Removing the effect of statistical uncertainty on dose-volume histograms from Monte Carlo dose calculations

Application of the adaptive Monte Carlo method for uncertainty evaluation in the determination of total testosterone in human serum by triple isotope dilution mass spectrometry

The measurement uncertainty is a crucial quantitative parameter for assessing the reliability of the result. The study aimed to propose a new budget for uncertainty evaluation of a reference measurement procedure for the determination of total testosterone in human serum. The adaptive Monte Carlo method (aMCM) was used for the propagation of probability distributions assigned to various input quantities to determine the uncertainty of the testosterone concentration. The basic principles of the propagation and the statistical analysis were described based on the experimental results of the quality control serum sample. The analysis of the number of Monte Carlo trials was discussed. The procedure of validation of the GUM uncertainty framework using the aMCM was also provided. The number of Monte Carlo trials was 2.974 × 106 when the results had stabilized. The total testosterone concentration was 16.02 nmol/L, and the standard uncertainty was 0.30 nmol/L. The coverage interval at coverage probability of 95% was 15.45 to 16.62 nmol/L, while the probability distribution for testosterone concentration was approximately described by a Gaussian distribution. The validation of results was not passed as the expanded uncertainty result obtained by the aMCM was slightly lower, about 7%, than that by the GUM uncertainty framework with consistent results of the concentration.

Maintaining dosimetric quality when switching to a Monte Carlo dose engine for head and neck volumetric-modulated arc therapy planning

Head and neck cancers present challenges in radiation treatment planning due to the large number of critical structures near the target(s) and highly heterogeneous tissue composition. While Monte Carlo (MC) dose calculations currently offer the most accurate approximation of dose deposition in tissue, the switch to MC presents challenges in preserving the parameters of care. The differences in dose‐to‐tissue were widely discussed in the literature, but mostly in the context of recalculating the existing plans rather than reoptimizing with the MC dose engine. Also, the target dose homogeneity received less attention. We adhere to strict dose homogeneity objectives in clinical practice. In this study, we started with 21 clinical volumetric‐modulated arc therapy (VMAT) plans previously developed in Pinnacle treatment planning system. Those plans were recalculated “as is” with RayStation (RS) MC algorithm and then reoptimized in RS with both collapsed cone (CC) and MC algorithms. MC statistical uncertainty (0.3%) was selected carefully to balance the dose computation time (1–2 min) with the planning target volume (PTV) dose‐volume histogram (DVH) shape approaching that of a “noise‐free” calculation. When the hot spot in head and neck MC‐based treatment planning is defined as dose to 0.03 cc, it is exceedingly difficult to limit it to 105% of the prescription dose, as we were used to with the CC algorithm. The average hot spot after optimization and calculation with RS MC was statistically significantly higher compared to Pinnacle and RS CC algorithms by 1.2 and 1.0 %, respectively. The 95% confidence interval (CI) observed in this study suggests that in most cases a hot spot of ≤107% is achievable. Compared to the 95% CI for the previous clinical plans recalculated with RS MC “as is” (upper limit 108%), in real terms this result is at least as good or better than the historic plans.

Denoising proton therapy Monte Carlo dose distributions in multiple tumor sites: A comparative neural networks architecture study

INTRODUCTION

Monte Carlo (MC) algorithms provide accurate modeling of dose calculation by simulating the delivery and interaction of many particles through patient geometry. Fast MC simulations using large number of particles are desirable as they can lead to reliable clinical decisions. In this work, we assume that faster simulations with fewer particles can approximate slower ones by denoising them with deep learning.

MATERIALS AND METHODS

We use mean squared error (MSE) as loss function to train networks (sNet and dUNet), with 2.5D and 3D setups considering volumes of 7 and 24 slices. Our models are trained on proton therapy MC dose distributions of six different tumor sites acquired from 50 patients. We provide networks with input MC dose distributions simulated using 1 × 10⁶ particles while keeping 1 × 10⁹ particles as reference.

RESULTS

On average over 10 new patients with different tumor sites, in 2.5D and 3D, our models recover relative residual error on target volume, ΔD₉₅^TV of 0.67 ± 0.43% and 1.32 ± 0.87% for sNet vs. 0.83 ± 0.53% and 1.66 ± 0.98% for dUNet, compared to the noisy input at 12.40 ± 4.06%. Moreover, the denoising time for a dose distribution is: < 9s and  < 1s for sNet vs. < 16s and  < 1.5s for dUNet in 2.5D and 3D, in comparison to about 100 min (MC simulation using 1 × 10⁹ particles).

CONCLUSION

We propose a fast framework that can successfully denoise MC dose distributions. Starting from MC doses with 1 × 10⁶ particles only, the networks provide comparable results as MC doses with1 × 10⁹ particles, reducing simulation time significantly.

Mitigating inherent noise in Monte Carlo dose distributions using dilated U-Net

PURPOSE

Monte Carlo (MC) algorithms offer accurate modeling of dose calculation by simulating the transport and interactions of many particles through the patient geometry. However, given their random nature, the resulting dose distributions have statistical uncertainty (noise), which prevents making reliable clinical decisions. This issue is partly addressable using a huge number of simulated particles but is computationally expensive as it results in significantly greater computation times. Therefore, there is a trade-off between the computation time and the noise level in MC dose maps. In this work, we address the mitigation of noise inherent to MC dose distributions using dilated U-Net - an encoder-decoder-styled fully convolutional neural network, which allows fast and fully automated denoising of whole-volume dose maps.

METHODS

We use mean squared error (MSE) as loss function to train the model, where training is done in 2D and 2.5D settings by considering a number of adjacent slices. Our model is trained on proton therapy MC dose distributions of different tumor sites (brain, head and neck, liver, lungs, and prostate) acquired from 35 patients. We provide the network with input MC dose distributions simulated using 1 × 10 6 particles while keeping 1 × 10 9 particles as reference.

RESULTS

After training, our model successfully denoises new MC dose maps. On average (averaged over five patients with different tumor sites), our model recovers D 95 of 55.99 Gy from the noisy MC input of 49.51 Gy, whereas the low noise MC (reference) offers 56.03 Gy. We observed a significant reduction in average RMSE (thresholded >10% max ref) for reference vs denoised (1.25 Gy) than reference vs input (16.96 Gy) leading to an improvement in signal-to-noise ratio (ISNR) by 18.06 dB. Moreover, the inference time of our model for a dose distribution is less than 10 s vs 100 min (MC simulation using 1 × 10 9 particles).

CONCLUSIONS

We propose an end-to-end fully convolutional network that can denoise Monte Carlo dose distributions. The networks provide comparable qualitative and quantitative results as the MC dose distribution simulated with 1 × 10 9 particles, offering a significant reduction in computation time.

Dosimetric impact of statistical uncertainty on Monte Carlo dose calculation algorithm in volumetric modulated arc therapy using Monaco TPS for three different clinical cases

Aim

To study the dosimetric impact of statistical uncertainty (SU) per plan on Monte Carlo (MC) calculation in Monaco™ treatment planning system (TPS) during volumetric modulated arc therapy (VMAT) for three different clinical cases.

Background

During MC calculation SU is an important factor to decide dose calculation accuracy and calculation time. It is necessary to evaluate optimal acceptance of SU for quality plan with reduced calculation time.

Materials and methods

Three different clinical cases as the lung, larynx, and prostate treated using VMAT technique were chosen. Plans were generated with Monaco™ V5.11 TPS with 2% statistical uncertainty. By keeping all other parameters constant, plans were recalculated by varying SU, 0.5%, 1%, 2%, 3%, 4%, and 5%. For plan evaluation, conformity index (CI), homogeneity index (HI), dose coverage to PTV, organ at risk (OAR) dose, normal tissue receiving dose ≥5 Gy and ≥10 Gy, integral dose (NTID), calculation time, gamma pass rate, calculation reproducibility and energy dependency were analyzed.

Results

CI and HI improve as SU increases from 0.5% to 5%. No significant dose difference was observed in dose coverage to PTV, OAR doses, normal tissue receiving dose ≥5 Gy and ≥10 Gy and NTID. Increase of SU showed decrease in calculation time, gamma pass rate and increase in PTV max dose. No dose difference was seen in calculation reproducibility and dependent on energy.

Conclusion

For VMAT plans, SU can be accepted from 1% to 3% per plan with reduced calculation time without compromising plan quality and deliverability by accepting variations in point dose within the target.

Measurement comparison and Monte Carlo analysis for volumetric-modulated arc therapy (VMAT) delivery verification using the ArcCHECK dosimetry system

The objective of this study is to validate the capabilities of a cylindrical diode array system for volumetric‐modulated arc therapy (VMAT) treatment quality assurance (QA). The VMAT plans were generated by the Eclipse treatment planning system (TPS) with the analytical anisotropic algorithm (AAA) for dose calculation. An in‐house Monte Carlo (MC) code was utilized as a validation tool for the TPS calculations and the ArcCHECK measurements. The megavoltage computed tomography (MVCT) of the ArcCHECK system was adopted for the geometry reconstruction in the TPS and for MC simulations. A 10×10 cm2 open field validation was performed for both the 6 and 10 MV photon beams to validate the absolute dose calibration of the ArcCHECK system and also the TPS dose calculations for this system. The impact of the angular dependency on noncoplanar deliveries was investigated with a series of 10×10 cm2 fields delivered with couch rotation 0° to 40°. The sensitivity of detecting the translational (1 to 10 mm) and the rotational (1° to 3°) misalignments was tested with a breast VMAT case. Ten VMAT plans (six prostate, H&N, pelvis, liver, and breast) were investigated to evaluate the agreement of the target dose and the peripheral dose among ArcCHECK measurements, and TPS and MC dose calculations. A customized acrylic plug holding an ion chamber was used to measure the dose at the center of the ArcCHECK phantom. Both the entrance and the exit doses measured by the ArcCHECK system with and without the plug agreed with the MC simulation to 1.0%. The TPS dose calculation with a 2.5 mm grid overestimated the exit dose by up to 7.2% when the plug was removed. The agreement between the MC and TPS calculations for the ArcCHECK without the plug improved significantly when a 1 mm dose calculation grid was used in the TPS. The noncoplanar delivery test demonstrated that the angular dependency has limited impact on the gamma passing rate (<1.2% drop) for the 2%–3% dose and 2 mm–3 mm DTA criteria. A 1° rotational misalignment introduces 11.3% (3%/3 mm) to 21.3% (1%/1 mm) and 0.2% (3%/3 mm) to 0.8% (1%/1 mm) Gamma passing rate drop for ArcCHECK system and MatriXX system, respectively. Both systems have comparable sensitivity to the AP misalignments. However, a 2 mm RL misalignment introduces gamma passing rate drop ranging from 0.9% (3%/3 mm) to 4.0% (1%/1 mm) and 5.0% (3%/3 mm) to 12.0% (1%/1 mm) for ArcCHECK and MatriXX measurements, respectively. For VMAT plan QA, the gamma analysis passing rates ranged from 96.1% (H&N case) to 99.9% (prostate case), when using the 3%/3 mm DTA criteria for the peripheral dose validation between the TPS and ArcCHCEK measurements. The peripheral dose validation between the MC simulation and ArcCHECK measurements showed at least 97.9% gamma passing rates. The central dose validation also showed an agreement within 2.2% between TPS/MC calculations and ArcCHECK measurements. The worst discrepancy was found in the H&N case, which is the most complex VMAT case. The ArcCHECK system is suitable for VMAT QA evaluation based on the sensitivity to detecting misalignments, the clinical impact of the angular dependency, and the correlation between the dose agreements in the peripheral region and the central region. This work also demonstrated the importance of carrying out a thorough validation of both the TPS and the dosimetry system prior to utilizing it for QA, and the value of having an independent dose calculation tool, such as the MC method, in clinical practice.

PACS number: 87.55.Qr

Monte Carlo simulation of contrast-enhanced whole brain radiotherapy on a CT scanner

PURPOSE

To perform a feasibility study of contrast-enhanced whole brain radiotherapy for treating patients with multiple brain metastasis using a conventional computed tomography (CT) scanner.

METHODS

The treatment dose was optimized to be applied in a single run using a maximum tube power of 5200 kWs at 140 kV. CT scans of a large and a small head were used as reference. Irradiation geometry, shielding, axial beam collimation, radial beam collimation, gantry tilt, and tube current for beam modulation were optimized using a Monte Carlo simulation and a contrast agent concentration of 5 mg/ml iodine in the tumor. The statistical uncertainty of the Monte Carlo simulation was corrected using back convolution.

RESULTS

Using a CT tube with a beam collimation of 28.8 mm, a mean tumor dose of 1.76 +/- 0.13 Gy was achieved, while the head bone dose was 2.61 +/- 0.18 Gy with a normal brain dose of 0.98 +/- 0.06 Gy, eye dose of 0.19 +/- 0.05 Gy, and lens dose of 0.15 +/- 0.03 Gy, respectively. Using a CT tube with dose modulation and a beam collimation of 40.0 mm, the mean tumor dose was 2.00 +/- 0.11 Gy with a head bone dose of 1.96 +/- 0.14 Gy, normal brain dose of 1.13 +/- 0.08 Gy, eye dose of 0.21 +/- 0.05 Gy, and lens dose of 0.16 +/- 0.02 Gy, respectively. Thus a standard CT scanner enables an effective tumor dose of 37.0 Gy to be administered in 13 fractions, while exposing healthy brain to an effective dose of 17.2 Gy and head bone to 69.3 Gy. Additional radial collimation implemented in the hardware improves the therapeutic tumor dose by 25.2% in relation to the bone dose.

CONCLUSIONS

Contrast-enhanced total brain radiotherapy is feasible using a conventional CT tube with optimized dose application.

The effect of statistical noise on IMRT plan quality and convergence for MC-based and MC-correction-based optimized treatment plans

Monte Carlo (MC) is rarely used for IMRT plan optimization outside of research centres due to the extensive computational resources or long computation times required to complete the process. Time can be reduced by degrading the statistical precision of the MC dose calculation used within the optimization loop. However, this eventually introduces optimization convergence errors (OCEs). This study determines the statistical noise levels tolerated during MC-IMRT optimization under the condition that the optimized plan has OCEs <100 cGy (1.5% of the prescription dose) for MC-optimized IMRT treatment plans.Seven-field prostate IMRT treatment plans for 10 prostate patients are used in this study. Pre-optimization is performed for deliverable beams with a pencil-beam (PB) dose algorithm. Further deliverable-based optimization proceeds using: (1) MC-based optimization, where dose is recomputed with MC after each intensity update or (2) a once-corrected (OC) MC-hybrid optimization, where a MC dose computation defines beam-by-beam dose correction matrices that are used during a PB-based optimization. Optimizations are performed with nominal per beam MC statistical precisions of 2, 5, 8, 10, 15, and 20%. Following optimizer convergence, beams are re-computed with MC using 2% per beam nominal statistical precision and the 2 PTV and 10 OAR dose indices used in the optimization objective function are tallied. For both the MC-optimization and OC-optimization methods, statistical equivalence tests found that OCEs are less than 1.5% of the prescription dose for plans optimized with nominal statistical uncertainties of up to 10% per beam. The achieved statistical uncertainty in the patient for the 10% per beam simulations from the combination of the 7 beams is ~3% with respect to maximum dose for voxels with D>0.5D(max). The MC dose computation time for the OC-optimization is only 6.2 minutes on a single 3 Ghz processor with results clinically equivalent to high precision MC computations.

Evaluation of uncertainty-based stopping criteria for monte carlo calculations of intensity-modulated radiotherapy and arc therapy patient dose distributions

PURPOSE

To formulate uncertainty-based stopping criteria for Monte Carlo (MC) calculations of intensity-modulated radiotherapy and intensity-modulated arc therapy patient dose distributions and evaluate their influence on MC simulation times and dose characteristics.

METHODS AND MATERIALS

For each structure of interest, stopping criteria were formulated as follows: sigma(rel) <or=sigma(rel,tol) or Dsigma(rel) <or=D(lim)sigma(rel,tol) within >or=95% of the voxels, where sigma(rel) represents the relative statistical uncertainty on the estimated dose, D. The tolerated uncertainty (sigma(rel,tol)) was 2%. The dose limit (D(lim)) equaled the planning target volume (PTV) prescription dose or a dose value related to the organ at risk (OAR) planning constraints. An intensity-modulated radiotherapy-lung, intensity-modulated radiotherapy-ethmoid sinus, and intensity-modulated arc therapy-rectum patient case were studied. The PTV-stopping criteria-based calculations were compared with the PTV+OAR-stopping criteria-based calculations.

RESULTS

The MC dose distributions complied with the PTV-stopping criteria after 14% (lung), 21% (ethmoid), and 12% (rectum) of the simulation times of a 100 million histories reference calculation, and increased to 29%, 44%, and 51%, respectively, by the addition of the OAR-stopping criteria. Dose-volume histograms corresponding to the PTV-stopping criteria, PTV+OAR-stopping criteria, and reference dose calculations were indiscernible. The median local dose differences between the PTV-stopping criteria and the reference calculations amounted to 1.4% (lung), 2.1% (ethmoid), and 2.5% (rectum).

CONCLUSIONS

For the patient cases studied, the MC calculations using PTV-stopping criteria only allowed accurate treatment plan evaluation. The proposed stopping criteria provided a flexible tool to assist MC patient dose calculations. The structures of interest and appropriate values of sigma(rel,tol) and D(lim) should be selected for each patient individually according to the clinical treatment planning goals.

Effects of Hounsfield number conversion on CT based proton Monte Carlo dose calculations

The Monte Carlo method provides the most accurate dose calculations on a patient computed tomography (CT) geometry. The increase in accuracy is, at least in part, due to the fact that instead of treating human tissues as water of various densities as in analytical algorithms, the Monte Carlo method allows human tissues to be characterized by elemental composition and mass density, and hence allows the accurate consideration of all relevant electromagnetic and nuclear interactions. On the other hand, the algorithm to convert CT Hounsfield numbers to tissue materials for Monte Carlo dose calculation introduces uncertainties. There is not a simple one to one correspondence between Hounsfield numbers and tissue materials. To investigate the effects of Hounsfield number conversion for proton Monte Carlo dose calculations, clinical proton treatment plans were simulated using the Geant4 Monte Carlo code. Three Hounsfield number to material conversion methods were studied. The results were compared in forms of dose volume histograms of gross tumor volume and clinical target volume. The differences found are generally small but can be dosimetrically significant. Further, different methods may cause deviations in the predicted proton beam range in particular for deep proton fields. Typically, slight discrepancies in mass density assignments play only a minor role in the target region, whereas more significant effects are caused by different assignments in elemental compositions. In the presence of large tissue inhomogeneities, for head and neck treatments, treatment planning decisions could be affected by these differences because of deviations in the predicted tumor coverage. Outside the target area, differences in elemental composition and mass density assignments both may play a role. This can lead to pronounced effects for organs at risk, in particular in the spread-out Bragg peak penumbra or distal regions. In addition, the significance of the elemental composition effect (dose to water vs. dose to tissue) is tissue-type dependent and is also affected by nuclear reactions.

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.

Reporting and analyzing statistical uncertainties in Monte Carlo-based treatment planning

PURPOSE

To investigate methods of reporting and analyzing statistical uncertainties in doses to targets and normal tissues in Monte Carlo (MC)-based treatment planning.

METHODS AND MATERIALS

Methods for quantifying statistical uncertainties in dose, such as uncertainty specification to specific dose points, or to volume-based regions, were analyzed in MC-based treatment planning for 5 lung cancer patients. The effect of statistical uncertainties on target and normal tissue dose indices was evaluated. The concept of uncertainty volume histograms for targets and organs at risk was examined, along with its utility, in conjunction with dose volume histograms, in assessing the acceptability of the statistical precision in dose distributions. The uncertainty evaluation tools were extended to four-dimensional planning for application on multiple instances of the patient geometry. All calculations were performed using the Dose Planning Method MC code.

RESULTS

For targets, generalized equivalent uniform doses and mean target doses converged at 150 million simulated histories, corresponding to relative uncertainties of less than 2% in the mean target doses. For the normal lung tissue (a volume-effect organ), mean lung dose and normal tissue complication probability converged at 150 million histories despite the large range in the relative organ uncertainty volume histograms. For "serial" normal tissues such as the spinal cord, large fluctuations exist in point dose relative uncertainties.

CONCLUSIONS

The tools presented here provide useful means for evaluating statistical precision in MC-based dose distributions. Tradeoffs between uncertainties in doses to targets, volume-effect organs, and "serial" normal tissues must be considered carefully in determining acceptable levels of statistical precision in MC-computed dose distributions.

Development and commissioning of a Monte Carlo photon beam model for Varian Clinac 2100EX linear accelerator

Monte Carlo modeling of a linear accelerator is the first and most important step in Monte Carlo dose calculations in radiotherapy. We developed a photon beam model for Varian 2100EX for dose calculation purposes using MCNP4C Monte Carlo code. Results of our modeling were in close agreement with our measurements. The effect of beam width on percentage depth doses and beam profiles was studied. Our results showed that electron beam width could be tuned using large field beam profile at the depth of maximum dose.

EUD-based radiotherapy treatment plan evaluation: incorporating physical and Monte Carlo statistical dose uncertainties

The purpose of this work is to quantify the impact of dose uncertainty on radiobiologically based treatment plan evaluation. Dose uncertainties are divided into two categories: physical and statistical. Physical dose uncertainty is associated with the systematic and/or random errors incurred during treatment planning and/or delivery. The dose uncertainty associated with Monte Carlo calculated dose distributions is deemed statistical and noted as artificial with respect to the actual delivered dose. We will refer to all dose uncertainties that arise from either calculation or delivery as stochastic. Both physical and statistical dose uncertainties are considered at the intra- and inter-voxel levels. To account for voxel dose uncertainty, we calculate the mean survival fraction (SF) for the random dose deposition. Mathematically, the expression for the mean survival fraction is identical to that used by Niemierko (1997 Med. Phys. 24 103-10) in defining equivalent uniform dose (EUD). To distinguish between spatial and probabilistic dose variations, we define equivalent stochastic dose (ESD) as a voxel dose that gives the mean expected survival fraction for the randomly deposited dose. For a probability density function f(D), that represents the probabilistic voxel dose, SF(ESD) can be calculated by convolving SF(D) with f(D). In the case where the probability density function follows a Gaussian distribution, an analytic expression is derived for SF(ESD). The derived expression is verified using the Monte Carlo method and ESD values calculated with varied radiosensitivities for cases of 60 and 70 Gy at 2 Gy per fraction. The analytic expression is also extended to account for a multi-voxel dose distribution that incorporates a spatial dose heterogeneity. The results show that survival fraction increases with an increased dose uncertainty. This reduction depends on radiobiological parameters attributed to tissue and tumour. For tissue, ESD drops to 55% of the mean physical dose when the dose has a 10% intra- and inter-voxel dose uncertainty and inhomogeneity.

Investigation of geometrical and scoring grid resolution for Monte Carlo dose calculations for IMRT

Monte Carlo based treatment planning of two different patient groups treated with step-and-shoot IMRT (head-and-neck and lung treatments) with different CT resolutions and scoring methods is performed to determine the effect of geometrical and scoring voxel sizes on DVHs and calculation times. Dose scoring is performed in two different ways: directly into geometrical voxels (or in a number of grouped geometrical voxels) or into scoring voxels defined by a separate scoring grid superimposed on the geometrical grid. For the head-and-neck cancer patients, more than 2% difference is noted in the right optical nerve when using voxel dimensions of 4 x 4 x 4 mm3 compared to the reference calculation with 1 x 1 x 2 mm3 voxel dimensions. For the lung cancer patients, 2% difference is noted in the spinal cord when using voxel dimensions of 4 x 4 x 10 mm3 compared to the 1 x 1 x 5 mm3 calculation. An independent scoring grid introduces several advantages. In cases where a relatively high geometrical resolution is required and where the scoring resolution is less important, the number of scoring voxels can be limited while maintaining a high geometrical resolution. This can be achieved either by grouping several geometrical voxels together into scoring voxels or by superimposing a separate scoring grid of spherical voxels with a user-defined radius on the geometrical grid. For the studied lung cancer cases, both methods produce accurate results and introduce a speed increase by a factor of 10-36. In cases where a low geometrical resolution is allowed, but where a high scoring resolution is required, superimposing a separate scoring grid on the geometrical grid allows a reduction in geometrical voxels while maintaining a high scoring resolution. For the studied head-and-neck cancer cases, calculations performed with a geometrical resolution of 2 x 2 x 2 mm3 and a separate scoring grid containing spherical scoring voxels with a radius of 2 mm produce accurate results and introduce a speed increase by a factor of 13. The scoring grid provides an additional degree of freedom for limiting calculation time and memory requirements by selecting optimized scoring and geometrical voxel dimensions in an independent way.

Effect of statistical uncertainties on Monte Carlo treatment planning

This paper reviews the effect of statistical uncertainties on radiotherapy treatment planning using Monte Carlo simulations. We discuss issues related to the statistical analysis of Monte Carlo dose calculations for realistic clinical beams using various variance reduction or time saving techniques. We discuss the effect of statistical uncertainties on dose prescription and monitor unit calculation for conventional treatment and intensity-modulated radiotherapy (IMRT) based on Monte Carlo simulations. We show the effect of statistical uncertainties on beamlet dose calculation and plan optimization for IMRT and other advanced treatment techniques such as modulated electron radiotherapy (MERT). We provide practical guidelines for the clinical implementation of Monte Carlo treatment planning and show realistic examples of Monte Carlo based IMRT and MERT plans.

Monte Carlo as a four-dimensional radiotherapy treatment-planning tool to account for respiratory motion

Four-dimensional (4D) radiotherapy is the explicit inclusion of the temporal changes in anatomy during the imaging, planning and delivery of radiotherapy. Temporal anatomic changes can occur for many reasons, though the focus of the current investigation was respiration motion for lung tumours. The aims of the current research were first to develop a 4D Monte Carlo methodology and second to apply this technique to an existing 4D treatment plan. A 4D CT scan consisting of a series of 3D CT image sets acquired at different respiratory phases was used. Deformable image registration was performed to map each CT set from the end-inhale respiration phase to the CT image sets corresponding with subsequent respiration phases. This deformable registration allowed the contours drawn on the end-inhale CT to be automatically drawn on the other respiratory phase CT image sets. A treatment plan was created on the end-inhale CT image set and then automatically created on each of the 3D CT image sets corresponding with subsequent respiration phases, based on the beam arrangement and dose prescription in the end-inhale plan. Dose calculation using Monte Carlo was simultaneously performed on each of the N (=8) 3D image sets with 1/N fewer particles per calculation than for a 3D plan. The dose distribution from each respiratory phase CT image set was mapped back to the end-inhale CT image set for analysis. This use of deformable image registration to merge all the statistically noisy dose distributions back onto one CT image set effectively yielded a 4D Monte Carlo calculation with a statistical uncertainty equivalent to a 3D calculation, with a similar calculation time for the 3D and 4D methods. Monte Carlo as a dose calculation tool for 4D radiotherapy planning has two advantages: (1) higher accuracy for calculation in electronic disequilibrium conditions, such as those encountered during lung radiotherapy, and (2) if deformable image registration is used, the calculation time for Monte Carlo is independent of the number of 3D CT image sets constituting a 4D CT, unlike other algorithms for which the calculation time scales linearly with the number of 3D CT image sets constituting a 4D CT.

Adaptive anisotropic diffusion filtering of Monte Carlo dose distributions

The Monte Carlo method is the most accurate method for radiotherapy dose calculations, if used correctly. However, any Monte Carlo dose calculation is burdened with statistical noise. In this paper, denoising of Monte Carlo dose distributions with a three-dimensional adaptive anisotropic diffusion method was investigated. The standard anisotropic diffusion method was extended by changing the filtering parameters adaptively according to the local statistical noise. Smoothing of dose distributions with different noise levels in an inhomogeneous phantom, a conventional and an IMRT treatment case is shown. The resultant dose distributions were analysed using several evaluating criteria. It is shown that the adaptive anisotropic diffusion method can reduce statistical noise significantly (two to five times, corresponding to the reduction of simulation time by a factor of up to 20), while preserving important gradients of the dose distribution well. The choice of free parameters of the method was found to be fairly robust.

Comparison of IMRT optimization based on a pencil beam and a superposition algorithm

To investigate the role of sophisticated dose calculation methods for treatment planning, we compared conventional pencil beam optimized 6 and 15 MV intensity-modulated treatment plans with optimizations based on the superposition technique. Five lung and five head and neck IMRT cases with spatial resolutions of bixels and dose voxels usually employed in clinical practice were considered for tumor volumes between 15 and 500 cm3. We investigated the systematic error of the pencil beam algorithm and the pencil beam induced error to the optimal solution of bixel weights. For the lung cases, the pencil beam overestimated the mean dose deposited inside the planning target volume (PTV) by about 8%, for small lung tumors even up to 20.6%. In the head and neck cases only a slight overestimation in mean PTV dose of 1.5% was observed. The optimization with the superposition method substantially improved the dose coverage of the considered radiation targets. Additionally, for the head and neck cases, the brainstem was significantly spared by about 4% mean PTV dose through the use of the superposition technique. Our studies showed that, in target regions with intricate tissue inhomogeneities, superposition or Monte Carlo techniques have to be used for the optimization and the final dose calculation of intensity-modulated treatment plans.

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.

Monte Carlo simulation for MLC-based intensity-modulated radiotherapy

This article describes photon beam Monte Carlo simulation for multi leaf collimator (MLC)-based intensity-modulated radiotherapy (IMRT). We present the general aspects of the Monte Carlo method for the non-Monte Carloist with an emphasis given to patient-specific radiotherapy application. Patient-specific application of the Monte Carlo method can be used for IMRT dose verification, inverse planning, and forward planning in conventional conformal radiotherapy. Because it is difficult to measure IMRT dose distributions in heterogeneous phantoms that approximate a patient, Monte Carlo methods can be used to verify IMRT dose distributions that are calculated using conventional methods. Furthermore, using Monte Carlo as the dose calculation method for inverse planning results in better-optimized treatment plans. We describe both aspects and present our recent results to illustrate the discussion. Finally, we present current issues related to clinical implementation of Monte Carlo dose calculation. Monte Carlo is the most recent, and most accurate, method of radiotherapy dose calculation. It is currently in the process of being implemented by various treatment planning vendors and will be available for clinical use in the immediate future.

The MLC tongue-and-groove effect on IMRT dose distributions

We have investigated the tongue-and-groove effect on the IMRT dose distributions for a Varian MLC. We have compared the dose distributions calculated using the intensity maps with and without the tongue-and-groove effect. Our results showed that, for one intensity-modulated treatment field, the maximum tongue-and-groove effect could be up to 10% of the maximum dose in the dose distributions. For an IMRT treatment with multiple gantry angles (> or = 5), the difference between the dose distributions with and without the tongue-and-groove effect was hardly visible, less than 1.6% for the two typical clinical cases studied. After considering the patient setup errors, the dose distributions were smoothed with reduced and insignificant differences between plans with and without the tongue-and-groove effect. Therefore, for a multiple-field IMRT plan (> or = 5), the tongue-and-groove effect on the IMRT dose distributions will be generally clinically insignificant due to the smearing effect of individual fields. The tongue-and-groove effect on an IMRT plan with small number of fields (< 5) will vary depending on the number of fields in a plan (coplanar or non-coplanar), the MLC leaf sequences and the patient setup uncertainty, and may be significant (> 5% of maximum dose) in some cases, especially when the patient setup uncertainty is small (< or = 2 mm).

The effect of statistical uncertainty on inverse treatment planning based on Monte Carlo dose calculation

The effect of the statistical uncertainty, or noise, in inverse treatment planning for intensity modulated radiotherapy (IMRT) based on Monte Carlo dose calculation was studied. Sets of Monte Carlo beamlets were calculated to give uncertainties at Dmax ranging from 0.2% to 4% for a lung tumour plan. The weights of these beamlets were optimized using a previously described procedure based on a simulated annealing optimization algorithm. Several different objective functions were used. It was determined that the use of Monte Carlo dose calculation in inverse treatment planning introduces two errors in the calculated plan. In addition to the statistical error due to the statistical uncertainty of the Monte Carlo calculation, a noise convergence error also appears. For the statistical error it was determined that apparently successfully optimized plans with a noisy dose calculation (3% 1sigma at Dmax), which satisfied the required uniformity of the dose within the tumour, showed as much as 7% underdose when recalculated with a noise-free dose calculation. The statistical error is larger towards the tumour and is only weakly dependent on the choice of objective function. The noise convergence error appears because the optimum weights are determined using a noisy calculation, which is different from the optimum weights determined for a noise-free calculation. Unlike the statistical error, the noise convergence error is generally larger outside the tumour, is case dependent and strongly depends on the required objectives.