Decomposition of integer matrices and multileaf collimator sequencing
نویسندگان
چکیده
منابع مشابه
Decomposition of integer matrices and multileaf collimator sequencing
In this paper we consider the problem of decomposing an integer matrix into a weighted sum of binary matrices that have the strict consecutive ones property. This problem is motivated by an application in cancer radiotherapy planning, namely the sequencing of multileaf collimators to realize a given intensity matrix. In addition we also mention another application in the design of public transp...
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An important method in cancer treatment is the use of high energetic radiation. In order to kill tumor cells the patient is exposed to radiation that is delivered by a linear accelerator whose beam head can be rotated about the treatment couch. Inevitably the healthy tissue surrounding the tumor is also exposed to some radiation. So the problem arises to arrange the treatment in a way such that...
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The multileaf collimator sequencing problem is an important component of the effective delivery of intensity modulated radiotherapy used in the treatment of cancer. The problem can be formulated as finding a decomposition of an integer matrix into a weighted sequence of binary matrices whose rows satisfy a consecutive ones property. In this paper we extend the state-of-the-art optimisation meth...
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We consider a problem dealing with the efficient delivery of Intensity Modulated Radiation Therapy (IMRT) to individual patients. IMRT treatment planning is usually performed in three phases. The first phase determines a set of beam angles through which radiation is delivered, followed by a second phase that determines an optimal radiation intensity profile (or fluence map). This intensity prof...
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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 mat...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2005
ISSN: 0166-218X
DOI: 10.1016/j.dam.2005.04.008