Experimental determination and verification of the parameters used in a proton pencil beam algorithm

Dose calculation in proton therapy using a discovery cross-domain generative adversarial network (DiscoGAN)

PURPOSE

Accurate dose calculation is a critical step in proton therapy. A novel machine learning-based approach was proposed to achieve comparable accuracy to that of Monte Carlo simulation while reducing the computational time.

METHODS

Computed tomography-based patient phantoms were used and three treatment sites were selected (thorax, head, and abdomen), comprising different beam pathways and beam energies. The training data were generated using Monte Carlo simulations. A discovery cross-domain generative adversarial network (DiscoGAN) was developed to perform the mapping between two domains: stopping power and dose, with HU values from CT images incorporated as auxiliary features. The accuracy of dose calculation was quantitatively evaluated in terms of mean relative error (MRE) and mean absolute error (MAE). The relationship between the DiscoGAN performance and other factors such as absolute dose, beam energy and location within the beam cross-section (center and off-center lines) was examined.

RESULTS

The DiscoGAN model is found to be effective in dose calculation. For the abdominal case, the MRE is found to 1.47% (mean), 3.30% (maximum) and 0.67% (minimum). For the thoracic case, the MRE is found to ~2.43% (mean), 4.80% (maximum) and 0.71% (minimum). For the head case, the MRE is found to ~2.83% (mean), 4.84% (maximum) and 1.01% (minimum). Comparable accuracy is found in the independent validation dataset (different CT images), achieving a mean MRE of ~1.65% (thorax), 4.02% (head) and 1.64% (abdomen). For the energy span between 80 and 130 MeV, no strong dependency of accuracy on beam energy is found. The results imply that no systematic deviation, either over-dose or under-dose, occurs between the predicted dose and raw dose.

CONCLUSION

The DiscoGAN framework demonstrates great potential as a tool for dose calculation in proton therapy, achieving comparable accuracy yet being more efficient relative to Monte Carlo simulation. Its comparison with the pencil beam algorithm (PBA) will be the next step of our research. If successful, our proposed approach is expected to find its use in more advanced applications such as inverse planning and adaptive proton therapy.

Experimental and Monte Carlo characterization of a dynamic collimation system prototype for pencil beam scanning proton therapy

PURPOSE

There has been a growing interest in the development of energy-specific collimators for low-energy pencil beam scanning (PBS) to reduce the lateral penumbra. One particular device that has been the focus of several recent published works is the dynamic collimation system (DCS), which provides energy-specific collimation by intercepting the scanned proton beam as it nears to target edge with a set of orthogonal trimmer blades. While several computational studies have shown that this dynamic collimator can provide additional healthy tissue sparing, there has not been any rigorous experimental work to benchmark the theoretical models used in these initial studies. Therefore, it was the purpose of this work to demonstrate an experimental method that could integrate an experimental prototype with a clinical PBS system and benchmark the Monte Carlo methods that have been used to model the DCS.

METHODS

An experimental DCS prototype was designed and built in house to actively collimate individual proton beamlets during PBS within a well-characterized experimental setup. Monte Carlo methods were initially used to assess construction tolerances and later benchmarked against measurements, including integral depth dose and lateral asymmetric beamlet profiles. The experimental apparatus and measurement geometry were modeled using MCNP6 benchmarked from measurements performed at the Northwestern Chicago Proton Center.

RESULTS

Gamma analysis tests were used to evaluate the agreement between the measured and simulated profiles with a strict 1 mm/1% criteria and 5% dose threshold. Excellent agreement was observed between the simulated and measured profiles, which included 1 mm/1% gamma analysis pass rates of at least 100% and 95% for the integral depth dose (IDD) profiles and lateral profiles, respectively. Differences in the relative profile shape were observed experimentally between beamlets collimated on- and off-axis, which was attributed to the partial transmission of the beam through an unfocused collimator. Exposure rates resulting from the activation of the device were monitored with survey meter measurements and were found to agree with Monte Carlo estimates of the exposure rate to within 20%.

CONCLUSION

A DCS prototype was constructed and integrated into a clinical dose delivery system. While the results of this work are not exhaustive, they demonstrate the effects of beam source divergence, device activation, and beamlet deflection during scanning, which were found to be successfully modeled using Monte Carlo methods and experimentally benchmarked. Excellent agreement was achieved between the simulated and measured lateral spot profiles of collimated beamlets delivered on- and off-axis in PBS. The Monte Carlo models adequately predicted the measured elevated plateau region in the integral depth-dose profiles from the low-energy scatter off the collimators.

Clinical commissioning of intensity-modulated proton therapy systems: Report of AAPM Task Group 185

Proton therapy is an expanding radiotherapy modality in the United States and worldwide. With the number of proton therapy centers treating patients increasing, so does the need for consistent, high-quality clinical commissioning practices. Clinical commissioning encompasses the entire proton therapy system's multiple components, including the treatment delivery system, the patient positioning system, and the image-guided radiotherapy components. Also included in the commissioning process are the x-ray computed tomography scanner calibration for proton stopping power, the radiotherapy treatment planning system, and corresponding portions of the treatment management system. This commissioning report focuses exclusively on intensity-modulated scanning systems, presenting details of how to perform the commissioning of the proton therapy and ancillary systems, including the required proton beam measurements, treatment planning system dose modeling, and the equipment needed.

Implementation of planar proton minibeam radiation therapy using a pencil beam scanning system: A proof of concept study

PURPOSE

Proton minibeam radiation therapy (pMBRT) is an innovative approach that combines the advantages of minibeam radiation therapy with the more precise ballistics of protons to further reduce the side effects of radiation. One of the main challenges of this approach is the generation of very narrow proton pencil beams with an adequate dose-rate to treat patients within a reasonable treatment time (several minutes) in existing clinical facilities. The aim of this study was to demonstrate the feasibility of implementing pMBRT by combining the pencil beam scanning (PBS) technique with the use of multislit collimators. This proof of concept study of pMBRT with a clinical system is intended to guide upcoming biological experiments.

METHODS

Monte Carlo simulations (TOPAS v3.1.p2) were used to design a suitable multislit collimator to implement planar pMBRT for conventional pencil beam scanning settings. Dose distributions (depth-dose curves, lateral profiles, Peak-to-Valley Dose Ratio (PVDR) and dose-rates) for different proton beam energies were assessed by means of Monte Carlo simulations and experimental measurements in a water tank using commercial ionization chambers and a new p-type silicon diode, the IBA RAZOR. An analytical intensity-modulated dose calculation algorithm designed to optimize the weight of individual Bragg peaks composing the field was also developed and validated.

RESULTS

Proton minibeams were then obtained using a brass multislit collimator with five slits measuring 2 cm × 400 μm in width with a center-to-center distance of 4 mm. The measured and calculated dose distributions (depth-dose curves and lateral profiles) showed a good agreement. Spread-out Bragg peaks (SOBP) and homogeneous dose distributions around the target were obtained by means of intensity modulation of Bragg peaks, while maintaining spatial fractionation at shallow depths. Mean dose-rates of 0.12 and 0.09 Gy/s were obtained for one iso-energy layer and a SOBP conditions in the presence of multislit collimator.

CONCLUSIONS

This study demonstrates the feasibility of implementing pMBRT on a PBS system. It also confirms the reliability of RAZOR detector for pMBRT dosimetry. This newly developed experimental methodology will support the design of future preclinical research with pMBRT.

Proton range verification in inhomogeneous tissue: Treatment planning system vs. measurement vs. Monte Carlo simulation

In particle radiotherapy, range uncertainty is an important issue that needs to be overcome. Because high-dose conformality can be achieved using a particle beam, a small uncertainty can affect tumor control or cause normal-tissue complications. From this perspective, the treatment planning system (TPS) must be accurate. However, there is a well-known inaccuracy regarding dose computation in heterogeneous media. This means that verifying the uncertainty level is one of the prerequisites for TPS commissioning. We evaluated the range accuracy of the dose computation algorithm implemented in a commercial TPS, and Monte Carlo (MC) simulation against measurement using a CT calibration phantom. A treatment plan was produced for eight different materials plugged into a phantom, and two-dimensional doses were measured using a chamber array. The measurement setup and beam delivery were simulated by MC code. For an infinite solid water phantom, the gamma passing rate between the measurement and TPS was 97.7%, and that between the measurement and MC was 96.5%. However, gamma passing rates between the measurement and TPS were 49.4% for the lung and 67.8% for bone, and between the measurement and MC were 85.6% for the lung and 100.0% for bone tissue. For adipose, breast, brain, liver, and bone mineral, the gamma passing rates computed by TPS were 91.7%, 90.6%, 81.7%, 85.6%, and 85.6%, respectively. The gamma passing rates for MC for adipose, breast, brain, liver, and bone mineral were 100.0%, 97.2%, 95.0%, 98.9%, and 97.8%, respectively. In conclusion, the described procedure successfully evaluated the allowable range uncertainty for TPS commissioning. The TPS dose calculation is inefficient in heterogeneous media with large differences in density, such as lung or bone tissue. Therefore, the limitations of TPS in heterogeneous media should be understood and applied in clinical practice.

Evaluation of the influence of double and triple Gaussian proton kernel models on accuracy of dose calculations for spot scanning technique

PURPOSE

The main purpose in this study was to present the results of beam modeling and how the authors systematically investigated the influence of double and triple Gaussian proton kernel models on the accuracy of dose calculations for spot scanning technique.

METHODS

The accuracy of calculations was important for treatment planning software (TPS) because the energy, spot position, and absolute dose had to be determined by TPS for the spot scanning technique. The dose distribution was calculated by convolving in-air fluence with the dose kernel. The dose kernel was the in-water 3D dose distribution of an infinitesimal pencil beam and consisted of an integral depth dose (IDD) and a lateral distribution. Accurate modeling of the low-dose region was important for spot scanning technique because the dose distribution was formed by cumulating hundreds or thousands of delivered beams. The authors employed a double Gaussian function as the in-air fluence model of an individual beam. Double and triple Gaussian kernel models were also prepared for comparison. The parameters of the kernel lateral model were derived by fitting a simulated in-water lateral dose profile induced by an infinitesimal proton beam, whose emittance was zero, at various depths using Monte Carlo (MC) simulation. The fitted parameters were interpolated as a function of depth in water and stored as a separate look-up table. These stored parameters for each energy and depth in water were acquired from the look-up table when incorporating them into the TPS. The modeling process for the in-air fluence and IDD was based on the method proposed in the literature. These were derived using MC simulation and measured data. The authors compared the measured and calculated absolute doses at the center of the spread-out Bragg peak (SOBP) under various volumetric irradiation conditions to systematically investigate the influence of the two types of kernel models on the dose calculations.

RESULTS

The authors investigated the difference between double and triple Gaussian kernel models. The authors found that the difference between the two studied kernel models appeared at mid-depths and the accuracy of predicting the double Gaussian model deteriorated at the low-dose bump that appeared at mid-depths. When the authors employed the double Gaussian kernel model, the accuracy of calculations for the absolute dose at the center of the SOBP varied with irradiation conditions and the maximum difference was 3.4%. In contrast, the results obtained from calculations with the triple Gaussian kernel model indicated good agreement with the measurements within ±1.1%, regardless of the irradiation conditions.

CONCLUSIONS

The difference between the results obtained with the two types of studied kernel models was distinct in the high energy region. The accuracy of calculations with the double Gaussian kernel model varied with the field size and SOBP width because the accuracy of prediction with the double Gaussian model was insufficient at the low-dose bump. The evaluation was only qualitative under limited volumetric irradiation conditions. Further accumulation of measured data would be needed to quantitatively comprehend what influence the double and triple Gaussian kernel models had on the accuracy of dose calculations.

A method for modeling laterally asymmetric proton beamlets resulting from collimation

PURPOSE

To introduce a method to model the 3D dose distribution of laterally asymmetric proton beamlets resulting from collimation. The model enables rapid beamlet calculation for spot scanning (SS) delivery using a novel penumbra-reducing dynamic collimation system (DCS) with two pairs of trimmers oriented perpendicular to each other.

METHODS

Trimmed beamlet dose distributions in water were simulated with MCNPX and the collimating effects noted in the simulations were validated by experimental measurement. The simulated beamlets were modeled analytically using integral depth dose curves along with an asymmetric Gaussian function to represent fluence in the beam's eye view (BEV). The BEV parameters consisted of Gaussian standard deviations (sigmas) along each primary axis (σ(x1),σ(x2),σ(y1),σ(y2)) together with the spatial location of the maximum dose (μ(x),μ(y)). Percent depth dose variation with trimmer position was accounted for with a depth-dependent correction function. Beamlet growth with depth was accounted for by combining the in-air divergence with Hong's fit of the Highland approximation along each axis in the BEV.

RESULTS

The beamlet model showed excellent agreement with the Monte Carlo simulation data used as a benchmark. The overall passing rate for a 3D gamma test with 3%/3 mm passing criteria was 96.1% between the analytical model and Monte Carlo data in an example treatment plan.

CONCLUSIONS

The analytical model is capable of accurately representing individual asymmetric beamlets resulting from use of the DCS. This method enables integration of the DCS into a treatment planning system to perform dose computation in patient datasets. The method could be generalized for use with any SS collimation system in which blades, leaves, or trimmers are used to laterally sharpen beamlets.

An empirical model for calculation of the collimator contamination dose in therapeutic proton beams

Collimators are used as lateral beam shaping devices in proton therapy with passive scattering beam lines. The dose contamination due to collimator scattering can be as high as 10% of the maximum dose and influences calculation of the output factor or monitor units (MU). To date, commercial treatment planning systems generally use a zero-thickness collimator approximation ignoring edge scattering in the aperture collimator and few analytical models have been proposed to take scattering effects into account, mainly limited to the inner collimator face component. The aim of this study was to characterize and model aperture contamination by means of a fast and accurate analytical model. The entrance face collimator scatter distribution was modeled as a 3D secondary dose source. Predicted dose contaminations were compared to measurements and Monte Carlo simulations. Measurements were performed on two different proton beam lines (a fixed horizontal beam line and a gantry beam line) with divergent apertures and for several field sizes and energies. Discrepancies between analytical algorithm dose prediction and measurements were decreased from 10% to 2% using the proposed model. Gamma-index (2%/1 mm) was respected for more than 90% of pixels. The proposed analytical algorithm increases the accuracy of analytical dose calculations with reasonable computation times.

Analytical linear energy transfer model including secondary particles: calculations along the central axis of the proton pencil beam

In proton therapy, the relative biological effectiveness (RBE) depends on various types of parameters such as linear energy transfer (LET). An analytical model for LET calculation exists (Wilkens' model), but secondary particles are not included in this model. In the present study, we propose a correction factor, L sec, for Wilkens' model in order to take into account the LET contributions of certain secondary particles. This study includes secondary protons and deuterons, since the effects of these two types of particles can be described by the same RBE-LET relationship. L sec was evaluated by Monte Carlo (MC) simulations using the GATE/GEANT4 platform and was defined by the ratio of the LET d distributions of all protons and deuterons and only primary protons. This method was applied to the innovative Pencil Beam Scanning (PBS) delivery systems and L sec was evaluated along the beam axis. This correction factor indicates the high contribution of secondary particles in the entrance region, with L sec values higher than 1.6 for a 220 MeV clinical pencil beam. MC simulations showed the impact of pencil beam parameters, such as mean initial energy, spot size, and depth in water, on L sec. The variation of L sec with these different parameters was integrated in a polynomial function of the L sec factor in order to obtain a model universally applicable to all PBS delivery systems. The validity of this correction factor applied to Wilkens' model was verified along the beam axis of various pencil beams in comparison with MC simulations. A good agreement was obtained between the corrected analytical model and the MC calculations, with mean-LET deviations along the beam axis less than 0.05 keV μm(-1). These results demonstrate the efficacy of our new correction of the existing LET model in order to take into account secondary protons and deuterons along the pencil beam axis.

Evaluation of monitor unit calculation based on measurement and calculation with a simplified Monte Carlo method for passive beam delivery system in proton beam therapy

Calibrating the dose per monitor unit (DMU) for individual patients is important to deliver the prescribed dose in radiation therapy. We have developed a DMU calculation method combining measurement data and calculation with a simplified Monte Carlo method for the double scattering system in proton beam therapy at the National Cancer Center Hospital East in Japan. The DMU calculation method determines the clinical DMU by the multiplication of three factors: a beam spreading device factor FBSD, a patient‐specific device factor FPSD, and a field‐size correction factor FFS(A). We compared the calculated and the measured DMU for 75 dose fields in clinical cases. The calculated DMUs were in agreement with measurements in ±1.1% for all of 25 fields in prostate cancer cases, and in ±3% for 94% of 50 fields in head and neck (H&N) and lung cancer cases, including irregular shape fields and small fields. Although the FBSD in the DMU calculations is dominant as expected, we found that the patient‐specific device factor and field‐size correction also contribute significantly to the calculated DMU. This DMU calculation method will be able to substitute the conventional DMU measurement for the majority of clinical cases with a reasonable calculation time required for clinical use.

PACS number: 87.55.kh

Use of gEUD for predicting ear and pituitary gland damage following proton and photon radiation therapy

OBJECTIVE

To determine the relationship between the dose to the inner ear or pituitary gland and radiation-induced late effects of skull base radiation therapy.

METHODS

140 patients treated between 2000 and 2008 were considered for this study. Hearing loss and endocrine dysfunction were retrospectively reviewed on pre- and post-radiation therapy audiometry or endocrine assessments. Two normal tissue complication probability (NTCP) models were considered (Lyman-Kutcher-Burman and log-logistic) whose parameters were fitted to patient data using receiver operating characteristics and maximum likelihood analysis. The method provided an estimation of the parameters of a generalized equivalent uniform dose (gEUD)-based NTCP after conversion of dose-volume histograms to equivalent doses.

RESULTS

All 140 patients had a minimum follow up of 26 months. 26% and 44% of patients experienced mild hearing loss and endocrine dysfunction, respectively. The fitted values for TD50 and γ50 ranged from 53.6 to 60.7 Gy and from 1.9 to 2.9 for the inner ear and were equal to 60.6 Gy and 4.9 for the pituitary gland, respectively. All models were ranked equal according to Akaike's information criterion.

CONCLUSION

Mean dose and gEUD may be used as predictive factors for late ear and pituitary gland late complications after skull base proton and photon radiation therapy.

ADVANCES IN KNOWLEDGE

In this study, we have reported mean dose effects and dose-response relationship of small organs at risk (partial volumes of the inner ear and pituitary gland), which could be useful to define optimal dose constraints resulting in an improved therapeutic ratio.

A novel method for experimental characterization of large-angle scattered particles in scanned carbon-ion therapy

PURPOSE

It is essential to consider large-angle scattered particles in dose calculation models for therapeutic carbon-ion beams. However, it is difficult to measure the small dose contribution from large-angle scattered particles. In this paper, the authors present a novel method to derive the parameters describing large-angle scattered particles from the measured results.

METHODS

The authors developed a new parallel-plate ionization chamber consisting of concentric electrodes. Since the sensitive volume of each channel is increased linearly with this type, it is possible to efficiently and easily detect small contributions from the large-angle scattered particles. The parameters describing the large-angle scattered particles were derived from pencil beam dose distribution in water measured with the new ionization chamber. To evaluate the validity of this method, the correction for the field-size dependence of the doses, "predicted-dose scaling factor," was calculated with the new parameters.

RESULTS

The predicted-dose scaling factor calculated with the new parameters was compared with the existing one. The difference between the new correction factor and the existing one was 1.3%. For target volumes of different sizes, the calculated dose distribution with the new parameters was in good agreement with the measured one.

CONCLUSIONS

Parameters describing the large-angle scattered particles can be efficiently and rapidly determined using the new ionization chamber. The authors confirmed that the field-size dependence of the doses could be compensated for by the new parameters. This method makes it possible to easily derive the parameters describing the large-angle scattered particles, while maintaining the dose calculation accuracy.

A fast Monte Carlo code for proton transport in radiation therapy based on MCNPX

An important requirement for proton therapy is a software for dose calculation. Monte Carlo is the most accurate method for dose calculation, but it is very slow. In this work, a method is developed to improve the speed of dose calculation. The method is based on pre-generated tracks for particle transport. The MCNPX code has been used for generation of tracks. A set of data including the track of the particle was produced in each particular material (water, air, lung tissue, bone, and soft tissue). This code can transport protons in wide range of energies (up to 200 MeV for proton). The validity of the fast Monte Carlo (MC) code is evaluated with data MCNPX as a reference code. While analytical pencil beam algorithm transport shows great errors (up to 10%) near small high density heterogeneities, there was less than 2% deviation of MCNPX results in our dose calculation and isodose distribution. In terms of speed, the code runs 200 times faster than MCNPX. In the Fast MC code which is developed in this work, it takes the system less than 2 minutes to calculate dose for 10(6) particles in an Intel Core 2 Duo 2.66 GHZ desktop computer.

Improving spot-scanning proton therapy patient specific quality assurance with HPlusQA, a second-check dose calculation engine

PURPOSE

The purpose of this study was to validate the use of HPlusQA, spot-scanning proton therapy (SSPT) dose calculation software developed at The University of Texas MD Anderson Cancer Center, as second-check dose calculation software for patient-specific quality assurance (PSQA). The authors also showed how HPlusQA can be used within the current PSQA framework.

METHODS

The authors compared the dose calculations of HPlusQA and the Eclipse treatment planning system with 106 planar dose measurements made as part of PSQA. To determine the relative performance and the degree of correlation between HPlusQA and Eclipse, the authors compared calculated with measured point doses. Then, to determine how well HPlusQA can predict when the comparisons between Eclipse calculations and the measured dose will exceed tolerance levels, the authors compared gamma index scores for HPlusQA versus Eclipse with those of measured doses versus Eclipse. The authors introduce the αβγ transformation as a way to more easily compare gamma scores.

RESULTS

The authors compared measured and calculated dose planes using the relative depth, z∕R × 100%, where z is the depth of the measurement and R is the proton beam range. For relative depths than less than 80%, both Eclipse and HPlusQA calculations were within 2 cGy of dose measurements on average. When the relative depth was greater than 80%, the agreement between the calculations and measurements fell to 4 cGy. For relative depths less than 10%, the Eclipse and HPlusQA dose discrepancies showed a negative correlation, -0.21. Otherwise, the correlation between the dose discrepancies was positive and as large as 0.6. For the dose planes in this study, HPlusQA correctly predicted when Eclipse had and had not calculated the dose to within tolerance 92% and 79% of the time, respectively. In 4 of 106 cases, HPlusQA failed to predict when the comparison between measurement and Eclipse's calculation had exceeded the tolerance levels of 3% for dose and 3 mm for distance-to-agreement.

CONCLUSIONS

The authors found HPlusQA to be reasonably effective (79% ± 10%) in determining when the comparison between measured dose planes and the dose planes calculated by the Eclipse treatment planning system had exceeded the acceptable tolerance levels. When used as described in this study, HPlusQA can reduce the need for patient specific quality assurance measurements by 64%. The authors believe that the use of HPlusQA as a dose calculation second check can increase the efficiency and effectiveness of the QA process.

Experimental verification of dose calculation using the simplified Monte Carlo method with an improved initial beam model for a beam-wobbling system

A beam delivery system using a single-radius-beam-wobbling method has been used to form a conformal irradiation field for proton radiotherapy in Japan. A proton beam broadened by the beam-wobbling system provides a non-Gaussian distribution of projection angle different in two mutually orthogonal planes with a common beam central axis, at a certain position. However, the conventional initial beam model for dose calculations has been using an approximation of symmetric Gaussian angular distribution with the same variance in both planes (called here a Gaussian model with symmetric variance (GMSV)), instead of the accurate one. We have developed a more accurate initial beam model defined as a non-Gaussian model with asymmetric variance (NonGMAV), and applied it to dose calculations using the simplified Monte Carlo (SMC) method. The initial beam model takes into account the different distances of two beam-wobbling magnets from the iso-center and also the different amplitudes of kick angle given by each magnet. We have confirmed that the calculation using the SMC with NonGMAV reproduced the measured dose distribution formed in air by a mono-energetic proton beam passing through a square aperture collimator better than with the GMSV and with a Gaussian model with asymmetric variance (GMAV) in which different variances of angular distributions are used in the two mutually orthogonal planes. Measured dose distributions in a homogeneous phantom formed by a modulated proton beam passing through a range shifter and an L-shaped range compensator, were consistent with calculations using the SMC with GMAV and NonGMAV, but in disagreement with calculations using the SMC with GMSV. Measured lateral penumbrae in a lateral direction were reproduced better by calculations using the SMC with NonGMAV than by those with GMAV, when an aperture collimator with a smaller opening was used. We found that such a difference can be attributed to the non-Gaussian angular distribution of the initial beam at a lateral position for the beam-wobbling system. Calculations using the SMC with NonGMAV are effective to reproduce dose distributions formed by a beam-wobbling system more accurately than that with GMSV or that with GMAV.

Application of the pencil-beam redefinition algorithm in heterogeneous media for proton beam therapy

In proton beam therapy, changes in the proton range due to lateral heterogeneity may cause serious errors in the dose distribution. In the present study, the pencilbeam redefinition algorithm (PBRA) was applied to proton beam therapy to address the problem of lateral density heterogeneity. In the calculation, the phase-space parameters were characterized for multiple range (i.e. proton energy) bins for given pencil beams. The particles that were included in each pencil beam were transported and redefined periodically until they had stopped. The redefined beams formed a detouring path that was different from that of the non-redefined pencil beams, and the path of each redefined beam was straight. The results calculated by the PBRA were compared with measured proton dose distributions in a heterogeneous slab phantom and an anthropomorphic phantom. Through the beam redefinition process, the PBRA was able to predict the measured proton-detouring effects. Therefore, the PBRA may allow improved calculation accuracy when dealing with lateral heterogeneities in proton therapy applications.

A generalized 2D pencil beam scaling algorithm for proton dose calculation in heterogeneous slab geometries

PURPOSE

Pencil beam algorithms are commonly used for proton therapy dose calculations. Szymanowski and Oelfke ["Two-dimensional pencil beam scaling: An improved proton dose algorithm for heterogeneous media," Phys. Med. Biol. 47, 3313-3330 (2002)] developed a two-dimensional (2D) scaling algorithm which accurately models the radial pencil beam width as a function of depth in heterogeneous slab geometries using a scaled expression for the radial kernel width in water as a function of depth and kinetic energy. However, an assumption made in the derivation of the technique limits its range of validity to cases where the input expression for the radial kernel width in water is derived from a local scattering power model. The goal of this work is to derive a generalized form of 2D pencil beam scaling that is independent of the scattering power model and appropriate for use with any expression for the radial kernel width in water as a function of depth.

METHODS

Using Fermi-Eyges transport theory, the authors derive an expression for the radial pencil beam width in heterogeneous slab geometries which is independent of the proton scattering power and related quantities. The authors then perform test calculations in homogeneous and heterogeneous slab phantoms using both the original 2D scaling model and the new model with expressions for the radial kernel width in water computed from both local and nonlocal scattering power models, as well as a nonlocal parameterization of Molière scattering theory. In addition to kernel width calculations, dose calculations are also performed for a narrow Gaussian proton beam.

RESULTS

Pencil beam width calculations indicate that both 2D scaling formalisms perform well when the radial kernel width in water is derived from a local scattering power model. Computing the radial kernel width from a nonlocal scattering model results in the local 2D scaling formula under-predicting the pencil beam width by as much as 1.4 mm (21%) at the depth of the Bragg peak for a 220 MeV proton beam in homogeneous water. This translates into a 32% dose discrepancy for a 5 mm Gaussian proton beam. Similar trends were observed for calculations made in heterogeneous slab phantoms where it was also noted that errors tend to increase with greater beam penetration. The generalized 2D scaling model performs well in all situations, with a maximum dose error of 0.3% at the Bragg peak in a heterogeneous phantom containing 3 cm of hard bone.

CONCLUSIONS

The authors have derived a generalized form of 2D pencil beam scaling which is independent of the proton scattering power model and robust to the functional form of the radial kernel width in water used for the calculations. Sample calculations made with this model show excellent agreement with expected values in both homogeneous water and heterogeneous phantoms.

Calibration of CT Hounsfield units for proton therapy treatment planning: use of kilovoltage and megavoltage images and comparison of parameterized methods

Proton beam range is of major concern, in particular, when images used for dose computations are artifacted (for example in patients with surgically treated bone tumors). We investigated several conditions and methods for determination of computed tomography Hounsfield unit (CT-HU) calibration curves, using two different conversion schemes. A stoichiometric methodology was used on either kilovoltage (kV) or megavoltage (MV) CT images and the accuracy of the calibration methods was evaluated. We then studied the effects of metal artifacts on proton dose distributions using metallic implants in rigid phantom mimicking clinical conditions. MV-CT images were used to evaluate relative proton stopping power in certain high density implants, and a methodology is proposed for accurate delineation and dose calculation, using a combined set of kV- and MV-CT images. Our results show good agreement between measurements and dose calculations or relative proton stopping power determination (<5%). The results also show that range uncertainty increases when only kV-CT images are used or when no correction is made on artifacted images. However, differences between treatment plans calculated on corrected kV-CT data and MV-CT data remained insignificant in the investigated patient case, even with streak artifacts and volume effects that reduce the accuracy of manual corrections.

Clinical implementation of a GPU-based simplified Monte Carlo method for a treatment planning system of proton beam therapy

We implemented the simplified Monte Carlo (SMC) method on graphics processing unit (GPU) architecture under the computer-unified device architecture platform developed by NVIDIA. The GPU-based SMC was clinically applied for four patients with head and neck, lung, or prostate cancer. The results were compared to those obtained by a traditional CPU-based SMC with respect to the computation time and discrepancy. In the CPU- and GPU-based SMC calculations, the estimated mean statistical errors of the calculated doses in the planning target volume region were within 0.5% rms. The dose distributions calculated by the GPU- and CPU-based SMCs were similar, within statistical errors. The GPU-based SMC showed 12.30-16.00 times faster performance than the CPU-based SMC. The computation time per beam arrangement using the GPU-based SMC for the clinical cases ranged 9-67 s. The results demonstrate the successful application of the GPU-based SMC to a clinical proton treatment planning.

Computation of doses for large-angle Coulomb scattering of proton pencil beams

In this work we present a study of the impact of considering higher order terms in Molière's multiple Coulomb scattering (MCS) theory for the purpose of calculating scanning proton pencil beam lateral dose profiles in water. The proton beam profile in air, just before entering the target medium, was modeled with a sum of Gaussians fitted with measured data. The subsequent proton scattering in water was described using the three-term Molière distribution, which covers both small- and large-angle scatterings. We compared measured and computed lateral dose profiles at the 2 cm and at the near-Bragg peak depths for proton pencil beams with energies of 72.5 MeV, 121.2 MeV, 163.9 MeV and 221.8 MeV. At shallow depths, the Coulomb interaction model provided a good description of the profiles for all energies, except for 221.8 MeV. At the near-Bragg peak depths, the Coulomb interaction model provided a good description of the profiles only for the 72.5 MeV. The observed discrepancies may be attributed to the additional contributions from nuclear interactions, which may be quantified only after an accurate description of the MCS. The analysis presented in this work did not require user-adjustable parameters and may be carried out in a similar way for any other media, depths and proton energies.

The grid-dose-spreading algorithm for dose distribution calculation in heavy charged particle radiotherapy

A new variant of the pencil-beam (PB) algorithm for dose distribution calculation for radiotherapy with protons and heavier ions, the grid-dose spreading (GDS) algorithm, is proposed. The GDS algorithm is intrinsically faster than conventional PB algorithms due to approximations in convolution integral, where physical calculations are decoupled from simple grid-to-grid energy transfer. It was effortlessly implemented to a carbon-ion radiotherapy treatment planning system to enable realistic beam blurring in the field, which was absent with the broad-beam (BB) algorithm. For a typical prostate treatment, the slowing factor of the GDS algorithm relative to the BB algorithm was 1.4, which is a great improvement over the conventional PB algorithms with a typical slowing factor of several tens. The GDS algorithm is mathematically equivalent to the PB algorithm for horizontal and vertical coplanar beams commonly used in carbon-ion radiotherapy while dose deformation within the size of the pristine spread occurs for angled beams, which was within 3 mm for a single 150-MeV proton pencil beam of 30 degrees incidence, and needs to be assessed against the clinical requirements and tolerances in practical situations.

A beam source model for scanned proton beams

A beam source model, i.e. a model for the initial phase space of the beam, for scanned proton beams has been developed. The beam source model is based on parameterized particle sources with characteristics found by fitting towards measured data per individual beam line. A specific aim for this beam source model is to make it applicable to the majority of the various proton beam systems currently available or under development, with the overall purpose to drive dose calculations in proton beam treatment planning. The proton beam phase space is characterized by an energy spectrum, radial and angular distributions and deflections for the non-modulated elementary pencil beam. The beam propagation through the scanning magnets is modelled by applying experimentally determined focal points for each scanning dimension. The radial and angular distribution parameters are deduced from measured two-dimensional fluence distributions of the elementary beam in air. The energy spectrum is extracted from a depth dose distribution for a fixed broad beam scan pattern measured in water. The impact of a multi-slab range shifter for energy modulation is calculated with an own Monte Carlo code taking multiple scattering, energy loss and straggling, non-elastic and elastic nuclear interactions in the slab assembly into account. Measurements for characterization and verification have been performed with the scanning proton beam system at The Svedberg Laboratory in Uppsala. Both in-air fluence patterns and dose points located in a water phantom were used. For verification, dose-in-water was calculated with the Monte Carlo code GEANT 3.21 instead of using a clinical dose engine with approximations of its own. For a set of four individual pencil beams, both with the full energy and range shifted, 96.5% (99.8%) of the tested dose points satisfied the 1%/1 mm (2%/2 mm) gamma criterion.

Extended collimator model for pencil-beam dose calculation in proton radiotherapy

We have developed a simple collimator model to improve the accuracy of penumbra behaviour in pencil-beam dose calculation for proton radiotherapy. In this model, transmission of particles through a three-dimensionally extended opening of a collimator is calculated in conjunction with phase-space distribution of the particles. Comparison of the dose distributions calculated using the new three-dimensional collimator model and the conventional two-dimensional model to lateral dose profiles experimentally measured with collimated proton beams showed the superiority of the new model over the conventional one.

A Fourier analysis on the maximum acceptable grid size for discrete proton beam dose calculation

We developed an analytical method for determining the maximum acceptable grid size for discrete dose calculation in proton therapy treatment plan optimization, so that the accuracy of the optimized dose distribution is guaranteed in the phase of dose sampling and the superfluous computational work is avoided. The accuracy of dose sampling was judged by the criterion that the continuous dose distribution could be reconstructed from the discrete dose within a 2% error limit. To keep the error caused by the discrete dose sampling under a 2% limit, the dose grid size cannot exceed a maximum acceptable value. The method was based on Fourier analysis and the Shannon-Nyquist sampling theorem as an extension of our previous analysis for photon beam intensity modulated radiation therapy [J. F. Dempsey, H. E. Romeijn, J. G. Li, D. A. Low, and J. R. Palta, Med. Phys. 32, 380-388 (2005)]. The proton beam model used for the analysis was a near monoenergetic (of width about 1% the incident energy) and monodirectional infinitesimal (nonintegrated) pencil beam in water medium. By monodirection, we mean that the proton particles are in the same direction before entering the water medium and the various scattering prior to entrance to water is not taken into account. In intensity modulated proton therapy, the elementary intensity modulation entity for proton therapy is either an infinitesimal or finite sized beamlet. Since a finite sized beamlet is the superposition of infinitesimal pencil beams, the result of the maximum acceptable grid size obtained with infinitesimal pencil beam also applies to finite sized beamlet. The analytic Bragg curve function proposed by Bortfeld [T. Bortfeld, Med. Phys. 24, 2024-2033 (1997)] was employed. The lateral profile was approximated by a depth dependent Gaussian distribution. The model included the spreads of the Bragg peak and the lateral profiles due to multiple Coulomb scattering. The dependence of the maximum acceptable dose grid size on the orientation of the beam with respect to the dose grid was also investigated. The maximum acceptable dose grid size depends on the gradient of dose profile and in turn the range of proton beam. In the case that only the phantom scattering was considered and that the beam was aligned with the dose grid, grid sizes from 0.4 to 6.8 mm were required for proton beams with ranges from 2 to 30 cm for 2% error limit at the Bragg peak point. A near linear relation between the maximum acceptable grid size and beam range was observed. For this analysis model, the resolution requirement was not significantly related to the orientation of the beam with respect to the grid.

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.

Experimental evaluation of validity of simplified Monte Carlo method in proton dose calculations

It is important for proton therapy to calculate dose distributions accurately in treatment planning. Dose calculations in the body for treatment planning are converted to dose distributions in water, and the converted calculations are then generally evaluated by the dose measurements in water. In this paper, proton dose calculations were realized for a phantom simulating a clinical heterogeneity. Both dose calculations in the phantom calculated by two dose calculation methods, the range-modulated pencil beam algorithm (RMPBA) and the simplified Monte Carlo (SMC) method, and dose calculations converted to dose distributions in water by the same two methods were verified experimentally through comparison with measured distributions, respectively. For the RMPBA, though the converted calculations in water agreed moderately well with the measured ones, the calculated results in the actual phantom produced large errors. This meant that dose calculations in treatment planning should be evaluated by the dose measurements not in water but in the body with heterogeneity. On the other hand, the results calculated in the phantom, even by the less rigorous SMC method, reproduced the experimental ones well. This finding showed that actual dose distributions in the body should be predicted by the SMC method.

Two-dimensional pencil beam scaling: an improved proton dose algorithm for heterogeneous media

New dose delivery techniques with proton beams, such as beam spot scanning or raster scanning, require fast and accurate dose algorithms which can be applied for treatment plan optimization in clinically acceptable timescales. The clinically required accuracy is particularly difficult to achieve for the irradiation of complex, heterogeneous regions of the patient's anatomy. Currently applied fast pencil beam dose calculations based on the standard inhomogeneity correction of pathlength scaling often cannot provide the accuracy required for clinically acceptable dose distributions. This could be achieved with sophisticated Monte Carlo simulations which are still unacceptably time consuming for use as dose engines in optimization calculations. We therefore present a new algorithm for proton dose calculations which aims to resolve the inherent problem between calculation speed and required clinical accuracy. First, a detailed derivation of the new concept, which is based on an additional scaling of the lateral proton fluence is provided. Then, the newly devised two-dimensional (2D) scaling method is tested for various geometries of different phantom materials. These include standard biological tissues such as bone, muscle and fat as well as air. A detailed comparison of the new 2D pencil beam scaling with the current standard pencil beam approach and Monte Carlo simulations, performed with GEANT, is presented. It was found that the new concept proposed allows calculation of absorbed dose with an accuracy almost equal to that achievable with Monte Carlo simulations while requiring only modestly increased calculation times in comparison to the standard pencil beam approach. It is believed that this new proton dose algorithm has the potential to significantly improve the treatment planning outcome for many clinical cases encountered in highly conformal proton therapy.

Empirical description and Monte Carlo simulation of fast neutron pencil beams as basis of a treatment planning system

The fast neutron beam, used for fast neutron therapy in Essen, is produced by the nuclear reaction of a 14 MeV cyclotron-based deuteron beam on a thick beryllium target. The resulting neutron beam has a continuous energy spectrum with a mean and a maximum energy equal to 5.5 and 18 MeV, respectively. The dose delivered to the patient is computed by a treatment planning system (TPS) based on an empirical model, in which the dose components (neutron and photon) are described by analytical functions. In order to improve the dose calculation, and thus to use the fast neutron beam for other applications (e.g., Boron Neutron Capture Enhancement of Fast Neutron Therapy), in this work we aim to develop a new TPS. For this purpose, a model based on pencil beams of mono-energetic neutrons has been created. The neutron energy ranged from 0.25 MeV up to 17.25 MeV by steps of 0.5 MeV in order to cover the energy range of the Essen facility. The Monte Carlo method was then used to simulate the transport of neutrons within such pencil beams in a homogeneous water phantom. By using Monte Carlo techniques, it is possible to distinguish the energy deposition due to a primary collision in water to that due to scattered neutrons. The energy deposition due to pencil beams of 2.224 MeV photons, coming from hydrogen neutron capture reaction in the phantom or in the collimator, was also determined. In order to complete this work, air filled cylinders have been introduced in the water phantom. It is shown that the resulting depth dose curves for primary neutrons can be easily derived using the homogeneous phantom, and that the description of the effect on scattered neutron dose distribution is more complex. In this work we demonstrate the relevance of Monte Carlo simulations of mono-energetic neutron pencil beams for purposes of neutron treatment planning. Some additional work is still required to describe a clinical situation (continuous energy neutron spectrum) as well as to experimentally validate the method described here.