Response to "in regard to "Tran A, Zhang J, Woods K, Yu V, Nguyen D, Gustafson G, Rosen L, Sheng K. Treatment planning comparison of IMPT, VMAT and 4π radiotherapy for prostate cases"".

In regard to our recently published paper entitled "Treatment planning comparison of IMPT, VMAT and 4π radiotherapy for prostate cases", a question was raised whether "4π" was used appropriately to describe the non-coplanar planning and delivery space. In this letter, the term use is explained from both theoretical and practical perspectives. It is concluded that the self-explanatory term provides a flexible description of non-coplanar radiotherapy with beam orientation optimization. Confusions with this term can be avoided by understanding the evolving and machine/patient specific nature of 4π planning

K-quantum Nonlinear Jaynes-Cummings Model in Two Trapped Ions

A k-quantum nonlinear Jaynes-Cummings model for two trapped ions interacting with laser beams resonant to k-th red side-band of center-of-mass mode, far from Lamb-Dicke regime, has been obtained. The exact analytic solution showed the existence of quantum collapses and revivals of the occupation of two atoms.Comment: 8 pages, 3 figure

Cochlea-sparing acoustic neuroma treatment with 4π radiation therapy.

PurposeThis study investigates whether 4π noncoplanar radiation therapy can spare the cochleae and consequently potentially improve hearing preservation in patients with acoustic neuroma who are treated with radiation therapy.Methods and materialsClinical radiation therapy plans for 30 patients with acoustic neuroma were included (14 stereotactic radiation surgery [SRS], 6 stereotactic radiation therapy [SRT], and 10 intensity modulated radiation therapy [IMRT]). The 4π plans were created for each patient with 20 optimal beams selected using a greedy column generation method and subsequently recalculated in Eclipse for comparison. Organ-at-risk (OAR) doses, homogeneity index, conformity, and tumor control probability (TCP) were compared. Normal tissue complication probability (NTCP) was calculated for sensorineural hearing loss (SNHL) at 3 and 5 years posttreatment. The dose for each plan was then escalated to achieve 99.5% TCP.Results4π significantly reduced the mean dose to both cochleae by 2.0 Gy (32%) for SRS, 3.2 Gy (29%) for SRT, and 10.0 Gy (32%) for IMRT. The maximum dose to both cochleae was also reduced with 4π by 1.6 Gy (20%), 2.2 Gy (15%), and 7.1 Gy (18%) for SRS, SRT, and IMRT plans, respectively. The reductions in mean/maximum brainstem dose with 4π were also statistically significant. Mean doses to other OARs were reduced by 19% to 56% on average. 4π plans had a similar CN and TCP, with a significantly higher average homogeneity index (0.93 vs 0.92) and significantly lower average NTCP for SNHL at both 3 years (30.8% vs 40.8%) and 5 years (43.3% vs 61.7%). An average dose escalation of approximately 116% of the prescription dose achieved 99.5% TCP, which resulted in 32.6% and 43.4% NTCP for SNHL at 3 years and 46.4% and 64.7% at 5 years for 4π and clinical plans, respectively.ConclusionsCompared with clinical planning methods, optimized 4π radiation therapy enables statistically significant sparing of the cochleae in acoustic neuroma treatment as well as lowering of other OAR doses, potentially reducing the risk of hearing loss

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

PurposeThe 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.MethodsStatistical 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.ResultsStatistical 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.ConclusionCompared 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