On the use of predictor-corrector method for coupled Monte Carlo burnup codes

This paper investigates the effect of the burnup coupling scheme on the numerical stability and accuracy of coupled Monte-Carlo depletion calculations. We show that in some cases, even the Predictor Corrector method with relatively short time steps can be numerically unstable. In addition, we present two possible extensions to the Euler predictor-corrector (PC) method, which is typically used in coupled burnup calculations. These modifications allow using longer time steps, while maintaining numerical stability and accuracy. © 2013 Elsevier Ltd. All rights reserved.

Numerical stability of the predictor-corrector method in Monte Carlo burnup calculations of critical reactors

Monte Carlo burnup codes use various schemes to solve the coupled criticality and burnup equations. Previous studies have shown that the simplest methods, such as the beginning-of-step and middle-of-step constant flux approximations, are numerically unstable in fuel cycle calculations of critical reactors. Here we show that even the predictor-corrector methods that are implemented in established Monte Carlo burnup codes can be numerically unstable in cycle calculations of large systems. © 2013 Elsevier Ltd. All rights reserved.

The stochastic implicit Euler method - A stable coupling scheme for Monte Carlo burnup calculations

Existing Monte Carlo burnup codes use various schemes to solve the coupled criticality and burnup equations. Previous studies have shown that the coupling schemes of the existing Monte Carlo burnup codes can be numerically unstable. Here we develop the Stochastic Implicit Euler method - a stable and efficient new coupling scheme. The implicit solution is obtained by the stochastic approximation at each time step. Our test calculations demonstrate that the Stochastic Implicit Euler method can provide an accurate solution to problems where the methods in the existing Monte Carlo burnup codes fail. © 2013 Elsevier Ltd. All rights reserved.

A stochastic model updating method for parameter variability quantification based on response surface models and Monte Carlo simulation

Stochastic model updating must be considered for quantifying uncertainties inherently existing in real-world engineering structures. By this means the statistical properties,instead of deterministic values, of structural parameters can be sought indicating the parameter variability. However, the implementation of stochastic model updating is much more complicated than that of deterministic methods particularly in the aspects of theoretical complexity and low computational efficiency. This study attempts to propose a simple and cost-efficient method by decomposing a stochastic updating process into a series of deterministic ones with the aid of response surface models and Monte Carlo simulation. The response surface models are used as surrogates for original FE models in the interest of programming simplification, fast response computation and easy inverse optimization. Monte Carlo simulation is adopted for generating samples from the assumed or measured probability distributions of responses. Each sample corresponds to an individual deterministic inverse process predicting the deterministic values of parameters. Then the parameter means and variances can be statistically estimated based on all the parameter predictions by running all the samples. Meanwhile, the analysis of variance approach is employed for the evaluation of parameter variability significance. The proposed method has been demonstrated firstly on a numerical beam and then a set of nominally identical steel plates tested in the laboratory. It is found that compared with the existing stochastic model updating methods, the proposed method presents similar accuracy while its primary merits consist in its simple implementation and cost efficiency in response computation and inverse optimization.

A cost-based optimization of a fiberboard pressing plant using Monte-Carlo simulation (a reliability program)

In this research the reliability and availability of fiberboard pressing plant is assessed and a cost-based optimization of the system using the Monte- Carlo simulation method is performed. The woodchip and pulp or engineered wood industry in Australia and around the world is a lucrative industry. One such industry is hardboard. The pressing system is the main system, as it converts the wet pulp to fiberboard. The assessment identified the pressing system has the highest downtime throughout the plant plus it represents the bottleneck in the process. A survey in the late nineties revealed there are over one thousand plants around the world, with the pressing system being a common system among these plants. No work has been done to assess or estimate the reliability of such a pressing system; therefore this assessment can be used for assessing any plant of this type.

Validation and automation of the DYNJAWS component module of the BEAMnrc Monte Carlo code

The purpose of this work is to validate and automate the use of DYNJAWS; a new component module (CM) in the BEAMnrc Monte Carlo (MC) user code. The DYNJAWS CM simulates dynamic wedges and can be used in three modes; dynamic, step-and-shoot and static. The step-and-shoot and dynamic modes require an additional input file defining the positions of the jaw that constitutes the dynamic wedge, at regular intervals during its motion. A method for automating the generation of the input file is presented which will allow for the more efficient use of the DYNJAWS CM. Wedged profiles have been measured and simulated for 6 and 10 MV photons at three field sizes (5 cm x 5 cm , 10 cm x10 cm and 20 cm x 20 cm), four wedge angles (15, 30, 45 and 60 degrees), at dmax and at 10 cm depth. Results of this study show agreement between the measured and the MC profiles to within 3% of absolute dose or 3 mm distance to agreement for all wedge angles at both energies and depths. The gamma analysis suggests that dynamic mode is more accurate than the step-and-shoot mode. The DYNJAWS CM is an important addition to the BEAMnrc code and will enable the MC verification of patient treatments involving dynamic wedges.

Comparison of scoring systems for invasive pests using ROC analysis and Monte Carlo simulation

Different international plant protection organisations advocate different schemes for conducting pest risk assessments. Most of these schemes use structured questionnaire in which experts are asked to score several items using an ordinal scale. The scores are then combined using a range of procedures, such as simple arithmetic mean, weighted averages, multiplication of scores, and cumulative sums. The most useful schemes will correctly identify harmful pests and identify ones that are not. As the quality of a pest risk assessment can depend on the characteristics of the scoring system used by the risk assessors (i.e., on the number of points of the scale and on the method used for combining the component scores), it is important to assess and compare the performance of different scoring systems. In this article, we proposed a new method for assessing scoring systems. Its principle is to simulate virtual data using a stochastic model and, then, to estimate sensitivity and specificity values from these data for different scoring systems. The interest of our approach was illustrated in a case study where several scoring systems were compared. Data for this analysis were generated using a probabilistic model describing the pest introduction process. The generated data were then used to simulate the outcome of scoring systems and to assess the accuracy of the decisions about positive and negative introduction. The results showed that ordinal scales with at most 5 or 6 points were sufficient and that the multiplication-based scoring systems performed better than their sum-based counterparts. The proposed method could be used in the future to assess a great diversity of scoring systems.

The development of Monte Carlo techniques for the verification of radiotherapy treatments

Radiotherapy is a cancer treatment modality in which a dose of ionising radiation is delivered to a tumour. The accurate calculation of the dose to the patient is very important in the design of an effective therapeutic strategy. This study aimed to systematically examine the accuracy of the radiotherapy dose calculations performed by clinical treatment planning systems by comparison againstMonte Carlo simulations of the treatment delivery. A suite of software tools known as MCDTK (Monte Carlo DICOM ToolKit) was developed for this purpose, and is capable of: • Importing DICOM-format radiotherapy treatment plans and producing Monte Carlo simulation input files (allowing simple simulation of complex treatments), and calibrating the results; • Analysing the predicted doses of and deviations between the Monte Carlo simulation results and treatment planning system calculations in regions of interest (tumours and organs-at-risk) and generating dose-volume histograms, so that conformity with dose prescriptions can be evaluated. The code has been tested against various treatment planning systems, linear acceleratormodels and treatment complexities. Six clinical head and neck cancer treatments were simulated and the results analysed using this software. The deviations were greatest where the treatment volume encompassed tissues on both sides of an air cavity. This was likely due to the method the planning system used to model low density media.

Monte Carlo simulations of dynamic radiotherapy treatments

The effects of tumour motion during radiation therapy delivery have been widely investigated. Motion effects have become increasingly important with the introduction of dynamic radiotherapy delivery modalities such as enhanced dynamic wedges (EDWs) and intensity modulated radiation therapy (IMRT) where a dynamically collimated radiation beam is delivered to the moving target, resulting in dose blurring and interplay effects which are a consequence of the combined tumor and beam motion. Prior to this work, reported studies on the EDW based interplay effects have been restricted to the use of experimental methods for assessing single-field non-fractionated treatments. In this work, the interplay effects have been investigated for EDW treatments. Single and multiple field treatments have been studied using experimental and Monte Carlo (MC) methods. Initially this work experimentally studies interplay effects for single-field non-fractionated EDW treatments, using radiation dosimetry systems placed on a sinusoidaly moving platform. A number of wedge angles (60º, 45º and 15º), field sizes (20 × 20, 10 × 10 and 5 × 5 cm2), amplitudes (10-40 mm in step of 10 mm) and periods (2 s, 3 s, 4.5 s and 6 s) of tumor motion are analysed (using gamma analysis) for parallel and perpendicular motions (where the tumor and jaw motions are either parallel or perpendicular to each other). For parallel motion it was found that both the amplitude and period of tumor motion affect the interplay, this becomes more prominent where the collimator tumor speeds become identical. For perpendicular motion the amplitude of tumor motion is the dominant factor where as varying the period of tumor motion has no observable effect on the dose distribution. The wedge angle results suggest that the use of a large wedge angle generates greater dose variation for both parallel and perpendicular motions. The use of small field size with a large tumor motion results in the loss of wedged dose distribution for both parallel and perpendicular motion. From these single field measurements a motion amplitude and period have been identified which show the poorest agreement between the target motion and dynamic delivery and these are used as the „worst case motion parameters.. The experimental work is then extended to multiple-field fractionated treatments. Here a number of pre-existing, multiple–field, wedged lung plans are delivered to the radiation dosimetry systems, employing the worst case motion parameters. Moreover a four field EDW lung plan (using a 4D CT data set) is delivered to the IMRT quality control phantom with dummy tumor insert over four fractions using the worst case parameters i.e. 40 mm amplitude and 6 s period values. The analysis of the film doses using gamma analysis at 3%-3mm indicate the non averaging of the interplay effects for this particular study with a gamma pass rate of 49%. To enable Monte Carlo modelling of the problem, the DYNJAWS component module (CM) of the BEAMnrc user code is validated and automated. DYNJAWS has been recently introduced to model the dynamic wedges. DYNJAWS is therefore commissioned for 6 MV and 10 MV photon energies. It is shown that this CM can accurately model the EDWs for a number of wedge angles and field sizes. The dynamic and step and shoot modes of the CM are compared for their accuracy in modelling the EDW. It is shown that dynamic mode is more accurate. An automation of the DYNJAWS specific input file has been carried out. This file specifies the probability of selection of a subfield and the respective jaw coordinates. This automation simplifies the generation of the BEAMnrc input files for DYNJAWS. The DYNJAWS commissioned model is then used to study multiple field EDW treatments using MC methods. The 4D CT data of an IMRT phantom with the dummy tumor is used to produce a set of Monte Carlo simulation phantoms, onto which the delivery of single field and multiple field EDW treatments is simulated. A number of static and motion multiple field EDW plans have been simulated. The comparison of dose volume histograms (DVHs) and gamma volume histograms (GVHs) for four field EDW treatments (where the collimator and patient motion is in the same direction) using small (15º) and large wedge angles (60º) indicates a greater mismatch between the static and motion cases for the large wedge angle. Finally, to use gel dosimetry as a validation tool, a new technique called the „zero-scan method. is developed for reading the gel dosimeters with x-ray computed tomography (CT). It has been shown that multiple scans of a gel dosimeter (in this case 360 scans) can be used to reconstruct a zero scan image. This zero scan image has a similar precision to an image obtained by averaging the CT images, without the additional dose delivered by the CT scans. In this investigation the interplay effects have been studied for single and multiple field fractionated EDW treatments using experimental and Monte Carlo methods. For using the Monte Carlo methods the DYNJAWS component module of the BEAMnrc code has been validated and automated and further used to study the interplay for multiple field EDW treatments. Zero-scan method, a new gel dosimetry readout technique has been developed for reading the gel images using x-ray CT without losing the precision and accuracy.

Marginal reversible jump Markov chain Monte Carlo with application to motor unit number estimation

Motor unit number estimation (MUNE) is a method which aims to provide a quantitative indicator of progression of diseases that lead to loss of motor units, such as motor neurone disease. However the development of a reliable, repeatable and fast real-time MUNE method has proved elusive hitherto. Ridall et al. (2007) implement a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm to produce a posterior distribution for the number of motor units using a Bayesian hierarchical model that takes into account biological information about motor unit activation. However we find that the approach can be unreliable for some datasets since it can suffer from poor cross-dimensional mixing. Here we focus on improved inference by marginalising over latent variables to create the likelihood. In particular we explore how this can improve the RJMCMC mixing and investigate alternative approaches that utilise the likelihood (e.g. DIC (Spiegelhalter et al., 2002)). For this model the marginalisation is over latent variables which, for a larger number of motor units, is an intractable summation over all combinations of a set of latent binary variables whose joint sample space increases exponentially with the number of motor units. We provide a tractable and accurate approximation for this quantity and also investigate simulation approaches incorporated into RJMCMC using results of Andrieu and Roberts (2009).

Monte Carlo verification of intensity modulated radiotherapy treatments using EPIDS

Purpose: Electronic Portal Imaging Devices (EPIDs) are available with most linear accelerators (Amonuk, 2002), the current technology being amorphous silicon flat panel imagers. EPIDs are currently used routinely in patient positioning before radiotherapy treatments. There has been an increasing interest in using EPID technology tor dosimetric verification of radiotherapy treatments (van Elmpt, 2008). A straightforward technique involves the EPID panel being used to measure the fluence exiting the patient during a treatment which is then compared to a prediction of the fluence based on the treatment plan. However, there are a number of significant limitations which exist in this Method: Resulting in a limited proliferation ot this technique in a clinical environment. In this paper, we aim to present a technique of simulating IMRT fields using Monte Carlo to predict the dose in an EPID which can then be compared to the measured dose in the EPID. Materials: Measurements were made using an iView GT flat panel a-SI EPfD mounted on an Elekta Synergy linear accelerator. The images from the EPID were acquired using the XIS software (Heimann Imaging Systems). Monte Carlo simulations were performed using the BEAMnrc and DOSXVZnrc user codes. The IMRT fieids to be delivered were taken from the treatment planning system in DICOMRT format and converted into BEAMnrc and DOSXYZnrc input files using an in-house application (Crowe, 2009). Additionally. all image processing and analysis was performed using another in-house application written using the Interactive Data Language (IDL) (In Visual Information Systems). Comparison between the measured and Monte Carlo EPID images was performed using a gamma analysis (Low, 1998) incorporating dose and distance to agreement criteria. Results: The fluence maps recorded by the EPID were found to provide good agreement between measured and simulated data. Figure 1 shows an example of measured and simulated IMRT dose images and profiles in the x and y directions. "A technique for the quantitative evaluation of dose distributions", Med Phys, 25(5) May 1998 S. Crowe, 1. Kairn, A. Fielding, "The Development of a Monte Carlo system to verify Radiotherapy treatment dose calculations", Radiotherapy & Oncology, Volume 92, Supplement 1, August 2009, Pages S71-S71.

Controlled Monte Carlo data generation for statistical damage identification employing Mahalanobis squared distance

The use of Mahalanobis squared distance–based novelty detection in statistical damage identification has become increasingly popular in recent years. The merit of the Mahalanobis squared distance–based method is that it is simple and requires low computational effort to enable the use of a higher dimensional damage-sensitive feature, which is generally more sensitive to structural changes. Mahalanobis squared distance–based damage identification is also believed to be one of the most suitable methods for modern sensing systems such as wireless sensors. Although possessing such advantages, this method is rather strict with the input requirement as it assumes the training data to be multivariate normal, which is not always available particularly at an early monitoring stage. As a consequence, it may result in an ill-conditioned training model with erroneous novelty detection and damage identification outcomes. To date, there appears to be no study on how to systematically cope with such practical issues especially in the context of a statistical damage identification problem. To address this need, this article proposes a controlled data generation scheme, which is based upon the Monte Carlo simulation methodology with the addition of several controlling and evaluation tools to assess the condition of output data. By evaluating the convergence of the data condition indices, the proposed scheme is able to determine the optimal setups for the data generation process and subsequently avoid unnecessarily excessive data. The efficacy of this scheme is demonstrated via applications to a benchmark structure data in the field.