Approximated multileaf collimator field segmentation

In intensity-modulated radiation therapy the aim is to realize given intensity distributions as a superposition of differently shaped fields. Multileaf collimators are used for field shaping. This segmentation task leads to discrete optimization problems, that are considered in this dissertation. A variety of algorithms for exact and approximated segmentation, for different objective functions and various technical as well as dosimetric constraints are developed

Approximated MLC shape matrix decomposition with interleaf collision constraint

Shape matrix decomposition is a subproblem in radiation therapy planning. A given fluence matrix A has to be decomposed into a sum of shape matrices corresponding to homogeneous fields that can be shaped by a multileaf collimator (MLC). We solve the problem of minimizing the delivery time for an approximation of A satisfying certain prescribed bounds, under the additional condition that the used MLC requires the interleaf collision constraint

Binary matrix decompositions without tongue-and-groove underdosage for radiation therapy planning

In the present paper we consider a particular case of the segmentation problem arising in the elaboration of radiation therapy plans. This problem consists in decomposing an integer matrix A into a nonnegative integer linear combination of some particular binary matrices called segments which represent fields that are deliverable with a multileaf collimator. For the radiation therapy context, it is desirable to find a decomposition that minimizes the beam-on time, that is the sum of the coefficients of the decomposition. Here we investigate a variant of this minimization problem with an additional constraint on the segments, called the tongue-and-groove constraint. Although this minimization problem under the condition that the used segments have to respect the tongue-and-groove constraint has already been studied, the complexity of it is still unknown. Here we prove that in the particular case where A is a binary matrix this problem is polynomially solvable. We provide a polynomial procedure that finds such a decomposition with minimal beam-on time. Furthermore, we show that the beam-on time of an optimal decomposition (but not the segmentation itself) can be found by determining the chromatic number of a related perfect graph

Approximated MLC shape matrix decomposition with interleaf collision constraint

Shape matrix decomposition is a subproblem in radiation therapy planning. A given fluence matrix A has to be decomposed into a sum of shape matrices corresponding to homogeneous fields that can be shaped by a multileaf collimator (MLC). We solve the problem of minimizing the delivery time for an approximation of A satisfying certain prescribed bounds, under the additional condition that the used MLC requires the interleaf collision constraint

A closest vector problem arising in radiation therapy planning

info:eu-repo/semantics/publishe

A closest vector problem arising in radiation therapy planning

In this paper we consider the following closest vector problem. We are given a set of 0-1 vectors, the generators, an integer vector, the target vector, and a nonnegative integer C. Among all vectors that can be written as nonnegative integer linear combinations of the generators, we seek a vector whose ℓ ∞-distance to the target vector does not exceed C, and whose ℓ 1-distance to the target vector is minimum. First, we observe that the problem can be solved in polynomial time provided the generators form a totally unimodular matrix. Second, we prove that this problem is NP-hard to approximate within an O(d) additive error, where d denotes the dimension of the ambient vector space. Third, we obtain a polynomial time algorithm that either proves that the given instance has no feasible solution, or returns a vector whose ℓ ∞-distance to the target vector is within an O(d√lnd) additive error of C and whose ℓ 1-distance to the target vector is within an O(d√dlnd) additive error of the optimum. This is achieved by randomly rounding an optimal solution to a natural LP relaxation. The closest vector problem arises in the elaboration of radiation therapy plans. In this context, the target is a nonnegative integer matrix and the generators are certain 0-1 matrices whose rows satisfy the consecutive ones property. Here we begin by considering the version of the problem in which the set of generators comprises all those matrices that have on each nonzero row a number of ones that is at least a certain constant. This set of generators encodes the so-called minimum separation constraint. We conclude by giving further results on the approximability of the problem in the context of radiation therapy. © 2010 Springer Science+Business Media, LLC.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Bevacizumab and platinum-based combinations for recurrent ovarian cancer: a randomised, open-label, phase 3 trial

International audienceState-of-the art therapy for recurrent ovarian cancer suitable for platinum-based re-treatment includes bevacizumab-containing combinations (eg, bevacizumab combined with carboplatin-paclitaxel or carboplatin-gemcitabine) or the most active non-bevacizumab regimen: carboplatin-pegylated liposomal doxorubicin. The aim of this head-to-head trial was to compare a standard bevacizumab-containing regimen versus carboplatin-pegylated liposomal doxorubicin combined with bevacizumab