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.

[Verification of the VEF photon beam model for dose calculations by the Voxel-Monte-Carlo-Algorithm]. / Verifikation des VEF-Strahlerkopfmodells für Photonen zur Dosisberechnung mit dem Voxel-Monte-Carlo-Algorithmus.

The VEF linac head model (VEF, virtual energy fluence) was developed at the University of Tübingen to determine the primary fluence for calculations of dose distributions in patients by the Voxel-Monte-Carlo-Algorithm (XVMC). This analytical model can be fitted to any therapy accelerator head by measuring only a few basic dose data; therefore, time-consuming Monte-Carlo simulations of the linac head become unnecessary. The aim of the present study was the verification of the VEF model by means of water-phantom measurements, as well as the comparison of this system with a common analytical linac head model of a commercial planning system (TMS, formerly HELAX or MDS Nordion, respectively). The results show that both the VEF and the TMS models can very well simulate the primary fluence. However, the VEF model proved superior in the simulations of scattered radiation and in the calculations of strongly irregular MLC fields. Thus, an accurate and clinically practicable tool for the determination of the primary fluence for Monte-Carlo-Simulations with photons was established, especially for the use in IMRT planning.

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.

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.

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.

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.

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.

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.

[IMCO(++)--a Monte Carlo based IMRT system]. / IMCO(++)--Ein Monte-Carlo-basiertes System für die IMRT.

The application of intensity modulated radiotherapy (IMRT) to dose escalation in the target volume sets particular demands in terms of accuracy of dose calculation. Dose calculation errors due to approximations are compensated by the optimization algorithm, a procedure that ultimately leads to incorrect fluence modulation. Such inaccuracies affect particularly the dose distribution in areas with secondary electron disequilibrium. In case tissues heterogeneity predominates, conventional dose calculation methods (such as Pencil Beam) can produce relative errors up to more than 10%. The accuracy can be significantly improved by the application of a Monte-Carlo (MC) algorithm. This paper describes a MC-based inverse treatment planning algorithm (IMCO++), based on a non-iterative approach with a feedback-controlling process. The convergence behavior of IMCO++ was investigated and the used MC dose-calculation codes MMms and XVMC were compared by means of a heterogeneous phantom. IMCO++ plans were optimized in various phantoms. All plans showed conformity in terms of dose distribution of the target volume and dose reduction in risk organs (according to the requirements of the target parameter), as well as a very fast convergence of the algorithm (in less than 10 optimization steps).