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In this lecture, we'll discuss
how linear optimization

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is used to design radiation
therapy treatments for cancer

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patients.

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Cancer is the
second leading cause

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of death in the United States,
second only to heart disease.

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There were an estimated 570,000
deaths in 2013 due to cancer.

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Additionally, over 1.6
million new cases of cancer

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will be diagnosed in the
United States in 2013.

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These trends are also
seen throughout the world.

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Worldwide, cancer is a
leading cause of death,

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with 8.2 million deaths in 2012.

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Cancer can be treated
using radiation therapy,

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where beams of
high-energy photons

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are fired into the patient
to kill cancerous cells.

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This is a very common
form of treatment

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for many types of cancers,
and in the United States,

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about half of all
cancer patients

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undergo some form of
radiation therapy.

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Radiation therapy has a history
going back to the late 1800s.

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X-rays were discovered by
Wilhelm Rontgen in 1895,

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who was later awarded the
first Nobel Prize in Physics.

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Shortly after the
discovery, X-rays

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started being used to
treat skin cancers.

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This image shows an x-ray
of Rontgen's wife's hand.

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You can see the
bones in her hand

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as well as her wedding
ring on her finger.

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A few years later
in 1898, radium

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was discovered by
Marie and Pierre Curie.

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They won the Nobel Prize
for this discovery in 1911.

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Radium started being used
to treat cancer, as well

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as other diseases.

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Later in the 1900s, the first
radiation delivery machines,

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called linear accelerators,
were developed.

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Then computed tomography, or CT
scans, were invented in 1971.

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These discoveries
led to the invention

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of Intensity Modulated
Radiation Therapy, or IMRT,

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in the early 1980s.

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The invention of
IMRT significantly

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improved the ability
of radiation therapy

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to target cancerous cells.

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To reach the tumor,
radiation passes

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through healthy tissue
and therefore damages

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both healthy and
cancerous tissue.

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This damage to
healthy tissue can

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lead to undesirable
side effects that

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reduce post-treatment
quality of life.

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For example, blistering
and burning of skin

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can occur because of the
damage to healthy skin cells.

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For this reason,
we want the dose

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to fit the tumor as
closely as possible

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to reduce the dose
to healthy tissue.

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This became possible with
the invention of IMRT.

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In IMRT, the intensity profile
of each beam is non-uniform.

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Before IMRT, each beam had
to have the same intensity,

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so the tumor could not
be targeted very well.

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But by using non-uniform
intensity profiles,

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the radiation dose can
better fit the tumor.

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Let's see what this looks like.

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In this image, we have
a person's body outlined

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in black, and then
the target, or tumor,

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and two critical
structures also outlined.

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We would like to maximize
the radiation to the target,

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while minimizing the
dose to healthy tissue,

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and especially to the
critical structures.

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Using traditional
radiation therapy,

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each of the three beams
has the same intensity

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throughout the beam.

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So to deliver enough
radiation to the tumor,

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we also have to deliver a
significant amount of radiation

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to the critical structures
and to other healthy tissue.

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But by using IMRT, we
can change the intensity

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throughout each beam
to make it non-uniform.

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Some pieces of
the beam will have

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a higher intensity than others.

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This allows us to deliver the
necessary amount of radiation

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to the tumor, while
minimizing the total radiation

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to healthy tissue, and thus,
the critical structures

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get significantly
less radiation.

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Each of the pieces of the beam
is referred to as a beamlet.

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So in IMRT, we
decide the intensity

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of each of the
beamlets so that we

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can target the
tumor with radiation

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while minimizing the
radiation to healthy tissue.

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So in designing
an IMRT treatment,

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the fundamental problem is
-- how should the beamlet

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intensities be selected to
deliver a therapeutic dose

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to the tumor and to minimize
damage to healthy tissue?

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This is the problem that
we'll address in this lecture,

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using linear optimization.