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.

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

Introduction: Recent advances in the planning and delivery of radiotherapy treatments have resulted in improvements in the accuracy and precision with which therapeutic radiation can be administered. As the complexity of the treatments increases it becomes more difficult to predict the dose distribution in the patient accurately. Monte Carlo (MC) methods have the potential to improve the accuracy of the dose calculations and are increasingly being recognised as the ‘gold standard’ for predicting dose deposition in the patient [1]. This project has three main aims: 1. To develop tools that enable the transfer of treatment plan information from the treatment planning system (TPS) to a MC dose calculation engine. 2. To develop tools for comparing the 3D dose distributions calculated by the TPS and the MC dose engine. 3. To investigate the radiobiological significance of any errors between the TPS patient dose distribution and the MC dose distribution in terms of Tumour Control Probability (TCP) and Normal Tissue Complication Probabilities (NTCP). The work presented here addresses the first two aims. Methods: (1a) Plan Importing: A database of commissioned accelerator models (Elekta Precise and Varian 2100CD) has been developed for treatment simulations in the MC system (EGSnrc/BEAMnrc). Beam descriptions can be exported from the TPS using the widespread DICOM framework, and the resultant files are parsed with the assistance of a software library (PixelMed Java DICOM Toolkit). The information in these files (such as the monitor units, the jaw positions and gantry orientation) is used to construct a plan-specific accelerator model which allows an accurate simulation of the patient treatment field. (1b) Dose Simulation: The calculation of a dose distribution requires patient CT images which are prepared for the MC simulation using a tool (CTCREATE) packaged with the system. Beam simulation results are converted to absolute dose per- MU using calibration factors recorded during the commissioning process and treatment simulation. These distributions are combined according to the MU meter settings stored in the exported plan to produce an accurate description of the prescribed dose to the patient. (2) Dose Comparison: TPS dose calculations can be obtained using either a DICOM export or by direct retrieval of binary dose files from the file system. Dose difference, gamma evaluation and normalised dose difference algorithms [2] were employed for the comparison of the TPS dose distribution and the MC dose distribution. These implementations are spatial resolution independent and able to interpolate for comparisons. Results and Discussion: The tools successfully produced Monte Carlo input files for a variety of plans exported from the Eclipse (Varian Medical Systems) and Pinnacle (Philips Medical Systems) planning systems: ranging in complexity from a single uniform square field to a five-field step and shoot IMRT treatment. The simulation of collimated beams has been verified geometrically, and validation of dose distributions in a simple body phantom (QUASAR) will follow. The developed dose comparison algorithms have also been tested with controlled dose distribution changes. Conclusion: The capability of the developed code to independently process treatment plans has been demonstrated. A number of limitations exist: only static fields are currently supported (dynamic wedges and dynamic IMRT will require further development), and the process has not been tested for planning systems other than Eclipse and Pinnacle. The tools will be used to independently assess the accuracy of the current treatment planning system dose calculation algorithms for complex treatment deliveries such as IMRT in treatment sites where patient inhomogeneities are expected to be significant. Acknowledgements: Computational resources and services used in this work were provided by the HPC and Research Support Group, Queensland University of Technology, Brisbane, Australia. Pinnacle dose parsing made possible with the help of Paul Reich, North Coast Cancer Institute, North Coast, New South Wales.

Development of empirical equations for irradiance profile of a standard parabolic trough collector using Monte Carlo ray tracing technique

Irradiance profile around the receiver tube (RT) of a parabolic trough collector (PTC) is a key effect of optical performance that affects the overall energy performance of the collector. Thermal performance evaluation of the RT relies on the appropriate determination of the irradiance profile. This article explains a technique in which empirical equations were developed to calculate the local irradiance as a function of angular location of the RT of a standard PTC using a vigorously verified Monte Carlo ray tracing model. A large range of test conditions including daily normal insolation, spectral selective coatings and glass envelop conditions were selected from the published data by Dudley et al. [1] for the job. The R2 values of the equations are excellent that vary in between 0.9857 and 0.9999. Therefore, these equations can be used confidently to produce realistic non-uniform boundary heat flux profile around the RT at normal incidence for conjugate heat transfer analyses of the collector. Required values in the equations are daily normal insolation, and the spectral selective properties of the collector components. Since the equations are polynomial functions, data processing software can be employed to calculate the flux profile very easily and quickly. The ultimate goal of this research is to make the concentrating solar power technology cost competitive with conventional energy technology facilitating its ongoing research.

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.

A sequential Monte Carlo framework for adaptive Bayesian model discrimination designs using mutual information

In this paper we present a unified sequential Monte Carlo (SMC) framework for performing sequential experimental design for discriminating between a set of models. The model discrimination utility that we advocate is fully Bayesian and based upon the mutual information. SMC provides a convenient way to estimate the mutual information. Our experience suggests that the approach works well on either a set of discrete or continuous models and outperforms other model discrimination approaches.

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.

Using narrow beam profiles to quantify focal spot size, for accurate Monte Carlo simulations of SRS/SRT systems

This study investigates the variation of photon field penumbra shape with initial electron beam diameter, for very narrow beams. A Varian Millenium MLC (Varian Medical Systems, Palo Alto, USA) and a Brainlab m3 microMLC (Brainlab AB. Feldkirchen, Germany) were used, with one Varian iX linear accelerator, to produce fields that were (nominally) 0.20 cm across. Dose profiles for these fields were measured using radiochromic film and compared with the results of simulations completed using BEAMnrc and DOSXYZnrc, where the initial electron beam was set to FWHM = 0.02, 0.10, 0.12, 0.15, 0.20 and 0.50 cm. Increasing the electron-beam FWHM produced increasing occlusion of the photon source by the closely spaced collimator leaves and resulted in blurring of the simulated profile widths from 0.26 to 0.64 cm, for the MLC, from 0.12 to 0.43 cm, for the microMLC. Comparison with measurement data suggested that the electron spot size in the clinical linear accelerator was between FWHM = 0.10 and 0.15 cm, encompassing the result of our previous output-factor based work, which identified a FWHM of 0.12. Investigation of narrow-beam penumbra variation has been found to be a useful procedure, with results varying noticeably with linear accelerator spot size and allowing FWHM estimates obtained using other methods to be verified.

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.

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.

Monte Carlo dosimetry for stereotactic radiosurgery

Stereotactic radiosurgery (SRS) treatments for brain cancers require small and precisely shaped photon beams. These beams can be generated by fitting a linear accelerator with a micro-multileaf collimator (mMLC) such as the BrainLAB m3, which offers greater flexibility for field shaping than standard SRS cone collimators

Field validation of controlled Monte Carlo data generation for statistical damage identification employing Mahalanobis squared distance

This article presents the field applications and validations for the controlled Monte Carlo data generation scheme. This scheme was previously derived to assist the Mahalanobis squared distance–based damage identification method to cope with data-shortage problems which often cause inadequate data multinormality and unreliable identification outcome. To do so, real-vibration datasets from two actual civil engineering structures with such data (and identification) problems are selected as the test objects which are then shown to be in need of enhancement to consolidate their conditions. By utilizing the robust probability measures of the data condition indices in controlled Monte Carlo data generation and statistical sensitivity analysis of the Mahalanobis squared distance computational system, well-conditioned synthetic data generated by an optimal controlled Monte Carlo data generation configurations can be unbiasedly evaluated against those generated by other set-ups and against the original data. The analysis results reconfirm that controlled Monte Carlo data generation is able to overcome the shortage of observations, improve the data multinormality and enhance the reliability of the Mahalanobis squared distance–based damage identification method particularly with respect to false-positive errors. The results also highlight the dynamic structure of controlled Monte Carlo data generation that makes this scheme well adaptive to any type of input data with any (original) distributional condition.

Angular distribution of carbon ion flux in a nanotube array during the plasma process by the Monte Carlo technique

Angular distribution of microscopic ion fluxes around nanotubes arranged into a dense ordered pattern on the surface of the substrate is studied by means of multiscale numerical simulation. The Monte Carlo technique was used to show that the ion current density is distributed nonuniformly around the carbon nanotubes arranged into a dense rectangular array. The nonuniformity factor of the ion current flux reaches 7 in dense (5× 1018 m-3) plasmas for a nanotube radius of 25 nm, and tends to 1 at plasma densities below 1× 1017 m-3. The results obtained suggest that the local density of carbon adatoms on the nanotube side surface, at areas facing the adjacent nanotubes of the pattern, can be high enough to lead to the additional wall formation and thus cause the single- to multiwall structural transition, and other as yet unexplained nanoscience phenomena.

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.