Gamma Knife® Perfexion™ (PFX) is used for delivering radiosurgery plans to treat lesions and tumours in the brain by means of selectively ionizing the tissue with high-energy beams of radiation. An important component of designing PFX treatments is the selection of points in the target structure at which to focus the radiation, called isocentres. This study applies skeletonization methods to select such isocentres. Our skeletonization technique identifies clusters of each target structure’s skeleton using distance coding methods. A user-defined number of isocentre locations are chosen from the skeletal clusters. The isocentres resulting from this approach are used as input to a sector duration optimization model that determines the optimal shot shapes and intensities for the radiation deposited at each isocentre. The results for seven clinical cases are presented. For each case, target structure dose and conformity meet clinical radiosurgery guidelines, while brainstem dose is kept to acceptable levels and other healthy organs are also spared.