Analysis of the applicability of two-dimensional detector arrays in terms of sampling rate and detector size to verify scanned intensity-modulated proton therapy plans

Purpose: The introduction of advanced treatment techniques in proton therapy, such as intensity-modulated proton therapy, leads to an increased need for patient-specific quality assurance, especially an accurate treatment plan verification becomes inevitable. In this study, signal theoretical analysis of dose distributions in scanned proton therapy is performed to investigate the feasibility and limits of two-dimensional (2D) detector arrays for treatment plan verification. Methods: 2D detector arrays are characterized by two main aspects: the distance between the single detectors on the array or the sampling frequency; and the lateral response functions of a single detector. The analysis is based on single spots, reference fields and on measured and calculated dose distributions of typical intensity-modulated proton therapy treatment plans with and without range shifter. Measurements were performed with Gafchromic EBT3 films (Ashland Speciality Ingredients G.P., Bridgewater, NJ, USA), the MatriXX PT detector array (IBA Dosimetry, Schwarzenbruck, Germany) and the OCTAVIUS detector array 1500XDR (PTW-Freiburg, Germany) at an IBA Proteus PLUS proton therapy system (Ion Beam Applications, Louvain-la-Neuve, Belgium). Dose calculations were performed with the treatment planning system RayStation 6 or 8 (RaySearch Laboratories, Sweden). Results: The Fourier analysis of the data of the treatment planning system and film measurements show maximum frequencies of 0.06/mm for the plan with range shifter and 0.083/mm for the plan without range shifter. According to the Nyquist theorem, this corresponds to minimum required sampling distances of 8.3 and 6 mm, respectively. By comparison, the sampling distances of the arrays of 7.6 mm (MatriXX PT) and 7.1 mm (OD1500XDR) are sufficient to reconstruct the dose distributions adequately from measurements if range shifters are used, whereas some fields of the plans without range shifter violated the Nyquist requirement. The lateral dose response functions of the single detectors within the arrays have clearly higher frequencies than the treatment plans and thus the volume effect only slightly influences the measurements. Consequently, the array measurements show high gamma passing rates with at least 96 % and a good agreement between the investigated line profiles. Conclusion: The results indicate that the detector dimensions and sampling distances of the arrays are in most studied cases adequate not to substantially influence the measurement process when they are used for analyzing typical intensity-modulated proton therapy treatment plans. Nevertheless, clinical conditions have been identified, for instance treatment plans without range shifter, under which the Nyquist theorem is violated such that a full representation of the dose distributions with the measurements is not feasible. In these cases, analysis of measurements is limited to pointwise comparisons.