Understanding the Influence of Photon Energy on 6MV Non Reference Dosimetry and CT Dosimetry using TLD and OSLD

Measurement of the absorbed dose from ionizing radiation in medical applications is an essential component to providing safe and reproducible patient care. There are a wide variety of tools available for measuring radiation dose; this work focuses on the characterization of two common, solid-state dosimeters in medical applications: thermoluminescent dosimeters (TLD) and optically stimulated luminescent dosimeters (OSLD). There were two main objectives to this work. The first objective was to evaluate the energy dependence of TLD and OSLD for non-reference measurement conditions in a radiotherapy environment. The second objective was to fully characterize the OSLD nanoDot in a CT environment, and to provide validated calibration procedures for CT dose measurement using OSLD. Current protocols for dose measurement using TLD and OSLD generally assume a constant photon energy spectrum within a nominal beam energy regardless of measurement location, tissue composition, or changes in beam parameters. Variations in the energy spectrum of therapeutic photon beams may impact the response of TLD and OSLD and could thereby result in an incorrect measure of dose unless these differences are accounted for. In this work, we used a Monte Carlo based model to simulate variations in the photon energy spectra of a Varian 6MV beam; then evaluated the impact of the perturbations in energy spectra on the response of both TLD and OSLD using Burlin Cavity Theory. Energy response correction factors were determined for a range of conditions and compared to measured correction factors with good agreement. When using OSLD for dose measurement in a diagnostic imaging environment, photon energy spectra are often referenced to a therapy-energy or orthovoltage photon beam – commonly 250kVp, Co-60, or even 6MV, where the spectra are substantially different. Appropriate calibration techniques specifically for the OSLD nanoDot in a CT environment have not been presented in the literature; furthermore the dependence of the energy response of the calibration energy has not been emphasized. The results of this work include detailed calibration procedures for CT dosimetry using OSLD, and a full characterization of this dosimetry system in a low-dose, low-energy setting.

Evaluation of PRESAGE® dosimeters for brachytherapy sources and the 3D dosimetry and characterization of the new AgX100 125I seed model

With continuous new improvements in brachytherapy source designs and techniques, method of 3D dosimetry for treatment dose verifications would better ensure accurate patient radiotherapy treatment. This study was aimed to first evaluate the 3D dose distributions of the low-dose rate (LDR) Amersham 6711 OncoseedTM using PRESAGE® dosimeters to establish PRESAGE® as a suitable brachytherapy dosimeter. The new AgX100 125I seed model (Theragenics Corporation) was then characterized using PRESAGE® following the TG-43 protocol. PRESAGE® dosimeters are solid, polyurethane-based, 3D dosimeters doped with radiochromic leuco dyes that produce a linear optical density response to radiation dose. For this project, the radiochromic response in PRESAGE® was captured using optical-CT scanning (632 nm) and the final 3D dose matrix was reconstructed using the MATLAB software. An Amersham 6711 seed with an air-kerma strength of approximately 9 U was used to irradiate two dosimeters to 2 Gy and 11 Gy at 1 cm to evaluate dose rates in the r=1 cm to r=5 cm region. The dosimetry parameters were compared to the values published in the updated AAPM Report No. 51 (TG-43U1). An AgX100 seed with an air-kerma strength of about 6 U was used to irradiate two dosimeters to 3.6 Gy and 12.5 Gy at 1 cm. The dosimetry parameters for the AgX100 were compared to the values measured from previous Monte-Carlo and experimental studies. In general, the measured dose rate constant, anisotropy function, and radial dose function for the Amersham 6711 showed agreements better than 5% compared to consensus values in the r=1 to r=3 cm region. The dose rates and radial dose functions measured for the AgX100 agreed with the MCNPX and TLD-measured values within 3% in the r=1 to r=3 cm region. The measured anisotropy function in PRESAGE® showed relative differences of up to 9% with the MCNPX calculated values. It was determined that post-irradiation optical density change over several days was non-linear in different dose regions, and therefore the dose values in the r=4 to r=5 cm regions had higher uncertainty due to this effect. This study demonstrated that within the radial distance of 3 cm, brachytherapy dosimetry in PRESAGE® can be accurate within 5% as long as irradiation times are within 48 hours.

Efficient methodologies for system matrix modelling in iterative image reconstruction for rotating high-resolution PET

A fully 3D iterative image reconstruction algorithm has been developed for high-resolution PET cameras composed of pixelated scintillator crystal arrays and rotating planar detectors, based on the ordered subsets approach. The associated system matrix is precalculated with Monte Carlo methods that incorporate physical effects not included in analytical models, such as positron range effects and interaction of the incident gammas with the scintillator material. Custom Monte Carlo methodologies have been developed and optimized for modelling of system matrices for fast iterative image reconstruction adapted to specific scanner geometries, without redundant calculations. According to the methodology proposed here, only one-eighth of the voxels within two central transaxial slices need to be modelled in detail. The rest of the system matrix elements can be obtained with the aid of axial symmetries and redundancies, as well as in-plane symmetries within transaxial slices. Sparse matrix techniques for the non-zero system matrix elements are employed, allowing for fast execution of the image reconstruction process. This 3D image reconstruction scheme has been compared in terms of image quality to a 2D fast implementation of the OSEM algorithm combined with Fourier rebinning approaches. This work confirms the superiority of fully 3D OSEM in terms of spatial resolution, contrast recovery and noise reduction as compared to conventional 2D approaches based on rebinning schemes. At the same time it demonstrates that fully 3D methodologies can be efficiently applied to the image reconstruction problem for high-resolution rotational PET cameras by applying accurate pre-calculated system models and taking advantage of the system's symmetries.

Modelling of the surface emission of the low magnetic field magnetar SGR 0418+5729

We perform a detailed modelling of the post-outburst surface emission of the low magnetic field magnetar SGR 0418+5729. The dipolar magnetic field of this source, B=6×1012G estimated from its spin-down rate, is in the observed range of magnetic fields for normal pulsars. The source is further characterized by a high pulse fraction and a single-peak profile. Using synthetic temperature distribution profiles, and fully accounting for the general-relativistic effects of light deflection and gravitational redshift, we generate synthetic X-ray spectra and pulse profiles that we fit to the observations. We find that asymmetric and symmetric surface temperature distributions can reproduce equally well the observed pulse profiles and spectra of SGR 0418. None the less, the modelling allows us to place constraints on the system geometry (i.e. the angles ψ and ξ that the rotation axis makes with the line of sight and the dipolar axis, respectively), as well as on the spot size and temperature contrast on the neutron star surface. After performing an analysis iterating between the pulse profile and spectra, as done in similar previous works, we further employed, for the first time in this context, a Markov-Chain Monte Carlo approach to extract constraints on the model parameters from the pulse profiles and spectra, simultaneously. We find that, to reproduce the observed spectrum and flux modulation: (a) the angles must be restricted to 65° ≲ ψ + ξ ≲ 125° or 235° ≲ ψ + ξ ≲ 295°; (b) the temperature contrast between the poles and the equator must be at least a factor of ∼6, and (c) the size of the hottest region ranges between 0.2 and 0.7 km (including uncertainties on the source distance). Lastly, we interpret our findings within the context of internal and external heating models.

Process systems modelling and applications in granulation: A review

Granulation is one of the fundamental operations in particulate processing and has a very ancient history and widespread use. Much fundamental particle science has occurred in the last two decades to help understand the underlying phenomena. Yet, until recently the development of granulation systems was mostly based on popular practice. The use of process systems approaches to the integrated understanding of these operations is providing improved insight into the complex nature of the processes. Improved mathematical representations, new solution techniques and the application of the models to industrial processes are yielding better designs, improved optimisation and tighter control of these systems. The parallel development of advanced instrumentation and the use of inferential approaches provide real-time access to system parameters necessary for improvements in operation. The use of advanced models to help develop real-time plant diagnostic systems provides further evidence of the utility of process system approaches to granulation processes. This paper highlights some of those aspects of granulation. (c) 2005 Elsevier Ltd. All rights reserved.

Modelling nucleation in wet granulation

Nucleation is the first stage in any granulation process where binder liquid first comes into contact with the powder. This paper investigates the nucleation process where binder liquid is added to a fine powder with a spray nozzle. The dimensionless spray flux approach of Hapgood et al. (Powder Technol. 141 (2004) 20) is extended to account for nonuniform spray patterns and allow for overlap of nuclei granules rather than spray drops. A dimensionless nuclei distribution function which describes the effects of the design and operating parameters of the nucleation process (binder spray characteristics, the nucleation area ratio between droplets and nuclei and the powder bed velocity) on the fractional surface area coverage of nuclei on a moving powder bed is developed. From this starting point, a Monte Carlo nucleation model that simulates full nuclei size distributions as a function of the design and operating parameters that were implemented in the dimensionless nuclei distribution function is developed. The nucleation model was then used to investigate the effects of the design and operating parameters on the formed nuclei size distributions and to correlate these effects to changes of the dimensionless nuclei distribution function. Model simulations also showed that it is possible to predict nuclei size distributions beyond the drop controlled nucleation regime in Hapgood's nucleation regime map. Qualitative comparison of model simulations and experimental nucleation data showed similar shapes of the nuclei size distributions. In its current form, the nucleation model can replace the nucleation term in one-dimensional population balance models describing wet granulation processes. Implementation of more sophisticated nucleation kinetics can make the model applicable to multi-dimensional population balance models.

Development of a dosage strategy in patients receiving enoxaparin by continuous intravenous infusion using modelling and simulation

Aim To develop an appropriate dosing strategy for continuous intravenous infusions (CII) of enoxaparin by minimizing the percentage of steady-state anti-Xa concentration (C-ss) outside the therapeutic range of 0.5-1.2 IU ml(-1). Methods A nonlinear mixed effects model was developed with NONMEM (R) for 48 adult patients who received CII of enoxaparin with infusion durations that ranged from 8 to 894 h at rates between 100 and 1600 IU h(-1). Three hundred and sixty-three anti-Xa concentration measurements were available from patients who received CII. These were combined with 309 anti-Xa concentrations from 35 patients who received subcutaneous enoxaparin. The effects of age, body size, height, sex, creatinine clearance (CrCL) and patient location [intensive care unit (ICU) or general medical unit] on pharmacokinetic (PK) parameters were evaluated. Monte Carlo simulations were used to (i) evaluate covariate effects on C-ss and (ii) compare the impact of different infusion rates on predicted C-ss. The best dose was selected based on the highest probability that the C-ss achieved would lie within the therapeutic range. Results A two-compartment linear model with additive and proportional residual error for general medical unit patients and only a proportional error for patients in ICU provided the best description of the data. Both CrCL and weight were found to affect significantly clearance and volume of distribution of the central compartment, respectively. Simulations suggested that the best doses for patients in the ICU setting were 50 IU kg(-1) per 12 h (4.2 IU kg(-1) h(-1)) if CrCL < 30 ml min(-1); 60 IU kg(-1) per 12 h (5.0 IU kg(-1) h(-1)) if CrCL was 30-50 ml min(-1); and 70 IU kg(-1) per 12 h (5.8 IU kg(-1) h(-1)) if CrCL > 50 ml min(-1). The best doses for patients in the general medical unit were 60 IU kg(-1) per 12 h (5.0 IU kg(-1) h(-1)) if CrCL < 30 ml min(-1); 70 IU kg(-1) per 12 h (5.8 IU kg(-1) h(-1)) if CrCL was 30-50 ml min(-1); and 100 IU kg(-1) per 12 h (8.3 IU kg(-1) h(-1)) if CrCL > 50 ml min(-1). These best doses were selected based on providing the lowest equal probability of either being above or below the therapeutic range and the highest probability that the C-ss achieved would lie within the therapeutic range. Conclusion The dose of enoxaparin should be individualized to the patients' renal function and weight. There is some evidence to support slightly lower doses of CII enoxaparin in patients in the ICU setting.

Modelling frontal discontinuities in wind fields

A Bayesian procedure for the retrieval of wind vectors over the ocean using satellite borne scatterometers requires realistic prior near-surface wind field models over the oceans. We have implemented carefully chosen vector Gaussian Process models; however in some cases these models are too smooth to reproduce real atmospheric features, such as fronts. At the scale of the scatterometer observations, fronts appear as discontinuities in wind direction. Due to the nature of the retrieval problem a simple discontinuity model is not feasible, and hence we have developed a constrained discontinuity vector Gaussian Process model which ensures realistic fronts. We describe the generative model and show how to compute the data likelihood given the model. We show the results of inference using the model with Markov Chain Monte Carlo methods on both synthetic and real data.

Neural Network Modelling with Input Uncertainty: Theory and Application

It is generally assumed when using Bayesian inference methods for neural networks that the input data contains no noise. For real-world (errors in variable) problems this is clearly an unsafe assumption. This paper presents a Bayesian neural network framework which accounts for input noise provided that a model of the noise process exists. In the limit where the noise process is small and symmetric it is shown, using the Laplace approximation, that this method adds an extra term to the usual Bayesian error bar which depends on the variance of the input noise process. Further, by treating the true (noiseless) input as a hidden variable, and sampling this jointly with the network’s weights, using a Markov chain Monte Carlo method, it is demonstrated that it is possible to infer the regression over the noiseless input. This leads to the possibility of training an accurate model of a system using less accurate, or more uncertain, data. This is demonstrated on both the, synthetic, noisy sine wave problem and a real problem of inferring the forward model for a satellite radar backscatter system used to predict sea surface wind vectors.

How much is corporate cash-pooling worth? Modelling and simulation

The paper analyzes a special corporate banking product, the so called cash-pool, which gained remarkable popularity in the recent years as firms try to centralize and manage their liquidity more efficiently. The novelty of this paper is the formalization of a valuation model which can serve as a basis for a Monte Carlo simulation to assess the most important benefits of the firms arising from the pooling of their cash holdings. The literature emphasizes several benefits of cash-pooling such as interest rate savings, economy of scale and reduced cash-flow volatility. The presented model focuses on the interest rate savings complemented with a new aspect: the reduced counterparty risk toward the bank. The main conclusion of the analysis is that the value of a cash-pool is higher in case of firms with large, diverse and volatile cash-flows having less access to the capital markets especially if the partner bank is risky and offers a high interest spread. It is also shown that cash-pooling is not the privilege of large multinational firms any more as the initial direct costs can be easily regained within a year even in the case of SMEs.

Advanced Applications of 3D Dosimetry and 3D Printing in Radiation Therapy

As complex radiotherapy techniques become more readily-practiced, comprehensive 3D dosimetry is a growing necessity for advanced quality assurance. However, clinical implementation has been impeded by a wide variety of factors, including the expense of dedicated optical dosimeter readout tools, high operational costs, and the overall difficulty of use. To address these issues, a novel dry-tank optical CT scanner was designed for PRESAGE 3D dosimeter readout, relying on 3D printed components and omitting costly parts from preceding optical scanners. This work details the design, prototyping, and basic commissioning of the Duke Integrated-lens Optical Scanner (DIOS).

The convex scanning geometry was designed in ScanSim, an in-house Monte Carlo optical ray-tracing simulation. ScanSim parameters were used to build a 3D rendering of a convex ‘solid tank’ for optical-CT, which is capable of collimating a point light source into telecentric geometry without significant quantities of refractive-index matched fluid. The model was 3D printed, processed, and converted into a negative mold via rubber casting to produce a transparent polyurethane scanning tank. The DIOS was assembled with the solid tank, a 3W red LED light source, a computer-controlled rotation stage, and a 12-bit CCD camera. Initial optical phantom studies show negligible spatial inaccuracies in 2D projection images and 3D tomographic reconstructions. A PRESAGE 3D dose measurement for a 4-field box treatment plan from Eclipse shows 95% of voxels passing gamma analysis at 3%/3mm criteria. Gamma analysis between tomographic images of the same dosimeter in the DIOS and DLOS systems show 93.1% agreement at 5%/1mm criteria. From this initial study, the DIOS has demonstrated promise as an economically-viable optical-CT scanner. However, further improvements will be necessary to fully develop this system into an accurate and reliable tool for advanced QA.

Pre-clinical animal studies are used as a conventional means of translational research, as a midpoint between in-vitro cell studies and clinical implementation. However, modern small animal radiotherapy platforms are primitive in comparison with conventional linear accelerators. This work also investigates a series of 3D printed tools to expand the treatment capabilities of the X-RAD 225Cx orthovoltage irradiator, and applies them to a feasibility study of hippocampal avoidance in rodent whole-brain radiotherapy.

As an alternative material to lead, a novel 3D-printable tungsten-composite ABS plastic, GMASS, was tested to create precisely-shaped blocks. Film studies show virtually all primary radiation at 225 kVp can be attenuated by GMASS blocks of 0.5cm thickness. A state-of-the-art software, BlockGen, was used to create custom hippocampus-shaped blocks from medical image data, for any possible axial treatment field arrangement. A custom 3D printed bite block was developed to immobilize and position a supine rat for optimal hippocampal conformity. An immobilized rat CT with digitally-inserted blocks was imported into the SmART-Plan Monte-Carlo simulation software to determine the optimal beam arrangement. Protocols with 4 and 7 equally-spaced fields were considered as viable treatment options, featuring improved hippocampal conformity and whole-brain coverage when compared to prior lateral-opposed protocols. Custom rodent-morphic PRESAGE dosimeters were developed to accurately reflect these treatment scenarios, and a 3D dosimetry study was performed to confirm the SmART-Plan simulations. Measured doses indicate significant hippocampal sparing and moderate whole-brain coverage.

Trajectory prediction uncertainty modelling for Air Traffic Management

The anticipated growth of air traffic worldwide requires enhanced Air Traffic Management (ATM) technologies and procedures to increase the system capacity, efficiency, and resilience, while reducing environmental impact and maintaining operational safety. To deal with these challenges, new automation and information exchange capabilities are being developed through different modernisation initiatives toward a new global operational concept called Trajectory Based Operations (TBO), in which aircraft trajectory information becomes the cornerstone of advanced ATM applications. This transformation will lead to higher levels of system complexity requiring enhanced Decision Support Tools (DST) to aid humans in the decision making processes. These will rely on accurate predicted aircraft trajectories, provided by advanced Trajectory Predictors (TP). The trajectory prediction process is subject to stochastic effects that introduce uncertainty into the predictions. Regardless of the assumptions that define the aircraft motion model underpinning the TP, deviations between predicted and actual trajectories are unavoidable. This thesis proposes an innovative method to characterise the uncertainty associated with a trajectory prediction based on the mathematical theory of Polynomial Chaos Expansions (PCE). Assuming univariate PCEs of the trajectory prediction inputs, the method describes how to generate multivariate PCEs of the prediction outputs that quantify their associated uncertainty. Arbitrary PCE (aPCE) was chosen because it allows a higher degree of flexibility to model input uncertainty. The obtained polynomial description can be used in subsequent prediction sensitivity analyses thanks to the relationship between polynomial coefficients and Sobol indices. The Sobol indices enable ranking the input parameters according to their influence on trajectory prediction uncertainty. The applicability of the aPCE-based uncertainty quantification detailed herein is analysed through a study case. This study case represents a typical aircraft trajectory prediction problem in ATM, in which uncertain parameters regarding aircraft performance, aircraft intent description, weather forecast, and initial conditions are considered simultaneously. Numerical results are compared to those obtained from a Monte Carlo simulation, demonstrating the advantages of the proposed method. The thesis includes two examples of DSTs (Demand and Capacity Balancing tool, and Arrival Manager) to illustrate the potential benefits of exploiting the proposed uncertainty quantification method.

Phase transitions and spatially ordered counterion association in ionic-lipid membranes: A statistical model

We propose a statistical model to account for the gel-fluid anomalous phase transitions in charged bilayer- or lamellae-forming ionic lipids. The model Hamiltonian comprises effective attractive interactions to describe neutral-lipid membranes as well as the effect of electrostatic repulsions of the discrete ionic charges on the lipid headgroups. The latter can be counterion dissociated (charged) or counterion associated (neutral), while the lipid acyl chains may be in gel (low-temperature or high-lateral-pressure) or fluid (high-temperature or low-lateral-pressure) states. The system is modeled as a lattice gas with two distinct particle types-each one associated, respectively, with the polar-headgroup and the acyl-chain states-which can be mapped onto an Ashkin-Teller model with the inclusion of cubic terms. The model displays a rich thermodynamic behavior in terms of the chemical potential of counterions (related to added salt concentration) and lateral pressure. In particular, we show the existence of semidissociated thermodynamic phases related to the onset of charge order in the system. This type of order stems from spatially ordered counterion association to the lipid headgroups, in which charged and neutral lipids alternate in a checkerboard-like order. Within the mean-field approximation, we predict that the acyl-chain order-disorder transition is discontinuous, with the first-order line ending at a critical point, as in the neutral case. Moreover, the charge order gives rise to continuous transitions, with the associated second-order lines joining the aforementioned first-order line at critical end points. We explore the thermodynamic behavior of some physical quantities, like the specific heat at constant lateral pressure and the degree of ionization, associated with the fraction of charged lipid headgroups.

Sampling phylogenetic tree space with the generalized Gibbs sampler

The generalized Gibbs sampler (GGS) is a recently developed Markov chain Monte Carlo (MCMC) technique that enables Gibbs-like sampling of state spaces that lack a convenient representation in terms of a fixed coordinate system. This paper describes a new sampler, called the tree sampler, which uses the GGS to sample from a state space consisting of phylogenetic trees. The tree sampler is useful for a wide range of phylogenetic applications, including Bayesian, maximum likelihood, and maximum parsimony methods. A fast new algorithm to search for a maximum parsimony phylogeny is presented, using the tree sampler in the context of simulated annealing. The mathematics underlying the algorithm is explained and its time complexity is analyzed. The method is tested on two large data sets consisting of 123 sequences and 500 sequences, respectively. The new algorithm is shown to compare very favorably in terms of speed and accuracy to the program DNAPARS from the PHYLIP package.