ABSTRACT
An MLC consists of metal leaves which can block the radiation. To each row of the intensity matrix there is associated a pair of leaves, a left leaf and a right leaf that can be moved in the direction of the row. The leaf positions of the collimators were modeled by certain 0-1-matrices called segments, where a 1-entry corresponds to a bixel receiving radiation and a 0-entry to a bixel covered by a leaf. This problem could be formulated as 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. The mathematical problem to solve was formulated by the following linear equation:
(1)
For medical and practical reasons, one aimed at minimizing the total irradiation time and the number of segments, and the segmentation problem could be formulated as follows:
Instance: A nonnegative integer m*n-matrix A. Problem: Find a segmentation such that: Total number of monitor unit (TNMU):
min . 1
The number of segments (NS): →k min . However, it was proved that the minimization of
the number of homogeneous fields that are needed is an NP-complete problem[1, 13]. That means no single algorithm is the most efficient for all clinical cases or intensity maps [14]. This suggests that it is desirable to have multiple algorithms available in the ARTS which will search through all embedded algorithms automatically and find the most efficient delivery sequence for a given intensity matrix[4, 15].
