The energy margin strategy for reducing dose variation due to setup uncertainty in intensity modulated proton therapy (IMPT) delivered with distal edge tracking (DET).

Intensity-modulated proton therapy (IMPT) can produce plans with similar target dose conformity but lower normal tissue dose than intensity-modulated X-ray therapy (IMXT). However, due to the finite range of proton beams in tissue, proton therapy treatment plans are usually more sensitive to setup uncertainties than X-ray therapy plans. In this work, the energy margin (EM) concept, which was initially developed for passive scattering proton therapy, was generalized to apply to IMPT treatment planning. The effectiveness of the EM method was evaluated on five head-and-neck cancer patients with distal edge tracking (DET) treatment plans by comparing the original plans (ORG) without an EM to those with an EM. Three beam arrangements were considered: 24 beams delivered over a 360° arc, 12 beams delivered over a 180° arc, and 12 beams delivered over two 90° fan angles. Setup uncertainty was modeled by sampling rigid translational shifts from a Gaussian distribution with a mean of 0 mm and standard deviation of 2 mm in all directions. Delivered dose distributions for all 30 fractions were recalculated using the Geant4 Monte Carlo code. Normalized total dose (NTD) for both the CTV and a ring structure surrounding the PTV were recorded. The plan quality comparison revealed that EM plans had the same CTV coverage but higher dose to the normal tissue than ORG plans. After the simulated delivery, ORG plans resulted in more than 3% underdosage to 5% of the CTV volume in all three beam arrangements, whereas the EM plans did not. Both ORG and EM plans did not produce more than 5% overdose to D2% of the ring structure. The use of an EM for IMPT treatment planning can substantially reduce sensitivity of the resulting dose distributions to setup uncertainty.

Investigation of probabilistic optimization for tomotherapy.

This work builds on a suite of studies related to the 'interplay', or lack thereof, for respiratory motion with helical tomotherapy (HT). It helps explain why HT treatments without active motion management had clinical outcomes that matched positive expectations. An analytical calculation is performed to illuminate the frequency range for which interplay-type dose errors could occur. Then, an experiment is performed which completes a suite of tests. The experiment shows the potential for a stable motion probability distribution function (PDF) with HT and respiratory motion. This PDF enables one to use a motion-robust or probabilistic optimization to intrinsically include respiratory motion into the treatment planning. The reason why HT is robust to respiratory motion is related to the beam modulation sampling of the tumor motion. Because active tracking-based motion management is more complicated for a variety of reasons, HT optimization that is robust to motion is a useful alternative for those many patients that cannot benefit from active motion management.

On the impact of longitudinal breathing motion randomness for tomotherapy delivery.

The purpose of this study is to explain the unplanned longitudinal dose modulations that appear in helical tomotherapy (HT) dose distributions in the presence of irregular patient breathing. This explanation is developed by the use of longitudinal (1D) simulations of mock and surrogate data and tested with a fully 4D HT delivered plan. The 1D simulations use a typical mock breathing function which allows more flexibility to adjust various parameters. These simplified simulations are then made more realistic by using 100 surrogate waveforms all similarly scaled to produce longitudinal breathing displacements. The results include the observation that, with many waveforms used simultaneously, a voxel-by-voxel probability of a dose error from breathing is found to be proportional to the realistically random breathing amplitude relative to the beam width if the PTV is larger than the beam width and the breathing displacement amplitude. The 4D experimental test confirms that regular breathing will not result in these modulations because of the insensitivity to leaf motion for low-frequency dynamics such as breathing. These modulations mostly result from a varying average of the breathing displacements along the beam edge gradients. Regular breathing has no displacement variation over many breathing cycles. Some low-frequency interference is also possible in real situations. In the absence of more sophisticated motion management, methods that reduce the breathing amplitude or make the breathing very regular are indicated. However, for typical breathing patterns and magnitudes, motion management techniques may not be required with HT because typical breathing occurs mostly between fundamental HT treatment temporal and spatial scales. A movement beyond only discussing margins is encouraged for intensity modulated radiotherapy such that patient and machine motion interference will be minimized and beneficial averaging maximized. These results are found for homogeneous and longitudinal on-axis delivery for unplanned longitudinal dose modulations.

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.

A phantom model demonstration of tomotherapy dose painting delivery, including managed respiratory motion without motion management.

The aim of the study was to demonstrate a potential alternative scenario for accurate dose-painting (non-homogeneous planned dose) delivery at 1 cm beam width with helical tomotherapy (HT) in the presence of 1 cm, three-dimensional, intra-fraction respiratory motion, but without any active motion management. A model dose-painting experiment was planned and delivered to the average position (proper phase of a 4DCT scan) with three spherical PTV levels to approximate dose painting to compensate for hypothetical hypoxia in a model lung tumor. Realistic but regular motion was produced with the Washington University 4D Motion Phantom. A small spherical Virtual Water phantom was used to simulate a moving lung tumor inside of the LUNGMAN anthropomorphic chest phantom to simulate realistic heterogeneity uncertainties. A piece of 4 cm Gafchromic EBT film was inserted into the 6 cm diameter sphere. TomoTherapy, Inc., DQA software was used to verify the delivery performed on a TomoTherapy Hi-Art II device. The dose uncertainty in the purposeful absence of motion management and in the absence of large, low frequency drifts (periods greater than the beam width divided by the couch velocity) or randomness in the breathing displacement yields very favorable results. Instead of interference effects, only small blurring is observed because of the averaging of many breathing cycles and beamlets and the avoidance of interference. Dose painting during respiration with helical tomotherapy is feasible in certain situations without motion management. A simple recommendation is to make respiration as regular as possible without low frequency drifting. The blurring is just small enough to suggest that it may be acceptable to deliver without motion management if the motion is equal to the beam width or smaller (at respiration frequencies) when registered to the average position.