Radiosurgery Treatment Planning via Nonlinear Programming

Abstract

The Gamma Knife is a highly specialized treatment unit that pro- vides an advanced stereotactic approach to the treatment of tumors, vascular malformations, and pain disorders within the head. Inside a shielded treatment unit, multiple beams of radiation are focussed into an approximately spherical volume, generating a high dose shot of ra- diation. The treatment planning process determines where to center the shots, how long to expose them for, and what size focussing hel- mets should be used, in order to cover the target with su cient dosage without overdosing normal tissue or surrounding sensitive structures. We outline a new approach that models the dose distribution nonlin- early, and uses a smoothing approach to treat discrete problem choices. The resulting nonlinear program is not convex and several heuristic ap- proaches are used to improve solution time and quality. The overall approach is fast and reliable; we give several results obtained from use in a clinical setting.