On the isotropic distribution of beam directions

Lech Papiez, Xiaoyi Lu, Mark Langer

Research output: Contribution to journalArticle

3 Scopus citations


The notion of an isotropic distribution of beam directions for three-dimensional radiotherapy is discussed. It has been thought that isotropic beam directions minimize the delivery of high dose to tissue outside the target volume. This paper demonstrates that beam arrangements that may be called most isotropic do not necessarily lead to the minimization of the high dose volume lying outside the target. This unexpected finding is related to results on abstract problems of the most symmetric distributions of finite number of points on the surface of the sphere, and optimal packings of circles on the surface of a sphere.

Original languageEnglish (US)
Pages (from-to)991-1000
Number of pages10
JournalMathematical Models and Methods in Applied Sciences
Issue number7
StatePublished - Oct 2000

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics

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