Dosimetry of cone-defined stereotactic radiosurgery fields with a commercial synthetic diamond detector

Purpose Small field x-ray beam dosimetry is difficult due to a lack of lateral electronic equilibrium, source occlusion, high dose gradients and detector volume averaging. Currently there is no single definitive detector recommended for small field dosimetry. The objective of this work was to evaluate the performance of a new commercial synthetic diamond detector, namely the PTW 60019 microDiamond, for the dosimetry of small x-ray fields as used in stereotactic radiosurgery (SRS). Methods Small field sizes were defined by BrainLAB circular cones (4 – 30 mm diameter) on a Novalis Trilogy linear accelerator and using the 6 MV SRS x-ray beam mode for all measurements. Percentage depth doses were measured and compared to an IBA SFD and a PTW 60012 E diode. Cross profiles were measured and compared to an IBA SFD diode. Field factors, Ω_(Q_clin,Q_msr)^(f_clin,f_msr ), were calculated by Monte Carlo methods using BEAMnrc and correction factors, k_(Q_clin,Q_msr)^(f_clin,f_msr ), were derived for the PTW 60019 microDiamond detector. Results For the small fields of 4 to 30 mm diameter, there were dose differences in the PDDs of up to 1.5% when compared to an IBA SFD and PTW 60012 E diode detector. For the cross profile measurements the penumbra values varied, depending upon the orientation of the detector. The field factors, Ω_(Q_clin,Q_msr)^(f_clin,f_msr ), were calculated for these field diameters at a depth of 1.4 cm in water and they were within 2.7% of published values for a similar linear accelerator. The corrections factors, k_(Q_clin,Q_msr)^(f_clin,f_msr ), were derived for the PTW 60019 microDiamond detector. Conclusions We conclude that the new PTW 60019 microDiamond detector is generally suitable for relative dosimetry in small 6 MV SRS beams for a Novalis Trilogy linear equipped with circular cones.

An experimental approach to air gap optimisation for a correction-less small field diode

Aim A recent Monte Carlo based study has shown that it is possible to design a diode that measures small field output factors equivalent to that in water. This is accomplished by placing an appropriate sized air gap above the silicon chip (1) with experimental results subsequently confirming that a particular Monte Carlo design was accurate (2). The aim of this work was to test if a new correction-less diode could be designed using an entirely experimental methodology. Method: All measurements were performed on a Varian iX at a depth of 5 cm, SSD of 95 cm and field sizes of 5, 6, 8, 10, 20 and 30 mm. Firstly, the experimental transfer of kq,clin,kq,msr from a commonly used diode detector (IBA, stereotactic field diode (SFD)) to another diode detector (Sun Nuclear, unshielded diode, (EDGEe)) was tested. These results were compared to Monte Carlo calculated values of the EDGEe. Secondly, the air gap above the EDGEe silicon chip was optimised empirically. Nine different air gap “tops” were placed above the EDGEe (air depth = 0.3, 0.6, 0.9 mm; air width = 3.06, 4.59, 6.13 mm). The sensitivity of the EDGEe was plotted as a function of air gap thickness for the field sizes measured. Results: The transfer of kq,clin,kq,msr from the SFD to the EDGEe was correct to within the simulation and measurement uncertainties. The EDGEe detector can be made “correction-less” for field sizes of 5 and 6 mm, but was ∼2% from being “correction-less” at field sizes of 8 and 10 mm. Conclusion Different materials will perturb small fields in different ways. A detector is only “correction-less” if all these perturbations happen to cancel out. Designing a “correction-less” diode is a complicated process, thus it is reasonable to expect that Monte Carlo simulations should play an important role.

The use of penumbrae to define and analyse non-standard fields

Aim A new method of penumbral analysis is implemented which allows an unambiguous determination of field size and penumbra size and quality for small fields and other non-standard fields. Both source occlusion and lateral electronic disequilibrium will affect the size and shape of cross-axis profile penumbrae; each is examined in detail. Method A new method of penumbral analysis is implemented where the square of the derivative of the cross-axis profile is plotted. The resultant graph displays two peaks in the place of the two penumbrae. This allows a strong visualisation of the quality of a field penumbra, as well as a mathematically consistent method of determining field size (distance between the two peak’s maxima), and penumbra (full-widthtenth-maximum of peak). Cross-axis profiles were simulated in a water phantom at a depth of 5 cm using Monte Carlo modelling, for field sizes between 5 and 30 mm. The field size and penumbra size of each field was calculated using the method above, as well as traditional definitions set out in IEC976. The effect of source occlusion and lateral electronic disequilibrium on the penumbrae was isolated by repeating the simulations removing electron transport and using an electron spot size of 0 mm, respectively. Results All field sizes calculated using the traditional and proposed methods agreed within 0.2 mm. The penumbra size measured using the proposed method was systematically 1.8 mm larger than the traditional method at all field sizes. The size of the source had a larger effect on the size of the penumbra than did lateral electronic disequilibrium, particularly at very small field sizes. Conclusion Traditional methods of calculating field size and penumbra are proved to be mathematically adequate for small fields. However, the field size definition proposed in this study would be more robust amongst other nonstandard fields, such as flattening filter free. Source occlusion plays a bigger role than lateral electronic disequilibrium in small field penumbra size.

Approximate Bayesian Computation for astronomical model analysis : a case study in galaxy demographics and morphological transformation at high redshift

Approximate Bayesian Computation’ (ABC) represents a powerful methodology for the analysis of complex stochastic systems for which the likelihood of the observed data under an arbitrary set of input parameters may be entirely intractable – the latter condition rendering useless the standard machinery of tractable likelihood-based, Bayesian statistical inference [e.g. conventional Markov chain Monte Carlo (MCMC) simulation]. In this paper, we demonstrate the potential of ABC for astronomical model analysis by application to a case study in the morphological transformation of high-redshift galaxies. To this end, we develop, first, a stochastic model for the competing processes of merging and secular evolution in the early Universe, and secondly, through an ABC-based comparison against the observed demographics of massive (Mgal > 1011 M⊙) galaxies (at 1.5 < z < 3) in the Cosmic Assembly Near-IR Deep Extragalatic Legacy Survey (CANDELS)/Extended Groth Strip (EGS) data set we derive posterior probability densities for the key parameters of this model. The ‘Sequential Monte Carlo’ implementation of ABC exhibited herein, featuring both a self-generating target sequence and self-refining MCMC kernel, is amongst the most efficient of contemporary approaches to this important statistical algorithm. We highlight as well through our chosen case study the value of careful summary statistic selection, and demonstrate two modern strategies for assessment and optimization in this regard. Ultimately, our ABC analysis of the high-redshift morphological mix returns tight constraints on the evolving merger rate in the early Universe and favours major merging (with disc survival or rapid reformation) over secular evolution as the mechanism most responsible for building up the first generation of bulges in early-type discs.

Model choice problems using approximate Bayesian computation with applications to pathogen transmission data sets

Analytically or computationally intractable likelihood functions can arise in complex statistical inferential problems making them inaccessible to standard Bayesian inferential methods. Approximate Bayesian computation (ABC) methods address such inferential problems by replacing direct likelihood evaluations with repeated sampling from the model. ABC methods have been predominantly applied to parameter estimation problems and less to model choice problems due to the added difficulty of handling multiple model spaces. The ABC algorithm proposed here addresses model choice problems by extending Fearnhead and Prangle (2012, Journal of the Royal Statistical Society, Series B 74, 1–28) where the posterior mean of the model parameters estimated through regression formed the summary statistics used in the discrepancy measure. An additional stepwise multinomial logistic regression is performed on the model indicator variable in the regression step and the estimated model probabilities are incorporated into the set of summary statistics for model choice purposes. A reversible jump Markov chain Monte Carlo step is also included in the algorithm to increase model diversity for thorough exploration of the model space. This algorithm was applied to a validating example to demonstrate the robustness of the algorithm across a wide range of true model probabilities. Its subsequent use in three pathogen transmission examples of varying complexity illustrates the utility of the algorithm in inferring preference of particular transmission models for the pathogens.

Design and experimental testing of air slab caps which convert commercial electron diodes into dual purpose, correction-free diodes for small field dosimetry

Purpose Two diodes which do not require correction factors for small field relative output measurements are designed and validated using experimental methodology. This was achieved by adding an air layer above the active volume of the diode detectors, which canceled out the increase in response of the diodes in small fields relative to standard field sizes. Methods Due to the increased density of silicon and other components within a diode, additional electrons are created. In very small fields, a very small air gap acts as an effective filter of electrons with a high angle of incidence. The aim was to design a diode that balanced these perturbations to give a response similar to a water-only geometry. Three thicknesses of air were placed at the proximal end of a PTW 60017 electron diode (PTWe) using an adjustable “air cap”. A set of output ratios (ORfclin Det ) for square field sizes of side length down to 5 mm was measured using each air thickness and compared to ORfclin Det measured using an IBA stereotactic field diode (SFD). k fclin, f msr Qclin,Qmsr was transferred from the SFD to the PTWe diode and plotted as a function of air gap thickness for each field size. This enabled the optimal air gap thickness to be obtained by observing which thickness of air was required such that k fclin, f msr Qclin,Qmsr was equal to 1.00 at all field sizes. A similar procedure was used to find the optimal air thickness required to make a modified Sun Nuclear EDGE detector (EDGEe) which s “correction-free” in small field relative dosimetry. In addition, the feasibility of experimentally transferring k fclin, f msr Qclin,Qmsr values from the SFD to unknown diodes was tested by comparing the experimentally transferred k fclin, f msr Qclin,Qmsr values for unmodified PTWe and EDGEe diodes to Monte Carlo simulated values. Results 1.0 mm of air was required to make the PTWe diode correction-free. This modified diode (PTWeair) produced output factors equivalent to those in water at all field sizes (5–50 mm). The optimal air thickness required for the EDGEe diode was found to be 0.6 mm. The modified diode (EDGEeair) produced output factors equivalent to those in water, except at field sizes of 8 and 10 mm where it measured approximately 2% greater than the relative dose to water. The experimentally calculated k fclin, f msr Qclin,Qmsr for both the PTWe and the EDGEe diodes (without air) matched Monte Carlo simulated results, thus proving that it is feasible to transfer k fclin, f msr Qclin,Qmsr from one commercially available detector to another using experimental methods and the recommended experimental setup. Conclusions It is possible to create a diode which does not require corrections for small field output factor measurements. This has been performed and verified experimentally. The ability of a detector to be “correction-free” depends strongly on its design and composition. A nonwater-equivalent detector can only be “correction-free” if competing perturbations of the beam cancel out at all field sizes. This should not be confused with true water equivalency of a detector.

SHM through flexible vibration sensing technologies and robust safety evaluation paradigm

This research has successfully developed a novel synthetic structural health monitoring system model that is cost-effective and flexible in sensing and data acquisition; and robust in the structural safety evaluation aspect for the purpose of long-term and frequent monitoring of large-scale civil infrastructure during their service lives. Not only did it establish a real-world structural monitoring test-bed right at the heart of QUT Gardens Point Campus but it can also facilitate reliable and prompt protection for any built infrastructure system as well as the user community involved.

Contributions to Bayesian experimental design

This thesis progresses Bayesian experimental design by developing novel methodologies and extensions to existing algorithms. Through these advancements, this thesis provides solutions to several important and complex experimental design problems, many of which have applications in biology and medicine. This thesis consists of a series of published and submitted papers. In the first paper, we provide a comprehensive literature review on Bayesian design. In the second paper, we discuss methods which may be used to solve design problems in which one is interested in finding a large number of (near) optimal design points. The third paper presents methods for finding fully Bayesian experimental designs for nonlinear mixed effects models, and the fourth paper investigates methods to rapidly approximate the posterior distribution for use in Bayesian utility functions.

Statistical methods for electromyography data and associated problems

This thesis proposes three novel models which extend the statistical methodology for motor unit number estimation, a clinical neurology technique. Motor unit number estimation is important in the treatment of degenerative muscular diseases and, potentially, spinal injury. Additionally, a recent and untested statistic to enable statistical model choice is found to be a practical alternative for larger datasets. The existing methods for dose finding in dual-agent clinical trials are found to be suitable only for designs of modest dimensions. The model choice case-study is the first of its kind containing interesting results using so-called unit information prior distributions.

Pre-processing for approximate Bayesian computation in image analysis

Most of the existing algorithms for approximate Bayesian computation (ABC) assume that it is feasible to simulate pseudo-data from the model at each iteration. However, the computational cost of these simulations can be prohibitive for high dimensional data. An important example is the Potts model, which is commonly used in image analysis. Images encountered in real world applications can have millions of pixels, therefore scalability is a major concern. We apply ABC with a synthetic likelihood to the hidden Potts model with additive Gaussian noise. Using a pre-processing step, we fit a binding function to model the relationship between the model parameters and the synthetic likelihood parameters. Our numerical experiments demonstrate that the precomputed binding function dramatically improves the scalability of ABC, reducing the average runtime required for model fitting from 71 hours to only 7 minutes. We also illustrate the method by estimating the smoothing parameter for remotely sensed satellite imagery. Without precomputation, Bayesian inference is impractical for datasets of that scale.

Estimating the burden of disease attributable to excess body weight in South Africa in 2000

Objective. To estimate the burden of disease attributable to excess body weight using the body mass index (BMI), by age and sex, in South Africa in 2000. Design. World Health Organization comparative risk assessment (CRA) methodology was followed. Re-analysis of the 1998 South Africa Demographic and Health Survey data provided mean BMI estimates by age and sex. Populationattributable fractions were calculated and applied to revised burden of disease estimates. Monte Carlo simulation-modelling techniques were used for the uncertainty analysis. Setting. South Africa. Subjects. Adults 30 years of age. Outcome measures. Deaths and disability-adjusted life years (DALYs) from ischaemic heart disease, ischaemic stroke, hypertensive disease, osteoarthritis, type 2 diabetes mellitus, and selected cancers. Results. Overall, 87% of type 2 diabetes, 68% of hypertensive disease, 61% of endometrial cancer, 45% of ischaemic stroke, 38% of ischaemic heart disease, 31% of kidney cancer, 24% of osteoarthritis, 17% of colon cancer, and 13% of postmenopausal breast cancer were attributable to a BMI 21 kg/m2. Excess body weight is estimated to have caused 36 504 deaths (95% uncertainty interval 31 018 - 38 637) or 7% (95% uncertainty interval 6.0 - 7.4%) of all deaths in 2000, and 462 338 DALYs (95% uncertainty interval 396 512 - 478 847) or 2.9% of all DALYs (95% uncertainty interval 2.4 - 3.0%). The burden in females was approximately double that in males. Conclusions. This study shows the importance of recognising excess body weight as a major risk to health, particularly among females, highlighting the need to develop, implement and evaluate comprehensive interventions to achieve lasting change in the determinants and impact of excess body weight.

Estimating the burden of disease attributable to physical inactivity in South Africa in 2000

Objectives. To quantify the burden of disease attributable to physical inactivity in persons 15 years or older, by age group and sex, in South Africa for 2000. Design. The global comparative risk assessment (CRA) methodology of the World Health Organization was followed to estimate the disease burden attributable to physical inactivity. Levels of physical activity for South Africa were obtained from the World Health Survey 2003. A theoretical minimum risk exposure of zero, associated outcomes, relative risks, and revised burden of disease estimates were used to calculate population-attributable fractions and the burden attributed to physical inactivity. Monte Carlo simulation-modelling techniques were used for the uncertainty analysis. Setting. South Africa. Subjects. Adults ≥ 15 years. Outcome measures. Deaths and disability-adjusted life years (DALYs) from ischaemic heart disease, ischaemic stroke, breast cancer, colon cancer, and type 2 diabetes mellitus. Results. Overall in adults ≥ 15 years in 2000, 30% of ischaemic heart disease, 27% of colon cancer, 22% of ischaemic stroke, 20% of type 2 diabetes, and 17% of breast cancer were attributable to physical inactivity. Physical inactivity was estimated to have caused 17 037 (95% uncertainty interval 11 394 - 20 407), or 3.3% (95% uncertainty interval 2.2 - 3.9%) of all deaths in 2000, and 176 252 (95% uncertainty interval 133 733 - 203 628) DALYs, or 1.1% (95% uncertainty interval 0.8 - 1.3%) of all DALYs in 2000. Conclusions. Compared with other regions and the global average, South African adults have a particularly high prevalence of physical inactivity. In terms of attributable deaths, physical inactivity ranked 9th compared with other risk factors, and 12th in terms of DALYs. There is a clear need to assess why South Africans are particularly inactive, and to ensure that physical activity/inactivity is addressed as a national health priority.

Multi-modal deformable medical image registration

Non-rigid image registration is an essential tool required for overcoming the inherent local anatomical variations that exist between images acquired from different individuals or atlases. Furthermore, certain applications require this type of registration to operate across images acquired from different imaging modalities. One popular local approach for estimating this registration is a block matching procedure utilising the mutual information criterion. However, previous block matching procedures generate a sparse deformation field containing displacement estimates at uniformly spaced locations. This neglects to make use of the evidence that block matching results are dependent on the amount of local information content. This paper presents a solution to this drawback by proposing the use of a Reversible Jump Markov Chain Monte Carlo statistical procedure to optimally select grid points of interest. Three different methods are then compared to propagate the estimated sparse deformation field to the entire image including a thin-plate spline warp, Gaussian convolution, and a hybrid fluid technique. Results show that non-rigid registration can be improved by using the proposed algorithm to optimally select grid points of interest.