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Purpose Respiratory movement, as one of the main challenges in proton therapy for pancreatic cancer patients, could not only lead to harm to normal tissues but also lead to failure of the tumor control, resulting in irreversible consequences. Including respiratory movements into the plan optimization, i.e. 4D robust optimization, may mitigate the interplay effect. However, 4D robust optimization considering images of all breathing phases is time-consuming and less efficient. This work aims to investigate the effect of the breathing phase number on the 4D robust optimization for pancreatic cancer intensity modulated proton therapy (IMPT) by examining plan quality and computational efficiency. Methods A total of 15 pancreatic cancer patients were retrospectively analyzed. In this study, both anterior-fields and posterior-fields plans were created for each patient. For each plan, six four-dimensional (4D) robust treatment planning strategies with different numbers of respiratory phases and one three-dimensional (3D) treatment plan were created. Optimization of the plans were performed on all ten phases (10phase plan), two extreme phases (2phase plan), two extreme phases plus an intermediate state (3phase plan), two extreme phases plus the 3D CT (3Aphase plan), six phases during the exhalation stage (6Exphase plan), six phases during the inhalation stage (6Inphase plan) and 3D Computed Tomography (CT) scan image (3D plan), respectively. 4D dynamic dose (4DDD) was then calculated to access the interplay effect by considering respiratory motion and dynamic beam delivery. Plan quality and dosimetric parameters for the target and organs at risk (OARs) were then analyzed. Results Compared to the 4D plans, 3D plan performed terribly in terms of target coverage and organs at risk. Target dose in anterior-fields plan varied slightly among all six 4D treatment planning strategies. Both the 6Exphase and 6Inphase plans demonstrated performance that was comparable to the 10phase plan in target coverage, outperforming the other five plans for anterior-fields plan. It’s basically the same for the posterior-fields plan. The six strategies showed similar OARs sparing effect for both anterior-fields and posterior-fields plan. Compared with the 10phase plan, the average decline rates of the optimization time of the six plans of 2phase, 3phase, 3Aphase, 6Exphase, 6Inphase, and 3D were 73.26 ± 6.54% vs. 74.48 ± 6.63%, 65.80 ± 7.89% vs. 65.81 ± 9.58%, 54.67 ± 11.52% vs. 65.75 ± 9.58%, 42.14 ± 13.57% vs. 39.63 ± 16.93%, 37.72 ± 11.70% vs. 40.79 ± 13.62% and 75.52 ± 8.21% vs. 80.67 ± 5.62%, respectively (anterior vs. posterior). With the decrease of the number of phases selected for optimization, the decline rates increased, while the other dosimetry parameters generally showed a deterioration trend. Conclusion In this study, a comprehensive evaluation of six 4D robust treatment planning strategies and one 3D treatment planning strategy for pancreatic cancer patients receiving IMPT was performed. The results showed that six 4D robust optimization strategies were comparable in common posterior field therapy. 2phase and 3phase (including 3Aphase) treatment planning strategies could replace the 10phase treatment planning strategy. It should be noted that patients with large motion amplitudes should receive special attention. The dosimetric performance of the 6Exphase and 6Inphase plans closely aligned with that of the 10phase plan in anterior fields. These plans offered a feasible alternative to 10phase treatment planning strategy by reducing optimization time while maintaining dose coverage of the target and protection of OARs. This research provides guidelines to reduce optimization time and improve clinical efficiency for pancreatic cancer IMPT.

Purpose The interplay effect between dynamic pencil proton beams and motion of the lung tumor presents a challenge in treating lung cancer patients in pencil beam scanning (PBS) proton therapy. The main purpose of the current study was to investigate the interplay effect on the volumetric repainting lung plans with beam delivery in alternating order (“down” and “up” directions), and explore the number of volumetric repaintings needed to achieve acceptable lung cancer PBS proton plan. Method The current retrospective study included ten lung cancer patients. The total dose prescription to the clinical target volume (CTV) was 70 Gy(RBE) with a fractional dose of 2 Gy(RBE). All treatment plans were robustly optimized on all ten phases in the 4DCT data set. The Monte Carlo algorithm was used for the 4D robust optimization, as well as for the final dose calculation. The interplay effect was evaluated for both the nominal (i.e., without repainting) as well as volumetric repainting plans. The interplay evaluation was carried out for each of the ten different phases as the starting phases. Several dosimetric metrics were included to evaluate the worst‐case scenario (WCS) and bandwidth based on the results obtained from treatment delivery starting in ten different breathing phases. Results The number of repaintings needed to meet the criteria 1 (CR1) of target coverage (D95% ≥ 98% and D99% ≥ 97%) ranged from 2 to 10. The number of repaintings needed to meet the CR1 of maximum dose (ΔD1% < 1.5%) ranged from 2 to 7. Similarly, the number of repaintings needed to meet CR1 of homogeneity index (ΔHI < 0.03) ranged from 3 to 10. For the target coverage region, the number of repaintings needed to meet CR1 of bandwidth (<100 cGy) ranged from 3 to 10, whereas for the high‐dose region, the number of repaintings needed to meet CR1 of bandwidth (<100 cGy) ranged from 1 to 7. Based on the overall plan evaluation criteria proposed in the current study, acceptable plans were achieved for nine patients, whereas one patient had acceptable plan with a minor deviation. Conclusion The number of repaintings required to mitigate the interplay effect in PBS lung cancer (tumor motion < 15 mm) was found to be highly patient dependent. For the volumetric repainting with an alternating order, a patient‐specific interplay evaluation strategy must be adopted. Determining the optimal number of repaintings based on the bandwidth and WCS approach could mitigate the interplay effect in PBS lung cancer treatment.

This study evaluated the dosimetric benefits of various four-dimensional (4D) robust optimization strategies for enhancing plan robustness in free-breathing stereotactic body radiotherapy (SBRT). For ten early-stage lung cancer patients, we generated four helical tomotherapy–SBRT plans (42 Gy/4 fractions) using 4D robust optimization based on 4D-computed tomography (CT) images from all ten phases (4D_10), six phases (4D_6), four phases (4D_4), and two phases (4D_2). Conventional internal target volume (ITV)–based plans served as a reference. Setup uncertainty robustness was assessed across all CT phases. We compared dose and target coverage (D 98% , V 100% ) for the gross tumor volume, doses to relevant organs at risk (OARs), and reductions in plan robustness for both nominal and perturbed scenarios. Optimization durations were recorded. All nominal plans met clinical criteria for targets and OARs. The 4D_10 plans exhibited the highest robustness in target coverage, with D 98% significantly different from ITV plans ( p  < 0.05) and V 100% significantly different from 4D_2 plans ( p  < 0.05). Optimization time increased linearly with the number of CT phases. Four-dimensional robust optimization enables free-breathing SBRT plans resilient to respiratory and setup uncertainties; however, limiting phase number may compromise robustness for certain tumors despite shorter optimization times.

Aircraft trajectory planning is affected by various uncertainties. Among them, those in weather prediction have a large impact on the aircraft dynamics. Trajectory planning that assumes a deterministic weather scenario can cause significant performance degradation and constraint violation if the actual weather conditions are significantly different from the assumed ones. The present study proposes a fundamental framework to plan four-dimensional optimal descent trajectories that are robust against uncertainties in weather-prediction data. To model the nature of the uncertainties, we utilize the Global Ensemble Forecast System, which provides a set of weather scenarios, also referred to as members. A robust trajectory planning problem is constructed based on the robust optimal control theory, which simultaneously considers a set of trajectories for each of the weather scenarios while minimizing the expected value of the overall operational costs. We validate the proposed planning algorithm with a numerical simulation, assuming an arrival route to Leipzig/Halle Airport in Germany. Comparison between the robust and the inappropriately-controlled trajectories shows the proposed robust planning strategy can prevent deteriorated costs and infeasible trajectories that violate operational constraints. The simulation results also confirm that the planning can deal with a wide range of cost-index and required-time-of-arrival settings, which help the operators to determine the best values for these parameters. The framework we propose is in a generic form, and therefore it can be applied to a wide range of scenario settings.

This study introduces a novel control framework based on the Takagi–Sugeno–Kang wavelet fuzzy neural network, integrating brain imitated network and cerebellar network. The proposed controller demonstrates high robustness, making it an excellent candidate for handling intricate nonlinear dynamics, effectively mapping input–output relationships and efficiently learning from data. To enhance its performance, the controller’s parameters are fine-tuned using Lyapunov stability theory. Compared to existing approaches, the proposed model exhibits superior learning capabilities and achieves outstanding performance metrics. Furthermore, the study applies this synchronization technique to the secure transmission of medical images. By encrypting a medical image into a chaotic trajectory before transmission, the system ensures data security. On the receiving end, the original image is successfully reconstructed using chaotic trajectory synchronization. Experimental results confirm the effectiveness and reliability of the proposed neural network model, as well as the encryption and decryption process. Specifically, the average_RMSE of the Takagi–Sugeno–Kang fuzzy wavelet brain cerebral controller (TFWBCC) method is 2.004 times smaller than the cerebellar model articulation controller (CMAC) method, 1.923 times smaller than the RCMAC method, 1.8829 times smaller than the TSKCMAC method, and 1.8153 times smaller than the brain emotional learning controller (BELC) method.