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Now, let's take a look at
a full example of a case.

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This is a head and neck
example, and the CT scans

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are shown on the right.

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There are a total
of 132,878 voxels.

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The target, or tumor,
has 9,777 voxels.

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There are five
critical structures

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that we want to minimize the
dose to-- the spinal cord,

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the brain, the brain
stem, the parotid glands,

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and the mandible or jaw.

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We're using five
beams, and each beam

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is composed of
about 60 beamlets.

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In total, there
are 328 beamlets.

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In this example, we want
the dose to the whole tumor

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to be between 70 and 77 gray.

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The spinal cord dose should
be no more than 45 gray,

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since significant damage to
any voxel in the spinal cord

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will result in loss of function.

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The brain stem dose should
be no more than 54 gray,

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and the mandible dose should
be no more than 70 gray.

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The average parotid gland dose
should be at most 26 gray.

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This constraint is
a little different,

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since the parotid gland
is a parallel structure.

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Significant damage
to any one voxel

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does not jeopardize function
of the entire organ.

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So what is our
optimization problem now?

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Again, our decisions are the
intensities of the beamlets.

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Our objective is to minimize the
total dose to healthy tissue.

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Our constraints are
limits on the tumor dose

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and upper bounds for the spinal
cord, brain stem, and mandible.

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We also have a constraint to
limit the average parotid dose

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to 26 gray.

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Lastly, all of our intensities,
or decision variables,

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should be non-negative.

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We solved this
optimization problem,

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and this plot shows the results.

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On the x-axis is the
dose, in gray, and on

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the y-axis is the
fraction of voxels

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that received that
dose or higher.

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Each line corresponds to
a different structure.

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We can see that for the tumor,
which is shown as the red line,

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100% of the voxels get a dose
of 70 gray, and 0% of the voxels

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get a dose of more than 77 gray.

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This is what our
constraint specified.

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While none of the
critical structures

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are getting very
high doses, it looks

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like the mandible, which
is shown as the blue line,

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is receiving the highest
dose of the healthy organs.

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In the next video, we'll
explore different solutions

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and the shadow prices
of our constraints.