A constrained least‐squares optimization method for external beam radiation therapy treatment planning

A method has been developed to optimize the selection of beam weights for external beam radiation therapy treatment planning. This method uses a matrix transformation method to achieve a least-squares fit to doses at preselected points in a target volume. This method is more general than the conventional least-squares method in that it allows one to incorporate as constraints maximum allowable doses delivered to critical organs, as well as the requirement that all beam weights be non-negative. A computer algorithm DOSEOPT has been written which takes a matrix of doses to various points from beams whose field sizes and orientations have been predetermined, and performs the constrained least-squares fit to desired doses in the target volume and maximum doses to critical organs. Implementation of this algorithm and its application to several cases are discussed.