Modeling and comparison of alternative approaches for sector duration optimization in a dedicated radiosurgery system

Stereotactic radiosurgery (SRS) is an effective technique to treat brain metastasis for which several inverse planning methods may be appropriate. We compare three different optimization models for segment duration optimization in SRS using Leksell Gamma Knife^® Icon^TM (Elekta, Stockholm, Sweden). We investigate (1) a linear programming approach, (2) a piecewise quadratic penalty approach, and (3) an unconstrained convex moment-based penalty approach. We examine the performances of these approaches using anonymized data from 14 previously treated cases. In addition, we investigate the important modeling question of selecting weights for the objective functions where we use a simulated annealing algorithm to determine these weights for each model. The inverse plans obtained via optimization models are compared against each other and against the clinical plans. The three inverse planning models can all yield optimal treatment plans in a reasonable amount of time and the treatment plans obtained by these models meet or exceed clinical guidelines while displaying high conformity.