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Optimizing Gamma Knife Radiosurgery through Mathematical Morphology

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.

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Optimizing Gamma Knife Radiosurgery through Mathematical Morphology

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  1. Optimizing Gamma Knife Radiosurgery through Mathematical Morphology Jeffrey Overbey Angela Kolve Nathan Hirtz

  2. 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.

  3. 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

  4. 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

  5. What is Gamma Knife Radiosurgery? http://www.ucsf.edu/gammakf/lgk_cutout2.jpg http://www.erheadquarters.com/episodes/8/images/allinhead2.jpg

  6. 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.

  7. Mathematical Morphologyand 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.

  8. Skeletonization http://www.cee.hw.ac.uk/hipr/html/skeleton.html

  9. Skeletonization http://www.esiee.fr/~coupriem/Sdi/resources/saha3_SC.gif

  10. Our Algorithms

  11. The Formula and Its Graph 0.7717657102 – 0.04046790807x + 0.2693164541y z = 1 – 0.1580097209 ln x – 9.032235572 ln y x = number of shotsy = percentage treatedz = preference value

  12. Analysis of the Model • Limitations • The shapes of the shots are not perfectly spherical. • The formula is based on a certain set of preferences.

  13. 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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