title: Optimization of rotational radiotherapy treatment planning.
abstract: OBJECTIVE
  Rotational therapy treatment planning for rotationally symmetric geometry of tumor and healthy tissue provides an important example of testing various approaches to optimizing dose distributions for therapeutic x-ray irradiations. In this article, dose distribution optimization is formulated as a variational problem. This problem is solved analytically and numerically.
  
  
  METHODS
  The classical Lagrange method is used to derive equations and inequalities that give necessary conditions for minimizing the mean-square deviation between the ideal dose distribution and the achievable dose distribution. The solution of the resulting integral equation with Cauchy kernel is used to derive analytical formulas for the minimizing irradiation intensity function.
  
  
  RESULTS
  The solutions are evaluated numerically and the graphs of the minimizing intensity functions and the corresponding dose distributions are presented.
  
  
  CONCLUSIONS
  The optimal solutions obtained using the mean-square criterion lead to significant underdosage in some areas of the tumor volume. Possible solutions to this shortcoming are investigated and medically more appropriate criteria for optimization are proposed for future investigations.
authors.affiliation: Indiana University Hospital, School of Medicine, Department of Radiation Oncology, Indianapolis 46202-5289, USA.
authors.forename: V
authors.initials: V
authors.lastname: Tulovsky
authors.forename: M
authors.initials: M
authors.lastname: Ringor
authors.forename: L
authors.initials: L
authors.lastname: Papiez
mesh_terms: D006801:Humans; D008433:Mathematics; D018787:Radiation Oncology; D011853:Radiobiology; D011874:Radiometry; D011879:Radiotherapy Dosage