The Gamma Knife radiosurgery treatment involves geometrically mapping for covering the tumor area in three dimensions so that the gamma rays can provide precise treatment to the affected area. The entire process has to be accurate in order to prevent the exposure of the gamma rays to the neighboring healthy tissues. When the tumor shape is irregular, it is difficult to ensure the coverage of the tumor region. We present, in this paper, a new approach to fit spheres in a bounded region based on maximum distance. Our proposed method for automating the gamma knife surgery planning is by using a geometrically-based Euclidean sphere packing optimization method. We implement our algorithm in Slicer3D using Python libraries. Experiments show that our algorithm produces reasonable dense packing of different irregular shapes.

Cancer treatment planning using SRS (Stereotactic Radio Surgery) uses approximate sphere packing algorithms by guiding multiple beams to treat a set of spherical cancerous regions. Usually volume data from CT/MRI scans is used to identify the cancerous region as set of voxels. Computationally optimal Sphere Packing is proven NP-Complete. So usually approximate sphere packing algorithms are used to find a set of non-intersecting spheres inside the region of interest (ROI). We implemented a greedy strategy where largest Euclidean spheres are found using distance transformation algorithm. The voxels inside of the largest Euclidean sphere are then subtracted from the ROI, and the next Euclidean sphere is found again from the subtracted volume. The process continues iteratively until we find the desired coverage. In this paper, our goal is to analyze the rotational invariance properties of resulting sphere-packing when the shape of the ROI is rotated. If our sphere packing algorithm generate spheres of identical radius before and after the rotation, then our algorithm could also be used for matching and tracking similar shapes across data sets of multiple patients. In this paper, we describe unique shape descriptors to show that our sphere packing algorithm has high degree of rotation invariance within ±epsilon. We estimate the value of epsilon in the data set for 30 patients by implementing these ideas using Slicer3D™ platform.