Spatial resolution of 2D ionization chamber arrays for IMRT dose verification: single-detector size and sampling step width

Abstract

The spatial resolution of 2D detector arrays equipped with ionization chambers or diodes, used for the dose verification of IMRT treatment plans, is limited by the size of the single detector and the centre-to-centre distance between the detectors. Optimization criteria with regard to these parameters have been developed by combining concepts of dosimetry and pattern analysis. The 2D-ARRAY Type 10024 (PTW-Freiburg, Germany), single-chamber cross section 5 x 5 mm(2), centre-to-centre distance between chambers in each row and column 10 mm, served as an example. Additional frames of given dose distributions can be taken by shifting the whole array parallel or perpendicular to the MLC leaves by, e.g., 5 mm. The size of the single detector is characterized by its lateral response function, a trapezoid with 5 mm top width and 9 mm base width. Therefore, values measured with the 2D array are regarded as sample values from the convolution product of the accelerator generated dose distribution and this lateral response function. Consequently, the dose verification, e.g., by means of the gamma index, is performed by comparing the measured values of the 2D array with the values of the convolution product of the treatment planning system (TPS) calculated dose distribution and the single-detector lateral response function. Sufficiently small misalignments of the measured dose distributions in comparison with the calculated ones can be detected since the lateral response function is symmetric with respect to the centre of the chamber, and the change of dose gradients due to the convolution is sufficiently small. The sampling step width of the 2D array should provide a set of sample values representative of the sampled distribution, which is achieved if the highest spatial frequency contained in this function does not exceed the 'Nyquist frequency', one half of the sampling frequency. Since the convolution products of IMRT-typical dose distributions and the single-detector lateral response function have no or very small frequency contributions beyond 0.1 mm(-1), the mathematical approach introduced by Nyquist and Shannon shows that the sampling frequency of 0.2 mm(-1) is appropriate. Overall it is shown that the spatial resolution of the 2D-ARRAY Type 10024 is appropriate for the dose verification of IMRT plans. The insights obtained are also applied in the discussion of other available two-dimensional detector arrays.

Dosimetric validation and clinical implementation of two 3D dose verification systems for quality assurance in volumetric‐modulated arc therapy techniques

“…Strictly, Mobius3D‐ and COMPASS‐calculated values in planar analysis should be convolved with the detector response function and then compared to MatriXX measurements (47) . This problem, described as a limitation of the present study, is not observed in measurement‐based dose reconstruction performed by COMPASS because the system inherently applies this correction.…”

Evaluation of semiempirical VMAT dose reconstruction on a patient dataset based on biplanar diode array measurements

“…The White Paper states: “Due to the highly irregular nature and limited resolution of the energy fluence matrix, deviations between calculated and measured dose in the Delta 4 detector positions are more frequent in the IMRT case, … Deviations are primarily localized to regions of the rapid dose changes, indicating distances to agreement less than the pixel size, i. e. $<6\hspace{0.17em}\text{mm}$.” It is clear that when the penumbra of individual segments is not represented with sufficient resolution, the superposition of many segments in a modulated beam would lead to rather inaccurate calculations. This is effectively equivalent to calculating modulated beams with a $6\times 6\hspace{0.17em}{\text{mm}}^2$ pixel size, while it is well established in the literature that segmented beam calculations require 2.5 mm voxel grid resolution to faithfully reproduce encountered gradients 28 , 29 , 30 . This explains poor dosimetric agreement for VMAT plans found in Table 2 and 4, 5, 6.…”

On flattening filter‐free portal dosimetry

“…The most commonly used dose distribution measurement devices currently available are film 5 , 6 (radiochromic), arrays 7 , 8 (both ion chamber and diodes), and EPIDs. Film has a high resolution, but its use is very time‐consuming; it needs time before scanning, the scanning itself, and a calibration process.…”