Purpose

Empirical relative biological effectiveness (RBE) models have been used to estimate the biological dose in proton therapy but do not adequately capture the factors influencing RBE values for treatment planning. We reformulate the McNamara RBE model such that it can be added as a linear biological dose fidelity term within our previously developed sensitivity-regularized and heterogeneity-weighted beam orientation optimization (SHBOO) framework.

Methods

Based on our SHBOO framework, we formulated the biological optimization problem to minimize total McNamara RBE dose to OARs. We solve this problem using two optimization algorithms: FISTA (McNam-FISTA) and Chambolle-Pock (McNam-CP). We compare their performances with a physical dose optimizer assuming RBE = 1.1 in all structures (PHYS-FISTA) and an LET-weighted dose model (LET-FISTA). Three head and neck patients were planned with the four techniques and compared on dosimetry and robustness.

Results

Compared to Phys-FISTA, McNam-CP was able to match CTV [HI, Dmax, D95%, D98%] by [0.00, 0.05%, 1.4%, 0.8%]. McNam-FISTA and McNam-CP were able to significantly improve overall OAR [Dmean, Dmax] by an average of [36.1%,26.4%] and [29.6%, 20.3%], respectively. Regarding CTV robustness, worst [Dmax, V95%, D95%, D98%] improvement of [-6.6%, 6.2%, 6.0%, 4.8%] was reported for McNam-FISTA and [2.7%, 2.7%, 5.3%, -4.3%] for McNam-CP under combinations of range and setup uncertainties. For OARs, worst [Dmax, Dmean] were improved by McNam-FISTA and McNam-CP by an average of [25.0%, 19.2%] and [29.5%, 36.5%], respectively. McNam-FISTA considerably improved dosimetry and CTV robustness compared to LET-FISTA, which achieved better worst-case OAR doses.

Conclusion

The four optimization techniques deliver comparable biological doses for the head and neck cases. Besides modest CTV coverage and robustness improvement, OAR biological dose and robustness were substantially improved with both McNam-FISTA and McNam-CP, showing potential benefit for directly incorporating McNamara RBE in proton treatment planning.

Existing volumetric modulated arc therapy (VMAT) optimization using coplanar arcs is highly efficient but usually dosimetrically inferior to intensity modulated radiation therapy (IMRT) with optimized non-coplanar beams. To achieve both dosimetric quality and delivery efficiency, we proposed in this study, a novel integrated optimization method for non-coplanar VMAT (4πVMAT). 4πVMAT with direct aperture optimization (DAO) was achieved by utilizing a least square dose fidelity objective, along with an anisotropic total variation term for regularizing the fluence smoothness, a single segment term for imposing simple apertures, and a group sparsity term for selecting beam angles. Continuous gantry/couch angle trajectories were selected using the Dijkstra's algorithm, where the edge and node costs were determined based on the maximal gantry rotation speed and the estimated fluence map at the current iteration, respectively. The couch-gantry-patient collision space was calculated based on actual machine geometry and a human subject 3D surface. Beams leading to collision are excluded from the DAO and beam trajectory selection (BTS). An alternating optimization strategy was implemented to solve the integrated DAO and BTS problem. The feasibility of 4πVMAT using one full-arc or two full-arcs was tested on nine patients with brain, lung, or prostate cancer. The plan was compared against a coplanar VMAT (2πVMAT) plan using one additional arc and collimator rotation. Compared to 2πVMAT, 4πVMAT reduced the average maximum and mean organs-at-risk dose by 9.63% and 3.08% of the prescription dose with the same target coverage. R50 was reduced by 23.0%. Maximum doses to the dose limiting organs, such as the brainstem, the major vessels, and the proximal bronchus, were reduced by 8.1 Gy (64.8%), 16.3 Gy (41.5%), and 19.83 Gy (55.5%), respectively. The novel 4πVMAT approach affords efficient delivery of non-coplanar arc trajectories that lead to dosimetric improvements compared with coplanar VMAT using more arcs.

Purpose

Volumetric modulated arc therapy (VMAT) is a widely employed radiation therapy technique, showing comparable dosimetry to static beam intensity modulated radiation therapy (IMRT) with reduced monitor units and treatment time. However, the current VMAT optimization has various greedy heuristics employed for an empirical solution, which jeopardizes plan consistency and quality. The authors introduce a novel direct aperture optimization method for VMAT to overcome these limitations.

Methods

The comprehensive VMAT (comVMAT) planning was formulated as an optimization problem with an L2-norm fidelity term to penalize the difference between the optimized dose and the prescribed dose, as well as an anisotropic total variation term to promote piecewise continuity in the fluence maps, preparing it for direct aperture optimization. A level set function was used to describe the aperture shapes and the difference between aperture shapes at adjacent angles was penalized to control MLC motion range. A proximal-class optimization solver was adopted to solve the large scale optimization problem, and an alternating optimization strategy was implemented to solve the fluence intensity and aperture shapes simultaneously. Single arc comVMAT plans, utilizing 180 beams with 2° angular resolution, were generated for a glioblastoma multiforme case, a lung (LNG) case, and two head and neck cases-one with three PTVs (H&N3PTV) and one with foue PTVs (H&N4PTV)-to test the efficacy. The plans were optimized using an alternating optimization strategy. The plans were compared against the clinical VMAT (clnVMAT) plans utilizing two overlapping coplanar arcs for treatment.

Results

The optimization of the comVMAT plans had converged within 600 iterations of the block minimization algorithm. comVMAT plans were able to consistently reduce the dose to all organs-at-risk (OARs) as compared to the clnVMAT plans. On average, comVMAT plans reduced the max and mean OAR dose by 6.59% and 7.45%, respectively, of the prescription dose. Reductions in max dose and mean dose were as high as 14.5 Gy in the LNG case and 15.3 Gy in the H&N3PTV case. PTV coverages measured by D95, D98, and D99 were within 0.25% of the prescription dose. By comprehensively optimizing all beams, the comVMAT optimizer gained the freedom to allow some selected beams to deliver higher intensities, yielding a dose distribution that resembles a static beam IMRT plan with beam orientation optimization.

Conclusions

The novel nongreedy VMAT approach simultaneously optimizes all beams in an arc and then directly generates deliverable apertures. The single arc VMAT approach thus fully utilizes the digital Linac's capability in dose rate and gantry rotation speed modulation. In practice, the new single VMAT algorithm generates plans superior to existing VMAT algorithms utilizing two arcs.

Ultra-high dose rate in radiotherapy (FLASH) has been shown to increase the therapeutic index with markedly reduced normal tissue toxicity and the same or better tumor cell killing. The challenge to achieve FLASH using x-rays, besides developing a high output linac, is to intensity-modulate the high-dose-rate x-rays so that the biological gain is not offset by the lack of physical dose conformity. In this study, we develop the ROtational direct Aperture optimization with a Decoupled ring-collimator (ROAD) to achieve simultaneous ultrafast delivery and complex dose modulation. The ROAD design includes a fast-rotating slip-ring linac and a decoupled collimator-ring with 75 pre-shaped multi-leaf-collimator (MLC) modules. The ring-source rotates at 1 rotation per second (rps) clockwise while the ring-collimator is either static or rotating at 1 rps counterclockwise, achieving 75 (ROAD-75) or 150 (ROAD-150) equal-angular beams for one full arc. The Direct Aperture Optimization (DAO) for ROAD was formulated to include a least-square dose fidelity, an anisotropic total variation term, and a single segment term. The FLASH dose (FD) and FLASH biological equivalent dose (FBED) were computed voxelwise, with the latter using a spatiotemporal model accounting for radiolytic oxygen depletion. ROAD was compared with clinical volumetric modulated arc therapy (VMAT) on a brain, a lung, a prostate, and a head and neck cancer patient. The mean dose rate of ROAD-75 and ROAD-150 are 76.2 Gy s^-1 and 112 Gy s^-1 respectively to deliver 25 Gy single-fraction dose in 1 s. With improved PTV homogeneity, ROAD-150 reduced (max, mean) OAR physical dose by (4.8 Gy, 6.3 Gy). The average R50 and integral dose of (VMAT, ROAD-75, ROAD-150) are (4.8, 3.2, 3.2) and (89, 57, 56) Gy×Liter, respectively. The FD and FBED showed model dependent FLASH effects. The novel ROAD design achieves ultrafast dose delivery and improves physical dosimetry compared with clinical VMAT, providing a potentially viable engineering solution for x-ray FLASH radiotherapy.

Despite significant dosimetric gains, clinical implementation of the 4π non-coplanar radiotherapy on the widely available C-arm gantry system is hindered by limited clearance, and the need to perform complex coordinated gantry and couch motion. A robotic radiotherapy platform would be conducive to such treatment but a new conflict between field size and MLC modulation resolution needs to be managed for versatile applications. This study investigates the dosimetry and delivery efficiency of purposefully creating many isocenters to achieve simultaneously high MLC modulation resolution and large tumor coverage. An integrated optimization framework was proposed for simultaneous beam orientation optimization (BOO), isocenter selection, and fluence map optimization (FMO). The framework includes a least-square dose fidelity objective, a total variation term for regularizing the fluence smoothness, and a group sparsity term for beam selection. A minimal number of isocenters were identified for efficient target coverage. Colliding beams excluded, high-resolution small-field 4π intensity-modulated radiotherapy (IMRT) treatment plans with 50 cm source-to-isocenter distance (SID-50) on 10 Head and Neck (H&N) cancer patients were compared with low-resolution large-field plans with 100 cm SID (SID-100). With the same or better target coverage, the average reduction of [Dmean, Dmax] of 20-beam SID-50 plans from 20-beam SID-100 plans were [2.09 Gy, 1.19 Gy] for organs at risk (OARs) overall, [3.05 Gy, 0.04 Gy] for parotid gland, [3.62 Gy, 5.19 Gy] for larynx, and [3.27 Gy, 1.10 Gy] for mandible. R50 and integral dose were reduced by 5.3% and 9.6%, respectively. Wilcoxon signed-rank test showed significant difference (p   <  0.05) in planning target volume (PTV) homogeneity, PTV Dmax, R50, Integral dose, and OAR Dmean and Dmax. The estimated delivery time of 20-beam [SID-50, SID-100] plans were [19, 18] min and [14, 9] min, assuming 5 fractions and 30 fractions, respectively. With clinically acceptable delivery efficiency, many-isocenter optimization is dosimetrically desirable for treating large targets with high modulation resolution on the robotic platform.

Purpose

Spot-scanning proton arc therapy (SPAT) is an emerging modality to improve plan conformality and delivery efficiency. A greedy and heuristic method is proposed in the existing SPAT algorithm to select energy layers and sequence energy switching with gantry rotation, which does not promise optimality in either dosimetry or efficiency. We aim to develop a method to solve the energy layer switching and dosimetry optimization problems in an integrated framework for SPAT.

Methods

In an integrated approach, energy layer optimization for spot-scanning proton arc therapy (ELO-SPAT) is formulated with a dose fidelity term, a group sparsity regularization, a log barrier regularization, and an energy sequencing (ES) penalty. The combination of L2,1/2-norm group sparsity regularization and log barrier function allows one energy layer being selected per control point. The ES regularization term sorts the delivery sequence from high energy to low energy to reduce the total energy layer switching time (ELST) and subsequently the total delivery time. Within the ES penalty, the gradient of layer weights between adjacent beams is first calculated along beam direction and then along energy direction. The gradients indicate energy switch patterns between two adjacent beams. The time-wise costly energy switch-up is more heavily penalized in the ES term. This ELO-SPAT method was tested on one frontal base-of-skull (BOS) patient, one chordoma (CHDM) patient with a simultaneous integrated boost, one bilateral head-and-neck (H&N) patient, and one lung (LNG) patient. We compared ELO-SPAT with intensity-modulated proton therapy (IMPT) using discrete beams and SPArc by Ding et al. For the two arc algorithms, both the plans with and without energy sequencing were created and compared.

Results

Energy layer optimization for spot-scanning proton arc therapy reduced the runtime of optimization by 84% on average compared with the greedy SPArc method. In both the ELO-SPAT plans with and without ES, one energy layer per control point was selected. Without ES regularization, the energy sequence was arbitrary, with around 40-60 switch-up for the tested cases. After adding ES regularization, the number of energy switch-up was reduced to less than 20. Compared with the energy sequenced SPArc plans, the ELO-SPAT plans with ES led to 24% less total ELST for synchrotron plans and 14% less for cyclotron plans. Both the ELO-SPAT and SPArc plans achieved better sparing compared with the IMPT plans for most Organs-at-risks (OARs), with or without ES. Without ES, the ELO-SPAT plans achieved further improvement of the OARs compared with the SPArc plans, with an averaged reduction of OAR [Dmean, Dmax] by [1.57, 3.34] GyRBE. Adding the ES regularization degraded the plan quality, but the ELO-SPAT plans still had comparable or slightly better sparing than the SPArc plans with ES, with an averaged reduction of OAR [Dmean, Dmax] by [1.42, 2.34] GyRBE.

Conclusion

We developed a computationally efficient spot-scanning proton arc optimization method, which solved energy layer selection and sequencing in an integrated framework, generating plans with good dosimetry and high delivery efficiency.