A genetic algorithm has been used to optimize the selection of beam weights for external beam three-dimensional conformal radiotherapy treatment planning. A fitness function is defined, which includes a difference function to achieve a least-square fit to doses at preselected points in a planning target volume, and a penalty item to constrain the maximum allowable doses delivered to critical organs. Adjustment between the dose uniformity within the target volume and the dose constraint to the critical structures can be achieved by varying the beam weight variables in the fitness function. A floating-point encoding schema and several operators, like uniform crossover, arithmetical crossover, geometrical crossover, Gaussian mutation and uniform mutation, have been used to evolve the population. Three different cases were used to verify the correctness of the algorithm and quality assessment based on dose-volume histograms and three-dimensional dose distributions were given. The results indicate that the genetic algorithm presented here has considerable potential.

The single isocenter for multiple-target (SIMT) technique has become a popular treatment technique for multiple brain metastases. We have implemented a method to obtain a nonuniform margin for SIMT technique. In this study, we further propose a method to determine the isocenter position so that the total expanded margin volume is minimal. Materials and method:Based on a statistical model, the relationship between nonuniform margin and the distance d (from isocenter to target point), setup uncertainties, and significance level was established. Due to the existence of rotational error, there is a nonlinear relationship between the margin volume and the isocenter position. Using numerical simulation, we study the relationship between optimal isocenter position and translational error, rotational error, and target size. In order to find the optimal isocenter position quickly, adaptive simulated annealing (ASA) algorithm was used. This method was implemented in the Pinnacle 3 treatment planning system and compared with isocenter at center-ofgeometric (COG), center-of -volume (COV), and center-of -surface (COS). Ten patients with multiple brain metastasis targets treated with the SIMT technique was selected for evaluation. Results: When the size of tumors is equal, the optimal isocenter obtained by ASA and numerical simulation coincides with COG, COV, and COS. When the size of tumors is different, the optimal isocenter is close to the large tumor. The position of COS point is closer to the optimal point than the COV point for nearly all cases.Moreover,in some cases the COS point can be approximately selected as the optimal point. The ASA algorithm can reduce the calculating time from several hours to tens of seconds for three or more tumors. Using multiple brain metastases targets, a series of volume difference and calculating time were obtained for various tumor number, tumor size, and separation distances. Compared with the margin volume with isocenter at COG, the margin volume for optimal point can be reduced by up to 27.7%. Conclusion: Optimal treatment isocenter selection of multiple targets with large differences could reduce the total margin volume. ASA algorithm can significantly improve the speed of finding the optimal isocenter. This method can be used for clinical isocenter selection and is useful for the protection of normal tissue nearby.

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Background: Recently, patient rotating devices for gantry-free radiotherapy, a new approach to implement external beam radiotherapy, have been introduced. When a patient is rotated in the horizontal position, gravity causes anatomic deformation. For treatment planning, one feasible method is to acquire simulation images at different horizontal rotation angles. Purpose: This study aimed to investigate the feasibility of synthesizing magnetic resonance (MR) images at patient rotation angles of 180 • (prone position) and 90 • (lateral position) from those at a rotation angle of 0 • (supine position) using deep learning. Methods: This study included 23 healthy male volunteers. They underwent MR imaging (MRI) in the supine position and then in the prone (23 volunteers) and lateral (16 volunteers) positions. T1-weighted fast spin echo was performed for all positions with the same parameters. Two two-dimensional deep learning networks, pix2pix generative adversarial network (pix2pix GAN) and CycleGAN, were developed for synthesizing MR images in the prone and lateral positions from those in the supine position, respectively. For the evaluation of the models, leave-one-out cross-validation was performed. The mean absolute error (MAE), Dice similarity coefficient (DSC), and Hausdorff distance (HD) were used to determine the agreement between the prediction and ground truth for the entire body and four specific organs. Results: For pix2pix GAN, the synthesized images were visually bad, and no quantitative evaluation was performed. The quantitative evaluation metrics of the body outlines calculated for the synthesized prone and lateral images using CycleGAN were as follows: MAE, 35.63 ± 3.98 and 40.45 ± 5.83, respectively; DSC, 0.97 ± 0.01 and 0.94 ± 0.01, respectively; and HD (in pixels), 16.74 ± 3.55 and 31.69 ± 12.03, respectively. The quantitative metrics of the bladder and prostate performed were also promising for both the prone and lateral images, with mean values >0.90 in DSC (p > 0.05).The mean DSC and HD values of the bilateral femur for the prone images were 0.96 and 3.63 (in pixels), respectively, and 0.78 and 12.65 (in pixels) for the lateral images, respectively (p < 0.05). Conclusions: The CycleGAN could synthesize the MRI at lateral and prone positions using images at supine position, and it could benefit gantry-free radiation therapy.