A graph-searching method for MLC leaf sequencing under constraints

Abstract

A new leaf-sequencing algorithm for step-and-shoot IMRT that is based on a graph-searching technique is described. An iterative process guided by a quantitative measure for the complexity of the initial or residual intensity pattern is used to identify the field segments shaped by a multileaf collimator (MLC). Given a user selected number of intensity levels, the algorithm searches deliverable segment candidates considering all intensity levels and two collimator positions separated by 90 degrees. The candidates for each intensity level are obtained as the least number of segments to cover the areas with equal or higher intensity. The shape of a deliverable segment is adjusted by leaving out certain beam elements for later delivery if this results in a simpler residual intensity pattern and the segment is still deliverable. For a MLC design that does not allow leaf interdigitation, it is initially assumed that a single segment cannot cover two disjoined areas. Among all candidates the segment with the greatest reduction of the complexity of the residual intensity distribution is chosen for the current step of iteration. The iterative process generates a set of deliverable segments of simply connected areas. These segments are combined later under specific MLC constraints. Different orders of segment combination are considered for minimizing the beam-on time. The final segments are sequenced to minimize the leaf travel. This algorithm has been tested using randomly generated intensity distributions and clinical cases for the Varian, Siemens, and Elekta MLC systems. The results show that as the number of intensity levels is increased, the numbers of segments and MUs increase only modestly. Using two collimator angles results in decreases in the required number of segments and the number of monitor units that can be as much as 20%.