The leaf sweep algorithm for an immobile and moving target as an optimal control problem in radiotherapy delivery

The variational problem of modelling the optimized dynamic delivery of intensity modulated radiation therapy is investigated. Motions of two jaws are determined that expose each point of the field for a predetermined amount of time and minimize the overall time of the radiation delivery. Variable initial and final conditions for jaw motions are admissible and constraints expressing limitations on speeds of jaw movements are included. Cases of dynamic intensity modulation for immobile as well as moving targets are investigated.