Methods and systems for automated volumetric modulated arc therapy (VMAT) for external radiation therapy

A system for performing volumetric modulated arc therapy (VMAT) treatment planning, the system comprising:

• one or more processors;
• and
• a memory to store computer code instructions, the computer code instructions when executed cause the one or more processors to:
• determine, using a current solution of a non-convex VMAT optimization problem, a search region defining, for each leaf of a plurality of leaves of a multi-leaf collimator (MLC), a corresponding spatial movement range, the current solution including a first set of positions for the plurality of leaves of the MLC;
• merge, for each spatial movement range of a corresponding leaf, beamlets associated with the spatial movement range;
• transform the non-convex VMAT optimization problem into a convex VMAT optimization based on the merging of beamlets associated with each spatial movement range;
• solve the convex VMAT optimization problem to determine a second set of positions for the plurality of leaves of the MLC;
• compare a performance of the second set of positions for the plurality of leaves of the MLC and a performance of the current solution with respect to solving the non-convex VMAT optimization problem;
• and
• modify, for each leaf of the plurality of leaves of the MLC, the corresponding spatial movement range, based on comparing the performance of the second set of positions for the plurality of leaves of the MLC and the performance of the current solution.

A computer readable non-transitory medium including computer code instructions stored thereon, the computer code instructions when executed cause one or more processors to:

• determine, using a current solution of a non-convex VMAT optimization problem, a search region defining, for each leaf of a plurality of leaves of a multi-leaf collimator (MLC), a corresponding spatial movement range, the current solution including a first set of positions for the plurality of leaves of the MLC;
• merge, for each spatial movement range of a corresponding leaf, beamlets associated with the spatial movement range;
• transform the non-convex VMAT optimization problem into a convex VMAT optimization based on the merging of beamlets associated with each spatial movement range;
• solve the convex VMAT optimization problem to determine a second set of positions for the plurality of leaves of the MLC;
• compare a performance of the second set of positions for the plurality of leaves of the MLC and a performance of the current solution with respect to solving the non-convex VMAT optimization problem;
• and
• modify, for each leaf of the plurality of leaves of the MLC, the corresponding spatial movement range, based on comparing the performance of the second set of positions for the plurality of leaves of the MLC and the performance of the current solution.