Decomposition of Matrices and Static Multileaf Collimators: A Survey

نویسندگان

  • Matthias Ehrgott
  • Horst W. Hamacher
  • Marc Nußbaum
چکیده

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.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The complexity of minimizing the number of shape matrices subject to minimal beam-on time in multileaf collimator field decomposition with bounded fluence

The use of multileaf collimators (MLCs) is a modern way to realize intensity modulated fields in radiotherapy. An important step in the treatment planning is the shape matrix decomposition: The desired fluence distribution, given by an integer matrix, has to be decomposed into a small number shape matrices, i.e. (0, 1)−matrices corresponding to the field shapes that can be delivered by the used...

متن کامل

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...

متن کامل

A new mathematical model for intensity matrix decomposition using multileaf collimator

Cancer is one of the major causes of death all over the globe and radiotherapy is considered one of its most effective treatment methods. Designing a radiotherapy treatment plan was done entirely manually in the past. RecentlyIntensity Modulated Radiation Therapy (IMRT) was introduced as a new technology with advanced medical equipmentin the recent years. IMRT provides the opportunity to delive...

متن کامل

Beam characteristic of P.E collimators Add-on multileaf collimator

  Introduction:    Multileaf collimators (MLCs) are computer-controlled devices which are Useful and cost-effective tools for conformal therapy and intensity modulation radiotherapy (IMRT). Nowadays MLCs are important and standard configuration of the new medical linear accelerators which are substitute of conventional Blocks and has eliminated the ...

متن کامل

Minimum Cardinality Matrix Decomposition into Consecutive-Ones Matrices: CP and IP Approaches

We consider the problem of decomposing an integer matrix into a positively weighted sum of binary matrices that have the consecutive-ones property. This problem is well-known and of practical relevance. It has an important application in cancer radiation therapy treatment planning: the sequencing of multileaf collimators to deliver a given radiation intensity matrix, representing (a component o...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2006