A practical and theoretical definition of very small field size for radiotherapy output factor measurements

Purpose This work introduces the concept of very small field size. Output factor (OPF) measurements at these field sizes require extremely careful experimental methodology including the measurement of dosimetric field size at the same time as each OPF measurement. Two quantifiable scientific definitions of the threshold of very small field size are presented. Methods A practical definition was established by quantifying the effect that a 1 mm error in field size or detector position had on OPFs, and setting acceptable uncertainties on OPF at 1%. Alternatively, for a theoretical definition of very small field size, the OPFs were separated into additional factors to investigate the specific effects of lateral electronic disequilibrium, photon scatter in the phantom and source occlusion. The dominant effect was established and formed the basis of a theoretical definition of very small fields. Each factor was obtained using Monte Carlo simulations of a Varian iX linear accelerator for various square field sizes of side length from 4 mm to 100 mm, using a nominal photon energy of 6 MV. Results According to the practical definition established in this project, field sizes < 15 mm were considered to be very small for 6 MV beams for maximal field size uncertainties of 1 mm. If the acceptable uncertainty in the OPF was increased from 1.0 % to 2.0 %, or field size uncertainties are 0.5 mm, field sizes < 12 mm were considered to be very small. Lateral electronic disequilibrium in the phantom was the dominant cause of change in OPF at very small field sizes. Thus the theoretical definition of very small field size coincided to the field size at which lateral electronic disequilibrium clearly caused a greater change in OPF than any other effects. This was found to occur at field sizes < 12 mm. Source occlusion also caused a large change in OPF for field sizes < 8 mm. Based on the results of this study, field sizes < 12 mm were considered to be theoretically very small for 6 MV beams. Conclusions Extremely careful experimental methodology including the measurement of dosimetric field size at the same time as output factor measurement for each field size setting and also very precise detector alignment is required at field sizes at least < 12 mm and more conservatively < 15 mm for 6 MV beams. These recommendations should be applied in addition to all the usual considerations for small field dosimetry, including careful detector selection.

GPU accelerated MCMC for modelling terrorist activity

The use of graphical processing unit (GPU) parallel processing is becoming a part of mainstream statistical practice. The reliance of Bayesian statistics on Markov Chain Monte Carlo (MCMC) methods makes the applicability of parallel processing not immediately obvious. It is illustrated that there are substantial gains in improved computational time for MCMC and other methods of evaluation by computing the likelihood using GPU parallel processing. Examples use data from the Global Terrorism Database to model terrorist activity in Colombia from 2000 through 2010 and a likelihood based on the explicit convolution of two negative-binomial processes. Results show decreases in computational time by a factor of over 200. Factors influencing these improvements and guidelines for programming parallel implementations of the likelihood are discussed.

Retrospective evaluation of dosimetric quality for prostate carcinomas treated with 3D conformal, intensity-modulated and volumetric-modulated arc radiotherapy

Introduction This study examines and compares the dosimetric quality of radiotherapy treatment plans for prostate carcinoma across a cohort of 163 patients treated across 5 centres: 83 treated with three-dimensional conformal radiotherapy (3DCRT), 33 treated with intensity-modulated radiotherapy (IMRT) and 47 treated with volumetric-modulated arc therapy (VMAT). Methods Treatment plan quality was evaluated in terms of target dose homogeneity and organ-at-risk sparing, through the use of a set of dose metrics. These included the mean, maximum and minimum doses; the homogeneity and conformity indices for the target volumes; and a selection of dose coverage values that were relevant to each organ-at-risk. Statistical significance was evaluated using two-tailed Welch’s T-tests. The Monte Carlo DICOM ToolKit software was adapted to permit the evaluation of dose metrics from DICOM data exported from a commercial radiotherapy treatment planning system. Results The 3DCRT treatment plans offered greater planning target volume dose homogeneity than the other two treatment modalities. The IMRT and VMAT plans offered greater dose reduction in the organs-at-risk: with increased compliance with recommended organ-at-risk dose constraints, compared to conventional 3DCRT treatments. When compared to each other, IMRT and VMAT did not provide significantly different treatment plan quality for like-sized tumour volumes. Conclusions This study indicates that IMRT and VMAT have provided similar dosimetric quality, which is superior to the dosimetric quality achieved with 3DCRT.

Characterising an ECG signal using statistical modelling : a feasibility study

For clinical use, in electrocardiogram (ECG) signal analysis it is important to detect not only the centre of the P wave, the QRS complex and the T wave, but also the time intervals, such as the ST segment. Much research focused entirely on qrs complex detection, via methods such as wavelet transforms, spline fitting and neural networks. However, drawbacks include the false classification of a severe noise spike as a QRS complex, possibly requiring manual editing, or the omission of information contained in other regions of the ECG signal. While some attempts were made to develop algorithms to detect additional signal characteristics, such as P and T waves, the reported success rates are subject to change from person-to-person and beat-to-beat. To address this variability we propose the use of Markov-chain Monte Carlo statistical modelling to extract the key features of an ECG signal and we report on a feasibility study to investigate the utility of the approach. The modelling approach is examined with reference to a realistic computer generated ECG signal, where details such as wave morphology and noise levels are variable.

Development of optical ray tracing model of a standard parabolic trough collector

Parabolic trough concentrator collector is the most matured, proven and widespread technology for the exploitation of the solar energy on a large scale for middle temperature applications. The assessment of the opportunities and the possibilities of the collector system are relied on its optical performance. A reliable Monte Carlo ray tracing model of a parabolic trough collector is developed by using Zemax software. The optical performance of an ideal collector depends on the solar spectral distribution and the sunshape, and the spectral selectivity of the associated components. Therefore, each step of the model, including the spectral distribution of the solar energy, trough reflectance, glazing anti-reflection coating and the absorber selective coating is explained and verified. Radiation flux distribution around the receiver, and the optical efficiency are two basic aspects of optical simulation are calculated using the model, and verified with widely accepted analytical profile and measured values respectively. Reasonably very good agreement is obtained. Further investigations are carried out to analyse the characteristics of radiation distribution around the receiver tube at different insolation, envelop conditions, and selective coating on the receiver; and the impact of scattered light from the receiver surface on the efficiency. However, the model has the capability to analyse the optical performance at variable sunshape, tracking error, collector imperfections including absorber misalignment with focal line and de-focal effect of the absorber, different rim angles, and geometric concentrations. The current optical model can play a significant role in understanding the optical aspects of a trough collector, and can be employed to extract useful information on the optical performance. In the long run, this optical model will pave the way for the construction of low cost standalone photovoltaic and thermal hybrid collector in Australia for small scale domestic hot water and electricity production.

High penetration of rooftop photovoltaic cells in low voltage distribution networks : voltage imbalance and improvement

Installation of domestic rooftop photovoltaic cells (PVs) is increasing due to feed–in tariff and motivation driven by environmental concerns. Even though the increase in the PV installation is gradual, their locations and ratings are often random. Therefore, such single–phase bi–directional power flow caused by the residential customers can have adverse effect on the voltage imbalance of a three–phase distribution network. In this chapter, a voltage imbalance sensitivity analysis and stochastic evaluation are carried out based on the ratings and locations of single–phase grid–connected rooftop PVs in a residential low voltage distribution network. The stochastic evaluation, based on Monte Carlo method, predicts a failure index of non–standard voltage imbalance in the network in presence of PVs. Later, the application of series and parallel custom power devices are investigated to improve voltage imbalance problem in these feeders. In this regard, first, the effectiveness of these two custom power devices is demonstrated vis–à–vis the voltage imbalance reduction in feeders containing rooftop PVs. Their effectiveness is investigated from the installation location and rating points of view. Later, a Monte Carlo based stochastic analysis is utilized to investigate their efficacy for different uncertainties of load and PV rating and location in the network. This is followed by demonstrating the dynamic feasibility and stability issues of applying these devices in the network.

Recursive pathways to marginal likelihood estimation with prior-sensitivity analysis

We investigate the utility to computational Bayesian analyses of a particular family of recursive marginal likelihood estimators characterized by the (equivalent) algorithms known as "biased sampling" or "reverse logistic regression" in the statistics literature and "the density of states" in physics. Through a pair of numerical examples (including mixture modeling of the well-known galaxy dataset) we highlight the remarkable diversity of sampling schemes amenable to such recursive normalization, as well as the notable efficiency of the resulting pseudo-mixture distributions for gauging prior-sensitivity in the Bayesian model selection context. Our key theoretical contributions are to introduce a novel heuristic ("thermodynamic integration via importance sampling") for qualifying the role of the bridging sequence in this procedure, and to reveal various connections between these recursive estimators and the nested sampling technique.

Computer simulation of scaffold degradation

Scaffolds are porous biocompatible materials with suitable microarchitectures that are designed to allow for cell adhesion, growth and proliferation. They are used in combination with cells in regenerative medicine to promote tissue regeneration by means of a controlled deposition of natural extracellular matrix by the hosted cells therein. This healing process is in many cases accompanied by scaffold degradation up to its total disappearance when the scaffold is made of a biodegradable material. This work presents a computational model that simulates the degradation of scaffolds. The model works with three-dimensional microstructures, which have been previously discretised into small cubic homogeneous elements, called voxels. The model simulates the evolution of the degradation of the scaffold using a Monte Carlo algorithm, which takes into account the curvature of the surface of the fibres. The simulation results obtained in this study are in good agreement with empirical degradation measurements performed by mass loss on scaffolds after exposure to an etching alkaline solution.

Random Gabor based templates for facial expression recognition in images with facial occlusion

Robust facial expression recognition (FER) under occluded face conditions is challenging. It requires robust algorithms of feature extraction and investigations into the effects of different types of occlusion on the recognition performance to gain insight. Previous FER studies in this area have been limited. They have spanned recovery strategies for loss of local texture information and testing limited to only a few types of occlusion and predominantly a matched train-test strategy. This paper proposes a robust approach that employs a Monte Carlo algorithm to extract a set of Gabor based part-face templates from gallery images and converts these templates into template match distance features. The resulting feature vectors are robust to occlusion because occluded parts are covered by some but not all of the random templates. The method is evaluated using facial images with occluded regions around the eyes and the mouth, randomly placed occlusion patches of different sizes, and near-realistic occlusion of eyes with clear and solid glasses. Both matched and mis-matched train and test strategies are adopted to analyze the effects of such occlusion. Overall recognition performance and the performance for each facial expression are investigated. Experimental results on the Cohn-Kanade and JAFFE databases demonstrate the high robustness and fast processing speed of our approach, and provide useful insight into the effects of occlusion on FER. The results on the parameter sensitivity demonstrate a certain level of robustness of the approach to changes in the orientation and scale of Gabor filters, the size of templates, and occlusions ratios. Performance comparisons with previous approaches show that the proposed method is more robust to occlusion with lower reductions in accuracy from occlusion of eyes or mouth.

Surface dosimetry for very small X-ray beams

Introduction The dose to skin surface is an important factor for many radiotherapy treatment techniques. It is known that TPS predicted surface doses can be significantly different from actual ICRP skin doses as defined at 70 lm. A number of methods have been implemented for the accurate determination of surface dose including use of specific dosimeters such as TLDs and radiochromic film as well as Monte Carlo calculations. Stereotactic radiosurgery involves delivering very high doses per treatment fraction using small X-ray fields. To date, there has been limited data on surface doses for these very small field sizes. The purpose of this work is to evaluate surface doses by both measurements and Monte Carlo calculations for very small field sizes. Methods All measurements were performed on a Novalis Tx linear accelerator which has a 6 MV SRS X-ray beam mode which uses a specially thin flattening filter. Beam collimation was achieved by circular cones with apertures that gave field sizes ranging from 4 to 30 mm at the isocentre. The relative surface doses were measured using Gafchromic EBT3 film which has the active layer at a depth similar to the ICRP skin dose depth. Monte Carlo calculations were performed using the BEAMnrc/EGSnrc Monte Carlo codes (V4 r225). The specifications of the linear accelerator, including the collimator, were provided by the manufacturer. Optimisation of the incident X-ray beam was achieved by an iterative adjustment of the energy, spatial distribution and radial spread of the incident electron beam striking the target. The energy cutoff parameters were PCUT = 0.01 MeV and ECUT = 0.700 - MeV. Directional bremsstrahlung splitting was switched on for all BEAMnrc calculations. Relative surface doses were determined in a layer defined in a water phantom of the same thickness and depth as compared to the active later in the film. Results Measured surface doses using the EBT3 film varied between 13 and 16 % for the different cones with an uncertainty of 3 %. Monte Carlo calculated surface doses were in agreement to better than 2 % to the measured doses for all the treatment cones. Discussion and conclusions This work has shown the consistency of surface dose measurements using EBT3 film with Monte Carlo predicted values within the uncertainty of the measurements. As such, EBT3 film is recommended for in vivo surface dose measurements.

A practical and theoretical definition of 'small field'

Introduction The consistency of measuring small field output factors is greatly increased by reporting the measured dosimetric field size of each factor, as opposed to simply stating the nominal field size [1] and therefore requires the measurement of cross-axis profiles in a water tank. However, this makes output factor measurements time consuming. This project establishes at which field size the accuracy of output factors are not affected by the use of potentially inaccurate nominal field sizes, which we believe establishes a practical working definition of a ‘small’ field. The physical components of the radiation beam that contribute to the rapid change in output factor at small field sizes are examined in detail. The physical interaction that dominates the cause of the rapid dose reduction is quantified, and leads to the establishment of a theoretical definition of a ‘small’ field. Methods Current recommendations suggest that radiation collimation systems and isocentre defining lasers should both be calibrated to permit a maximum positioning uncertainty of 1 mm [2]. The proposed practical definition for small field sizes is as follows: if the output factor changes by ±1.0 % given a change in either field size or detector position of up to ±1 mm then the field should be considered small. Monte Carlo modelling was used to simulate output factors of a 6 MV photon beam for square fields with side lengths from 4.0 to 20.0 mm in 1.0 mm increments. The dose was scored to a 0.5 mm wide and 2.0 mm deep cylindrical volume of water within a cubic water phantom, at a depth of 5 cm and SSD of 95 cm. The maximum difference due to a collimator error of ±1 mm was found by comparing the output factors of adjacent field sizes. The output factor simulations were repeated 1 mm off-axis to quantify the effect of detector misalignment. Further simulations separated the total output factor into collimator scatter factor and phantom scatter factor. The collimator scatter factor was further separated into primary source occlusion effects and ‘traditional’ effects (a combination of flattening filter and jaw scatter etc.). The phantom scatter was separated in photon scatter and electronic disequilibrium. Each of these factors was plotted as a function of field size in order to quantify how each affected the change in small field size. Results The use of our practical definition resulted in field sizes of 15 mm or less being characterised as ‘small’. The change in field size had a greater effect than that of detector misalignment. For field sizes of 12 mm or less, electronic disequilibrium was found to cause the largest change in dose to the central axis (d = 5 cm). Source occlusion also caused a large change in output factor for field sizes less than 8 mm. Discussion and conclusions The measurement of cross-axis profiles are only required for output factor measurements for field sizes of 15 mm or less (for a 6 MV beam on Varian iX linear accelerator). This is expected to be dependent on linear accelerator spot size and photon energy. While some electronic disequilibrium was shown to occur at field sizes as large as 30 mm (the ‘traditional’ definition of small field [3]), it has been shown that it does not cause a greater change than photon scatter until a field size of 12 mm, at which point it becomes by far the most dominant effect.

A diode for correction-less small field output factor measurements

Introduction Due to their high spatial resolution diodes are often used for small field relative output factor measurements. However, a field size specific correction factor [1] is required and corrects for diode detector over-response at small field sizes. A recent Monte Carlo based study has shown that it is possible to design a diode detector that produces measured relative output factors that are equivalent to those in water. This is accomplished by introducing an air gap at the upstream end of the diode [2]. The aim of this study was to physically construct this diode by placing an ‘air cap’ on the end of a commercially available diode (the PTW 60016 electron diode). The output factors subsequently measured with the new diode design were compared to current benchmark small field output factor measurements. Methods A water-tight ‘cap’ was constructed so that it could be placed over the upstream end of the diode. The cap was able to be offset from the end of the diode, thus creating an air gap. The air gap width was the same as the diode width (7 mm) and the thickness of the air gap could be varied. Output factor measurements were made using square field sizes of side length from 5 to 50 mm, using a 6 MV photon beam. The set of output factor measurements were repeated with the air gap thickness set to 0, 0.5, 1.0 and 1.5 mm. The optimal air gap thickness was found in a similar manner to that proposed by Charles et al. [2]. An IBA stereotactic field diode, corrected using Monte Carlo calculated kq,clin,kq,msr values [3] was used as the gold standard. Results The optimal air thickness required for the PTW 60016 electron diode was 1.0 mm. This was close to the Monte Carlo predicted value of 1.15 mm2. The sensitivity of the new diode design was independent of field size (kq,clin,kq,msr = 1.000 at all field sizes) to within 1 %. Discussion and conclusions The work of Charles et al. [2] has been proven experimentally. An existing commercial diode has been converted into a correction-less small field diode by the simple addition of an ‘air cap’. The method of applying a cap to create the new diode leads to the diode being dual purpose, as without the cap it is still an unmodified electron diode.

The importance of accurate beam data measurement for SRT/SRS treatment planning

Introduction This study investigated the sensitivity of calculated stereotactic radiotherapy and radiosurgery doses to the accuracy of the beam data used by the treatment planning system. Methods Two sets of field output factors were acquired using fields smaller than approximately 1 cm2, for inclusion in beam data used by the iPlan treatment planning system (Brainlab, Feldkirchen, Germany). One set of output factors were measured using an Exradin A16 ion chamber (Standard Imaging, Middleton, USA). Although this chamber has a relatively small collecting volume (0.007 cm3), measurements made in small fields using this chamber are subject to the effects of volume averaging, electronic disequilibrium and chamber perturbations. The second, more accurate, set of measurements were obtained by applying perturbation correction factors, calculated using Monte Carlo simulations according to a method recommended by Cranmer-Sargison et al. [1] to measurements made using a 60017 unshielded electron diode (PTW, Freiburg, Germany). A series of 12 sample patient treatments were used to investigate the effects of beam data accuracy on resulting planned dose. These treatments, which involved 135 fields, were planned for delivery via static conformal arcs and 3DCRT techniques, to targets ranging from prostates (up to 8 cm across) to meningiomas (usually more than 2 cm across) to arterioveinous malformations, acoustic neuromas and brain metastases (often less than 2 cm across). Isocentre doses were calculated for all of these fields using iPlan, and the results of using the two different sets of beam data were evaluated. Results While the isocentre doses for many fields are identical (difference = 0.0 %), there is a general trend for the doses calculated using the data obtained from corrected diode measurements to exceed the doses calculated using the less-accurate Exradin ion chamber measurements (difference\0.0 %). There are several alarming outliers (circled in the Fig. 1) where doses differ by more than 3 %, in beams from sample treatments planned for volumes up to 2 cm across. Discussion and conclusions These results demonstrate that treatment planning dose calculations for SRT/SRS treatments can be substantially affected when beam data for fields smaller than approximately 1 cm2 are measured inaccurately, even when treatment volumes are up to 2 cm across.

The effect of very small air gaps on small field dosimetry

The purpose of this study was to investigate the effect of very small air gaps (less than 1 mm) on the dosimetry of small photon fields used for stereotactic treatments. Measurements were performed with optically stimulated luminescent dosimeters (OSLDs) for 6 MV photons on a Varian 21iX linear accelerator with a Brainlab lMLC attachment for square field sizes down to 6 mm 9 6 mm. Monte Carlo simulations were performed using EGSnrc C++ user code cavity. It was found that the Monte Carlo model used in this study accurately simulated the OSLD measurements on the linear accelerator. For the 6 mm field size, the 0.5 mm air gap upstream to the active area of the OSLD caused a 5.3 % dose reduction relative to a Monte Carlo simulation with no air gap...

Origins of the observed asymmetry in out-of-field dose from a linac fitted with an external micro-MLC

Objective Recently, Taylor et al. reported that use of the BrainLAB m3 microMLC, for stereotactic radiosurgery, results in a decreased out-of-field dose in the direction of leaf-motion compared to the outof- field dose measured in the direction orthogonal to leaf-motion [1]. It was recommended that, where possible, patients should be treated with their superior–inferior axes aligned with the microMLCs leafmotion direction, to minimise out-of-field doses [1]. This study aimed, therefore, to examine the causes of this asymmetry in outof- field dose and, in particular, to establish that a similar recommendation need not be made for radiotherapy treatments delivered by linear accelerators without external micro-collimation systems. Methods Monte Carlo simulations were used to study out-of-field dose from different linear accelerators (the Varian Clinacs 21iX and 600C and the Elekta Precise) with and without internal MLCs and external microMLCs [2]. Results Simulation results for the Varian Clinac 600C linear accelerator with BrainLAB m3 microMLC confirm Taylor et als [1] published experimental data. The out-of-field dose in the leaf motion direction is deposited by lower energy (more obliquely scattered) photons than the out-of-field dose in the orthogonal direction. Linear accelerators without microMLCs produce no asymmetry in out-offield dose. Conclusions The asymmetry in out-of-field dose previously measured by Taylor et al. [1] results from the shielding characteristics of the BrainLAB m3 microMLC device and is not produced by the linear accelerator to which it is attached.