Resolution-Complete Inverse Treatment Planning in Radiosurgery

Treatment planning in radiosurgery and radiation therapy involves a large number of medical and technical constraints. The main technical constraints stem from the gantry kinematics and the type of collimator available. The gantry kinematics (i.e. number and spatial arrangement of movable joint axes) determines the type of motion which can be performed by the therapeutic beam. The collimator determines the shape of the beam. We describe a new method for treatment planning which relies on a hardwareindependent intermediate treatment plan. This abstract plan is computed as an inverse plan, namely a plan, for which it can be decided via complete methods whether the given constraints can be satis ed. The intermediate plan does not take into account speci c hardware requirements. Instead, we show that the plan computed for this intermediate layer can be resolved into executable plans for common systems. In particular, it is shown how the generated intermediate plans can be resolved into minimal-time plans for both jaw collimator systems and multi-leaf collimators. Interestingly, this computation of minimum time paths is possible in a complete way based on the Gilmore-Gomory algorithm. Here (low) polynomial computing time can be achieved, which is not possible for the original application of the Gilmore-Gomory algorithm. The described planning method allows for transparent and uniform inverse planning. Completeness properties with respect to satis ability of medical constraints and minimum-time paths are a further bene t of this new method.