Fourier deconvolution reveals the role of the Lorentz function as the convolution kernel of narrow photon beams.

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.

Mapping radiation quality inside photon-irradiated absorbers by means of a twin-chamber method.

In photon-beam radiotherapy, the absorbed dose in an irradiated object contains a contribution by energy-degraded photons originating from Compton scatter processes at parts of the treatment head and within the absorber itself. These low-energy spectral components may lead to changes in the response of non-ideally water-equivalent radiation detectors, such as Si diodes and radiographic films, in the water/tissue dose conversion factors and in the relative biological effectiveness (RBE). As a simple means of accounting for these changes in spectral quality, the Monte Carlo calculated fraction of the kerma or absorbed dose contributed by scattered photons with energies not exceeding a certain cut-off value has previously been proposed as a useful parameter. In this paper, we present an equivalent experimental approach, providing a means for the spatial mapping of radiation quality. Its applicability will be demonstrated for the case of (60)Co and 6 MV photons. A twin-chamber combination of a Farmer type ionization chamber, equipped with a graphited PMMA outer electrode, and a chamber of the same design, but with an outer electrode made from copper, has been developed. The measured quantity is the signal ratio (SR) of the copper wall and graphited wall chambers. A correlation between the SR and the fraction of the air kerma respectively of the absorbed dose to water, contributed by photons with energies not exceeding 200 keV, has been established at a Theratron 780-C (60)Co teletherapy unit and at a Siemens Primus 6 MV linear accelerator. We also describe a two-dimensional version of the twin-chamber method using the PTW 2D-Array 256. Typical trends of parameter SR with depth and off-axis distance in water-equivalent phantoms have been observed. Thereby, a simple experimental method for the space-resolved assessment of the dose fraction attributable to low-energy Compton scattered photons can be presented as an innovative instrument of describing radiation quality in radiotherapy.

A new reference-type ionization chamber with direction-independent response for use in small-field photon-beam dosimetry - An experimental and Monte Carlo study.

The frequently applied narrow and non-standard transverse dose profiles of intensity modulated photon-beam radiotherapy, lacking lateral secondary electron equilibrium, require the use of high-resolution dosimetry detectors, and small air-filled detectors are recommended as the reference detectors for cross-calibration of the high-resolution detectors. The present study focuses on the dosimetric properties of a novel cylindrical ionization chamber, the PTW Semiflex 3D 31021. The chamber's effective point of measurement was found to lie at (0.41±0.04) r downstream the tip of the inner surface of the spherical front wall in the axial orientation and (0.46±0.04) r upstream the chamber axis in the radial orientation. Due to its symmetrical design, the sigma values of its lateral dose response functions for all chamber's orientations are the same (2.10±0.05mm). The polarity correction factors obtained in this work do not exceed 0.1% and the saturation correction factor was below 1% up to a dose-per-pulse value of 0.956mGy. The radiation quality correction factor kQ of the chamber as a function of the tissue-phantom-ratio, TPR20,10, has been calculated by Monte Carlo simulation and has been determined experimentally at the German Metrology Institute (Physikalisch-Technische Bundesanstalt, PTB). The values of the non-reference condition correction factor kNR have been Monte-Carlo-calculated for use of the chamber at various depths and field sizes.

Dosimetric characteristics of an unshielded p-type Si diode: linearity, photon energy dependence and spatial resolution.

The unshielded Si diode PTW 60012, used for accurate measurements of the transversal dose profiles of narrow photon beams, has been investigated with regard to its linearity, photon energy dependence and spatial resolution. The diode shows a slight supralinearity, i.e., increase of the response with pulse dose, by 3% over the pulse dose range 0.1 to 0.8 mGy. In p-type silicon, supralinearity results from the increased chance for radiation-induced electrons to escape recombination when the pulse dose increases. Over the energy range from 6 to 15 MV, the response decreases by about 4%. This small variation of the response results from partial compensation between the influences of the secondary electron energy on the mass stopping power ratio silicon/water and on electron backscattering from the silicon chip. The lateral response function of the examined diode has a full half width of 1.3 mm. Dose profiles of 5 mm half-width can still be recorded with negligible error.

The output factor correction as function of the photon beam field size - direct measurement and calculation from the lateral dose response functions of gas-filled and solid detectors.

The first aim of this study has been to extend the systematic experimental study of the field size dependence of the output factor correction for three micro-ionization chambers (PTW 31014, PTW 31022 and IBA Razor chamber), two silicon diodes (PTW 60017 and IBA Razor Diode) and the synthetic diamond detector microDiamond (PTW 60019) in a 6 MV photon beam down to an effective field side length of 2.6mm, and to summarize the present knowledge of this factor by treating it as a function of the dosimetric field size. In order to vary the dosimetric field size over this large range, output factors measurements were performed at source-to-surface distances of 60cm and 90cm. Since the output factors obtained with the organic scintillation detector Exradin W1 (Standard Imaging, Middleton, USA) at all field sizes closely agreed with those measured by EBT3 radiochromic films (ISP Corp, Wayne, USA), the scintillation detector served as the reference detector. The measured output correction factors reflect the influences of the volume averaging and density effects upon the uncorrected output factor values. In case of the microDiamond detector these opposing influences result in output factor correction values less than 1 for moderately small field sizes and larger than 1 for very small field sizes. Our results agree with most of the published experimental as well as Monte-Carlo simulated data within detector-specific limits of uncertainty. The dosimetric field side length has been identified as a reliable determinant of the output factor correction, and typical functional curve shapes of the field-size dependent output factor correction vs. dosimetric field side length have been associated with gas-filled, silicon diode and synthetic diamond detectors. The second aim of this study has been a novel, semi-empirical approach to calculate the field-size dependent output correction factors of small photon detectors by convolving film measured true dose profile data with measured lateral response functions of the detectors. To achieve this, the set of previously published 2D lateral dose response functions was complemented by those of the novel detectors PTW PinPoint chamber 31022 (PTW Freiburg, Freiburg, Germany), Razor chamber and Razor Diode (IBA Dosimetry, Schwarzenbruck, Germany). The output correction factors calculated from the lateral dose response functions closely fit with the directly measured output correction factors, thus supporting the latter by an independent method.

2D convolution kernels of ionization chambers used for photon-beam dosimetry in magnetic fields: the advantage of small over large chamber dimensions.

This study aims at developing an optimization strategy for photon-beam dosimetry in magnetic fields using ionization chambers. Similar to the familiar case in the absence of a magnetic field, detectors should be selected under the criterion that their measured 2D signal profiles M(x,y) approximate the absorbed dose to water profiles D(x,y) as closely as possible. Since the conversion of D(x,y) into M(x,y) is known as the convolution with the 'lateral dose response function' K(x-ξ, y-η) of the detector, the ideal detector would be characterized by a vanishing magnetic field dependence of this convolution kernel (Looe et al 2017b Phys. Med. Biol. 62 5131-48). The idea of the present study is to find out, by Monte Carlo simulation of two commercial ionization chambers of different size, whether the smaller chamber dimensions would be instrumental to approach this aim. As typical examples, the lateral dose response functions in the presence and absence of a magnetic field have been Monte-Carlo modeled for the new commercial ionization chambers PTW 31021 ('Semiflex 3D', internal radius 2.4 mm) and PTW 31022 ('PinPoint 3D', internal radius 1.45 mm), which are both available with calibration factors. The Monte-Carlo model of the ionization chambers has been adjusted to account for the presence of the non-collecting part of the air volume near the guard ring. The Monte-Carlo results allow a comparison between the widths of the magnetic field dependent photon fluence response function K M(x-ξ, y-η) and of the lateral dose response function K(x-ξ, y-η) of the two chambers with the width of the dose deposition kernel K D(x-ξ, y-η). The simulated dose and chamber signal profiles show that in small photon fields and in the presence of a 1.5 T field the distortion of the chamber signal profile compared with the true dose profile is weakest for the smaller chamber. The dose responses of both chambers at large field size are shown to be altered by not more than 2% in magnetic fields up to 1.5 T for all three investigated chamber orientations.

The 1D lateral dose response functions of photon-dosimetry detectors in magnetic fields-measurement and Monte-Carlo simulation.

The present study is concerned with clinical photon-beam dosimetry at radiotherapy units combined with magnetic resonance imaging devices. Due to the superposed constant magnetic field, the deflections of the secondary electron trajectories by the Lorentz force not only influence the 2D dose distribution, D(x,y), in water phantoms, but furthermore modify the secondary electron transport within the detectors and thereby the detectors' signal profiles, M(x,y), across the photon beams. This second effect can be represented by the lateral dose response function, K(x,y), the convolution kernel transforming D(x,y) into M(x,y) via the convolution M(x,y) = D(x,y) * K(x,y). The 1D functions K(x) of a set of commercial gas-filled and solid-state photon-beam detectors were experimentally determined using a slit beam geometry together with a constant, homogeneous magnetic field of up to 1.42 T. As predicted by a recent Monte-Carlo study (Looe et al 2017b Phys. Med. Biol. 62 5131-48), the functions K(x) of these detectors are shown experimentally to be distorted in magnetic field. For the larger Semiflex 3D 31021 chamber, the FWHM value of K(x) decreases from 4.9 mm for the field free (0 T) case to 4.8 mm in 0.35 T and 4.1 mm in 1.42 T magnetic field, whereas the FWHM value of the smaller PinPoint 3D 31022 chamber decreases from 2.8 mm for the field free case to 2.6 mm in 1.42 T magnetic field. The FWHM values of the semiconductor detectors are not modified in magnetic fields. Additionally, the symmetry of K(x) is shown to be distorted in magnetic field. Using a 10 mm wide field as example, the signal profiles, M(x), predicted by the measured and simulated K(x) by convolution with D(x) (measured with EBT3 film) agree within 3% of the maximum value to the measured M(x) for all detectors, except for the silicon diode detector if the measured K(x) was used, where deviations of around 5% were observed at the field border.

Reference conditions for ion-chamber based HDR brachytherapy dosimetry and for the calibration of high-resolution solid detectors.

The aim of this study has been to develop a two-step method of in-phantom dosimetry around a brachytherapy 192Ir photon source. The first step is to measure the absorbed dose rate to water with a calibrated ionization chamber under reference conditions, the second to cross-calibrate, under these conditions, small solid-state detectors such as silicon diodes, synthetic diamond or scintillation detectors suited for spatially resolved dose rate measurements at other, particularly at smaller source axis distances in the water phantom. This two-step approach constitutes a method for in-phantom dosimetry in brachytherapy, analogous to the "small calibration field" commonly used in teletherapy to provide the reference conditions for the cross-calibration of high-resolution detectors. Under reference conditions, all known corrections for radiation quality, volume averaging and position of the chamber's effective point of measurement (EPOM) have to be applied. The study is therefore particularly devoted to (1) the experimental determination of the position of the source axis, (2) a general formulation for the volume averaging correction factor of small ionization chambers and (3) the experimental determination of the EPOM positions for the PinPoint chamber 31014 and the 3D-PinPoint chamber PTW 31022 (both PTW Freiburg, Germany). The distance of 30mm from the source axis was chosen as the reference condition for cross calibrations. This concept is realized with the instrumentation available in a hospital, a scanning-type water phantom, a software package for small field dosimetry and detectors typically used in clinical routine dosimetry. The present development of a method of in-phantom dose measurement under 192Ir brachytherapy conditions was performed in recognition of the primary role of dose calculations, e.g. according to the AAPM TG43 recommendations. But in addition, the methodology tested here is paving a practicable way for the experimental check of typical dose values under clinical conditions, should the need arise.

Magnetic fields are causing small, but significant changes of the radiochromic EBT3 film response to 6 MV photons.

The optical density (OD) of EBT3 radiochromic films (Ashland Specialty Ingredients, Bridgewater, NJ, USA) exposed to absorbed doses to water up to D = 20 Gy in magnetic fields of B = 0.35 and 1.42 T was measured in the three colour channels of an Epson Expression 10000XL flatbed scanner. A 7 cm wide water phantom with fixed film holder was placed between the pole shoes of a constant-current electromagnet with variable field strength and was irradiated by a 6 MV photon beam whose axis was directed at right angles with the field lines. The doses at the film position at water depth 5 cm were measured with a calibrated ionization chamber when the magnet was switched off and were converted to the doses in presence of the magnetic field via the monitor units and by a Monte Carlo-calculated correction accounting for the slight change of the depth dose curves in magnetic fields. In the presence of the 0.35 and 1.42 T fields small negative changes of the OD values at given absorbed doses to water occurred and just significantly exceeded the uncertainty margin given by the stochastic and the uncorrected systematic deviations. This change can be described by a +2.1% change of the dose values needed to produce a given optical density in the presence of a 1.42 T field. The thereby modified OD versus D function remained unchanged irrespective of whether the original short film side-the preference direction of the monomer crystals of the film-was directed parallel or orthogonal to the magnetic field. The 'orientation effect', the difference between the optical densities measured in the 'portrait' or 'landscape' film positions on the scanner bed caused by the reflection of polarised light in the scanner's mirror system, remained unaltered after EBT3 film exposure in magnetic fields. An independent optical bench investigation of EBT3 films exposed to doses of 10 and 20 Gy at 0.35 and 1.42 T showed that the direction of the electric vector of polarised light experiencing the largest transmission through EBT3 films remained unaltered after film exposure in the magnetic fields. The observed small modification of the OD versus D curve of the radiochromic film EBT3 in the range up to 20 Gy and 1.42 T, hardly exceeding the experimental uncertainty margin, numerically confirms other recent studies on EBT3 film. A stronger magnetic field effect had been observed with the previous product EBT2 exposed to 60Co gamma radiation at 0.35 T.

Determination of the active volumes of solid-state photon-beam dosimetry detectors using the PTB proton microbeam.

PURPOSE: This study aims at the experimental determination of the diameters and thicknesses of the active volumes of solid-state photon-beam detectors for clinical dosimetry. The 10 MeV proton microbeam of the PTB (Physikalisch-Technische Bundesanstalt, Braunschweig) was used to examine two synthetic diamond detectors, type microDiamond (PTW Freiburg, Germany), and the silicon detectors Diode E (PTW Freiburg, Germany) and Razor Diode (Iba Dosimetry, Germany). The knowledge of the dimensions of their active volumes is essential for their Monte Carlo simulation and their applications in small-field photon-beam dosimetry. METHODS: The diameter of the active detector volume was determined from the detector current profile recorded by radially scanning the proton microbeam across the detector. The thickness of the active detector volume was determined from the detector's electrical current, the number of protons incident per time interval and their mean stopping power in the active volume. The mean energy of the protons entering this volume was assessed by comparing the measured and the simulated influence of the thickness of a stack of aluminum preabsorber foils on the detector signal. RESULTS: For all detector types investigated, the diameters measured for the active volume closely agreed with the manufacturers' data. For the silicon Diode E detector, the thickness determined for the active volume agreed with the manufacturer's data, while for the microDiamond detectors and the Razor Diode, the thicknesses measured slightly exceeded those stated by the manufacturers. DISCUSSION: The PTB microbeam facility was used to analyze the diameters and thicknesses of the active volumes of photon dosimetry detectors for the first time. A new method of determining the thickness values with an uncertainty of ±10% was applied. The results appear useful for further consolidating detailed geometrical knowledge of the solid-state detectors investigated, which are used in clinical small-field photon-beam dosimetry.

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

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.

The energy dependence of the lateral dose response functions of detectors with various densities in photon-beam dosimetry.

The lateral dose response function is a general characteristic of the volume effect of a detector used for photon dosimetry in a water phantom. It serves as the convolution kernel transforming the true absorbed dose to water profile, which would be produced within the undisturbed water phantom, into the detector-measured signal profile. The shape of the lateral dose response function characterizes (i) the volume averaging attributable to the detector's size and (ii) the disturbance of the secondary electron field associated with the deviation of the electron density of the detector material from the surrounding water. In previous work, the characteristic dependence of the shape of the lateral dose response function upon the electron density of the detector material was studied for 6 MV photons by Monte Carlo simulation of a wall-less voxel-sized detector (Looe et al 2015 Phys. Med. Biol. 60 6585-07). This study is here continued for 60Co gamma rays and 15 MV photons in comparison with 6 MV photons. It is found (1) that throughout these photon spectra the shapes of the lateral dose response functions are retaining their characteristic dependence on the detector's electron density, and (2) that their energy-dependent changes are only moderate. This appears as a practical advantage because the lateral dose response function can then be treated as practically invariant across a clinical photon beam in spite of the known changes of the photon spectrum with increasing distance from the beam axis.

Evaluation of water-mimicking solid phantom materials for use in HDR and LDR brachytherapy dosimetry.

In modern HDR or LDR brachytherapy with photon emitters, fast checks of the dose profiles generated in water or a water-equivalent phantom have to be available in the interest of patient safety. However, the commercially available brachytherapy photon sources cover a wide range of photon emission spectra, and the range of the in-phantom photon spectrum is further widened by Compton scattering, so that the achievement of water-mimicking properties of such phantoms involves high requirements on their atomic composition. In order to classify the degree of water equivalence of the numerous commercially available solid water-mimicking phantom materials and the energy ranges of their applicability, the radial profiles of the absorbed dose to water, D w, have been calculated using Monte Carlo simulations in these materials and in water phantoms of the same dimensions. This study includes the HDR therapy sources Nucletron Flexisource Co-60 HDR (60Co), Eckert und Ziegler BEBIG GmbH CSM-11 (137Cs), Implant Sciences Corporation HDR Yb-169 Source 4140 (169Yb) as well as the LDR therapy sources IsoRay Inc. Proxcelan CS-1 (131Cs), IsoAid Advantage I-125 IAI-125A (125I), and IsoAid Advantage Pd-103 IAPd-103A (103Pd). Thereby our previous comparison between phantom materials and water surrounding a Varian GammaMed Plus HDR therapy 192Ir source (Schoenfeld et al 2015) has been complemented. Simulations were performed in cylindrical phantoms consisting of either water or the materials RW1, RW3, Solid Water, HE Solid Water, Virtual Water, Plastic Water DT, Plastic Water LR, Original Plastic Water (2015), Plastic Water (1995), Blue Water, polyethylene, polystyrene and PMMA. While for 192Ir, 137Cs and 60Co most phantom materials can be regarded as water equivalent, for 169Yb the materials Plastic Water LR, Plastic Water DT and RW1 appear as water equivalent. For the low-energy sources 106Pd, 131Cs and 125I, only Plastic Water LR can be classified as water equivalent.

The "collimator monitoring fill factor" of a two-dimensional detector array, a measure of its ability to detect collimation errors.

PURPOSE: Two-dimensional detector arrays are routinely used for constancy checks and treatment plan verification in photon-beam radiotherapy. In addition to the spatial resolution of the dose profiles, the "coverage" of the radiation field with respect to the detection of any beam collimation deficiency appears as the second characteristic feature of a detector array. The here proposed "collimator monitoring fill factor" (CM fill factor) has been conceived to serve as a quantitative characteristic of this "coverage". METHODS: The CM fill factor is defined as the probability of a 2D array to detect any collimator position error. Therefore, it is represented by the ratio of the "sensitive area" of a single detector, in which collimator position errors are detectable, and the geometrical "cell area" associated with this detector within the array. Numerical values of the CM fill factor have been Monte Carlo simulated for 2D detector arrays equipped with air-vented ionization chambers, liquid-filled ionization chambers and diode detectors and were compared with the "FWHM fill factor" defined by Gago-Arias et al. (2012). RESULTS: For arrays with vented ionization chambers, the differences between the CM fill factor and the FWHM fill factor are moderate, but occasionally the latter exceeds unity. For narrower detectors such as liquid-filled ionization chambers and Si diodes and for small sampling distances, large differences between the FWHM fill factor and the CM fill factor have been observed. These differences can be explained by the shapes of the fluence response functions of these narrow detectors. CONCLUSIONS: A new parameter "collimator monitoring fill factor" (CM fill factor), applicable to quantitate the collimator position error detection probability of a 2D detector array, has been proposed. It is designed as a help in classifying the clinical performance of two-dimensional detector arrays in photon-beam radiotherapy.

Magnetic field influences on the lateral dose response functions of photon-beam detectors: MC study of wall-less water-filled detectors with various densities.

The distortion of detector reading profiles across photon beams in the presence of magnetic fields is a developing subject of clinical photon-beam dosimetry. The underlying modification by the Lorentz force of a detector's lateral dose response function-the convolution kernel transforming the true cross-beam dose profile in water into the detector reading profile-is here studied for the first time. The three basic convolution kernels, the photon fluence response function, the dose deposition kernel, and the lateral dose response function, of wall-less cylindrical detectors filled with water of low, normal and enhanced density are shown by Monte Carlo simulation to be distorted in the prevailing direction of the Lorentz force. The asymmetric shape changes of these convolution kernels in a water medium and in magnetic fields of up to 1.5 T are confined to the lower millimetre range, and they depend on the photon beam quality, the magnetic flux density and the detector's density. The impact of this distortion on detector reading profiles is demonstrated using a narrow photon beam profile. For clinical applications it appears as favourable that the magnetic flux density dependent distortion of the lateral dose response function, as far as secondary electron transport is concerned, vanishes in the case of water-equivalent detectors of normal water density. By means of secondary electron history backtracing, the spatial distribution of the photon interactions giving rise either directly to secondary electrons or to scattered photons further downstream producing secondary electrons which contribute to the detector's signal, and their lateral shift due to the Lorentz force is elucidated. Electron history backtracing also serves to illustrate the correct treatment of the influences of the Lorentz force in the EGSnrc Monte Carlo code applied in this study.

The 'cutting away' of potential secondary electron tracks explains the effects of beam size and detector wall density in small-field photon dosimetry.

The well-known field-size dependent overresponse in small-field photon-beam dosimetry of solid-state detectors equipped with very thin sensitive volumes, such as the PTW microDiamond, cannot be caused by the photon and electron interactions within these sensitive layers because they are only a few micrometers thick. The alternative explanation is that their overresponse is caused by the combination of two effects, the modification of the secondary electron fluence profile (i) by a field size too small to warrant lateral secondary electron equilibrium and (ii) by the density-dependent electron ranges in the structural detector materials placed in front of or backing the sensitive layer. The present study aims at the numerical demonstration and visualization of this combined mechanism. The lateral fluence profiles of the secondary electrons hitting a 1 µm thick scoring layer were Monte-Carlo simulated by modelling their generation and transport in the upstream or downstream adjacent layers of thickness 0.6 mm and densities from 0.0012 to 3 g cm-3, whose atomic composition was constantly kept water-like. The scoring layer/adjacent layer sandwich was placed in an infinite water phantom irradiated by circular 60Co, 6 MV and 15 MV photon beams with diameters from 3 to 40 mm. The interpretation starts from the ideal case of lateral secondary electron equilibrium, where the Fano theorem excludes any density effect. If the field size is then reduced, electron tracks potentially originating from source points outside the field border will then be numerically 'cut away'. This geometrical effect reduces the secondary electron fluence at the field center, but the magnitude of this reduction also varies with the density-dependent electron ranges in the adjacent layers. This combined mechanism, which strongly depends on the photon spectrum, explains the field size and material density effect on the response of detectors with very thin sensitive layers used in small-field photon-beam dosimetry.

The practical application of scintillation dosimetry in small-field photon-beam radiotherapy.

Plastic scintillation detectors are a new instrument of stereotactic photon-beam dosimetry. The clinical application of the plastic scintillation detector Exradin W1 at the Siemens Artiste and Elekta Synergy accelerators is a matter of current interest. In order to reduce the measurement uncertainty, precautions have to be taken with regard to the geometrical arrangement of the scintillator, the light-guide fiber and the photodiode in the radiation field. To determine the "Cerenkov light ratio" CLR with a type A uncertainty below 1%, the Cerenkov calibration procedure for small-field measurements based on the two-channel spectral method was used. Output factors were correctly measured with the W1 for field sizes down to 0.5×0.5cm2 with a type A uncertainty of 1.8%. Measurements of small field dose profiles and percentage depth dose curves were carried out with the W1 using automated water phantom profile scans, and a type A uncertainty for dose maxima of 1.4% was achieved. The agreement with a synthetic diamond detector (microDiamond, PTW Freiburg) and a plane parallel ionization chamber (Roos chamber, PTW Freiburg) in relative dose measurements was excellent. In oversight of all results, the suitability of the plastic scintillation detector Exradin W1 for clinical dosimetry under stereotactic conditions, in particular the tried and tested procedures for CLR determination, output factor measurement and automated dose profile scans in water phantoms, have been confirmed.

Two-dimensional ionization chamber arrays for IMRT plan verification.

In this paper we describe a concept for dosimetric treatment plan verification using two-dimensional ionization chamber arrays. Two different versions of the 2D-ARRAY (PTW-Freiburg, Germany) will be presented, a matrix of 16 x 16 chambers (chamber cross section 8 mm x 8 mm; the distance between chamber centers, 16 mm) and a matrix of 27 x 27 chambers (chamber cross section 5 mm x 5 mm; the distance between chamber centers is 10 mm). The two-dimensional response function of a single chamber is experimentally determined by scanning it with a slit beam. For dosimetric plan verification, the expected two-dimensional distribution of the array signals is calculated via convolution of the planned dose distribution, obtained from the treatment planning system, with the two-dimensional response function of a single chamber. By comparing the measured two-dimensional distribution of the array signals with the expected one, a distribution of deviations is obtained that can be subjected to verification criteria, such as the gamma index criterion. As an example, this verification method is discussed for one sequence of an IMRT plan. The error detection capability is demonstrated in a case study. Both versions of two-dimensional ionization chamber arrays, together with the developed treatment plan verification strategy, have been found to provide a suitable and easy-to-handle quality assurance instrument for IMRT.

The dose-area product, a new parameter for the dosimetry of narrow photon beams.

In the dosimetry of narrow photon fields with side lengths of the order of 1 cm, the traditional parametrisation via the absolute dose on the beam axis and the relative lateral dose distribution has to deal with the difficulty to find sufficiently small detectors and to adjust them accurately on the narrow-beam axis. This can be avoided by reconsidering the parametrisation, using as normalization factor the surface integral of the dose in the plane perpendicular to the beam axis, abbreviated as the "dose-area product" (DAP). We investigated and confirmed the ability of a large-area parallel-plate ionisation chamber, with a sensitive volume shaped as a flat cylinder of 81.6 mm diameter and 2 mm thickness, to perform the integration over the full lateral dose profile of narrow photon beams with side lengths up to 5 cm. The lateral adjustment of this large-area detector relative to a narrow photon beam is not critical. The large-area ionisation chamber was calibrated in terms of the DAP by reference to a 0.3 cm3 ionisation chamber. A field-size dependent "modified output factor" was defined as the ratio of the DAP measured at 5 cm phantom depth for 100 cm SSD, and the monitor reading. A prominent phenomenon of narrow photon fields is the field-size and source-distance independence of the relative axial profile of the DAP as function of the thickness of a pre-absorber or of the depth in a phantom. For narrow-beam treatment planning in IMRT, the DAP is combined with the energy- and field size-dependent relative lateral dose distribution which is represented, for example, by a Gaussian convolution kernel. Another useful feature of the DAP is the possibility of its direct control during patient irradiation by means of an on-line monitor with spatial resolution, arranged in the accessory holder.

Changes of the optical characteristics of radiochromic films in the transition from EBT3 to EBT-XD films.

A new type of radiochromic film, the EBT-XD film, has been introduced with the aim to reduce the orientation effect and the lateral response artifact occurring in the use of radiochromic films together with flatbed scanners. The task of the present study is to quantify the changes of optical characteristics involved with the transition from the well-known EBT3 films to the new EBT-XD films, using the optical bench arrangement already applied by Schoenfeld et al (2014 Phys. Med. Biol. 59 3575-97). Largely reduced polarization effects and the almost complete loss of the anisotropy of the scattered light produced in a radiation-exposed film have been observed. The Rayleigh-Debye-Gans theory is used to understand these optical changes as arising from the reduced length-to-width ratio of the LiPCDA polymer crystals in the active layer of the EBT-XD film. The effect of these changes on the flatbed scanning artifacts will be shortly addressed, but treated in more detail in a further paper.