A Network Approach for Intensity Modulated Arc Therapy (IMAT)

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A Network Approach for Intensity Modulated Arc
Therapy (IMAT)

• Athula D. A. Gunawardena, Michael C. Ferris and
  Robert R. Meyer
• University of Wisconsin-Whitewater, and
• University of Wisconsin-Madison

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Radiotherapy 100 years

• 1896 - Emil Herman Grubbé uses radiation to
  treat breast cancer - less than one month after
  public announcement of Roentgens discovery of
  X-rays
• 1975 - Mark P. Carol, M.D. develops initial idea
  for IMRT
• 1992 - Computer technology advances allow Carol
  to prototype the Peacock IMRT system.
• 1996 - FDA approval won for Carols system

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Radiotherapy Impact and Challenges

• gt 1 million cases of cancer each year in U.S.,
  and many times that number in other countries
• Approximately 40 of U.S. patients with cancer
  are treated with radiation therapy
• Minimizing radiation dose to nearby healthy
• organs at risk (OARs) very difficult

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Radiation Therapy Goals

• High Level Goals Achieve prescribed radiation to
  tumor while minimizing dose to the surrounding
  organs
• Some Additional Goals
• Minimize time patient spends on the treatment
  couch.
• Minimize beam-on time (time radiation beam in
  on )
• Minimize treatment planning time

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Intensity Modulated Radiation Therapy A
complex RT procedure

• Radiation delivered from 4-9 angles
• selected from 360 possible angles
• For each of these 4-9 angles,
• Intensity Modulated Radiotherapy (IMRT) uses
  50-200 small radiation beamlets each of which is
  allowed to have a
• different radiation intensity
• Different beamlet intensities achieved via
  multiple apertures at each angle

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Leaf Sequencing in IMRT
Multileaf Collimator
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Common Machine Specific Constraints on Shapes

• Single Interval Constraint
• - Any nonzero row of an achievable shape
  contains a single interval of ones
• Inter-Digitization Constraint
• -Opposite adjacent leaves cannot cross each
  other

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Intensity Modulated Arc Therapy (IMAT)A
rotational IMRT system

• A1 , A2,, AP I-maps
• K3 the number of sweeps along the arc
• Would like

• A2

• A1

• A3

• A

• AP

• AP-1

• Introduced by C. X. Yu in 1995 as an alternative
  to Tomo Therapy

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Leaf Sequencing in IMAT

• Input
• A1 , A2,, AP nonnegative real matrices
• K the number of sweeps through an
  arc(i.e., of shapes per I-map)
• D maximum allowable leaf movement between
  two adjacent angles

• Variables
• ?i1,, ?iK beam weights for segmentation of
  Ai, I1, , P
• Si1,, SiK binary shape matrices for Ai

• Maximum allowable leaf movement between Si,j and
  Si1,j ? D, MLM(Si,j and Si1,j )? D, and
• other constraints on Sij.

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Clinical Prostate Maps
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• Row-Non-Convexity Measure

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Network Models

• Assignment Problems
• Transportation Problems
• Shortest Path Problems
• Maximum Flow Problems
• Critical Path in Project Plan Networks
• Minimum Cost Flow Problems

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Intensity Map
Segmentation Error Map

• Angle 200

• Angle 260

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