Optimization of leaf positions when shaping a radiation field with a multileaf collimator

Computer-controlled multileaf collimators are receiving increasing acceptance for clinical use in radiation therapy due to their efficiency in shaping radiation fields. Because of the physical leaf width of the multileaf collimator, a smooth field contour prescribed by a physician is approximated by a staircase-shaped field boundary. The point of intersection with the prescribed field contour determines the error of the approximation and may affect the outcome of the treatment. This article provides analytically optimized solutions for leaf positioning based on two different geometric object functions.