In IMRT; the clinician specifies certain characteristics of the desired dose distribution by introducing objective functions for the tumor and for the critical organs close to the tumor. A discretization of the incident beams and of the treatment volume of the patient is performed and an optimization problem is formulated. In general; the IMRT problem is large-scale and has a non-convex nature; often with linear and non-linear constraints. In this study we investigate how the Hessian affects the optimization performance for a quasi-Newton algorithm used in a commercial treatment planning system. Currently; the initial Hessian fed into the algorithm is diagonal. The influence of including more accurate curvature information; represented as off-diagonal elements; is explored for three patient cases.
A more accurate initial Hessian results in a much faster progress of optimization than when using a diagonal initial Hessian. Furthermore; the optimal beam profiles differ significantly; with an accurate Hessian they are very jagged compared to the smooth profiles obtained with a diagonal Hessian. Jagged profiles are; in general; not desirable since they are harder to deliver; but for a certain class of IMRT problems they are preferable. The results also indicate that the IMRT problem is an ill-posed inverse problem in the sense that very different fluence profiles can produce almost identical dose distributions.