Detector response

In radiotherapy dosimetry it is well known that the characteristics of a detector may affect its response to ionizing radiation considerably. For example, the particle fluence that is sampled by the detector differs, sometimes substantially, from the fluence that exists in a homogeneous medium in the absence of the detector. This is caused by the size, shape and materials in the detector, which result in deviations from the ideal small volume concept underlying the Bragg–Gray principle. For a real detector, the application of Bragg–Gray cavity theory based on medium-to-detector stopping-power ratios requires a modification using perturbation correction factors. All dosimetry protocols for conventional reference dosimetry based on a theoretical determination of all perturbation correction factors necessary to correct the detector response from the calibration beam quality to the user’s beam quality explicitly or implicitly include such perturbation correction factors [1, 2, 39, 40]. When measurements are performed in CPE or TCPE conditions, any variation in stopping-power ratio

is evaluated independently of perturbation correction factors for wall effects, the presence, if any, of a central electrode, electron in-scattering effects, volume of the medium displaced by the detector, etc. [41], all assumed to be small and independent. In recent years there has been a renewed interest in accurate determinations of perturbation correction factors for ionization chambers. In particular, Monte Carlo methods have analysed in detail the various types of perturbation effects in a stepwise fashion [42–44], leading to a total perturbation correction factor for an ionization chamber in a given beam quality.

Studies on perturbation effects of small ionization chambers in small static beams are scarce. One of the earliest comprehensive studies pertaining to this area is the work by Crop et al. [45]. The results of this Monte Carlo study, of which the data at the centre of a 0.8 cm × 0.8 cm field are shown in Fig. 6, indicated that the central electrode and wall perturbation correction factors were, even though different from those in a broad beam, close to unity. The major perturbations were caused by the volume averaging effect and the difference between the mass density of the detector and that of the medium, and both corrections were rather large and of similar size. The perturbations were considerably larger for off-axis measurements. This shows that for small fields, perturbation effects even for small detectors are considerably larger than for conventional ionization chambers in broad beams. In the smallest fields of interest, some perturbations become so large

0.55 symbols), and according to the model of Palmans [38] (curves) for field sizes between 4 cm and 12 cm and nominal photon beam energies between 4 MV and 10 MV (reproduced from Ref. [38] with the permission of the American Association of Physicists in Medicine).

that the various contributions to the overall perturbation correction factors are no longer independent. This situation, which differs from broad beam conditions, undermines our current approach of applying Bragg–Gray cavity theory. Monte Carlo calculations based on a ratio of absorbed dose to water and absorbed dose to the detector material for the entire detector geometry are then preferable for calculating an overall conversion factor. It might still be of scientific interest to study the contributions in a stepwise fashion but not with the aim of proposing independent values for the various factors that could be reproduced via different routes. Decreasing the relative detector-to-beam size, misalignments, or primary photon source size can in addition, lead to unpredictably large effects. Figure 7 illustrates the uncertainty contribution to the absorbed dose determination using a PTW 60012 diode due to a uniformly distributed displacement error of 1 mm in all directions perpendicular to the beam axis.

FIG. 6. Contributions to the Monte Carlo calculated overall perturbation correction factor in the centre of a 0.8 cm × 0.8 cm field in a 6 MV photon beam resulting from the non-water equivalence of the wall (p_wall ), the presence of the central electrode (p_cel ), the perturbation from replacing water with air (p_a,w ) and volume averaging (p_vol ) for two types of PinPoint chambers (PP16 = PTW 31016 and PP06 = PTW 31006 with nominal volumes of 0.016 cm³ and 0.015 cm³, respectively) and two electron spot sizes (6G and 20G = 0.6 mm and 2.0 mm FWHM, respectively). The data are not in any particular order and the dotted lines serve only the purpose of visually connecting data points that represent the same contributing factor. Note that, for comparison, the value of the total perturbation correction factor p_tot in a 10 cm × 10 cm field amounts to 0.99 (reproduced from Ref. [45] with the permission of IOP Publishing).

FIG. 7. Uncertainty contribution to the absorbed dose determination using a PTW 60012 diode due to a uniformly distributed displacement error of 1 mm in all directions perpendicular to the beam axis only calculated by Monte Carlo (reproduced from Ref. [46] with the permission of IOP Publishing).

More recently, a number of authors have studied the components of small field perturbation factors by Monte Carlo simulations in a more systematic way [47–50]. Scott et al. [47] defined the ratio of absorbed dose to water at the measurement point in the water phantom and the mean absorbed dose over a volume of water replacing the entire detector’s sensitive volume as the volume averaging correction factor. Any other factor is then related to the non-water equivalence of detector materials in the sensitive volume, the electrodes and the encapsulation. It was then observed that, next to volume averaging, the main additional contribution to small field perturbation factors is the difference in density between the detector materials and water, especially in the variation of perturbation factors with field size. Not only is the density of the material in the sensitive volume of importance, but so is that of surrounding materials such as the epoxy encapsulation of diode detectors [51, 52], thin metallic electrodes and presence of small air gaps [53].

Differences in interaction data, while important in the overall conversion factor, are found to make only a small contribution to the variation of the perturbation correction factor with field size. Following up on those observations, Monte Carlo studies have investigated the possibility of compensating for small field perturbations by ‘mass density compensation’ [54, 55].

It is emphasized that small solid state detectors may also exhibit some level of volume averaging, which, considering their size, is shown only for the smallest therapeutic fields, i.e. those smaller than 1 cm [47, 56–58]. For these detectors, other perturbation effects may play a role as well (e.g. backscattering from metallic electrodes). The energy and angular dependence of some detectors, such as diodes, plays an important role. Owing to the fact that silicon has a higher mass energy absorption coefficient than water, unshielded diodes over-respond in large fields because of the significant phantom scatter component of low energy photons. The consequence is an underestimation of field output factors when they are normalized to a large field size (e.g. the conventional 10 cm × 10 cm reference field). In large fields, the over-response is usually compensated by adding a layer of high Z material around the sides and the bottom of the silicon chip that filters out the low energy scattered photons. These high Z caps are, however, undesirable in very small fields, as they may cause large perturbation effects that are difficult to determine accurately even with Monte Carlo calculations, as detector-to-detector differences are complicated to simulate [59].