title: Maximizing the probability of satisfying the clinical goals in radiation therapy treatment planning under setup uncertainty.
abstract: OBJECTIVE
  This paper introduces a method that maximizes the probability of satisfying the clinical goals in intensity-modulated radiation therapy treatments subject to setup uncertainty.
  
  
  METHODS
  The authors perform robust optimization in which the clinical goals are constrained to be satisfied whenever the setup error falls within an uncertainty set. The shape of the uncertainty set is included as a variable in the optimization. The goal of the optimization is to modify the shape of the uncertainty set in order to maximize the probability that the setup error will fall within the modified set. Because the constraints enforce the clinical goals to be satisfied under all setup errors within the uncertainty set, this is equivalent to maximizing the probability of satisfying the clinical goals. This type of robust optimization is studied with respect to photon and proton therapy applied to a prostate case and compared to robust optimization using an a priori defined uncertainty set.
  
  
  RESULTS
  Slight reductions of the uncertainty sets resulted in plans that satisfied a larger number of clinical goals than optimization with respect to a priori defined uncertainty sets, both within the reduced uncertainty sets and within the a priori, nonreduced, uncertainty sets. For the prostate case, the plans taking reduced uncertainty sets into account satisfied 1.4 (photons) and 1.5 (protons) times as many clinical goals over the scenarios as the method taking a priori uncertainty sets into account.
  
  
  CONCLUSIONS
  Reducing the uncertainty sets enabled the optimization to find better solutions with respect to the errors within the reduced as well as the nonreduced uncertainty sets and thereby achieve higher probability of satisfying the clinical goals. This shows that asking for a little less in the optimization sometimes leads to better overall plan quality.
authors.affiliation: RaySearch Laboratories, Sveavägen 44, Stockholm SE-111 34, Sweden.
authors.forename: Albin
authors.initials: A
authors.lastname: Fredriksson
authors.affiliation: Optimization and Systems Theory, Department of Mathematics, KTH Royal Institute of Technology, Stockholm SE-100 44, Sweden.
authors.forename: Anders
authors.initials: A
authors.lastname: Forsgren
authors.affiliation: RaySearch Laboratories, Sveavägen 44, Stockholm SE-111 34, Sweden.
authors.forename: Björn
authors.initials: B
authors.lastname: Hårdemark
mesh_terms: D006801:Humans; D008297:Male; D017785:Photons / Q000627:therapeutic use; D011336:Probability; D011379:Prognosis; D011467:Prostate / Q000528:radiation effects; D061766:Proton Therapy / Q000379:methods; D011874:Radiometry / Q000379:methods; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D050397:Radiotherapy, Intensity-Modulated / Q000379:methods*; D016896:Treatment Outcome; D035501:Uncertainty; D011522:Protons
chemical_list: D011522:Protons