Realtime Optimization and Planning for Prostate Implants

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Real-time Optimization and Planning for Prostate
Implants

• Bruce Thomadsen
• University of Wisconsin
• Madison

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Conflict of Interest

• That the author knows of, he has no conflicts of
  interest for this presentation.

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Learning Objectives

• To understand the nature of optimization for
  interstitial implants.
• To understand the optimization process.
• To understand real-time optimization

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Limitations

• Will only discuss low dose-rate implants, since
  high dose-rate brachytherapy optimization for
  prostate is the same as for any HDR implant.

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Definitions

• Real time quickly enough that you dont feel
  youve waited too long.
• Optimization a process that produces the dose
  distribution you desire or close enough.

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As of Now

• Both definitions change with time.
• Real time depends on our expectations.
• Optimization depends on our desires and how
  close we feel that we need to get to it.

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More Careful Definition

• Real-time optimization is often used to mean
  real-time correction of dosimetry.
• Not optimization.
• Reassessment of the location of seeds already
  implanted compared to the desired locations.
• Allows replanning using whatever means were used
  in the first place.

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Real-time Reassessment

• Commercially, available with the Nucletron
  FIRST/SPOT ultrasound system, and near for
  VariSeed.
• Research using cone-beam CT.

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Real-time ReassessmentProcess

• Plan the case and start the implant.
• At intervals, re-image and correct the dose
  distribution for the actual location of the
  sources implanted.
• Replan where to place remaining sources to
  compensate for the real locations already used.

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Real-time ReassessmentLimitations

• Visualization of sources.
• Movement of sources by implantation of other
  sources.
• Time for replanning.

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Real-time ReassessmentLimitations

• Also, it is not clear that the reassessments
  actually goes through optimization rather than
  simply recalculation.

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Old QuestionOptimize or Uniformly Load

• 1. Uniform dose or hot center?
• 2. Uniform dose how uniform?
• at what price?

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Optimization Approaches

• Intellectual
• Rules
• Stochastic
• Deductive
• Heuristic
• Analytic

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Intellectual Optimization

• Trial and evaluation during treatment plan.
• Not particularly fast but certainly live time.
• Not what the organizer had in mind for me to
  address

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Rules

• For example, Manchester spherical implant rules
  (1/4 source in core 3/4 source on periphery)
• Again, not the topic of this talk

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Stochastic Optimization

• Examples simulated annealing or genetic
  algorithm
• Because they are iterative, they tend to take
  relatively long
• No guarantee that they find the optimum, only an
  adequate solution (if one exists, and maybe not
  the best).

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Objective Functions

• All stochastic, and many other optimization
  methods, use objective functions to evaluate how
  good a trial is.
• An example might be simply (dose desired-dose
  achieved).
• The goal would be to minimize this function.

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Objective Functions (cont.)

• Can also include doses to normal tissue,
  uniformity, etc.
• Example
• F(Dosedesired-Doseachieved)x
• (Dosenormal-Tolerance)/Homogeneity Factor

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Simulated Annealing

• Starts with a random placement of sources in the
  possible solutions.
• Evaluate the objective function.
• Change some source positions.
• Evaluate the objective function
• If the objective function is acceptable, stop.
• If the objective function is not, go back to 3,
  starting from the better distribution.

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Simulated Annealing (cont.)

• At first there can be big changes in source
  positions, either in number of sources or in the
  location of the sources.
• At each iteration, the size of the changes
  decreases.
• The process improves the value for the objective
  function, or at least doesnt make it worse.

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Simulated Annealing (cont.)

• Can nestle into a local minimum.
• To avoid that, sometimes in the middle a large
  change is allowed.

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Genetic Algorithms

• Start with an arbitrary distribution and make a
  continuous chain of the positions. Calculate the
  objective function.
• Pick another arbitrary distribution, and
  calculate the objective function.
• Mate the two distributions as on the next slide.

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Genetic Algorithm (cont.)
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Genetic Algorithm (cont.)

• Evaluate the objective functions,and pick the
  best two of the four, and mate them, or mate the
  best with a different random distribution.
• Continue iteratively, occasionally throwing in
  random changes (mutations).
• Stop when the objective function is adequate.

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Deductive (Numerical) Methods

• An example is Branch and Bound
• First the problem is solved with each possible
  source position optimized with a fractional
  occupancy
• This is easy, mathematically, but of course is
  physically ridiculous.
• However, calculating the objective function for
  this case gives the best value that function
  could ever have.

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Branch and Bound

• One source position (any) is picked, and for the
  two possibilities, a source present (1) or source
  absent (0), the objective function is evaluated.
• This has defined two paths, (present/absent).
• The path with the better objective function is
  followed, and another position picked for the 0/1
  options.
• Again the better picked, and so on.

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Branch and Bound Tree
Warren DSouza
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Branch and Bound (cont.)

• At each branching, the objective function gets
  worse because we are replacing fractional
  occupancy with integer.
• If the objective function is worse than the value
  at the end of any other path, go back to the best
  value, and continue the process there.

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Branch and Bound (cont.)

• The process can either continue until an adequate
  value for the objective function is found
  (relatively quick) or the best value (longer)
• Does not test all possibilities.
• Can give the true optimum.
• Faster than stochastic methods.

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Heuristic

• Example the Greedy Algorithm
• Process
• Establish a region
• Calculate the adjoint function for the region

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Adjoint Function

• Determines the contribution to the average dose
  in the region from a source placed at the test
  point.
• The adjoint function maps this out for all space
  (or in the case of a prostate implant, for all
  possible source positions).

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Whole ROI Adjoint Distribution for a 2D
image-slice
Target
Rectum
Normal tissue
Sua Yoo
Urethra
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Combining All Adjoints

• Plot each function simply sequentially for all
  source positions (top to bottom, left to right).
• Find the position with the highest ratio of dose
  to target to dose to the normal structures.
• Place a source there.

Sua Yoo
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Adjoint Ratio

• Best location is with lowest ratio

Sua Yoo
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Greedy Algorithm

• Process
• After placing a source in the first location, see
  if dose criteria are met. (yes-stop no-proceed)
• Exclude locations within a specified isodose
  surface.
• Pick the next best position in the allowed
  volume.
• See if dose criteria are met. (yes-stop
  no-proceed)
• Increase the exclusion isodose value and set up
  the new excluded volume.

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Greedy Algorithm

• Process
• Continue until dose criteria are met.
• Advantage Because the process is not iterative
  (trying distributions that dont work), the
  algorithm is very fast (100 5000 times faster
  than branch and bound)
• Disadvantage Not a true optimization, only
  adequacy (but not that different results).

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Analytic Methods

• Analytic methods would be solving an equation for
  the source positions.
• There is not much going on in this arena.

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Real-time Optimization

• Real-time optimization would be optimization that
  would be fast enough that
• It could be performed intraoperatively.
• It could correct the plan continually to make up
  for differences between the last version of the
  plan and the actual placement of the sources
  since then.
• It would also require rapid, accurate, and
  sensitive imaging of seeds.

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Real-time OptimizationWhere Are We?

• Approaching possibility.
• The heuristic approach is fast enough and good
  enough. (In a few years, computers may be fast
  enough for other approaches to be feasible. Dont
  forget, we are talking about potentially 20-100
  optimizations).
• Imaging is very rapidly improving (or at least
  was in 2002-2003)

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Real-time OptimizationWhere Will We Be?

• The question remains, and will for a long time
  Does all this improve results (survival and
  quality of life)?