Optimizing Gamma Knife Radiosurgery through Mathematical Morphology Jeffrey Overbey Angela Kolve Nathan Hirtz What is Gamma Knife Radiosurgery? Used to treat brain tumors. Delivers a high dose of ionizing radiation from 201 cobalt-60 beams. These beams intersect in an approximately spherical shape. Each dose of radiation is called a shot. What is Gamma Knife Radiosurgery? Beams emanate from collimator helmet. 4 interchangeable outer helmets. Beam sizes are 4, 8, 14, or 18mm in diameter. The target point, or center of the shot, is called the isocenter. http://www.mc.uky.edu/gammaknife/images/gdraw.jpg What is Gamma Knife Radiosurgery? The “edge” of each shot is called the 50% isodose line (50% IDL). Beyond the 50% IDL, the radiation level is less than 50% of that at the isocenter, and is not considered damaging. http://w3.uokhsc.edu/neurosurgery/gamma/gamkni2.jpg What is Gamma Knife Radiosurgery? http://www.ucsf.edu/gammakf/lgk_cutout2.jpg http://www.erheadquarters.com/episodes/8/ images/allinhead2.jpg The Problem Given a volume, find the most optimal method for arranging spheres of 4, 8, 14, and 18mm in diameter given the following conditions: At least 90% of the volume is occupied. No spheres overlap. No spheres protrude outside the target volume. Mathematical Morphology and Skeletonization Morphology is a field of study with applications in computer vision, handwriting recognition, and image processing. Skeletonization is a morphological process that reduces an image to its most basic linear structure. Skeletonization http://www.cee.hw.ac.uk/hipr/html/skeleton.html Skeletonization http://www.esiee.fr/~coupriem/Sdi/resources/saha3_SC.gif Our Algorithms The Formula and Its Graph 0.7717657102 – 0.04046790807x + 0.2693164541y z= 1 – 0.1580097209 ln x – 9.032235572 ln y x = number of shots y = percentage treated z = preference value Analysis of the Model Limitations The shapes of the shots are not perfectly spherical. The formula is based on a certain set of preferences. Analysis of the Model Benefits At least 90% of the target volume is covered. Largely confines untreated tissue to a small area. Overlapping areas of strong radiation from 2 or more shots is avoided. Represents a compromise between minimum number of shots and area of target volume covered.
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