Decomposition of Matrices and Static Multileaf Collimators: A Survey

Technical Report, Reports in Wirtschaftsmathematik, Number 101, Technische Universität Kaiserslautern, Available at http://kluedo.ub.uni-kl.de/volltexte/2006/2033/, 2006

Authors

• Matthias Ehrgott
• Horst W. Hamacher
• Marc Nußbaum

Abstract

Multileaf Collimators (MLC) consist of (currently 20-100) pairs of movable metal leaves which are used to block radiation in Intensity Modulated Radiation Therapy (IMRT). The leaves modulate a uniform source of radiation to achieve given intensity profiles. The modulation process is modeled by the decomposition of a given non-negative integer matrix into a non-negative linear combination of matrices with the (strict) consecutive ones property. In this paper we review some results and algorithms which can be used to minimize the time a patient is exposed to radiation (corresponding to the sum of coefficients in the linear combination), the set-up time (corresponding to the number of matrices used in the linear combination), and other objectives which contribute to an improved radiation therapy.

BibTeX

 
@TechReport{ EhrgottEtAl:MultileafSurvey, 
   title = { Decomposition of Matrices and Static Multileaf Collimators: A Survey }, 
   author = { Matthias Ehrgott and Horst W. Hamacher and Marc Nußbaum },     
   series = { Reports in Wirtschaftsmathematik },  
   number = { 101 }, 
   institution = { Technische Universität Kaiserslautern },       
   note = { Available at http://kluedo.ub.uni-kl.de/volltexte/2006/2033/ },  
   year = 2006, 
} 

---

This publication belongs to the project DeNDeMA.