Monte Carlo Calculated Dose Distributions Research Articles

On the de-noising of Monte Carlo calculated dose distributions

This paper presents an algorithm for de-noising Monte Carlo calculated dose distributions for use in radiation treatment planning. The algorithm is a three-dimensional generalization of a Savitzky–Golay digital filter and uses an adaptive smoothing window size to reduce the probability for systematic bias. The paper also introduces five accuracy criteria that are relevant for the expected clinical use of Monte Carlo techniques, which can be used to evaluate the performance of smoothing algorithms. Using these accuracy criteria it is demonstrated that the smoothing algorithm presented here decreases the uncertainty of Monte Carlo calculated dose distributions. The corresponding decrease in necessary particle tracks ranges from a factor of 2 to a factor of 20, depending on the accuracy criterion used. It is shown that very short Monte Carlo simulations combined with smoothing deliver satisfactory dose distributions and may therefore be extremely valuable for the initial trial and error phase of the radiation treatment planning process.

Significance of hypoxia for tumor response to radiation: Mathematical modeling and analysis of local control and clonogenic assay data

Various hypotheses for radiation local tumorcontrol probability (ltcp) were modeled, and assessed against local tumorcontrol (LTC) and clonogenic assay (CA) data. For head-and-neck tumors receiving low-LET external-beam irradiation, the best model was a Poisson ltcp accounting for cell repopulation, hypoxia, and tumor volume dependence of radiosensitivity (α). This confirmed that hypoxia is limiting LTC of these tumors, with the magnitude depending upon tumor volume. However, LTC of cervical carcinoma receiving external-beam irradiation and brachytherapy was well described by a model not accounting for hypoxia. Furthermore, when the survival fraction at 2 Gy ( SF 2 ) and colony forming efficiency (CFE) measured for individual patients were incorporated into this model, very good correlation with LTC was seen (p=0.0004). After multivariate analysis, this model was the best independent prognostic factor for LTC and patient survival. Furthermore, no difference in prediction was seen when a model based on birth-and-death stochastic theory was used. Two forms of hypoxia are known to be present in tumors: diffusion-limited, chronic hypoxia (CH), and acute, transient hypoxia (TH). A modeling study on WiDr multicellular spheroids showed that the CH effect on LTC is significantly lower than expected from CA. This could arise from energy charge depletion accompanying CH, reducing the number of proliferating clonogenic cells that can repair radiation damage, and thus mitigating the radioresistance of CH cells. This suggests that TH, rather than CH, may be the limiting factor for in vivo LTC. Finally, by computing ltcp using Monte Carlo calculated dose distributions, it was shown that Monte Carlo statistical noise can cause an underestimation of ltcp, with the magnitude depending upon the model hypotheses.

Monte Carlo evaluation of tissue inhomogeneity effects in the treatment of the head and neck

Purpose: To use Monte Carlo dose calculation to assess the degree to which tissue inhomogeneities in the head and neck affect static field conformal, computed tomography (CT)-based 6-MV photon treatment plans. Methods and Materials: We retrospectively studied the three-dimensional treatment plans that had been used for the treatment of 5 patients with tumors in the nasopharyngeal or paranasal sinus regions. Two patients had large surgical cavities. The plans were designed with a clinical treatment planning system that uses a measurement-based pencil-beam dose-calculation algorithm with an equivalent path-length inhomogeneity correction. Each plan employs conformally-shaped 6-MV photon beams. Patient anatomy and electron densities were obtained from the treatment planning CT images. For each plan, the dose distribution was recalculated with the Monte Carlo method, utilizing the same beam geometry and CT images. The Monte Carlo method accurately accounts for the perturbation effects of local tissue heterogeneities. The Monte Carlo calculated dose distributions were compared with those from the clinical treatment planning system. Results: The degree to which tissue inhomogeneity affects the dose distributions of individual fields varies with the specific anatomic geometry, especially the size and location of air cavities in relation to the beam orientation and field size. Most of the beam apertures completely enclose the air cavities within or adjacent to the gross tumor volume (GTV). Equivalent squares (including blocking) ranged from approximately 5 to 9.5 cm. A common feature observed for individual fields is that the Monte Carlo calculated doses to tissue directly behind and within an air cavity are lower. However, after combining the fields employed in each treatment plan, the overall dose distribution shows only small differences between the two methods. For all 5 patients, the Monte Carlo calculated treatment plans showed a slightly lower dose received by the 95% of target volume (D 95) than the plans calculated with the pencil-beam algorithm. The average difference in the target volume encompassed by the prescription isodose line was less than 2.2%. The difference between the dose-volume histograms (DVHs) of the GTV was generally small. For the brainstem and chiasm, the DVHs of the two plans were similar. For the spinal cord, differences in the details of the DHV and the dose to 1 cc (D 1cc) of the structure were observed, with Monte Carlo calculation generally predicting increased dose indices to the spinal cord. However, these changes are not expected to be clinically significant. Conclusion: For 6-MV photons, the effects of both normal tissue inhomogeneities and surgical air cavities on the target coverage were adequately accounted for by conventional pencil beam methods for all of the cases studied. Although differences in details of the DVHs of the normal structures were observed, depending on whether Monte Carlo or pencil-beam algorithm was used for calculation, these differences are not expected to be clinically significant. In general, the pencil-beam calculation corrected for primary attenuation by the equivalent pathlength is a sufficiently accurate method for head-and-neck treatment planning using 6-MV photons.

Investigation of variance reduction techniques for Monte Carlo photondose calculation using XVMC

Several variance reduction techniques, such as photon splitting, electronhistory repetition, Russian roulette and the use of quasi-random numbers areinvestigated and shown to significantly improve the efficiency of the recentlydeveloped XVMC Monte Carlo code for photon beams in radiation therapy. It isdemonstrated that it is possible to further improve the efficiency byoptimizing transport parameters such as electron energy cut-off, maximumelectron energy step size, photon energy cut-off and a cut-off for kermaapproximation, without loss of calculation accuracy. These methods increasethe efficiency by a factor of up to 10 compared with the initial XVMCray-tracing technique or a factor of 50 to 80 compared with EGS4/PRESTA.Therefore, a common treatment plan (6 MV photons, 10×10 cm2 fieldsize, 5 mm voxel resolution, 1% statistical uncertainty) can be calculatedwithin 7 min using a single CPU 500 MHz personal computer. If therequirement on the statistical uncertainty is relaxed to 2%, the calculationtime will be less than 2 min. In addition, a technique ispresented which allows for the quantitative comparison of Monte Carlocalculated dose distributions and the separation of systematic and statisticalerrors. Employing this technique it is shown that XVMC calculations agree withEGSnrc on a sub-per cent level for simulations in the energy and material rangeof interest for radiation therapy.

Evaluation of a commercial three-dimensional electron beam treatment planning system.

We evaluated a commercial three-dimensional (3D) electron beam treatment planning system (CADPLAN V.2.7.9) using both experimentally measured and Monte Carlo calculated dose distributions to compare with those predicted by CADPLAN calculations. Tests were carried out at various field sizes and electron beam energies from 6 to 20 MeV. For a homogeneous water phantom the agreement between measured and CADPLAN calculated dose distributions is very good except at the phantom surface. CADPLAN is able to predict hot and cold spots caused by a simple 3D inhomogeneity but unable to predict dose distributions for a more complex geometry where CADPLAN underestimates dose changes caused by inhomogeneity. We discussed possible causes for the inaccuracy in the CADPLAN dose calculations. In addition, we have tested CADPLAN treatment monitor unit and electron cut-out factor calculations and found that CADPLAN predictions generally agree with manual calculations.

Dose calculation models for proton treatment planning using a dynamic beam delivery system: an attempt to include density heterogeneity effects in the analytical dose calculation

The gantry for proton radiotherapy at the Paul Scherrer Institute (PSI) is designed specifically for the spot-scanning technique. Use of this technique to its full potential requires dose calculation algorithms which are capable of precisely simulating each scanned beam individually. Different specialized analytical dose calculations have been developed, which attempt to model the effects of density heterogeneities in the patient's body on the dose. Their accuracy has been evaluated by a comparison with Monte Carlo calculated dose distributions in the case of a simple geometrical density interface parallel to the beam and typical anatomical situations. A specialized ray casting model which takes range dilution effects (broadening of the spectrum of proton ranges) into account has been found to produce results of good accuracy. This algorithm can easily be implemented in the iterative optimization procedure used for the calculation of the optimal contribution of each individual scanned pencil beam. In most cases an elemental pencil beam dose calculation has been found to be most accurate. Due to the long computing time, this model is currently used only after the optimization procedure as an alternative method of calculating the dose.

Monte Carlo calculated dose distribution for endovascular HDR brachytherapy with Ir-192

Background and purpose: For endovascular HDR brachytherapy, very thin sources are required and the dose is specified at a short distance to the source centre down to 1.5 mm. The source which is used in the Nucletron HDR Selectron stepping source afterloader is treated by most dose calculation algorithms in clinical use as a point source, although its dimensions are large compared to these dose specification distances. Furthermore, inaccuracies might be introduced because consecutive dwell positions show an overlap of sources if the step size is smaller than the active length of the source. Materials and methods: In order to quantify these inaccuracies, we used the EGS4 Monte Carlo code to generate the dose distribution with 0.5 mm spatial resolution for a single source. From this, translation and superposition were used to calculate dose distributions for multiple dwell positions. The results are compared with those of other Monte Carlo computations and of a commercial brachytherapy planning system. Results and conclusions: Our Monte Carlo calculations showed that secondary electrons have no relevant influence on the dose distribution and that errors up to 25% are made when using the point source approximation for irradiations with a single dwell position. However, when three or more dwell positions are used with equal dwell times, the total error becomes negligibly small because the errors from subsequent dwell positions compensate each other. At distances larger than 5 mm, there is a good match between the Monte Carlo data and those of point source algorithms for all clinical relevant cases.

The role of phantom and treatment head generated bremsstrahlung in high-energy electron beam dosimetry

An analytical expression has been derived for the phantom generated bremsstrahlung photons in plane-parallel monoenergetic electron beams normally incident on material of any atomic number (Be, , Al, Cu and U). The expression is suitable for the energy range from 1 to 50 MeV and it is solely based on known scattering power and radiative and collision stopping power data for the material at the incident electron energy. The depth dose distribution due to the bremsstrahlung generated by the electrons in the phantom is derived by convolving the bremsstrahlung energy fluence produced in the phantom with a simple analytical energy deposition kernel. The kernel accounts for both electrons and photons set in motion by the bremsstrahlung photons. The energy loss by the primary electrons, the build-up of the electron fluence and the generation, attenuation and absorption of bremsstrahlung photons are all taken into account in the analytical formula. The longitudinal energy deposition kernel is derived analytically and it is consistent with both the classical biexponential relation describing the photon depth dose distribution and the exponential attenuation of the primary photons. For comparison Monte Carlo calculated energy deposition distributions using ITS3 code were used. Good agreement was found between the results with the analytical expression and the Monte Carlo calculation. For tissue equivalent materials, the maximum total energy deposition differs by less than 0.2% from Monte Carlo calculated dose distributions. The result can be used to estimate the depth dependence of phantom generated bremsstrahlung in different materials in therapeutic electron beams and the bremsstrahlung production in different electron absorbers such as scattering foils, transmission monitors and photon and electron collimators. By subtracting the phantom generated bremsstrahlung from the total bremsstrahlung background the photon contamination generated in the treatment head can be determined to allow accurate dosimetry of heavily photon contaminated electron beams.