Optimization of Gamma Knife Radiosurgery

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Optimization of Gamma Knife Radiosurgery

• Michael Ferris
• University of Wisconsin, Computer Sciences
• David Shepard
• University of Maryland School of Medicine

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Overview

• Details of machine and problem
• Formulation
• modeling dose
• shot / target optimization
• Results
• Two-dimensional data
• Real patient (three-dimensional) data

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The Leksell Gamma Knife
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Problem characteristics

• Machine has 201 radiation sources focussed on one
  location
• Very accurate dose delivery
• Benefits of computer solution
• uniformity of treatment plan
• better treatment plan
• faster determination of plan

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Problem outline

• Target volume (from MRI or CT)
• Maximum number of shots to use
• Which size shots to use
• Where to place shots
• How long to deliver shot for
• Conform to Target (50 isodose curve)
• Real-time optimization

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Two-dimensional example
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Ideal Optimization
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Dose calculation

• Measure dose at distance from shot center
• Fit a nonlinear curve to these measurements
• Functional form from literature, 6 parameters to
  fit via least-squares

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8mm shot
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18mm shot
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MIP Approach

• A-priori fix possible shot locations

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MIP Problem
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Size Problem

• Dose(NonTarget) Dose(Rind)
• Too many shots
• Generate grid of large shots
• grid spacing
• grid offset
• Small shots randomly placed nr boundary
• Proportion of each?

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Features of MIP

• Large amounts of data/integer variables
• Shot location on 1mm grid too restrictive
• Time consuming, even with restrictions and CPLEX
• but ... have guarantee of global optimality

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Nonlinear Approach
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Two-stage approach

• Approximate via arctan
• First, solve with approximation, then fix shot
  widths and reoptimize

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3D slice image
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Slice 3
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Axial slice
Manual Computer Optimized
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Axial slice
Manual Computer Optimized
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Coronal slice
Manual Computer Optimized
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Sagittal slice
Manual Computer Optimized
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Challenges

• Integration into real system
• Reduction of optimization time
• What if scenarios?
• Improve the objective function
• Change number of shots
• Global versus local solutions