Matthias Fippel

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.

A virtual photon energy fluence model for Monte Carlo dose calculation.

The presented virtual energy fluence (VEF) model of the patient-independent part of the medical linear accelerator heads, consists of two Gaussian-shaped photon sources and one uniform electron source. The planar photon sources are located close to the bremsstrahlung target (primary source) and to the flattening filter (secondary source), respectively. The electron contamination source is located in the plane defining the lower end of the filter. The standard deviations or widths and the relative weights of each source are free parameters. Five other parameters correct for fluence variations, i.e., the horn or central depression effect. If these parameters and the field widths in the X and Y directions are given, the corresponding energy fluence distribution can be calculated analytically and compared to measured dose distributions in air. This provides a method of fitting the free parameters using the measurements for various square and rectangular fields and a fixed number of monitor units. The next step in generating the whole set of base data is to calculate monoenergetic central axis depth dose distributions in water which are used to derive the energy spectrum by deconvolving the measured depth dose curves. This spectrum is also corrected to take the off-axis softening into account. The VEF model is implemented together with geometry modules for the patient specific part of the treatment head (jaws, multileaf collimator) into the XVMC dose calculation engine. The implementation into other Monte Carlo codes is possible based on the information in this paper. Experiments are performed to verify the model by comparing measured and calculated dose distributions and output factors in water. It is demonstrated that open photon beams of linear accelerators from two different vendors are accurately simulated using the VEF model. The commissioning procedure of the VEF model is clinically feasible because it is based on standard measurements in air and water. It is also useful for IMRT applications because a full Monte Carlo simulation of the treatment head would be too time-consuming for many small fields.

A pencil beam algorithm for intensity modulated proton therapy derived from Monte Carlo simulations

A pencil beam algorithm as a component of an optimization algorithm for intensity modulated proton therapy (IMPT) is presented. The pencil beam algorithm is tuned to the special accuracy requirements of IMPT, where in heterogeneous geometries both the position and distortion of the Bragg peak and the lateral scatter pose problems which are amplified by the spot weight optimization. Heterogeneity corrections are implemented by a multiple raytracing approach using fluence-weighted sub-spots. In order to derive nuclear interaction corrections, Monte Carlo simulations were performed. The contribution of long ranged products of nuclear interactions is taken into account by a fit to the Monte Carlo results. Energy-dependent stopping power ratios are also implemented. Scatter in optional beam line accessories such as range shifters or ripple filters is taken into account. The collimator can also be included, but without additional scattering. Finally, dose distributions are benchmarked against Monte Carlo simulations, showing 3%/1 mm agreement for simple heterogeneous phantoms. In the case of more complicated phantoms, principal shortcomings of pencil beam algorithms are evident. The influence of these effects on IMPT dose distributions is shown in clinical examples.

A Monte Carlo dose calculation algorithm for proton therapy

A Monte Carlo (MC) code (VMCpro) for treatment planning in proton beam therapy of cancer is introduced. It is based on ideas of the Voxel Monte Carlo algorithm for photons and electrons and is applicable to human tissue for clinical proton energies. In the present paper the implementation of electromagnetic and nuclear interactions is described. They are modeled by a Class II condensed history algorithm with continuous energy loss, ionization, multiple scattering, range straggling, delta-electron transport, nuclear elastic proton nucleus scattering and inelastic proton nucleus reactions. VMCpro is faster than the general purpose MC codes FLUKA by a factor of 13 and GEANT4 by a factor of 35 for simulations in a phantom with inhomogeneities. For dose calculations in patients the speed improvement is larger, because VMCpro has only a weak dependency on the heterogeneity of the calculation grid. Dose distributions produced with VMCpro are in agreement with GEANT4 results. Integrated or broad beam depth dose curves show maximum deviations not larger than 1% or 0.5 mm in regions with large dose gradients for the examples presented here.

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.

VMC++, a fast MC algorithm for Radiation Treatment planning

This paper gives a short description of VMC++, a recent C++ re-implementation of the VMC [1] and XVMC [2, 3] code systems that incorporates a variety of improvements, and answers the questions concerning speed and accuracy given in the paper by Rogers and Mohan [4].

Efficient particle transport simulation through beam modulating devices for Monte Carlo treatment planning

For Monte Carlo treatment planning it is essential to model efficiently patient dependent beam modifying devices, e.g., Multi-Leaf Collimators (MLC). Therefore a Monte Carlo geometry tracking procedure is presented allowing the simulation of photon and electron transport through these devices within short calculation time. The tracking procedure is based on elemental regions, on surfaces (mainly planes) to separate the regions as well as on bit patterns and bit masks to identify the regions. Photon cross sections for photoelectric absorption, Compton scattering and pair production as well as electron stopping powers and ranges are provided by the Physical Reference Data of the National Institute of Standards and Technology (NIST). The tracking procedure is implemented in c + + with object-oriented design based on c + + class hierarchies and inheritance. Using the geometry technique, several MLC models are constructed. Some of them take into account tongue-and-groove effects as well as curved leaf ends. The models are integrated into the Monte Carlo dose calculation engine XVMC for treatment planning. The system is tested by comparing different MLC implementations and by verification with measurement.

Smoothing Monte Carlo calculated dose distributions by iterative reduction of noise

A smoothing algorithm based on an optimization procedure is presented and evaluated for single electron and photon beams and a full intensity modulated radiation therapy (IMRT) delivery. The algorithm iteratively reduces the statistical noise of Monte Carlo (MC) calculated dose distributions. It is called IRON (iterative reduction of noise). By varying the dose in each voxel, the algorithm minimizes the second partial derivatives of dose with respect to X, Y and Z. An additional restoration term ensures that too large dose changes are prevented. IRON requires a MC calculated one-dimensional or three-dimensional dose distribution with or without known statistical uncertainties as input. The algorithm is tested using three different treatment plan examples, a photon beam dose distribution in water, an IMRT plan of a real patient and an electron beam dose distribution in a water phantom with inhomogeneities. It is shown that smoothing can lead to an additional reduction of MC calculation time by factors of 2 to 10. This is especially useful if MC dose calculation is part of an inverse treatment planning system. In addition to this, it is shown that smoothing a noisy dose distribution may introduce some bias into the final dose values by converting the statistical uncertainty of the dose distribution into a systematic deviation of the dose value.

Study on the Tongue and Groove Effect of the Elekta Multileaf Collimator Using Monte Carlo Simulation and Film Dosimetry

Background:Nowadays, multileaf collimation of the treatment fields from medical linear accelerators is a common option. Due to the design of the leaf sides, the tongue and groove effect occurs for certain multileaf collimator applications such as the abutment of fields where the beam edges are defined by the sides of the leaves.Material and Methods:In this study, the tongue and groove effect was measured for two pairs of irregular multileaf collimator fields that were matched along leaf sides in two steps. Measurements were made at 10 cm depth in a polystyrene phantom using Kodak EDR2 films for a photon beam energy of 6 MV on an Elekta Sli-plus accelerator. To verify the measurements, full Monte Carlo simulations were done. In the simulations, the design of the leaf sides was taken into account and one component module of BEAM code was modified to correctly simulate the Elekta multileaf collimator.Results and Conclusion:The results of measurements and simulations are in good agreement and within the tolerance of film dosimetry.Hintergrund:Heutzutage werden zunehmend Lamellenkollimatoren für die Kollimierung von Strahlenfeldern eingesetzt. Zwar erreicht man mit Lamellenkollimatoren eine bessere Anpassung der Dosisverteilung an die Form des Zielvolumens, jedoch ist ihre Verwendung auch mit einigen Problemen bei der Dosisberechnung verbunden. Eines dieser Probleme, der Nut-und-Feder-Effekt, wird in dieser Arbeit untersucht. Dieser Effekt ist besonders bedeutsam, wenn Feldanschlüsse zweier Felder bei einer Bestrahlung vorgesehen sind.Material und Methodik:Zur Untersuchung dieses Effekts wurden zwei Konfigurationen mit unregelmäßigen Paarfeldern eingesetzt. Die Messungen erfolgten in einem Polystyrol-Phantom mit Kodak-EDR2-Filmen bei 6-MV-Photonenstrahlung an einem Elekta- Linearbeschleuniger (Sli-plus). Um die Messungen zu verifizieren, wurde der Beschleunigerkopf mit Hilfe des BEAM-Programms modelliert. Zur Berücksichtigung des Nut-und-Feder-Effekts wurde das BEAM-Programm entsprechend der Bauart des Elekta-Kollimators modifiziert.Ergebnisse und Schlussfolgerung:Messungen und Dosisberechnungen der Monte-Carlo-Simulation ergaben eine gute Übereinstimmung.

Off-axis chamber response in the depth of photon dose maximum

Measurements as well as Monte Carlo simulations are presented to investigate the deviation between the dose to water and the value measured by an ionization chamber. These deviations are evaluated at different depths (1.5 and 10 cm) and at an off-axis position of 15 cm. It is shown that an ionization chamber can produce a measuring signal, which is up to 2.5% too low, compared to the dose, when measurements are performed at shallow depths and far off-axis. The reason for this underresponse is found in the variation of the wall correction factor. As a result of the variation of the radiation spectra with depth and position the dose to the air volume, which originates from the wall, varies and therefore changes the wall correction factor.