In this article, we study the modulation of intensity matrices arising in cancer radiation therapy using multileaf collimators. This problem can be formulated by decomposing a given m n integer matrix into a positive linear combination of (0, 1) matrices with the strict consecutive 1’s property in rows. We consider a special case in which no technical constraints have to be taken into account. ...

We consider the problem of decomposing Intensity Modulated Radiation Therapy (IMRT) fluence maps using rectangular apertures. A fluence map can be represented as an integer matrix, which denotes the intensity profile to be delivered to a patient through a given beam angle. We consider IMRT treatment machinery that can form rectangular apertures using conventional jaws, and hence, do not need so...

Intensity-modulated radiation therapy (IMRT) requires the determination of the appropriate multileaf collimator settings to deliver an intensity map. The purpose of this work was to attempt to reduce the number of segments required for IMRT delivery and the number of monitor units required to deliver an intensity map. An intensity map may be written as a matrix. Leaf sequencing was formulated a...

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...

With the rapid progress of tissue engineering and regenerative medicine, the cell-friendly construction of a 3D extracellular matrix in a precisely controlled manner is needed. This biomimicry of the native extracellular matrix replicates major aspects of the native cellular microenvironment. Herein, we design a polyethylene glycol (PEG) based hydrogel combined with caging chemistry, which coul...

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...