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In the previous video, we saw
that the mandible, or jawbone,

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received the highest dose out of
all of the critical structures.

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The mean mandible
dose was 11.3 gray.

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So how can we reduce this?

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One approach is to modify
our objective function.

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Our current objective
is to minimize

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the sum of the total dose
to each critical structure.

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So we're minimizing the sum of
the total dose to the brain,

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plus the total dose
to the brain stem,

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plus a total dose
to the spinal cord,

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plus the total dose
to the parotid glands,

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plus the total dose
to the mandible.

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We could instead
change our objective

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to make the total dose to
the mandible more important.

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This can be done by weighting
the term for the mandible.

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By giving the mandible
dose a weight of 10,

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the total dose to the mandible
becomes 10 times more important

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in our objective
than the total dose

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to the other
critical structures.

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If we solve our problem
with this new objective,

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we get the solution
shown in this figure.

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The dose to the tumor, shown as
the red line, does not change.

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It still stays within the
constraints we've defined.

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For each of the
critical structures,

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the solution with the
previous objective

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is shown as a dotted
line, and the new solution

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with the weighted objective
is shown as a solid line.

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We can see that the dose to
the mandible, shown in blue,

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has significantly
decreased by adding

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a weight in the objective.

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However, the dose to
other critical structures

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has increased, especially to the
parotid glands, shown in black,

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and to the spinal
cord, shown in green.

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This shows how you can
modify the objective

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to capture different trade-offs
that might be desirable

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to different decision-makers
or for different patients.

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Another way to
explore trade-offs

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is to modify the constraints.

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For example, by relaxing
the mandible maximum dose

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constraint or by allowing the
maximum dose to the mandible

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to be higher, we may improve
our total healthy tissue dose.

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We would like to know how
much the objective changes

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for different constraints.

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This can be answered by
looking at the shadow

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prices of the constraints.

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Recall that we have a constraint
limiting the total dose

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for each voxel in each
critical structure.

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This table shows the highest
shadow price for any one voxel

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in each critical structure.

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The parotid glands and the brain
stem have shadow prices of 0.

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This means that we're not
even giving the maximum amount

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of radiation allowed
to these structures,

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so modifying the constraints
is not beneficial.

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The spinal cord has a
shadow price of 96.911.

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This means that by
increasing the radiation

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to one voxel of the
spinal cord by one unit,

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we can decrease
the total radiation

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to other critical
structures by 96.9 units.

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The mandible has the highest
shadow price of 7,399.72.

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So if a slight increase in the
mandible dose to a single voxel

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is acceptable, the total healthy
tissue dose can be reduced.

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Keep in mind that this
is the total reduction

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across all voxels
in the objective.

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We've seen in this video that by
modifying the formulation, both

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the objective and
the constraints,

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we can explore different
trade-offs in our problem.