Effect of CT electron density identification on Monte Carlo simulations of radiotherapeutic treatments

Introduction: The accurate identification of tissue electron densities is of great importance for Monte Carlo (MC) dose calculations. When converting patient CT data into a voxelised format suitable for MC simulations, however, it is common to simplify the assignment of electron densities so that the complex tissues existing in the human body are categorized into a few basic types. This study examines the effects that the assignment of tissue types and the calculation of densities can have on the results of MC simulations, for the particular case of a Siemen’s Sensation 4 CT scanner located in a radiotherapy centre where QA measurements are routinely made using 11 tissue types (plus air). Methods: DOSXYZnrc phantoms are generated from CT data, using the CTCREATE user code, with the relationship between Hounsfield units (HU) and density determined via linear interpolation between a series of specified points on the ‘CT-density ramp’ (see Figure 1(a)). Tissue types are assigned according to HU ranges. Each voxel in the DOSXYZnrc phantom therefore has an electron density (electrons/cm3) defined by the product of the mass density (from the HU conversion) and the intrinsic electron density (electrons /gram) (from the material assignment), in that voxel. In this study, we consider the problems of density conversion and material identification separately: the CT-density ramp is simplified by decreasing the number of points which define it from 12 down to 8, 3 and 2; and the material-type-assignment is varied by defining the materials which comprise our test phantom (a Supertech head) as two tissues and bone, two plastics and bone, water only and (as an extreme case) lead only. The effect of these parameters on radiological thickness maps derived from simulated portal images is investigated. Results & Discussion: Increasing the degree of simplification of the CT-density ramp results in an increasing effect on the resulting radiological thickness calculated for the Supertech head phantom. For instance, defining the CT-density ramp using 8 points, instead of 12, results in a maximum radiological thickness change of 0.2 cm, whereas defining the CT-density ramp using only 2 points results in a maximum radiological thickness change of 11.2 cm. Changing the definition of the materials comprising the phantom between water and plastic and tissue results in millimetre-scale changes to the resulting radiological thickness. When the entire phantom is defined as lead, this alteration changes the calculated radiological thickness by a maximum of 9.7 cm. Evidently, the simplification of the CT-density ramp has a greater effect on the resulting radiological thickness map than does the alteration of the assignment of tissue types. Conclusions: It is possible to alter the definitions of the tissue types comprising the phantom (or patient) without substantially altering the results of simulated portal images. However, these images are very sensitive to the accurate identification of the HU-density relationship. When converting data from a patient’s CT into a MC simulation phantom, therefore, all possible care should be taken to accurately reproduce the conversion between HU and mass density, for the specific CT scanner used. Acknowledgements: This work is funded by the NHMRC, through a project grant, and supported by the Queensland University of Technology (QUT) and the Royal Brisbane and Women's Hospital (RBWH), Brisbane, Australia. The authors are grateful to the staff of the RBWH, especially Darren Cassidy, for assistance in obtaining the phantom CT data used in this study. The authors also wish to thank Cathy Hargrave, of QUT, for assistance in formatting the CT data, using the Pinnacle TPS. Computational resources and services used in this work were provided by the HPC and Research Support Group, QUT, Brisbane, Australia.

Monte Carlo simulations of small field output factors in solid phantoms

Introduction Total scatter factor (or output factor) in megavoltage photon dosimetry is a measure of relative dose relating a certain field size to a reference field size. The use of solid phantoms has been well established for output factor measurements, however to date these phantoms have not been tested with small fields. In this work, we evaluate the water equivalency of a number of solid phantoms for small field output factor measurements using the EGSnrc Monte Carlo code. Methods The following small square field sizes were simulated using BEAMnrc: 5, 6, 7, 8, 10 and 30 mm. Each simulated phantom geometry was created in DOSXYZnrc and consisted of a silicon diode (of length and width 1.5 mm and depth 0.5 mm) submersed in the phantom at a depth of 5 g/cm2. The source-to-detector distance was 100 cm for all simulations. The dose was scored in a single voxel at the location of the diode. Interaction probabilities and radiation transport parameters for each material were created using custom PEGS4 files. Results A comparison of the resultant output factors in the solid phantoms, compared to the same factors in a water phantom are shown in Fig. 1. The statistical uncertainty in each point was less than or equal to 0.4 %. The results in Fig. 1 show that the density of the phantoms affected the output factor results, with higher density materials (such as PMMA) resulting in higher output factors. Additionally, it was also calculated that scaling the depth for equivalent path length had negligible effect on the output factor results at these field sizes. Discussion and conclusions Electron stopping power and photon mass energy absorption change minimally with small field size [1]. Also, it can be seen from Fig. 1 that the difference from water decreases with increasing field size. Therefore, the most likely cause for the observed discrepancies in output factors is differing electron disequilibrium as a function of phantom density. When measuring small field output factors in a solid phantom, it is important that the density is very close to that of water.

Effects of collimator backscatter in an Elekta linac by Monte Carlo simulation

The effects of radiation backscattered from the secondary collimators into the monitor chamber in an Elekta linac (producing 6 and 10 MV photon beams) are investigated using BEAMnrc Monte Carlo simulations. The degree and effects of this backscattered radiation are assessed by evaluating the changes to the calculated dose in the monitor chamber, and by determining a correction factor for those changes. Additionally, the fluency and energy characteristics of particles entering the monitor chamber from the downstream direction are evaluated by examining BEAMnrc phase-space data. It is shown that the proportion of particles backscattered into the monitor chamber is small (<0.35 %), for all field sizes studied. However, when the backscatter plate is removed from the model linac, these backscattered particles generate a noticeable increase in dose to the monitor chamber (up to approximate to 2.4 % for the 6 MV beam and up to 4.4 % for the 10 MV beam). With its backscatter plate in place, the Elekta linac (operating at 6 and 10 MV) is subject to negligible variation of monitor chamber dose with field size. At these energies, output variations in photon beams produced by the clinical Elekta linear accelerator can be attributed to head scatter alone. Corrections for field-size-dependence of monitor chamber dose are not necessary when running Monte Carlo simulations of the Elekta linac operating at 6 and 10 MV.

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.

Experimental evaluation of MCDTK, the Monte Carlo DICOM Tool-Kit

The Monte Carlo DICOM Tool-Kit (MCDTK) is a software suite designed for treatment plan dose verification, using the BEAMnrc and DOSXYZnrc Monte Carlo codes. MCDTK converts DICOM-format treatment plan information into Monte Carlo input files and compares the results of Monte Carlo treatment simulations with conventional treatment planning dose calculations. In this study, a treatment is planned using a commercial treatment planning system, delivered to a pelvis phantom containing ten thermoluminescent dosimeters and simulated using BEAMnrc and DOSXYZnrc using inputs derived from MCDTK. The dosimetric accuracy of the Monte Carlo data is then evaluated via comparisons with the dose distribution obtained from the treatment planning system as well as the in-phantom point dose measurements. The simulated beam arrangement produced by MCDTK is found to be in geometric agreement with the planned treatment. An isodose display generated from the Monte Carlo data by MCDTK shows general agreement with the isodose display obtained from the treatment planning system, except for small regions around density heterogeneities in the phantom, where the pencil-beam dose calculation performed by the treatment planning systemis likely to be less accurate. All point dose measurements agree with the Monte Carlo data obtained using MCDTK, within confidence limits, and all except one of these point dose measurements show closer agreement with theMonte Carlo data than with the doses calculated by the treatment planning system. This study provides a simple demonstration of the geometric and dosimetric accuracy ofMonte Carlo simulations based on information from MCDTK.

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-based diode design for correction-less small field dosimetry

Due to their small collecting volume diodes are commonly used in small field dosimetry. However the relative sensitivity of a diode increases with decreasing small field size. Conversely, small air gaps have been shown to cause a significant decrease in the sensitivity of a detector as the field size is decreased. Therefore this study uses Monte Carlo simulations to look at introducing air upstream to diodes such that they measure with a constant sensitivity across all field sizes in small field dosimetry. Varying thicknesses of air were introduced onto the upstream end of two commercial diodes (PTW 60016 photon diode and PTW 60017 electron diode), as well as a theoretical unenclosed silicon chip using field sizes as small as 5 mm × 5 mm . The metric D_(w,Q)/D_(Det,Q) used in this study represents the ratio of the dose to a point of water to the dose to the diode active volume, for a particular field size and location. The optimal thickness of air required to provide a constant sensitivity across all small field sizes was found by plotting D_(w,Q)/D_(Det,Q) as a function of introduced air gap size for various field sizes, and finding the intersection point of these plots. That is, the point at which D_(w,Q)/D_(Det,Q) was constant for all field sizes was found. The optimal thickness of air was calculated to be 3.3 mm, 1.15 mm and 0.10 mm for the photon diode, electron diode and unenclosed silicon chip respectively. The variation in these results was due to the different design of each detector. When calculated with the new diode design incorporating the upstream air gap, k_(Q_clin 〖,Q〗_msr)^(f_clin 〖,f〗_msr ) was equal to unity to within statistical uncertainty (0.5 %) for all three diodes. Cross-axis profile measurements were also improved with the new detector design. The upstream air gap could be implanted on the commercial diodes via a cap consisting of the air cavity surrounded by water equivalent material. The results for the unclosed silicon chip show that an ideal small field dosimetry diode could be created by using a silicon chip with a small amount of air above it.

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.

A comparison of surface doses for very small field size x-ray beams : Monte Carlo calculations and radiochromic film measurements

Stereotactic radiosurgery treatments involve the delivery of very high doses for a small number of fractions. To date, there is limited data in terms of the skin dose for the very small field sizes used in these treatments. In this work, we determine relative surface doses for small size circular collimators as used in stereotactic radiosurgery treatments. Monte Carlo calculations were performed using the BEAMnrc code with a model of the Novalis 15 Trilogy linear accelerator and the BrainLab circular collimators. The surface doses were calculated at the ICRU skin dose depth of 70 m all using the 6 MV SRS x-ray beam. The calculated surface doses varied between 15 – 12% with decreasing values as the field size increased from 4 to 30 mm. In comparison, surface doses were measured using Gafchromic EBT3 film positioned at the surface of a Virtual Water phantom. The absolute agreement between calculated and measured surface doses was better than 2.5% which is well within the 20 uncertainties of the Monte Carlo calculations and the film measurements. Based on these results, we have shown that the Gafchromic EBT3 film is suitable for surface dose estimates in very small size fields as used in SRS.

The influence of Monte Carlo source parameters on detector design and dose perturbation in small field dosimetry

To obtain accurate Monte Carlo simulations of small radiation fields, it is important model the initial source parameters (electron energy and spot size) accurately. However recent studies have shown that small field dosimetry correction factors are insensitive to these parameters. The aim of this work is to extend this concept to test if these parameters affect dose perturbations in general, which is important for detector design and calculating perturbation correction factors. The EGSnrc C++ user code cavity was used for all simulations. Varying amounts of air between 0 and 2 mm were deliberately introduced upstream to a diode and the dose perturbation caused by the air was quantified. These simulations were then repeated using a range of initial electron energies (5.5 to 7.0 MeV) and electron spot sizes (0.7 to 2.2 FWHM). The resultant dose perturbations were large. For example 2 mm of air caused a dose reduction of up to 31% when simulated with a 6 mm field size. However these values did not vary by more than 2 % when simulated across the full range of source parameters tested. If a detector is modified by the introduction of air, one can be confident that the response of the detector will be the same across all similar linear accelerators and the Monte Carlo modelling of each machine is not required.

Assessment on the effect of pollution abatement on environmental efficiency with Markov chain Monte Carlo simulation

Both environmental economists and policy makers have shown a great deal of interest in the effect of pollution abatement on environmental efficiency. In line with the modern resources available, however, no contribution is brought to the environmental economics field with the Markov chain Monte Carlo (MCMC) application, which enables simulation from a distribution of a Markov chain and simulating from the chain until it approaches equilibrium. The probability density functions gained prominence with the advantages over classical statistical methods in its simultaneous inference and incorporation of any prior information on all model parameters. This paper concentrated on this point with the application of MCMC to the database of China, the largest developing country with rapid economic growth and serious environmental pollution in recent years. The variables cover the economic output and pollution abatement cost from the year 1992 to 2003. We test the causal direction between pollution abatement cost and environmental efficiency with MCMC simulation. We found that the pollution abatement cost causes an increase in environmental efficiency through the algorithm application, which makes it conceivable that the environmental policy makers should make more substantial measures to reduce pollution in the near future.

A pseudo-marginal sequential Monte Carlo algorithm for random effects models in Bayesian sequential design

A computationally efficient sequential Monte Carlo algorithm is proposed for the sequential design of experiments for the collection of block data described by mixed effects models. The difficulty in applying a sequential Monte Carlo algorithm in such settings is the need to evaluate the observed data likelihood, which is typically intractable for all but linear Gaussian models. To overcome this difficulty, we propose to unbiasedly estimate the likelihood, and perform inference and make decisions based on an exact-approximate algorithm. Two estimates are proposed: using Quasi Monte Carlo methods and using the Laplace approximation with importance sampling. Both of these approaches can be computationally expensive, so we propose exploiting parallel computational architectures to ensure designs can be derived in a timely manner. We also extend our approach to allow for model uncertainty. This research is motivated by important pharmacological studies related to the treatment of critically ill patients.