Optimization of motion management parameters in a synchrotron‐based spot scanning system

Abstract Purpose To quantify the effects of combining layer‐based repainting and respiratory gating as a strategy to mitigate the dosimetric degradation caused by the interplay effect between a moving target and dynamic spot‐scanning proton delivery. Methods An analytic routine modeled three‐dimensional dose distributions of pencil‐beam proton plans delivered to a moving target. Spot positions and weights were established for a single field to deliver 100 cGy to a static, 15‐cm deep, 3‐cm radius spherical clinical target volume with a 1‐cm isotropic internal target volume expansion. The interplay effect was studied by modeling proton delivery from a clinical synchrotron‐based spot scanning system and respiratory target motion, patterned from surrogate patient breathing traces. Motion both parallel and orthogonal to the beam scanning direction was investigated. Repainting was modeled using a layer‐based technique. For each of 13 patient breathing traces, the dose from 20 distinct delivery schemes (combinations of four gate window amplitudes and five repainting techniques) was computed. Delivery strategies were inter‐compared based on target coverage, dose homogeneity, high dose spillage, and delivery time. Results Notable degradation and variability in plan quality were observed for ungated delivery. Decreasing the gate window reduced this variability and improved plan quality at the expense of longer delivery times. Dose deviations were substantially greater for motion orthogonal to the scan direction when compared with parallel motion. Repainting coupled with gating was effective at partially restoring dosimetric coverage at only a fraction of the delivery time increase associated with very small gate windows alone. Trends for orthogonal motion were similar, but more complicated, due to the increased severity of the interplay. Conclusions Layer‐based repainting helps suppress the interplay effect from intra‐gate motion, with only a modest penalty in delivery time. The magnitude of the improvement in target coverage is strongly influenced by individual patient breathing patterns and the tumor motion trajectory.


| INTRODUCTION
The potential of charged particle beams in providing highly conformal, targeted therapy has long been recognized. [1][2][3] Compared with photon beams, charged particles exhibit a well-defined penetration range in a patient, thus reducing unnecessary radiation dose distal to the intended target. Energy deposition rapidly increases near the end of a charged particle track at the location of the so-called Bragg Peak, potentially allowing for a larger ratio of target to normal tissue dose. 4 Technological advances have spurred the proliferation of proton therapy as an increasingly conventional treatment modality. 5 Modern facilities almost exclusively feature pencil-beam scanning, 6 in which a small beamlet of fixed energy (corresponding to a specific depth) is scanned over the lateral extent of the target. Once the layer is completed, the system switches energy to a more proximal depth, and the target is again laterally scanned. This process is completed until the prescribed dose has been fully delivered. Treatment planning systems (TPS) optimize the number of energy layers, the positions of the beamlets in each layer, and the relative weightings of each spot delivery. Pencil-beam scanning has advantages over the more traditional passively scattered approach including the ability to simultaneously shape both the proximal and distal boundaries of a target, the reduction of patient-specific overhead in the form of custom apertures, and the ability to delivery intensity-modulated proton therapy (IMPT). 4 Along with these benefits, however, pencil-beam scanning introduces the potential for deleterious interplay effects between the highly modulated delivery and a mobile target, 7 whereas the time independence of passively scattered deliveries render these treatments much more robust to target motion.
The interplay effect in spot scanning has been shown to induce clinically relevant dosimetric defects in single fraction deliveries. This has demonstrated both in general simulations 8,9 and in 4DCT studies on lung patients. 10,11 In this latter approach, the spots from a given field are divided temporally across all the 4DCT phases, dose is calculated on these phases, and the total dose is accumulated back to a reference phase. As spot sizes continue to decrease to achieve higher target conformality, the interplay effect is expected to increase in severity. 12,13 A number of techniques have been proposed to address the interplay effect. Beam gating, in which the beam is automatically enabled or terminated based on the continuous monitoring of a target motion surrogate, is a standard method of motion management in radiotherapy. 14 It requires the placement of either internal or external fiducial markers, 15,16 corresponding real-time tracking infrastructure, and upfront acquisition of 4D images at simulation. While gating has a history of successfully reducing the size of treatment volumes required to cover moving targets, 17 suboptimal results are possible when it is applied to spot-scanned proton treatments.
Residual motion inside the gate can still disrupt dosimetric homogeneity, 18 and complex target shapes and deliveries can render erratic results. 19 Moreover, long treatment times are possible from the combined dynamics of beam-off and accelerator recharge (for synchrotron systems) periods. 20 Repainting, in which the treatment plan is subdivided and delivered in multiple iterations, provides an alternative to gating. Multiple delivery passes over the moving target are intended to smooth the dose by reducing the fractional effects of misplaced spots. [21][22][23][24] Unlike gating, repainting does not attempt to limit the magnitude of spot position deviations from their ideal/ planned location in the target. Target tracking has also been investigated as a means of nullifying the interplay effect. 25 While these techniques show promise, there remain substantial technical challenges and the potential to deliver significant unintended dose to surrounding normal tissue (or substantially lower dose to the target).
Limitations of predictive tracking algorithms, anatomical heterogeneities upstream of the target, and relative motion between surrounding normal tissues and the target can all contribute to these effects. 26,27 With such a range of motion management options and associated configurable parameters, it is difficult to determine the optimal clinical solution for interplay effect reduction. Combined gating and repainting has been shown to offer added interplay reduction benefits in cyclotron delivery systems. 19 As the severity of the interplay effect is dependent on delivery dynamics, 28 however, it is important to characterize these effects and their associated countermeasures for different delivery systems. In this work, the relative effectiveness of gating, repainting, and combined gating/repainting is quantified for a representative spherical target and beam delivery using a synchrotron-based system (Hitachi Ltd. Hitachi, Japan). Full three-dimensional dose distributions on a quasi-continuous mobile target in a water phantom were calculated and analyzed using dose volume histograms (DVH) metrics. Furthermore, the average and variability in expected dosimetric outcomes were determined by incorporating realistic target motion, modeled with a set of surrogate patient breathing traces, in multiple directions. Recommendations are suggested for the utilization of these motion mitigation strategies in pencil-beam proton therapy. To comprehensively study interplay effects and mitigation strategies amidst these complicating factors, an in-house numeric simulation was developed to perform pencil-beam proton dose calculations on moving targets. These three-dimensional dose calculations were performed with high spatial resolution (0.75 mm) in a flat, homogeneous water phantom. This idealized geometry allows for the isolation of true interplay effects without convolution of independent effects such as range modulation due to mobile heterogeneities. The analytic calculation engine was based on models detailed in our TPS documentation 29 (Eclipse, Varian), in which primary, secondary, and recoil particles are considered. 30,31 The depth dose was modeled using a corrected Bethe formula approach, and was parameterized by the incident proton energy and its intrinsic energy spread. Lateral scattering was governed by a double Gaussian dependence, which was fit to Moliere theory in water. Monte Carlo simulations of proton beams in water were used to fit the individual model coefficients for the highest spatial dose calculation accuracy. Beam divergence was modeled assuming a 245-cm source-to-isocenter distance. The incident proton beams were modeled using symmetric, two-dimensional Gaussian profiles in air. These energy-dependent profiles were generated by Monte Carlo simulations of our spot scanning nozzle, and ranged between 3 and 6 mm σ

2.B | Target motion models
Our 4D dose calculation has the capability of simulating arbitrary target motion in three dimensions. In this study, one-dimensional motion trajectories were analyzed independently. The trajectories considered were confined to the plane orthogonal to the central axis of the individual pencil beams. Directions in this plane can be referenced to the primary pencil-beam scanning axis. In our system, the beam rasters back and forth in this direction as it paints a given energy layer, only making a perpendicular step to the next row of spots between subsequent sweeps. The two separate target motion directions considered in this work were "parallel" and "orthogonal"

2.C | Delivery timing parameterization
The temporal characteristics of the proton beam delivery strongly influence interplay effects, and vary from system to system. The parameters used in this work, shown in Table I   were simulated.

2.E | Dosimetric analysis
In each case, dose volume histograms (DVH) were computed for the target volume. The information contained in the DVH curves was distilled into a more compact form by computing both the target   In a format analogous to Fig. 6, the homogeneity index of the CTV for parallel (a) and orthogonal (b) motion is presented in Fig. 7. There is a general trend towards better dose homogeneity and lower patient-topatient variability with longer delivery times. Orthogonal target motion is again associated with greater plan degradation than parallel motion.
For parallel motion, the three curves are nearly coincident for treatment times below 150 s, albeit with erratic behavior in the repainting-only curve. At longer delivery times, a shift toward greater dose homogeneity and smaller error bars is visible in the combined gating and repainting vs gating-only curve. This shift and error bar reduction is also visible across the full range of delivery times for orthogonal target motion.
Repainting alone also provides the most dramatic reduction of dose heterogeneity for small deliver time increases.
The volume outside the ITV receiving prescription dose is plotted in Fig. 8    T A B L E 1 Delivery timing parameters. Dose distributions resulting from interplay effects are sensitive to the timing characteristics of the delivery system. The parameters used in this work were modeled after our synchrotron system. A study performed by Schätti et al. 19 indicated that combined gating and repainting increased the safety and robustness of spot scanning motion management when compared to gating alone. This simulation aspect of this work was performed by assuming a cyclotron-based delivery, an irregular breathing model obtained from a single patient, and dose metric comparisons were based on analysis of a single two-dimensional plane near the central lateral plane of the target. As the magnitude of the interplay effect is dependent on machine delivery characteristics such as spot size, beam current, energy switching times, and scanning speed, it is valuable to characterize these effects in different delivery systems and under a variety of clinical scenarios. In this work, we provide data to aid in the clinical implementation of a motion management program for a spot scanning, synchrotron-based Hitachi delivery system. Additionally, by incorporating statistical analysis on the results obtained from 13 irregular patient breathing models, motion management parameters could be more optimally tuned to account for the natural spread of patient breathing characteristics. Finally, as interplay is dependent on target depth, a single two-dimensional plane may not capture all relevant effects. We compliment previous work in two dimensions by extending our analysis to the full three-dimensional target volume.

| CONCLUSION
A quasi-continuous simulation of arbitrary target motion in a water phantom has been developed for spot scanning proton plans delivered using a Hitachi synchrotron-based system. This has enabled calculation of the 4D dose accumulation for a variety of circumstances, including different target motion directions, patient breathing patterns, and motion mitigation strategies. Plan quality, as measured by target coverage, target homogeneity, and prescription dose spillage outside the ITV, is substantial better for target motion parallel to the primary pencil-beam scanning axis as opposed to the case when this scanning axis is rotated 90 degrees. Averaged over 13 patient breathing traces normalized to nominal 1-cm peak-to-peak amplitude, the combination of gating and layer-based repainting allows for a shorter treatment delivery time and/or superior average plan quality with less variability when compared with gating or repainting alone.
Clinical constraints and individualized objectives should be considered when optimizing the specific gate and repainting parameters.
Looking ahead, our simulation infrastructure will allow for comparison with measured dose distributions, as well as investigation into additional dependences such as target size, prescription dose, breathing amplitude, and complex three-dimensional motion patterns.

ACKNOWLEDG MENTS
This work was supported in part by a grant from Varian Medical Systems.

CONFLI CT OF INTEREST
No conflicts of interest.