A new algorithm for optimal multileaf collimator field segmentation

Abstract

We present a new efficient leaf sequencing algorithm for the generation of intensity maps by a nonnegative combination of segments. Intensity maps describe the intensity modulation of beams in radiotherapy. We only study the static case (step and shoot). We exactly optimize the total number of monitor units and heuristically optimize the number of segments. We present a short exact proof for a formula giving the smallest total number of monitor units and describe a class of algorithms yielding this minimal value. A special member of this class provides a solution with a very small number of segments.

Integrating column generation in a method to compute a discrete representation of the non-dominated set of multi-objective linear programmes

“…We observe that, as the number of generated columns increases, the computation effort for solving RMP-RNBISub increases as well. We apply the segmentation algorithm by Engel (2005) to the optimal intensity patterns generated by the standard RNBI method. The results show that the intensity patterns (after discretisation by rounding to integers) can be reproduced with an average Table 2, the total monitor units for delivering the segmented patterns (an average of 408.8 MUs) is much higher than that of the segment patterns generated by column generation (an average of 76.7 and 123.8 MUs for CG-40 and CG-100, respectively).…”

Decomposition of matrices and static multileaf collimators: a survey

“…Thus we conclude that Xia and Verhey (1998) is inferior to the other algorithms. Baatar et al (2005) and Engel (2005) are roughly equal in speed. Both guarantee optimal DT , the latter performs better in terms of DC, finding the best value for all instances.…”

“…In combination with Lemma 2.1, this yields the optimality of their solution algorithm MULTIPAIR for the unconstrained DT problem, which is, again, a validity proof of the sweep algorithm. The same bounding argument as in Kamath et al (2003) is used by Engel (2005) in his TNMU algorithm (total number of monitor units). Instead of using trajectories, he bases his work directly on the M × (N + 1) difference matrix…”

“…Problem Remarks Baatar et al (2005) unconstrained guarantees min DT , heuristic for DC Engel (2005) gnconstrained guarantees min DT , heuristic for DC Xia and Verhey (1998) unconstrained heuristic for DC Baatar et al (2005) constrained guarantees min DT , heuristic for DC Kalinowski (2005) constrained guarantees min DT , heuristic for DC Siochi (1999) constrained guarantees min DT , heuristic for T T Xia and Verhey (1998) constrained heuristic for DC Table 1: List of algorithms tested.…”

“…Gunawardena et al (2006) propose a difference-matrix metaheuristic to obtain solutions with small DC as well as small DT values. The metaheuristsic uses multiple start local search with a heuristic that sequentially extracts segments Y k based on results of Engel (2005). They consider multiple constraints on the segments, including interleaf and innerleaf motion constraints.…”