This work presents the implementation of an optimization methodology that generates a trajectory simultaneous with treatment plan optimization (simTr-VMAT).


 The simTr-VMAT trajectories were compared against these random trajectories based on a quality metric that prefers trajectories with few control points and low objective function value over long, inefficient trajectories.


 For the lung patient, the simTr-VMAT plan resulted in a decrease of the mean dose of 1.5 and 1.0 Gy to the heart and ipsilateral lung, respectively.  For the glioblastoma patient, the simTr-VMAT plan resulted in improved planning target volume coverage with a decrease in mean dose to the eyes, lens, nose, and contralateral temporal lobe between 2 and 7 Gy.  The simTr-VMAT treatment plans ranked at the 99.6, 96.3, and 99.4 percentiles compared to the distribution of randomly generated trajectories for the lung, glioblastoma, and prostate patients, respectively.


 The simTr-VMAT optimization methodology resulted in treatment plans with equivalent or improved dosimetric outcomes compared to coplanar VMAT treatment plans, with the trajectories resulting from the optimization ranking among the optimal trajectories for each patient case.
simTr-VMAT
The optimization algorithm is based on the column generation approach, in which a treatment plan is iteratively constructed through the solution of a subproblem called the "pricing problem." 
column generation approach
The optimization algorithm is based on the column generation approach, in which a treatment plan is iteratively constructed through the solution of a subproblem called the "pricing problem."  The property of the pricing problem to rank candidate apertures based on their associated price is leveraged to select an optimal aperture while simultaneously determining the trajectory path. 
pricing problem
Simultaneous trajectory generation and volumetric modulated arc therapy optimization.PURPOSE
 Trajectory-based treatment planning involves the combination of a gantry-couch trajectory with volumetric modulated arc therapy (VMAT) treatment plan optimization.  This work presents the implementation of an optimization methodology that generates a trajectory simultaneous with treatment plan optimization (simTr-VMAT).


 The optimization algorithm is based on the column generation approach, in which a treatment plan is iteratively constructed through the solution of a subproblem called the "pricing problem."  The property of the pricing problem to rank candidate apertures based on their associated price is leveraged to select an optimal aperture while simultaneously determining the trajectory path.  A progressively increasing gantry-couch grid resolution is used to provide an initial coarse sampling of the angular solution space while maintaining fine control point spacing with the final treatment plan.  The trajectory optimization was applied and compared to coplanar VMAT treatment plans for a lung patient, a glioblastoma patient, and a prostate patient.  Algorithm validation was performed through the generation of 5000 random trajectories and optimization using column generation VMAT for each patient case, representing the solution space for the trajectory optimization problem.  The simTr-VMAT trajectories were compared against these random trajectories based on a quality metric that prefers trajectories with few control points and low objective function value over long, inefficient trajectories.


 For the lung patient, the simTr-VMAT plan resulted in a decrease of the mean dose of 1.5 and 1.0 Gy to the heart and ipsilateral lung, respectively.  For the glioblastoma patient, the simTr-VMAT plan resulted in improved planning target volume coverage with a decrease in mean dose to the eyes, lens, nose, and contralateral temporal lobe between 2 and 7 Gy.  The prostate patient showed no clinically relevant dosimetric improvement.  The simTr-VMAT treatment plans ranked at the 99.6, 96.3, and 99.4 percentiles compared to the distribution of randomly generated trajectories for the lung, glioblastoma, and prostate patients, respectively.


 CONCLUSION
 The simTr-VMAT optimization methodology resulted in treatment plans with equivalent or improved dosimetric outcomes compared to coplanar VMAT treatment plans, with the trajectories resulting from the optimization ranking among the optimal trajectories for each patient case.
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