|dc.description.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.||en