Optimizing Gamma Knife Radiosurgery through Mathematical Morphology

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Optimizing Gamma Knife Radiosurgery through
Mathematical Morphology

• Jeffrey Overbey
• Angela Kolve
• Nathan Hirtz

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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.

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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
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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.jp
g
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What is Gamma Knife Radiosurgery?
http//www.ucsf.edu/gammakf/lgk_cutout2.jpg
http//www.erheadquarters.com/episodes/8/images/a
llinhead2.jpg
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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.

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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.

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Skeletonization
http//www.cee.hw.ac.uk/hipr/html/skeleton.html
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Skeletonization
http//www.esiee.fr/coupriem/Sdi/resources/saha3_
SC.gif
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Our Algorithms
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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
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Analysis of the Model

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

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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.