Iterative regularization in intensity‐modulated radiation therapy optimization

A common way to solve intensity‐modulated radiation therapy (IMRT) optimization problems is to use a beamlet‐based approach. The approach is usually employed in a three‐step manner: first a beamlet‐weight optimization problem is solved, then the fluence profiles are converted into step‐and‐shoot segments, and finally postoptimization of the segment weights is performed. A drawback of beamlet‐based approaches is that beamlet‐weight optimization problems are ill‐conditioned and have to be regularized in order to produce smooth fluence profiles that are suitable for conversion. The purpose of this paper is twofold: first, to explain the suitability of solving beamlet‐based IMRT problems by a BFGS quasi‐Newton sequential quadratic programming method with diagonal initial Hessian estimate, and second, to empirically show that beamlet‐weight optimization problems should be solved in relatively few iterations when using this optimization method. The explanation of the suitability is based on viewing the optimization method as an iterative regularization method. In iterative regularization, the optimization problem is solved approximately by iterating long enough to obtain a solution close to the optimal one, but terminating before too much noise occurs. Iterative regularization requires an optimization method that initially proceeds in smooth directions and makes rapid initial progress. Solving ten beamlet‐based IMRT problems with dose‐volume objectives and bounds on the beamlet‐weights, we find that the considered optimization method fulfills the requirements for performing iterative regularization. After segment‐weight optimization, the treatments obtained using 35 beamlet‐weight iterations outperform the treatments obtained using 100 beamlet‐weight iterations, both in terms of objective value and of target uniformity. We conclude that iterating too long may in fact deteriorate the quality of the deliverable plan.