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IE521 Advanced Optimization
Lecture 4
Dr. Zeliha Akc
¸a
October 2011
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I
Bertsimas 2.3  2.7
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Problem of the Week
RADIATION TREATMENT
I
Radiation therapy is a technique used in the treatment of most cancer.
I
Radiation is depositted to the part of the body with tumor. Doctors decide the
amount radiation required in the treatment.
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Objective is to give the prescribed amount of radiation to the cancerous regions
(tumors) and minimum amount of radiation to noncancerous tissues.
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Radiation affects the DNA’s of cells and reduces their ability to multiply.
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Cancerous cells are more susceptible to radiation.
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Radiation is given via beams with different angles and intensity.
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Beams affect the entry regions the most. While the distance to entry increases
the affect of radiation reduces.
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The design of radiation therapy is very delicate.
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Aim is to select the best set of beams with right intensity in order to give the best
possible way of prescribed amount of radiation to tumor.
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View Full Document Radiation Treatment
I
The radiation machine deliver beams with different angles to the
patients body.
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Exposure time of the beam is determined and is called as the
intensity.
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2 main techniques are used: conformal therapy (in the shape of
tumor), intensitymodulated radiation therapy (region divided into
small rectangles).
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Region is divided into small rectangles that are called voxel.
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Construct intensity matrix for each voxel.
A
ij
of
A
: Weight of beam
j
to be applied to voxel
i
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Optimization in Radiation Therapy
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Constructing dose matrix is to plan the theatment in backwards.
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3 different voxels: Target
T
, critical
C
, normal
N
.
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For each voxel, objective function coefﬁcients are determined:
c
T
,
c
N
,
c
C
.
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Big penalties may be set for normal voxels.
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View Full Document Radyo Terapi LP Modeli
Decision Variables:
w
=
weight of beam vector
x
T
=
dose for target voxels
x
N
=
dose for normal voxels
x
C
=
dose for critical voxels
Parameters:
x
U
T
=
dose upper bnd for target voxels
x
L
T
=
dose lower bnd for target voxels
x
U
N
=
dose upper bnd for normal voxels
x
U
C
=
dose upper bnd for critical voxels
A
T
,
A
N
,
A
C
=
Dose matrices
min
w
,
x
T
,
x
N
,
x
C
C
T
N
x
N
s.t.
x
T
=
A
T w
x
N
=
A
N w
x
C
=
A
Cw
x
N
≤
x
U
N
x
C
≤
x
U
C
x
L
T
≤
x
T
≤
x
U
T
w
≥
0
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Optimization in Radiation Therapy
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To kill cancerous cells in a tumor radiation therapy is used.
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Radiation is applied to 3 regions.
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This note was uploaded on 01/09/2012 for the course IE 521 taught by Professor Zelihaakça during the Fall '11 term at Fatih Üniversitesi.
 Fall '11
 ZelihaAkça
 Optimization

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