Denoising of Monte Carlo dose calculations: smoothing capabilities versus introduction of systematic bias.

In order to evaluate the performance of denoising algorithms applied to Monte Carlo calculated dose distributions, conventional evaluation methods (rms difference, 1% and 2% difference) can be used. However, it is illustrated that these evaluation methods sometimes underestimate the introduction of bias, since possible bias effects are averaged out over the complete dose distribution. In the present work, a new evaluation method is introduced based on a sliding window superimposed on a difference dose distribution (reference dose-noisy/denoised dose). To illustrate its importance, a new denoising technique (ANRT) is presented based upon a combination of the principles of bilateral filtering and Savitzky-Golay filters. This technique is very conservative in order to limit the introduction of bias in high dose gradient regions. ANRT is compared with IRON for three challenging cases, namely an electron and photon beam impinging on heterogeneous phantoms and two IMRT treatment plans of head-and-neck cancer patients to determine the clinical relevance of the obtained results. For the electron beam case, IRON outperforms ANRT concerning the smoothing capabilities, while no differences in systematic bias are observed. However, for the photon beam case, although ANRT and IRON perform equally well on the conventional evaluation tests (rms difference, 1% and 2% difference), IRON clearly introduces much more bias in the penumbral regions while ANRT seems to introduce no bias at all. When applied to the IMRT patient cases, both denoising methods perform equally well regarding smoothing and bias introduction. This is probably caused by the summation of a large set of different beam segments, decreasing dose gradients compared to a single beam. A reduction in calculation time without introducing large systematic bias can shorten a Monte Carlo treatment planning process considerably and is therefore very useful for the initial trial and error phase of the treatment planning process.

A comparison of Monte Carlo dose calculation denoising techniques.

Recent studies have demonstrated that Monte Carlo (MC) denoising techniques can reduce MC radiotherapy dose computation time significantly by preferentially eliminating statistical fluctuations ('noise') through smoothing. In this study, we compare new and previously published approaches to MC denoising, including 3D wavelet threshold denoising with sub-band adaptive thresholding, content adaptive mean-median-hybrid (CAMH) filtering, locally adaptive Savitzky-Golay curve-fitting (LASG), anisotropic diffusion (AD) and an iterative reduction of noise (IRON) method formulated as an optimization problem. Several challenging phantom and computed-tomography-based MC dose distributions with varying levels of noise formed the test set. Denoising effectiveness was measured in three ways: by improvements in the mean-square-error (MSE) with respect to a reference (low noise) dose distribution; by the maximum difference from the reference distribution and by the 'Van Dyk' pass/fail criteria of either adequate agreement with the reference image in low-gradient regions (within 2% in our case) or, in high-gradient regions, a distance-to-agreement-within-2% of less than 2 mm. Results varied significantly based on the dose test case: greater reductions in MSE were observed for the relatively smoother phantom-based dose distribution (up to a factor of 16 for the LASG algorithm); smaller reductions were seen for an intensity modulated radiation therapy (IMRT) head and neck case (typically, factors of 2-4). Although several algorithms reduced statistical noise for all test geometries, the LASG method had the best MSE reduction for three of the four test geometries, and performed the best for the Van Dyk criteria. However, the wavelet thresholding method performed better for the head and neck IMRT geometry and also decreased the maximum error more effectively than LASG. In almost all cases, the evaluated methods provided acceleration of MC results towards statistically more accurate results.

Investigation of photon beam output factors for conformal radiation therapy--Monte Carlo simulations and measurements.

The purpose of this study was to investigate beam output factors (OFs) for conformal radiation therapy and to compare the OFs measured with different detectors with those simulated with Monte Carlo methods. Four different detectors (diode, diamond, pinpoint and ionization chamber) were used to measure photon beam OFs in a water phantom at a depth of 10 cm with a source-surface distance (SSD) of 100 cm. Square fields with widths ranging from 1 cm to 15 cm were observed; the OF for the different field sizes was normalized to that measured at a 5 cm x 5 cm field size at a depth of 10 cm. The BEAM/EGS4 program was used to simulate the exact geometry of a 6 MV photon beam generated by the linear accelerator, and the DOSXYZ-code was implemented to calculate the OFs for all field sizes. Two resolutions (0.1 cm and 0.5 cm voxel size) were chosen here. In addition, to model the detector four kinds of material, water, air, graphite or silicon, were placed in the corresponding voxels. Profiles and depth dose distributions resulting from the simulation show good agreement with the measurements. Deviations of less than 2% can be observed. The OF measured with different detectors in water vary by more than 35% for 1 cm x 1 cm fields. This result can also be found for the simulated OF with different voxel sizes and materials. For field sizes of at least 2 cm x 2 cm the deviations between all measurements and simulations are below 3%. This demonstrates that very small fields have a bad effect on dosimetric accuracy and precision. Finally, Monte Carlo methods can be significant in determining the OF for small fields.

[Verification of a fast Monte Carlo dose calculation algorithm by EGSnrc using the statistical separation method]. / Verifikation eines schnellen Monte-Carlo-Dosisberechnungsverfahrens durch EGSnrc anhand der statistischen Separationsmethode.

The recently developed XVMC code, a fast Monte Carlo (MC) algorithm to calculate the dose of photon and electron beams in treatment planning, was compared to EGSnrc, an enhanced version of the well-known EGS4 system. Because of the numerous and accurate verification measurements, this system can be considered as golden standard. The comparison was performed using phantoms consisting of water, lung tissue and bone. Dose profile and difference distributions showed good agreement within the accuracy requirements. Because deviations between the results of two MC algorithms are caused by systematic errors and statistical fluctuations, a separation method was used to quantify the systematic discrepancies. Using this method, it could be shown that there was good agreement between the three dimensional dose distributions, calculated with XVMC and EGSnrc, if maximum systematic deviation of 2% are accepted.

[Monte Carlo simulation of a dynamic multileaf collimator:implementation and applications]. / Monte-Carlo-Simulation von Multileafkollimatoren mit gekrümmten Lamellenenden.

A model for the simulation of the accelerator heads of two identical linear accelerators was designed at the University Hospital of Tübingen, using the BEAM program developed at the National Research Council of Canada. Both linear accelerators are equipped with multileaf collimators (MLCs) and backup jaws (y-direction) with curved leaf-ends. The accelerator models were divided into two parts. The first part consisted of target, primary collimator, flattening filter, monitor chamber, and mirror. After the Monte Carlo simulation of these parts, the phase-space characteristics below the mirror were stored in a file and used as source for the second part of the accelerator head (jaw, MLC). The electron source was assumed to deliver a gaussian energy spectrum, with parallel direction to the beam axis. With this electron source, there was good agreement between the measured and simulated depth dose curves in water, with difference < 2%. A new module was created for the BEAM program to simulate backup jaws, while the standard MLCQ module from BEAM was used to simulate a MLC with curved leaf-ends. As a result, MLCs and backup jaws with curved leaf-ends make the shoulder of the y-profile higher than the straight-end MLCs.

[Foundations of the Monte Carlo method for dose calculation in radiotherapy]. / Grundlagen der Monte-Carlo-Methode für die Dosisberechnung in der Strahlentherapie.

Monte Carlo (MC) methods applied in dose calculation are based on fundamental principles of radiation interaction with matter. In contrast to other methods, the accuracy of dose calculation achievable with MC depends only on the determination of the beam quality and the interaction coefficients. Using MC techniques it is possible to predict the dose for clinical photon and electron beams with an accuracy of > +/- 2%. Especially for inhomogeneous regions like head, neck, and lung, the MC technique can significantly improve the accuracy compared to conventional algorithms. Therefore, in the present paper the basic features of the MC method are reviewed in the context of treatment planning in radiation therapy. The main shortcoming in the past, i.e., that MC algorithms are too slow to be acceptable for clinical purposes, could be solved by using faster computers and by introducing new variance reduction (VR) techniques. These techniques decrease the statistical fluctuations without increasing the number of particle histories. Therefore, MC calculation times in the order of a few minutes are possible. A brief overview of VR methods is provided.

Film dosimetric verification of the Voxel Monte Carlo (VMC) algorithm with electron beam dose distributions.

Monte Carlo (MC) methods have the potential to predict radiation-therapy doses more accurately than any conventional technique, but normal MC simulations are very time consuming. Therefore, a fast MC code (Voxel Monte Carlo; VMC) was developed especially for radiation therapy purposes and experiments with the comparable precision were performed to demonstrate its accuracy. In the present study the dose distributions measured with film dosimetry in a cylindrical phantom were compared with calculations derived by VMC. The phantom consisted of 18 circular shaped PMMA slabs with a diameter of 20 cm and a thickness of approx. 1 cm. The films were placed between the slabs, and the whole phantom was irradiated with electron beams of different energies (6 MeV, 10 MeV, 18 MeV). The measured optical density distributions were then converted into dose distributions using characteristic curves of the film. Taking into account experimental uncertainties and statistical calculation fluctuations, agreement was found between measurements and VMC simulations with a maximal deviation of 3 mm on isodose curves for 18 MeV.

[Determination of the human tissue interaction parameters for Monte Carlo dose calculations in radiotherapy]. / Bestimmung der Wechselwirkungsparameter des menschlichen Gewebes für Monte-Carlo-Dosisberechnungen in der Strahlentherapie.

BACKGROUND: Monte Carlo dose calculation techniques for clinical photon and electron beams potentially predict the dose with an accuracy of better than +/- 2%. However, to achieve this precision, knowledge of the interaction properties in each volume element is essential. MATERIAL AND METHODS: In the present paper a method for mass density to total cross section conversion is described. This method is based on a detailed analysis of the interaction data for body tissues (ICRU Report 46) and allows the conversion without knowing the atomic composition. RESULTS: The analysis resulted in various fit functions allowing the calculation of interaction parameters for arbitrary materials using the corresponding cross sections in water. CONCLUSION: Together with standard procedures to calculate mass densities from a given CT number distribution, the method represents an effective and accurate algorithm to determine photon interaction coefficients, electron stopping powers as well as electron scatter parameters.

Investigation of variance reduction techniques for Monte Carlo photon dose calculation using XVMC.

Several variance reduction techniques, such as photon splitting, electron history repetition, Russian roulette and the use of quasi-random numbers are investigated and shown to significantly improve the efficiency of the recently developed XVMC Monte Carlo code for photon beams in radiation therapy. It is demonstrated that it is possible to further improve the efficiency by optimizing transpon parameters such as electron energy cut-off, maximum electron energy step size, photon energy cut-off and a cut-off for kerma approximation, without loss of calculation accuracy. These methods increase the efficiency by a factor of up to 10 compared with the initial XVMC ray-tracing technique or a factor of 50 to 80 compared with EGS4/PRESTA. Therefore, a common treatment plan (6 MV photons, 10 x 10 cm2 field size, 5 mm voxel resolution, 1% statistical uncertainty) can be calculated within 7 min using a single CPU 500 MHz personal computer. If the requirement on the statistical uncertainty is relaxed to 2%, the calculation time will be less than 2 min. In addition, a technique is presented which allows for the quantitative comparison of Monte Carlo calculated dose distributions and the separation of systematic and statistical errors. Employing this technique it is shown that XVMC calculations agree with EGSnrc on a sub-per cent level for simulations in the energy and material range of interest for radiation therapy.

Fast Monte Carlo dose calculation for photon beams based on the VMC electron algorithm.

A new Monte Carlo algorithm for 3D photon dose calculation in radiation therapy is presented, which is based on the previously developed Voxel Monte Carlo (VMC) for electron beams. The main result is that this new version of VMC (now called XVMC) is more efficient than EGS4/PRESTA photon dose calculation by a factor of 15-20. Therefore, a standard treatment plan for photons can be calculated by Monte Carlo in about 20 min. on a "normal" personal computer. The improvement is caused mainly by the fast electron transport algorithm and ray tracing technique, and an initial ray tracing method to calculate the number of electrons created in each voxel by the primary photon beam. The model was tested in comparison to calculations by EGS4 using several fictive phantoms. In most cases a good coincidence has been found between both codes. Only within lung substitute dose differences have been observed.

Experimental investigation of a fast Monte Carlo photon beam dose calculation algorithm.

An experimental verification of the recently developed XVMC code, a fast Monte Carlo algorithm to calculate dose distributions of photon beams in treatment planning, is presented. The treatment head is modelled by a point source with energy distribution (primary photons) and an additional head scatter contribution. Utility software is presented, allowing the determination of the parameters for this model using a single measured depth dose curve in water. The simple beam model is considered to be a starting point for more complex models being planned for future versions of the code. This paper is mainly focused on the influence of the different techniques on variance reduction and material property determination for dose distributions. It is demonstrated that XVMC and the simple beam model reproduce measured (by a diamond detector) relative dose distributions with an accuracy of better than +/-2% in various homogeneous and inhomogeneous phantoms. Furthermore, relative dose distributions in solid state phantoms have been measured by film. Also for these cases, measured and calculated dose distributions agree within experimental uncertainty. The short calculation time (depending on voxel resolution, statistical accuracy, field size and energy, a span of 1 min to 1 h using a present-day personal computer) and an interface to a commercial planning system will allow the implementation of the code for routine treatment planning of clinical electron and photon beams.

Electron beam dose calculations with the VMC algorithm and the verification data of the NCI working group.

The accuracy of the Monte Carlo algorithm for fast electron dose calculation, VMC, is demonstrated by comparing calculations with measurements performed by a working group of the National Cancer Institute (NCI) of the USA. For both energies investigated, 9 and 20 MeV, the measurements in water are taken to determine the energy spectra of the Varian Clinac 1800 accelerator. For the majority of the experiments a good agreement is found between measurements and VMC calculations. However, in some cases deviations have been observed, which could be explained by the incompletely known geometry on the one hand and by inconsistent data on the other hand. As a reference, dose distributions calculated by the MDAH pencil-beam algorithm are also presented. It is shown that, especially near low- or high-density inhomogeneities, large dose overestimations and underestimations are calculated by using a pencil-beam approach, whereas VMC is able to reproduce the correct doses for these cases also.

3D electron dose calculation using a Voxel based Monte Carlo algorithm (VMC).

A new model for calculating electron beam dose has been developed. The algorithm is based on a two- or three-dimensional geometry defined by computerized tomography (CT) images. The Monte Carlo technique was used to solve the electron transport equation. However, in contrast to conventional Monte Carlo models (EGS4) several approximations and simplifications in the description of elementary electron processes were introduced reducing in this manner the computational time by a factor of about 35 without significant loss in accuracy. The Monte Carlo computer program does not need any precalculated data. The random access memory required is about 16 Mbytes for a 128(2) X 50 matrix, depending on the resolution of the CT cube. The Voxel Monte Carlo model (VMC) was tested in comparison to calculations by EGS4 and the "Hogstrom algorithm" (MDAH) using several fictive phantoms. In all cases a good coincidence has been found between EGS4 and VMC, especially near tissue inhomogeneities, whereas the MDAH algorithm has produced dose underestimations of up to 40%.