Tomographic detection of photon pairs produced from high-energy X-rays for the monitoring of radiotherapy dosing.

Measuring the radiation dose reaching a patient's body is difficult. Here we report a technique for the tomographic reconstruction of the location of photon pairs originating from the annihilation of positron-electron pairs produced by high-energy X-rays travelling through tissue. We used Monte Carlo simulations on pre-recorded data from tissue-mimicking phantoms and from a patient with a brain tumour to show the feasibility of this imaging modality, which we named 'pair-production tomography', for the monitoring of radiotherapy dosing. We simulated three image-reconstruction methods, one applicable to a pencil X-ray beam scanning through a region of interest, and two applicable to the excitation of tissue volumes via broad beams (with temporal resolution sufficient to identify coincident photon pairs via filtered back projection, or with higher temporal resolution sufficient for the estimation of a photon's time-of-flight). In addition to the monitoring of radiotherapy dosing, we show that image contrast resulting from pair-production tomography is highly proportional to the material's atomic number. The technique may thus also allow for element mapping and for soft-tissue differentiation.

Technical note: Multi-MATE, a high-throughput platform for automated image-guided small-animal irradiation.

BACKGROUND: Small animal irradiation is essential to study the radiation response of new interventions before or parallel to human therapy. Image-guided radiotherapy (IGRT) and intensity-modulated radiotherapy (IMRT) are recently adopted in small animal irradiation to more closely mimic human treatments. However, sophisticated techniques require exceedingly high time, resources, and expertize that are often impractical. PURPOSE: We propose a high throughput and high precision platform named Multiple Mouse Automated Treatment Environment (Multi-MATE) to streamline image-guided small animal irradiation. METHODS: Multi-MATE consists of six parallel and hexagonally arranged channels, each equipped with a transfer railing, a 3D-printed immobilization pod, and an electromagnetic control unit, computer-controlled via an Arduino interface. The mouse immobilization pods are transferred along the railings between the home position outside the radiation field and the imaging/irradiation position at the irradiator isocenter. All six immobilization pods are transferred to the isocenter in the proposed workflow for parallel CBCT scans and treatment planning. The immobilization pods are then sequentially transported to the imaging/therapy position for dose delivery. The positioning reproducibility of Multi-MATE are evaluated using CBCT and radiochromic films. RESULTS: While parallelizing and automating the image-guided small animal radiation delivery, Multi-MATE achieved the average pod position reproducibility of 0.17 ± 0.04 mm in the superior-inferior direction, 0.20 ± 0.04 mm in the left-right direction, and 0.12 ± 0.02mm in the anterior-posterior direction in repeated CBCT tests. Additionally, in image-guided dose delivery tasks, Multi-MATE demonstrated the positioning reproducibility of 0.17 ± 0.06 mm in the superior-inferior direction, 0.19 ± 0.06 mm in the left-right direction. CONCLUSIONS: We designed, fabricated, and tested a novel automated irradiation platform, Multi-MATE to accelerate and automate image-guided small animal irradiation. The automated platform minimizes human operation and achieves high setup reproducibility and image-guided dose delivery accuracy. Multi-MATE thus removes a major barrier to implementing high-precision preclinical radiation research.

DeepMC: a deep learning method for efficient Monte Carlo beamlet dose calculation by predictive denoising in magnetic resonance-guided radiotherapy.

Emerging magnetic resonance (MR) guided radiotherapy affords significantly improved anatomy visualization and, subsequently, more effective personalized treatment. The new therapy paradigm imposes significant demands on radiation dose calculation quality and speed, creating an unmet need for the acceleration of Monte Carlo (MC) dose calculation. Existing deep learning approaches to denoise the final plan MC dose fail to achieve the accuracy and speed requirements of large-scale beamlet dose calculation in the presence of a strong magnetic field for online adaptive radiotherapy planning. Our deep learning dose calculation method, DeepMC, addresses these needs by predicting low-noise dose from extremely noisy (but fast) MC-simulated dose and anatomical inputs, thus enabling significant acceleration. DeepMC simultaneously reduces MC sampling noise and predicts corrupted dose buildup at tissue-air material interfaces resulting from MR-field induced electron return effects. Here we demonstrate our model's ability to accelerate dose calculation for daily treatment planning by a factor of 38 over traditional low-noise MC simulation with clinically meaningful accuracy in deliverable dose and treatment delivery parameters. As a post-processing approach, DeepMC provides compounded acceleration of large-scale dose calculation when used alongside established MC acceleration techniques in variance reduction and graphics processing unit-based MC simulation.

ROAD: ROtational direct Aperture optimization with a Decoupled ring-collimator for FLASH radiotherapy.

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.

Many-isocenter optimization for robotic 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.

Technical Note: Robust individual thermoluminescence dosimeter tracking using optical fingerprinting.

PURPOSE: The thermoluminescence dosimeter (TLD) has desirable features including low cost, reusability, small size, and relatively low energy dependence. However, the commonly available poly-crystal TLDs (e.g., TLD-100) exhibit high interdetector variability that requires individual calibration for high detection accuracy. To improve individual TLD tracking robustness, we developed an optical fingerprinting method to identify the TLD-100 chips. METHODS: Seven hundred and fifty-two images were initially captured using a digital microscope camera to build a feature library for both facets of 376 TLD-100 chips. A median intensity thresholding method was used to segment images into foreground and background. The affine transformation was used to register the segmented images to the same position. The fingerprint of each image was calculated from its registered image. All fingerprints were then recorded in an Elasticsearch® search database. The TLD fingerprint match was tested three times when the library was established and repeated once 20 months later. All chips were irradiated at 0, 1, 4, and 8 Gy on a calibrated clinical MV linac to establish the individual calibration curve. RESULTS: The true positive rate of identifying TLDs based on their optical fingerprints was 100% at initialization of the inventory. After 20 months and multiple deployments for characterization, calibration, and dose measurement, the true positive match rate dropped to 99% with zero false-positive matches. The TLDs exhibited high self-consistency in the dose-response test with R2 between 0.988 and 1 with linear regression. CONCLUSIONS: The TLD-100 chips surface textures are unique and sufficient to support accurate identification based on the optical fingerprinting. This method provides inexpensive and robust management of the TLDs for individual calibration and dosimetry.

A sparse orthogonal collimator for small animal intensity-modulated radiation therapy. Part II: hardware development and commissioning.

PURPOSE: A dose-modulation device for small animal radiotherapy is required to use clinically analogous treatment techniques, which will likely increase the translatability of preclinical research results. Because the clinically used multileaf collimator (MLC) is impractical for miniaturization, we have developed a simpler, better-suited sparse orthogonal collimator (SOC) for delivering small animal intensity-modulated radiation therapy (IMRT) using a rectangular aperture optimization (RAO) treatment planning system. METHODS: The SOC system was modeled in computer-aided design software and fabricated with machined tungsten leaves and three-dimensional (3D) printed leaf housing. A graphical user interface was developed for controlling and calibrating the SOC leaves, which are driven by Arduino-controlled stepper motors. A Winston-Lutz test was performed to assess mechanical alignment, and abutting field and grid dose patterns were created to analyze intra- and intercalibration leaf positioning error. Leaf transmission and penumbra were measured over the full range of gantry angles and leaf positions, respectively. Three SOC test plans were delivered, and film measurements were compared to the intended dose distributions. The differences in maximum, mean, and minimum, as well as pixelwise absolute dose differences, were compared for each structure, and a gamma analysis was performed for the target structures using criteria of 4% dose difference and 0.3 mm distance to agreement. RESULTS: The Winston-Lutz test revealed maximum directional offsets between the SOC and primary collimator axes of 0.53 mm at 0° and 0.68 mm over the full 360°. Upper and lower abutting field patterns had maximum dose deviations of 18.8 ± 3.1% and 15.5 ± 2.9%, respectively, and grid patterns showed intra- and intercalibration repeatability of 93% and 91%, respectively. Extremely low midleaf (0.15 ± 0.05%) and interleaf (0.27 ± 0.22%) transmission was measured, with no significant rotational variation. The average penumbra was ~0.8 mm for all leaves at field center, with a range of 0.17 mm for all leaf positions. A highly concave test plan was delivered with a ~ 95% gamma analysis pass rate, and a realistic mouse phantom liver irradiation plan achieved a pass rate of ~98%. A highly complex dose distribution was also created with 551 SOC apertures averaging 2.4 mm in size. CONCLUSIONS: A sparse orthogonal collimator was developed and commissioned, with promising preliminary dosimetry results. The SOC design, with its limited moving components and high dose-modulation resolution, is ideal for delivering high-quality small animal IMRT with our RAO-based treatment planning system.

Parallel beamlet dose calculation via beamlet contexts in a distributed multi-GPU framework.

PURPOSE: Dose calculation is one of the most computationally intensive, yet essential tasks in the treatment planning process. With the recent interest in automatic beam orientation and arc trajectory optimization techniques, there is a great need for more efficient model-based dose calculation algorithms that can accommodate hundreds to thousands of beam candidates at once. Foundational work has shown the translation of dose calculation algorithms to graphical processing units (GPUs), lending to remarkable gains in processing efficiency. But these methods provide parallelization of dose for only a single beamlet, serializing the calculation of multiple beamlets and under-utilizing the potential of modern GPUs. In this paper, the authors propose a framework enabling parallel computation of many beamlet doses using a novel beamlet context transformation and further embed this approach in a scalable network of multi-GPU computational nodes. METHODS: The proposed context-based transformation separates beamlet-local density and TERMA into distinct beamlet contexts that independently provide sufficient data for beamlet dose calculation. Beamlet contexts are arranged in a composite context array with dosimetric isolation, and the context array is subjected to a GPU collapsed-cone convolution superposition procedure, producing the set of beamlet-specific dose distributions in a single pass. Dose from each context is converted to a sparse representation for efficient storage and retrieval during treatment plan optimization. The context radius is a new parameter permitting flexibility between the speed and fidelity of the dose calculation process. A distributed manager-worker architecture is constructed around the context-based GPU dose calculation approach supporting an arbitrary number of worker nodes and resident GPUs. Phantom experiments were executed to verify the accuracy of the context-based approach compared to Monte Carlo and a reference CPU-CCCS implementation for single beamlets and broad beams composed by addition of beamlets. Dose for representative 4π beam sets was calculated in lung and prostate cases to compare its efficiency with that of an existing beamlet-sequential GPU-CCCS implementation. Code profiling was also performed to evaluate the scalability of the framework across many networked GPUs. RESULTS: The dosimetric accuracy of the context-based method displays <1.35% and 2.35% average error from the existing serialized CPU-CCCS algorithm and Monte Carlo simulation for beamlet-specific PDDs in water and slab phantoms, respectively. The context-based method demonstrates substantial speedup of up to two orders of magnitude over the beamlet-sequential GPU-CCCS method in the tested configurations. The context-based framework demonstrates near linear scaling in the number of distributed compute nodes and GPUs employed, indicating that it is flexible enough to meet the performance requirements of most users by simply increasing the hardware utilization. CONCLUSIONS: The context-based approach demonstrates a new expectation of performance for beamlet-based dose calculation methods. This approach has been successful in accelerating the dose calculation process for very large-scale treatment planning problems - such as automatic 4π IMRT beam orientation and VMAT arc trajectory selection, with hundreds of thousands of beamlets - in clinically feasible timeframes. The flexibility of this framework makes it as a strong candidate for use in a variety of other very large-scale treatment planning tasks and clinical workflows.

A sparse orthogonal collimator for small animal intensity-modulated radiation therapy part I: Planning system development and commissioning.

PURPOSE: To achieve more translatable preclinical research results, small animal irradiation needs to more closely simulate human radiotherapy. Although the clinical gold standard is intensity-modulated radiation therapy (IMRT), the direct translation of this method for small animals is impractical. In this study we describe the treatment planning system for a novel dose modulation device to address this challenge. METHODS: Using delineated target and avoidance structures, a rectangular aperture optimization (RAO) problem was formulated to penalize deviations from a desired dose distribution and limit the number of selected rectangular apertures. RAO was used to create IMRT plans with highly concave targets in the mouse brain, and the plan quality was compared to that using a hypothetical miniaturized multileaf collimator (MLC). RAO plans were also created for a realistic application of mouse whole liver irradiation and for a highly complex two-dimensional (2D) dose distribution as a proof-of-principle. Beam commissioning data, including output and off-axis factors and percent depth dose (PDD) curves, were acquired for our small animal irradiation system and incorporated into the treatment planning system. A plan post-processing step was implemented for aperture size-specific dose recalculation and aperture weighting reoptimization. RESULTS: The first RAO test case achieved highly conformal doses to concave targets in the brain, with substantially better dose gradient, conformity, and target dose homogeneity than the hypothetical miniaturized MLC plans. In the second test case, a highly conformal dose to the liver was achieved with significant sparing of the kidneys. RAO also successfully replicated a complex 2D dose distribution with three prescription dose levels. Energy spectra for field sizes 1 to 20 mm were calculated to match the measured PDD curves, with maximum and mean dose deviations of 4.47 ± 0.30% and 1.71 ± 0.18%. The final reoptimization of aperture weightings for the complex RAO test plan was able to reduce the maximum and mean dose deviations between the optimized and recalculated dose distributions from 10.3% to 6.6% and 4.0% to 2.8%, respectively. CONCLUSIONS: Using the advanced optimization techniques, complex IMRT plans were achieved using a simple dose modulation device. Beam commissioning data were incorporated into the treatment planning process to more accurately predict the resulting dose distribution. This platform substantially reduces the gap in treatment plan quality between clinical and preclinical radiotherapy, potentially increasing the value and flexibility of small animal studies.

Single-arc VMAT optimization for dual-layer MLC.

Dual-layer multi-leaf collimator (DLMLC) has recently attracted renewed interest due to its good balance among resolution, low leakage, and high fabricability. However, existing progressive sampling based volumetric modulated arc therapy (VMAT) algorithm is ineffective for DLMLC, requiring more arcs to achieve dosimetry comparable to VMAT plans with higher resolution single-layer MLC (SLMLC). In this study, we develop a novel single-arc VMAT optimization framework to take advantage of the unique DLMLC characteristics fully. Direct aperture optimization (DAO) for single-arc DLMLC VMAT was formulated as a least square dose fidelity objective, along with an anisotropic total variation term to regulate the fluence smoothness and a single segment term for forming simple apertures. The DAO was solved through alternating optimization approach. The DLMLC deliverability constraint and the MLC leaf speed constraint were formulated as the optimization constraints and solved using a graph optimization algorithm. Feasibility of the proposed framework was tested on a brain, a lung, and a prostate cancer patient. The framework was further adapted for a simultaneous integrated boost (SIB) case. The single-arc DLMLC-10 mm (leaf width) plan was compared against single-arc SLMLC VMAT plans including SLMLC-5mm, SLMLC-10mm, and SLMLC with 10 mm leaf width and 5 mm leaf step size (SLMLC-10mm-5mm). Compared with the SLMLC-10mm plan and the SLMLC-10mm-5mm plan, with the same target coverage, the DLMLC-10 mm plan reduced R50 by 30.7% and 10.0%, the average max OAR dose by 5.79% and 3.7% of the prescription dose, and the average mean OAR dose by 4.18% and 2.1% of the prescription dose, respectively. The plan quality is comparable to that of the SLMLC-5mm plan. The novel single-arc VMAT optimization framework for DLMLC utilizes two MLC layers to improve the effective modulation resolution and afford more sophisticated modulation. Consequently, DLMLC VMAT achieves superior dosimetry to SLMLC VMAT with the same leaf width.

Robust beam orientation optimization for intensity-modulated proton therapy.

PURPOSE: Dose conformality and robustness are equally important in intensity modulated proton therapy (IMPT). Despite the obvious implication of beam orientation on both dosimetry and robustness, an automated, robust beam orientation optimization algorithm has not been incorporated due to the problem complexity and paramount computational challenge. In this study, we developed a novel IMPT framework that integrates robust beam orientation optimization (BOO) and robust fluence map optimization (FMO) in a unified framework. METHODS: The unified framework is formulated to include a dose fidelity term, a heterogeneity-weighted group sparsity term, and a sensitivity regularization term. The L2, 1/2-norm group sparsity is used to reduce the number of active beams from the initial 1162 evenly distributed noncoplanar candidate beams, to between two and four. A heterogeneity index, which evaluates the lateral tissue heterogeneity of a beam, is used to weigh the group sparsity term. With this index, beams more resilient to setup uncertainties are encouraged. There is a symbiotic relationship between the heterogeneity index and the sensitivity regularization; the integrated optimization framework further improves beam robustness against both range and setup uncertainties. This Sensitivity regularization and Heterogeneity weighting based BOO and FMO framework (SHBOO-FMO) was tested on two skull-base tumor (SBT) patients and two bilateral head-and-neck (H&N) patients. The conventional CTV-based optimized plans (Conv) with SHBOO-FMO beams (SHBOO-Conv) and manual beams (MAN-Conv) were compared to investigate the beam robustness of the proposed method. The dosimetry and robustness of SHBOO-FMO plan were compared against the manual beam plan with CTV-based voxel-wise worst-case scenario approach (MAN-WC). RESULTS: With SHBOO-FMO method, the beams with superior range robustness over manual beams were selected while the setup robustness was maintained or improved. On average, the lowest [D95%, V95%, V100%] of CTV were increased from [93.85%, 91.06%, 70.64%] in MAN-Conv plans, to [98.62%, 98.61%, 96.17%] in SHBOO-Conv plans with range uncertainties. With setup uncertainties, the average lowest [D98%, D95%, V95%, V100%] of CTV were increased from [92.06%, 94.83%, 94.31%, 78.93%] in MAN-Conv plans, to [93.54%, 96.61%, 97.01%, 91.98%] in SHBOO-Conv plans. Compared with the MAN-WC plans, the final SHBOO-FMO plans achieved comparable plan robustness and better OAR sparing, with an average reduction of [Dmean, Dmax] of [6.31, 6.55] GyRBE for the SBT cases and [1.89, 5.08] GyRBE for the H&N cases from the MAN-WC plans. CONCLUSION: We developed a novel method to integrate robust BOO and robust FMO into IMPT optimization for a unified solution of both BOO and FMO, generating plans with superior dosimetry and good robustness.

Performance Comparison of Knowledge-Based Dose Prediction Techniques Based on Limited Patient Data.

PURPOSE: The accuracy of dose prediction is essential for knowledge-based planning and automated planning techniques. We compare the dose prediction accuracy of 3 prediction methods including statistical voxel dose learning, spectral regression, and support vector regression based on limited patient training data. METHODS: Statistical voxel dose learning, spectral regression, and support vector regression were used to predict the dose of noncoplanar intensity-modulated radiation therapy (4π) and volumetric-modulated arc therapy head and neck, 4π lung, and volumetric-modulated arc therapy prostate plans. Twenty cases of each site were used for k-fold cross-validation, with k = 4. Statistical voxel dose learning bins voxels according to their Euclidean distance to the planning target volume and uses the median to predict the dose of new voxels. Distance to the planning target volume, polynomial combinations of the distance components, planning target volume, and organ at risk volume were used as features for spectral regression and support vector regression. A total of 28 features were included. Principal component analysis was performed on the input features to test the effect of dimension reduction. For the coplanar volumetric-modulated arc therapy plans, separate models were trained for voxels within the same axial slice as planning target volume voxels and voxels outside the primary beam. The effect of training separate models for each organ at risk compared to all voxels collectively was also tested. The mean squared error was calculated to evaluate the voxel dose prediction accuracy. RESULTS: Statistical voxel dose learning using separate models for each organ at risk had the lowest root mean squared error for all sites and modalities: 3.91 Gy (head and neck 4π), 3.21 Gy (head and neck volumetric-modulated arc therapy), 2.49 Gy (lung 4π), and 2.35 Gy (prostate volumetric-modulated arc therapy). Compared to using the original features, principal component analysis reduced the 4π prediction error for head and neck spectral regression (-43.9%) and support vector regression (-42.8%) and lung support vector regression (-24.4%) predictions. Principal component analysis was more effective in using all/most of the possible principal components. Separate organ at risk models were more accurate than training on all organ at risk voxels in all cases. CONCLUSION: Compared with more sophisticated parametric machine learning methods with dimension reduction, statistical voxel dose learning is more robust to patient variability and provides the most accurate dose prediction method.

A novel optimization framework for VMAT with dynamic gantry couch rotation.

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.