# Optimizing Gamma Knife Radiosurg by pengxiang

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```									Optimizing Gamma Knife Radiosurgery
through
Mathematical Morphology

Jeffrey Overbey
Angela Kolve
Nathan Hirtz
What is Gamma Knife

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
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
The “edge” of each
shot is called the 50%
isodose line (50%
IDL).
Beyond the 50% IDL,
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

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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