Annals of Operations Research

, Volume 119, Issue 1, pp 247–260

Radiosurgery Treatment Planning via Nonlinear Programming

  • Michael C. Ferris
  • Jinho Lim
  • David M. Shepard

DOI: 10.1023/A:1022951027498

Cite this article as:
Ferris, M.C., Lim, J. & Shepard, D.M. Annals of Operations Research (2003) 119: 247. doi:10.1023/A:1022951027498


The Gamma Knife is a highly specialized treatment unit that provides 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 radiation. The treatment planning process attempts to cover the tumor with sufficient dosage without overdosing normal tissue or surrounding sensitive structures. An optimization problem is formulated that determines where to center the shots, for how long to expose each shot on the target, and what size focussing helmets should be used. We outline a new approach that models the dose distribution nonlinearly, and uses a smoothing approach to treat discrete problem choices. The resulting nonlinear program is not convex and several heuristic approaches 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.

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Michael C. Ferris
    • 1
  • Jinho Lim
    • 2
  • David M. Shepard
    • 3
  1. 1.Computer Sciences DepartmentUniversity of WisconsinMadisonUSA
  2. 2.Department of Industrial EngineeringUniversity of WisconsinMadisonUSA
  3. 3.Department of Radiation OncologyUniversity of Maryland School of MedicineBaltimoreUSA