Selection of coplanar or noncoplanar beams using three-dimensional optimization based on maximum beam separation and...

The design of an appropriate set of multiple fixed fields to achieve a steep dose gradient at the tumor edge, with minimal normal tissue exposure, is a very difficult problem, since a virtually infinite number of possible beam orientations exists. In practice we have selected beams in an iterative and often time-consuming process. This work proposes an optimization method, based on geometric and dose elements, to effectively arrive at a set of beam orientations.

Beams are selected by minimizing a goal function including an angle function (beam separation for steep dose gradient at target edge) and a length function (related to normal tissue dose volume histogram). The relative importance of these two factors may be adjusted depending on the clinic situation. The model is flexible and can include case specific practical anatomic and physical considerations.

In extremely simple situations, the goal function yields results consistent with well-known analytical solutions. When applied to more complex clinical situations, it provides clinically reasonable solutions similar to those empirically developed by the clinician. The optimization process takes approximately 25 min on a UNIX workstation.

The optimization scheme provides a practical means for rapidly designing multiple field coplanar or noncoplanar treatments. It overcomes limitations in human three-dimensional visualization such as trying to visualize beam directions and keeping track of the hinge angle between beams while accounting for anatomic/machine constraints. In practice, it has been used as a starting point for physicians to make modifications, based on their clinical judgment.