The two-dimensional lateral dose profiles D(x, y) of narrow photon beams, typically used for beamlet-based IMRT, stereotactic radiosurgery and tomotherapy, can be regarded as resulting from the convolution of a two-dimensional rectangular function R(x, y), which represents the photon fluence profile within the field borders, with a rotation-symmetric convolution kernel K(r). This kernel accounts not only for the lateral transport of secondary electrons and small-angle scattered photons in the absorber, but also for the 'geometrical spread' of each pencil beam due to the phase-space distribution of the photon source. The present investigation of the convolution kernel was based on an experimental study of the associated line-spread function K(x). Systematic cross-plane scans of rectangular and quadratic fields of variable side lengths were made by utilizing the linear current versus dose rate relationship and small energy dependence of the unshielded Si diode PTW 60012 as well as its narrow spatial resolution function. By application of the Fourier convolution theorem, it was observed that the values of the Fourier transform of K(x) could be closely fitted by an exponential function exp(-2pilambdanu(x)) of the spatial frequency nu(x). Thereby, the line-spread function K(x) was identified as the Lorentz function K(x) = (lambda/pi)[1/(x(2) + lambda(2))], a single-parameter, bell-shaped but non-Gaussian function with a narrow core, wide curve tail, full half-width 2lambda and convenient convolution properties. The variation of the 'kernel width parameter' lambda with the photon energy, field size and thickness of a water-equivalent absorber was systematically studied. The convolution of a rectangular fluence profile with K(x) in the local space results in a simple equation accurately reproducing the measured lateral dose profiles. The underlying 2D convolution kernel (point-spread function) was identified as K(r) = (lambda/2pi)[1/(r(2) + lambda(2))](3/2), fitting experimental results as well. These results are discussed in terms of their use for narrow-beam treatment planning.
Purpose: In this work it is shown that the volume effect of ionization chamber can be corrected by the application of a van‐Cittert iterative deconvolution algorithm. Methods: Due to their volume effect the reading of an ionisation chamber s(x) can be considered as a convolution of the true dose distribution d(x) with the lateral response function r(x) of the detector. A prominent effect of this convolution is the broadening of profile measurements in the penumbra region. For the analysis a Lorentz‐type response function a bell shaped function with wide tails and free parameter l is assumed. Representations of the “true” dose distribution are measured with a diode detector (detector with minimal spatial spread of r(x)). The free parameter for the response function l is found by systematical variation and subsequent application of an iterative deconvolution algorithm. The iterative procedure consists of a sequence of approximations for n(x) which quickly converges towards the desired true d(x). Each n(x) is numerically convolved with r(x) and from the comparison of the result with s(x), the next approximation n+1(x) is derived. The best estimate for r(x) is found for the 1 resulting in the best approximation of d(x). Results: For cylindrical ionisation chambers with different radii and volume effect the lateral response functions for 6 and 15 MV photon radiation and a variety of field sizes have been analyzed. It is shown that the penumbra broadening can be revoked with a sufficient accuracy. Conclusions: By an iterative deconvolution algorithm with a pre‐defined Lorentz‐shaped lateral response function can calculate an approximation of the true dose distribution from ionization chamber measurements. The resulting corrected dose profiles may act as the input for base data determination for treatment planning systems and may thus improve the accuracy of calculated dose distributions.
Purpose: The characteristics of the StarCheck system are evaluated. Method and Materials: The StarCheck (T10032, PTW‐Freiburg, Germany) consists of 512 ionisation chambers arranged in both main axes, as well as in both diagonal directions (chamber entrance window 2mm × 8 mm, height 5 mm, center‐to‐center distance 3mm). To allow a high spatial resolution, the narrow side is oriented perpendicular to the axes. Additional detectors are arranged within a 10 cm × 10 cm, 20 cm × 20 cm and 26 cm × 26 cm square. The center‐to‐center distance for the latter one is 5 mm, thus enabling a MLC position verification for MLCs down to 5 mm projection width. For all chambers within these square arrangements the chamber size is 4 mm × 4 mm with a height of 5 mm. Results: The effective point of measurement was found to be 7.5 mm under the surface of the array. Within an uncertainty of +/−0.1 mm no difference could be found between 6 and 15 MV. Output factor measurements utilizing the central chamber of the array showed no significant deviation from diode measurements for field sizes larger than 2 cm × 2 cm. Checks such as daily stability of accelerator output, field flatness and symmetry, light‐radiation field coincidence and MLC calibration or energy checks have been performed. The measurements agreed well with our standard systems 2D‐ARRAY 729 and QC6‐Plus (both PTW‐Freiburg, Germany). Furthermore the system allows on‐line adjustments e.g. during maintenance of the accelerator. Conclusion: The StarCheck proofed itself as a reliable and easy to handle measurement device which can be used for daily routine quality assurance as well as for maintenance adjustments of the accelerator. Due to the small detector cross section on the main axes, penumbra measurements can be performed with sufficient accuracy.
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