Combining Monte Carlo methods with coherent wave optics for the simulation of phase-sensitive X-ray imaging

Phase-sensitive X-ray imaging shows a high sensitivity towards electron density variations, making it well suited for imaging of soft tissue matter. However, there are still open questions about the details of the image formation process. Here, a framework for numerical simulations of phase-sensitive X-ray imaging is presented, which takes both particle- and wave-like properties of X-rays into consideration. A split approach is presented where we combine a Monte Carlo method (MC) based sample part with a wave optics simulation based propagation part, leading to a framework that takes both particle- and wave-like properties into account. The framework can be adapted to different phase-sensitive imaging methods and has been validated through comparisons with experiments for grating interferometry and propagation-based imaging. The validation of the framework shows that the combination of wave optics and MC has been successfully implemented and yields good agreement between measurements and simulations. This demonstrates that the physical processes relevant for developing a deeper understanding of scattering in the context of phase-sensitive imaging are modelled in a sufficiently accurate manner. The framework can be used for the simulation of phase-sensitive X-ray imaging, for instance for the simulation of grating interferometry or propagation-based imaging.

Forward treatment planning for modulated electron radiotherapy (MERT) employing Monte Carlo methods

PURPOSE This paper describes the development of a forward planning process for modulated electron radiotherapy (MERT). The approach is based on a previously developed electron beam model used to calculate dose distributions of electron beams shaped by a photon multi leaf collimator (pMLC). METHODS As the electron beam model has already been implemented into the Swiss Monte Carlo Plan environment, the Eclipse treatment planning system (Varian Medical Systems, Palo Alto, CA) can be included in the planning process for MERT. In a first step, CT data are imported into Eclipse and a pMLC shaped electron beam is set up. This initial electron beam is then divided into segments, with the electron energy in each segment chosen according to the distal depth of the planning target volume (PTV) in beam direction. In order to improve the homogeneity of the dose distribution in the PTV, a feathering process (Gaussian edge feathering) is launched, which results in a number of feathered segments. For each of these segments a dose calculation is performed employing the in-house developed electron beam model along with the macro Monte Carlo dose calculation algorithm. Finally, an automated weight optimization of all segments is carried out and the total dose distribution is read back into Eclipse for display and evaluation. One academic and two clinical situations are investigated for possible benefits of MERT treatment compared to standard treatments performed in our clinics and treatment with a bolus electron conformal (BolusECT) method. RESULTS The MERT treatment plan of the academic case was superior to the standard single segment electron treatment plan in terms of organs at risk (OAR) sparing. Further, a comparison between an unfeathered and a feathered MERT plan showed better PTV coverage and homogeneity for the feathered plan, with V95% increased from 90% to 96% and V107% decreased from 8% to nearly 0%. For a clinical breast boost irradiation, the MERT plan led to a similar homogeneity in the PTV compared to the standard treatment plan while the mean body dose was lower for the MERT plan. Regarding the second clinical case, a whole breast treatment, MERT resulted in a reduction of the lung volume receiving more than 45% of the prescribed dose when compared to the standard plan. On the other hand, the MERT plan leads to a larger low-dose lung volume and a degraded dose homogeneity in the PTV. For the clinical cases evaluated in this work, treatment plans using the BolusECT technique resulted in a more homogenous PTV and CTV coverage but higher doses to the OARs than the MERT plans. CONCLUSIONS MERT treatments were successfully planned for phantom and clinical cases, applying a newly developed intuitive and efficient forward planning strategy that employs a MC based electron beam model for pMLC shaped electron beams. It is shown that MERT can lead to a dose reduction in OARs compared to other methods. The process of feathering MERT segments results in an improvement of the dose homogeneity in the PTV.

The Utilization of Classical Spin Monte Carlo Methods to Simulate the Magnetic Behavior of Extended Three-Dimensional Cubic Networks Incorporating M(II) Ions with an S = 5/2 Ground State Spin

The numerical simulations of the magnetic properties of extended three-dimensional networks containing M(II) ions with an S = 5/2 ground-state spin have been carried out within the framework of the isotropic Heisenberg model. Analytical expressions fitting the numerical simulations for the primitive cubic, diamond, together with (10−3) cubic networks have all been derived. With these empirical formulas in hands, we can now extract the interaction between the magnetic ions from the experimental data for these networks. In the case of the primitive cubic network, these expressions are directly compared with those from the high-temperature expansions of the partition function. A fit of the experimental data for three complexes, namely [(N(CH3)4][Mn(N3)] 1, [Mn(CN4)]n 2, and [FeII(bipy)3][MnII2(ox)3] 3, has been carried out. The best fits were those obtained using the following parameters, J = −3.5 cm-1, g = 2.01 (1); J = −8.3 cm-1, g = 1.95 (2); and J = −2.0 cm-1, g = 1.95 (3).

Treatment planning aspects and Monte Carlo methods in proton therapy

Over the last years, the interest in proton radiotherapy is rapidly increasing. Protons provide superior physical properties compared with conventional radiotherapy using photons. These properties result in depth dose curves with a large dose peak at the end of the proton track and the finite proton range allows sparing the distally located healthy tissue. These properties offer an increased flexibility in proton radiotherapy, but also increase the demand in accurate dose estimations. To carry out accurate dose calculations, first an accurate and detailed characterization of the physical proton beam exiting the treatment head is necessary for both currently available delivery techniques: scattered and scanned proton beams. Since Monte Carlo (MC) methods follow the particle track simulating the interactions from first principles, this technique is perfectly suited to accurately model the treatment head. Nevertheless, careful validation of these MC models is necessary. While for the dose estimation pencil beam algorithms provide the advantage of fast computations, they are limited in accuracy. In contrast, MC dose calculation algorithms overcome these limitations and due to recent improvements in efficiency, these algorithms are expected to improve the accuracy of the calculated dose distributions and to be introduced in clinical routine in the near future.

Comparison of monte carlo collimator transport methods for photon treatment planning in radiotherapy

The aim of this work was a Monte Carlo (MC) based investigation of the impact of different radiation transport methods in collimators of a linear accelerator on photon beam characteristics, dose distributions, and efficiency. Thereby it is investigated if it is possible to use different simplifications in the radiation transport for some clinical situations in order to save calculation time.

Monte Carlo implementation, validation, and characterization of a 120 leaf MLC

Recently, the new high definition multileaf collimator (HD120 MLC) was commercialized by Varian Medical Systems providing high resolution in the center section of the treatment field. The aim of this work is to investigate the characteristics of the HD120 MLC using Monte Carlo (MC) methods.

An efficient framework for photon Monte Carlo treatment planning

Currently photon Monte Carlo treatment planning (MCTP) for a patient stored in the patient database of a treatment planning system (TPS) can usually only be performed using a cumbersome multi-step procedure where many user interactions are needed. This means automation is needed for usage in clinical routine. In addition, because of the long computing time in MCTP, optimization of the MC calculations is essential. For these purposes a new graphical user interface (GUI)-based photon MC environment has been developed resulting in a very flexible framework. By this means appropriate MC transport methods are assigned to different geometric regions by still benefiting from the features included in the TPS. In order to provide a flexible MC environment, the MC particle transport has been divided into different parts: the source, beam modifiers and the patient. The source part includes the phase-space source, source models and full MC transport through the treatment head. The beam modifier part consists of one module for each beam modifier. To simulate the radiation transport through each individual beam modifier, one out of three full MC transport codes can be selected independently. Additionally, for each beam modifier a simple or an exact geometry can be chosen. Thereby, different complexity levels of radiation transport are applied during the simulation. For the patient dose calculation, two different MC codes are available. A special plug-in in Eclipse providing all necessary information by means of Dicom streams was used to start the developed MC GUI. The implementation of this framework separates the MC transport from the geometry and the modules pass the particles in memory; hence, no files are used as the interface. The implementation is realized for 6 and 15 MV beams of a Varian Clinac 2300 C/D. Several applications demonstrate the usefulness of the framework. Apart from applications dealing with the beam modifiers, two patient cases are shown. Thereby, comparisons are performed between MC calculated dose distributions and those calculated by a pencil beam or the AAA algorithm. Interfacing this flexible and efficient MC environment with Eclipse allows a widespread use for all kinds of investigations from timing and benchmarking studies to clinical patient studies. Additionally, it is possible to add modules keeping the system highly flexible and efficient.

Monte Carlo simulation of a dynamic MLC: implementation and applications

PURPOSE: Study of behavior and influence of a multileaf collimator (MLC) on dose calculation, verification, and portal energy spectra in the case of intensity-modulated fields obtained with a step-and-shoot or a dynamic technique. METHODS: The 80-leaf MLC for the Varian Clinac 2300 C/D was implemented in a previously developed Monte Carlo (MC) based multiple source model (MSM) for a 6 MV photon beam. Using this model and the MC program GEANT, dose distributions, energy fluence maps and energy spectra at different portal planes were calculated for three different MLC applications. RESULTS: The comparison of MC-calculated dose distributions in the phantom and portal plane, with those measured with films showed an agreement within 3% and 1.5 mm for all cases studied. The deviations mainly occur in the extremes of the intensity modulation. The MC method allows to investigate, among other aspects, dose components, energy fluence maps, tongue-and-groove effects and energy spectra at portal planes. CONCLUSION: The MSM together with the implementation of the MLC is appropriate for a number of investigations in intensity-modulated radiation therapy (IMRT).

Monte Carlo based beam model using a photon MLC for modulated electron radiotherapy

PURPOSE Modulated electron radiotherapy (MERT) promises sparing of organs at risk for certain tumor sites. Any implementation of MERT treatment planning requires an accurate beam model. The aim of this work is the development of a beam model which reconstructs electron fields shaped using the Millennium photon multileaf collimator (MLC) (Varian Medical Systems, Inc., Palo Alto, CA) for a Varian linear accelerator (linac). METHODS This beam model is divided into an analytical part (two photon and two electron sources) and a Monte Carlo (MC) transport through the MLC. For dose calculation purposes the beam model has been coupled with a macro MC dose calculation algorithm. The commissioning process requires a set of measurements and precalculated MC input. The beam model has been commissioned at a source to surface distance of 70 cm for a Clinac 23EX (Varian Medical Systems, Inc., Palo Alto, CA) and a TrueBeam linac (Varian Medical Systems, Inc., Palo Alto, CA). For validation purposes, measured and calculated depth dose curves and dose profiles are compared for four different MLC shaped electron fields and all available energies. Furthermore, a measured two-dimensional dose distribution for patched segments consisting of three 18 MeV segments, three 12 MeV segments, and a 9 MeV segment is compared with corresponding dose calculations. Finally, measured and calculated two-dimensional dose distributions are compared for a circular segment encompassed with a C-shaped segment. RESULTS For 15 × 34, 5 × 5, and 2 × 2 cm(2) fields differences between water phantom measurements and calculations using the beam model coupled with the macro MC dose calculation algorithm are generally within 2% of the maximal dose value or 2 mm distance to agreement (DTA) for all electron beam energies. For a more complex MLC pattern, differences between measurements and calculations are generally within 3% of the maximal dose value or 3 mm DTA for all electron beam energies. For the two-dimensional dose comparisons, the differences between calculations and measurements are generally within 2% of the maximal dose value or 2 mm DTA. CONCLUSIONS The results of the dose comparisons suggest that the developed beam model is suitable to accurately reconstruct photon MLC shaped electron beams for a Clinac 23EX and a TrueBeam linac. Hence, in future work the beam model will be utilized to investigate the possibilities of MERT using the photon MLC to shape electron beams.

Recent Advances in Adaptive Sampling and Reconstruction for Monte Carlo Rendering

Monte Carlo integration is firmly established as the basis for most practical realistic image synthesis algorithms because of its flexibility and generality. However, the visual quality of rendered images often suffers from estimator variance, which appears as visually distracting noise. Adaptive sampling and reconstruction algorithms reduce variance by controlling the sampling density and aggregating samples in a reconstruction step, possibly over large image regions. In this paper we survey recent advances in this area. We distinguish between “a priori” methods that analyze the light transport equations and derive sampling rates and reconstruction filters from this analysis, and “a posteriori” methods that apply statistical techniques to sets of samples to drive the adaptive sampling and reconstruction process. They typically estimate the errors of several reconstruction filters, and select the best filter locally to minimize error. We discuss advantages and disadvantages of recent state-of-the-art techniques, and provide visual and quantitative comparisons. Some of these techniques are proving useful in real-world applications, and we aim to provide an overview for practitioners and researchers to assess these approaches. In addition, we discuss directions for potential further improvements.

Denoising Your Monte Carlo Renders: Recent Advances in Image Space-Adaptive Sampling and Reconstruction

With the ongoing shift in the computer graphics industry toward Monte Carlo rendering, there is a need for effective, practical noise-reduction techniques that are applicable to a wide range of rendering effects and easily integrated into existing production pipelines. This course surveys recent advances in image-space adaptive sampling and reconstruction algorithms for noise reduction, which have proven very effective at reducing the computational cost of Monte Carlo techniques in practice. These approaches leverage advanced image-filtering techniques with statistical methods for error estimation. They are attractive because they can be integrated easily into conventional Monte Carlo rendering frameworks, they are applicable to most rendering effects, and their computational overhead is modest.

Monte Carlo dose calculation improvements for low energy electron beams using eMC

The electron Monte Carlo (eMC) dose calculation algorithm in Eclipse (Varian Medical Systems) is based on the macro MC method and is able to predict dose distributions for high energy electron beams with high accuracy. However, there are limitations for low energy electron beams. This work aims to improve the accuracy of the dose calculation using eMC for 4 and 6 MeV electron beams of Varian linear accelerators. Improvements implemented into the eMC include (1) improved determination of the initial electron energy spectrum by increased resolution of mono-energetic depth dose curves used during beam configuration; (2) inclusion of all the scrapers of the applicator in the beam model; (3) reduction of the maximum size of the sphere to be selected within the macro MC transport when the energy of the incident electron is below certain thresholds. The impact of these changes in eMC is investigated by comparing calculated dose distributions for 4 and 6 MeV electron beams at source to surface distance (SSD) of 100 and 110 cm with applicators ranging from 6 x 6 to 25 x 25 cm(2) of a Varian Clinac 2300C/D with the corresponding measurements. Dose differences between calculated and measured absolute depth dose curves are reduced from 6% to less than 1.5% for both energies and all applicators considered at SSD of 100 cm. Using the original eMC implementation, absolute dose profiles at depths of 1 cm, d(max) and R50 in water lead to dose differences of up to 8% for applicators larger than 15 x 15 cm(2) at SSD 100 cm. Those differences are now reduced to less than 2% for all dose profiles investigated when the improved version of eMC is used. At SSD of 110 cm the dose difference for the original eMC version is even more pronounced and can be larger than 10%. Those differences are reduced to within 2% or 2 mm with the improved version of eMC. In this work several enhancements were made in the eMC algorithm leading to significant improvements in the accuracy of the dose calculation for 4 and 6 MeV electron beams of Varian linear accelerators.

Monte Carlo Dose Calculation on Deforming Anatomy

This article presents the implementation and validation of a dose calculation approach for deforming anatomical objects. Deformation is represented by deformation vector fields leading to deformed voxel grids representing the different deformation scenarios. Particle transport in the resulting deformed voxels is handled through the approximation of voxel surfaces by triangles in the geometry implementation of the Swiss Monte Carlo Plan framework. The focus lies on the validation methodology which uses computational phantoms representing the same physical object through regular and irregular voxel grids. These phantoms are chosen such that the new implementation for a deformed voxel grid can be compared directly with an established dose calculation algorithm for regular grids. Furthermore, separate validation of the aspects voxel geometry and the density changes resulting from deformation is achieved through suitable design of the validation phantom. We show that equivalent results are obtained with the proposed method and that no statistically significant errors are introduced through the implementation for irregular voxel geometries. This enables the use of the presented and validated implementation for further investigations of dose calculation on deforming anatomy.