Comparison of linear and nonlinear programming approaches for "worst case dose" and "minmax" robust optimization of intensity-modulated proton therapy dose distributions.

Robust optimization of intensity-modulated proton therapy (IMPT) takes uncertainties into account during spot weight optimization and leads to dose distributions that are resilient to uncertainties. Previous studies demonstrated benefits of linear programming (LP) for IMPT in terms of delivery efficiency by considerably reducing the number of spots required for the same quality of plans. However, a reduction in the number of spots may lead to loss of robustness. The purpose of this study was to evaluate and compare the performance in terms of plan quality and robustness of two robust optimization approaches using LP and nonlinear programming (NLP) models. The so-called "worst case dose" and "minmax" robust optimization approaches and conventional planning target volume (PTV)-based optimization approach were applied to designing IMPT plans for five patients: two with prostate cancer, one with skull-based cancer, and two with head and neck cancer. For each approach, both LP and NLP models were used. Thus, for each case, six sets of IMPT plans were generated and assessed: LP-PTV-based, NLP-PTV-based, LP-worst case dose, NLP-worst case dose, LP-minmax, and NLP-minmax. The four robust optimization methods behaved differently from patient to patient, and no method emerged as superior to the others in terms of nominal plan quality and robustness against uncertainties. The plans generated using LP-based robust optimization were more robust regarding patient setup and range uncertainties than were those generated using NLP-based robust optimization for the prostate cancer patients. However, the robustness of plans generated using NLP-based methods was superior for the skull-based and head and neck cancer patients. Overall, LP-based methods were suitable for the less challenging cancer cases in which all uncertainty scenarios were able to satisfy tight dose constraints, while NLP performed better in more difficult cases in which most uncertainty scenarios were hard to meet tight dose limits. For robust optimization, the worst case dose approach was less sensitive to uncertainties than was the minmax approach for the prostate and skull-based cancer patients, whereas the minmax approach was superior for the head and neck cancer patients. The robustness of the IMPT plans was remarkably better after robust optimization than after PTV-based optimization, and the NLP-PTV-based optimization outperformed the LP-PTV-based optimization regarding robustness of clinical target volume coverage. In addition, plans generated using LP-based methods had notably fewer scanning spots than did those generated using NLP-based methods.

Validation of a track repeating algorithm for intensity modulated proton therapy: clinical cases study.

Monte Carlo (MC) methods are acknowledged as the most accurate technique to calculate dose distributions. However, due its lengthy calculation times, they are difficult to utilize in the clinic or for large retrospective studies. Track-repeating algorithms, based on MC-generated particle track data in water, accelerate dose calculations substantially, while essentially preserving the accuracy of MC. In this study, we present the validation of an efficient dose calculation algorithm for intensity modulated proton therapy, the fast dose calculator (FDC), based on a track-repeating technique. We validated the FDC algorithm for 23 patients, which included 7 brain, 6 head-and-neck, 5 lung, 1 spine, 1 pelvis and 3 prostate cases. For validation, we compared FDC-generated dose distributions with those from a full-fledged Monte Carlo based on GEANT4 (G4). We compared dose-volume-histograms, 3D-gamma-indices and analyzed a series of dosimetric indices. More than 99% of the voxels in the voxelized phantoms describing the patients have a gamma-index smaller than unity for the 2%/2 mm criteria. In addition the difference relative to the prescribed dose between the dosimetric indices calculated with FDC and G4 is less than 1%. FDC reduces the calculation times from 5 ms per proton to around 5 µs.

Analysis of the track- and dose-averaged LET and LET spectra in proton therapy using the geant4 Monte Carlo code.

PURPOSE: The motivation of this study was to find and eliminate the cause of errors in dose-averaged linear energy transfer (LET) calculations from therapeutic protons in small targets, such as biological cell layers, calculated using the geant 4 Monte Carlo code. Furthermore, the purpose was also to provide a recommendation to select an appropriate LET quantity from geant 4 simulations to correlate with biological effectiveness of therapeutic protons. METHODS: The authors developed a particle tracking step based strategy to calculate the average LET quantities (track-averaged LET, LETt and dose-averaged LET, LETd) using geant 4 for different tracking step size limits. A step size limit refers to the maximally allowable tracking step length. The authors investigated how the tracking step size limit influenced the calculated LETt and LETd of protons with six different step limits ranging from 1 to 500 µm in a water phantom irradiated by a 79.7-MeV clinical proton beam. In addition, the authors analyzed the detailed stochastic energy deposition information including fluence spectra and dose spectra of the energy-deposition-per-step of protons. As a reference, the authors also calculated the averaged LET and analyzed the LET spectra combining the Monte Carlo method and the deterministic method. Relative biological effectiveness (RBE) calculations were performed to illustrate the impact of different LET calculation methods on the RBE-weighted dose. RESULTS: Simulation results showed that the step limit effect was small for LETt but significant for LETd. This resulted from differences in the energy-deposition-per-step between the fluence spectra and dose spectra at different depths in the phantom. Using the Monte Carlo particle tracking method in geant 4 can result in incorrect LETd calculation results in the dose plateau region for small step limits. The erroneous LETd results can be attributed to the algorithm to determine fluctuations in energy deposition along the tracking step in geant 4. The incorrect LETd values lead to substantial differences in the calculated RBE. CONCLUSIONS: When the geant 4 particle tracking method is used to calculate the average LET values within targets with a small step limit, such as smaller than 500 µm, the authors recommend the use of LETt in the dose plateau region and LETd around the Bragg peak. For a large step limit, i.e., 500 µm, LETd is recommended along the whole Bragg curve. The transition point depends on beam parameters and can be found by determining the location where the gradient of the ratio of LETd and LETt becomes positive.

Monte Carlo fast dose calculator for proton radiotherapy: application to a voxelized geometry representing a patient with prostate cancer.

The Monte Carlo method is used to provide accurate dose estimates in proton radiation therapy research. While it is more accurate than commonly used analytical dose calculations, it is computationally intense. The aim of this work was to characterize for a clinical setup the fast dose calculator (FDC), a Monte Carlo track-repeating algorithm based on GEANT4. FDC was developed to increase computation speed without diminishing dosimetric accuracy. The algorithm used a database of proton trajectories in water to calculate the dose of protons in heterogeneous media. The extrapolation from water to 41 materials was achieved by scaling the proton range and the scattering angles. The scaling parameters were obtained by comparing GEANT4 dose distributions with those calculated with FDC for homogeneous phantoms. The FDC algorithm was tested by comparing dose distributions in a voxelized prostate cancer patient as calculated with well-known Monte Carlo codes (GEANT4 and MCNPX). The track-repeating approach reduced the CPU time required for a complete dose calculation in a voxelized patient anatomy by more than two orders of magnitude, while on average reproducing the results from the Monte Carlo predictions within 2% in terms of dose and within 1 mm in terms of distance.

A TRACK-REPEATING ALGORITHM FOR FAST MONTE CARLO DOSE CALCULATIONS OF PROTON RADIOTHERAPY.

Monte Carlo codes are utilized for accurate dose calculations in proton radiation therapy research. While they are superior in accuracy to commonly used analytical dose calculations, they require significantly longer computation times. The aim of this work is to characterize a Monte Carlo track-repeating algorithm to increase computation speed without compromising dosimetric accuracy. The track-repeating approach reduced the CPU time required for a complete dose calculation in voxelized patient anatomy by more than two orders of magnitude, while on average reproducing the results from the traditional Monte Carlo approach within 4% dose difference and within 1-mm distance to agreement.