Three-dimensional optimization of treatment planning for gamma unit treatment system

During a treatment using the Leksell gamma unit, the physician and physicist need to determine a treatment plan by changing the parameters such as collimator sizes, the position of isocenters and isocenters' weights. This is a complex problem because the set of parameters is large, especially when targets are geometrically close to a critical structure. For this reason, we present here an optimization algorithm, namely the multiplier penalty method, to mathematically determine those parameters. Two cases are presented in this article: the first one is really planned by a physicist in a clinical treatment, and is redone in our optimization algorithm to show the effectiveness of this method; the second one is theoretical where a critical structure is placed close to the target volume. The results show that this method achieves an excellent conformation to the specified isodose curve with the contour of the target volume, allowing minimal damage to surrounding healthy tissue.