Session Item

The aim of the work was to determine the spatial frequency content of small radiation fields and planar dose distributions common in SRT, to ensure that the Nyquist-Shannon sampling theorem is fulfilled by detector arrays used for pre-treatment patient specific quality assurance.

One-dimensional dose profiles of 5x5 mm² to 60x60 mm² photon beams (Varian TrueBeam, 10 MV FFF, SSD = 90 cm, 10 cm depth in water) and common planar SRT dose distributions were sampled with high resolution and fitted to interpolate data sets with arbitrary sampling distances. The data sets were transformed by Discrete Fourier Transformation and examined for aliasing effects using the amplitude spectrum. The resulting Nyquist frequencies per field size or dose distribution were validated by evaluating the energy densities of the data sets under the assumption that 99.95 %, 99.97 % or 99.99 % of the spectral energy density can be assigned to the actual signal.

In addition, stereotactic VMAT plans were measured with the SRS MapCHECK (Sun Nuclear Corp. Melbourne, FL, USA) at the native sampling resolution (3.5 mm lat./long. and 2.49 mm diagonal), as well as at the double sampling resolution (1.75 mm lat./long. and 2.49 mm diagonal), which was achieved by merging two longitudinally shifted measurements. Both measured dose distributions were compared to that of the treatment plans by γ index analysis (1 mm, 1 %, TH 10%).

The Nyquist frequencies of static beams averaged over all methods suggest required sampling distances of (2.2±0.8) mm for a 5 mm beam, (2.3±0.6) mm for a 10 mm beam, (2.5±0.6) mm for a 20 mm beam, (3.3±0.9) mm for a 40 mm beam and (4.0±1.1) mm for a 60 mm beam. The required sampling distance for the SRT treatment plans proved to be (2.4 ±0.5) mm, i.e. slightly larger than the results of the smallest beam segments due to beam accumulation.

The results of the γ index analysis of the measurements with single and double detector density showed no significant differences.

The Nyquist frequency of small, static radiation fields suggests a required sampling distance upwards of (2.2±0.8) mm. The required sampling distance of a detector array additionally increases with the distance parameter of the commonly used γ index analysis and signal perturbation effects, such as volume averaging (Poppe et al. 2007), at the cost of sensitivity to errors. The theoretical analysis was validated by comparing measurements with a detector array matching the Nyquist frequency within uncertainty and repeated measurements with oversampling detector density. Consequently, previously published recommendations of 2.5 mm sampling distance for treatment verification measurements (Dempsey et al. 2005, Poppe et al. 2007) could be confirmed for SRT cases by theoretical analysis.