Objective.Dynamic trajectory radiotherapy (DTRT) and dynamic mixed-beam arc therapy (DYMBARC) exploit non-coplanarity and, for DYMBARC, simultaneously optimized photon and electron beams. Margin concepts to account for set-up uncertainties during delivery are ill-defined for electron fields. We develop robust optimization for DTRT&DYMBARC and compare dosimetric plan quality and robustness for both techniques and both optimization strategies for four cases.Approach.Cases for different treatment sites and clinical target volume (CTV) to planning target volume (PTV) margins,m, were investigated. Dynamic gantry-table-collimator photon paths were optimized to minimize PTV/organ-at-risk (OAR) overlap in beam\'s-eye-view and minimize potential photon multileaf collimator (MLC) travel. For DYMBARC plans, non-isocentric partial electron arcs or static fields with shortened source-to-surface distance (80 cm) were added. Direct aperture optimization (DAO) was used to simultaneously optimize MLC-based intensity modulation for both photon and electron beams yielding deliverable PTV-based DTRT&DYMBARC plans. Robust-optimized plans used the same paths/arcs/fields. DAO with stochastic programming was used for set-up uncertainties with equal weights in all translational directions and magnitudeδsuch thatm= 0.7δ. Robust analysis considered random errors in all directions with or without an additional systematic error in the worst 3D direction for the adjacent OARs.Main results.Electron contribution was 7%-41% of target dose depending on the case and optimization strategy for DYMBARC. All techniques achieved similar CTV coverage in the nominal (no error) scenario. OAR sparing was overall better in the DYMBARC plans than in the DTRT plans and DYMBARC plans were generally more robust to the considered uncertainties. OAR sparing was better in the PTV-based than in robust-optimized plans for OARs abutting or overlapping with the target volume, but more affected by uncertainties.Significance.Better plan robustness can be achieved with robust optimization than with margins. Combining electron arcs/fields with non-coplanar photon trajectories further improves robustness and OAR sparing.

UNASSIGNED: Dynamic trajectory radiotherapy (DTRT) has been shown to improve healthy tissue sparing compared to volumetric arc therapy (VMAT). This study aimed to assess and compare the robustness of DTRT and VMAT treatment-plans for head and neck (H&N) cancer to patient-setup (PS) and machine-positioning uncertainties.
UNASSIGNED: The robustness of DTRT and VMAT plans previously created for 46 H&N cases, prescribed 50-70 Gy to 95 % of the planning-target-volume, was assessed. For this purpose, dose distributions were recalculated using Monte Carlo, including uncertainties in PS (translation and rotation) and machine-positioning (gantry-, table-, collimator-rotation and multi-leaf collimator (MLC)). Plan robustness was evaluated by the uncertainties\' impact on normal tissue complication probabilities (NTCP) for xerostomia and dysphagia and on dose-volume endpoints. Differences between DTRT and VMAT plan robustness were compared using Wilcoxon matched-pair signed-rank test (α = 5 %).
UNASSIGNED: Average NTCP for moderate-to-severe xerostomia and grade ≥ II dysphagia was lower for DTRT than VMAT in the nominal scenario (0.5 %, p = 0.01; 2.1 %, p < 0.01) and for all investigated uncertainties, except MLC positioning, where the difference was not significant. Average differences compared to the nominal scenario were ≤ 3.5 Gy for rotational PS (≤ 3°) and machine-positioning (≤ 2°) uncertainties, <7 Gy for translational PS uncertainties (≤ 5 mm) and < 20 Gy for MLC-positioning uncertainties (≤ 5 mm).
UNASSIGNED: DTRT and VMAT plan robustness to the investigated uncertainties depended on uncertainty direction and location of the structure-of-interest to the target. NTCP remained on average lower for DTRT than VMAT even when considering uncertainties.

We compared dynamic trajectory radiotherapy (DTRT) to state-of-the-art volumetric modulated arc therapy (VMAT) for 46 head and neck cancer cases. DTRT had lower dose to salivary glands and swallowing structure, resulting in lower predicted xerostomia and dysphagia compared to VMAT. DTRT is deliverable on C-arm linacs with high dosimetric accuracy.

BACKGROUND: Non-coplanar techniques have shown to improve the achievable dose distribution compared to standard coplanar techniques for multiple treatment sites but finding optimal beam directions is challenging. Dynamic collimator trajectory radiotherapy (colli-DTRT) is a new intensity modulated radiotherapy technique that uses non-coplanar partial arcs and dynamic collimator rotation.
OBJECTIVE: To solve the beam angle optimization (BAO) problem for colli-DTRT and non-coplanar VMAT (NC-VMAT) by determining the table-angle and the gantry-angle ranges of the partial arcs through iterative 4π fluence map optimization (FMO) and beam direction elimination.
METHODS: BAO considers all available beam directions sampled on a gantry-table map with the collimator angle aligned to the superior-inferior axis (colli-DTRT) or static (NC-VMAT). First, FMO is performed, and beam directions are scored based on their contributions to the objective function. The map is thresholded to remove the least contributing beam directions, and arc candidates are formed by adjacent beam directions with the same table angle. Next, FMO and arc candidate trimming, based on objective function penalty score, is performed iteratively until a desired total gantry angle range is reached. Direct aperture optimization on the final set of colli-DTRT or NC-VMAT arcs generates deliverable plans. colli-DTRT and NC-VMAT plans were created for seven clinically-motivated cases with targets in the head and neck (two cases), brain, esophagus, lung, breast, and prostate. colli-DTRT and NC-VMAT were compared to coplanar VMAT plans as well as to class-solution non-coplanar VMAT plans for the brain and head and neck cases. Dosimetric validation was performed for one colli-DTRT (head and neck) and one NC-VMAT (breast) plan using film measurements.
RESULTS: Target coverage and conformity was similar for all techniques. colli-DTRT and NC-VMAT plans had improved dosimetric performance compared to coplanar VMAT for all treatment sites except prostate where all techniques were equivalent. For the head and neck and brain cases, mean dose reduction-in percentage of the prescription dose-to parallel organs was on average 0.7% (colli-DTRT), 0.8% (NC-VMAT) and 0.4% (class-solution) compared to VMAT. The reduction in D2% for the serial organs was on average 1.7% (colli-DTRT), 2.0% (NC-VMAT) and 0.9% (class-solution). For the esophagus, lung, and breast cases, mean dose reduction to parallel organs was on average 0.2% (colli-DTRT) and 0.3% (NC-VMAT) compared to VMAT. The reduction in D2% for the serial organs was on average 1.3% (colli-DTRT) and 0.9% (NC-VMAT). Estimated delivery times for colli-DTRT and NC-VMAT were below 4 min for a full gantry angle range of 720°, including transitions between arcs, except for the brain case where multiple arcs covered the whole table angle range. These times are in the same order as the class-solution for the head and neck and brain cases. Total optimization times were 25%-107% longer for colli-DTRT, including BAO, compared to VMAT.
CONCLUSIONS: We successfully developed dosimetrically motivated BAO for colli-DTRT and NC-VMAT treatment planning. colli-DTRT and NC-VMAT are applicable to multiple treatment sites, including body sites, with beneficial or equivalent dosimetric performances compared to coplanar VMAT and reasonable delivery times.

BACKGROUND: To improve organ at risk (OAR) sparing, dynamic trajectory radiotherapy (DTRT) extends VMAT by dynamic table and collimator rotation during beam-on. However, comprehensive investigations regarding the impact of the gantry-table (GT) rotation gradient on the DTRT plan quality have not been conducted.
OBJECTIVE: To investigate the impact of a user-defined GT rotation gradient on plan quality of DTRT plans in terms of dosimetric plan quality, dosimetric robustness, deliverability, and delivery time.
METHODS: The dynamic trajectories of DTRT are described by GT and gantry-collimator paths. The GT path is determined by minimizing the overlap of OARs with planning target volume (PTV). This approach is extended to consider a GT rotation gradient by means of a maximum gradient of the path ( G m a x ${G}_{max}$ ) between two adjacent control points ( G = | Δ table angle / Δ gantry angle | $G = | \\Delta {{\\mathrm{table\\ angle}}/\\Delta {\\mathrm{gantry\\ angle}}} |$ ) and maximum absolute change of G ( Δ G m a x ${{\\Delta}}{G}_{max}$ ). Four DTRT plans are created with different maximum G&∆G: G m a x ${G}_{max}$ & Δ G m a x ${{\\Delta}}{G}_{max}$  = 0.5&0.125 (DTRT-1), 1&0.125 (DTRT-2), 3&0.125 (DTRT-3) and 3&1‍(DTRT-4), including 3-4 dynamic trajectories, for three clinically motivated cases in the head and neck and brain region (A, B, and C). A reference VMAT plan for each case is created. For all plans, plan quality is assessed and compared. Dosimetric plan quality is evaluated by target coverage, conformity, and OAR sparing. Dosimetric robustness is evaluated against systematic and random patient-setup uncertainties between ± 3 mm $ \\pm 3\\ {\\mathrm{mm}}$ in the lateral, longitudinal, and vertical directions, and machine uncertainties between ± 4 ∘ $ \\pm 4^\\circ \\ $ in the dynamically rotating machine components (gantry, table, collimator rotation). Delivery time is recorded. Deliverability and delivery accuracy on a TrueBeam are assessed by logfile analysis for all plans and additionally verified by film measurements for one case. All dose calculations are Monte Carlo based.
RESULTS: The extension of the DTRT planning process with user-defined G m a x & Δ G m a x ${G}_{max}\\& {{\\Delta}}{G}_{max}$ to investigate the impact of the GT rotation gradient on plan quality is successfully demonstrated. With increasing G m a x & Δ G m a x ${G}_{max}\\& {{\\Delta}}{G}_{max}$ , slight (case C, D m e a n , p a r o t i d l . ${D}_{mean,\\ parotid\\ l.}$ : up to‍-1‍Gy) and substantial (case A, D 0.03 c m 3 , o p t i c n e r v e r . ${D}_{0.03c{m}^3,\\ optic\\ nerve\\ r.}$ : up to -9.3 Gy, case‍B, D m e a n , b r a i n $\\ {D}_{mean,\\ brain}$ : up to -4.7‍Gy) improvements in OAR sparing are observed compared to VMAT, while maintaining similar target coverage. All plans are delivered on the TrueBeam. Expected and actual machine position values recorded in the logfiles deviated by <0.2° for gantry, table and collimator rotation. The film measurements agreed by >96% (2%‍global/2 mm Gamma passing rate) with the dose calculation. With increasing G m a x & Δ G m a x ${G}_{max}\\& {{\\Delta}}{G}_{max}$ , delivery time is prolonged by <2 min/trajectory (DTRT-4) compared to VMAT and DTRT-1. The DTRT plans for case A and B and the VMAT plan for case C plan reveal the best dosimetric robustness for the considered uncertainties.
CONCLUSIONS: The impact of the GT rotation gradient on DTRT plan quality is comprehensively investigated for three cases in the head and neck and brain region. Increasing freedom in this gradient improves dosimetric plan quality at the cost of increased delivery time for the investigated cases. No clear dependency of GT rotation gradient on dosimetric robustness is observed.

Objective.The purpose of this study is to develop a treatment planning process (TPP) for non-isocentric dynamic trajectory radiotherapy (DTRT) using dynamic gantry rotation, collimator rotation, table rotation, longitudinal, vertical and lateral table translations and intensity modulation and to validate the dosimetric accuracy.Approach.The TPP consists of two steps. First, a path describing the dynamic gantry rotation, collimator rotation and dynamic table rotation and translations is determined. Second, an optimization of the intensity modulation along the path is performed. We demonstrate the TPP for three use cases. First, a non-isocentric DTRT plan for a brain case is compared to an isocentric DTRT plan in terms of dosimetric plan quality and delivery time. Second, a non-isocentric DTRT plan for a craniospinal irradiation (CSI) case is compared to a multi-isocentric intensity modulated radiotherapy (IMRT) plan. Third, a non-isocentric DTRT plan for a bilateral breast case is compared to a multi-isocentric volumetric modulated arc therapy (VMAT) plan. The non-isocentric DTRT plans are delivered on a TrueBeam in developer mode and their dosimetric accuracy is validated using radiochromic films.Main results.The non-isocentric DTRT plan for the brain case is similar in dosimetric plan quality and delivery time to the isocentric DTRT plan but is expected to reduce the risk of collisions. The DTRT plan for the CSI case shows similar dosimetric plan quality while reducing the delivery time by 45% in comparison with the IMRT plan. The DTRT plan for the breast case showed better treatment plan quality in comparison with the VMAT plan. The gamma passing rates between the measured and calculated dose distributions are higher than 95% for all three plans.Significance.The versatile benefits of non-isocentric DTRT are demonstrated with three use cases, namely reduction of collision risk, reduced setup and delivery time and improved dosimetric plan quality.