

We report a mathematically rigorous formulation for the qualitative evaluation of beam matching between linear accelerators.