Optimizing Radiation Treatment Planning for Tumors Using IMRT

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Optimizing Radiation Treatment Planning for
Tumors Using IMRT

• Laura D. Goadrich
• Industrial Engineering Department of Computer
  Sciences at University of Wisconsin-Madison
• April 19, 2004

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Overview

• Radiotherapy motivation
• Conformal radiotherapy
• IMRT
• Mechanical constraints
• MIP method
• Input/output
• Langer, et. al. Approach
• Monoshape constraints
• Implementation results
• References

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Motivation

• 1.2 million new cases of cancer each year in U.S.
  (times 10 globally)
• Half undergo radiation therapy
• Some are treated with implants, but most with
  external beams obtained using radiotherapy
  treatments.

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Radiotherapy Motivation

• Used to fight many types of cancer in almost
  every part of the body
• Approximately 40 of patients with cancer needs
  radiation therapy sometime during the course of
  their disease
• Over half of those patients who receive
  radiotherapy are treated with an aim to cure the
  patient
• to treat malignancies
• to shrink the tumor or to provide temporary
  relief of symptoms
• In the use of radiation, organ and function
  preservation are important aims (minimize risk to
  organs at risk (OAR)).

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Planning Radiotherapy- CAT scan

• Conduct scans of the section of the body
  containing the tumor
• Allows physicians to see the OAR and surrounding
  bodily structures

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Planning Radiotherapy- tumor volume contouring

• Isolating the tumor from the surrounding OAR is
  vital to ensure the patient receives minimal
  damage from the radiotherapy
• Identifying the dimensions of the tumor is vital
  to creating the intensity maps (identifying where
  to focus the radiation)

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Planning Radiotherapy- beam angles and creating
intensity maps

• Multiple angles are used to create a full
  treatment plan to treat one tumor.
• Through a sequence of leaf movements, intensity
  maps are obtained

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Option 1 Conformal Radiotherapy

• The beam of radiation used in treatment is a 10
  cm square.
• Utilizes a uniform beam of radiation
• ensures the target is adequately covered
• however does nothing to avoid critical structures
  except usage of some blocks

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Option 2 IMRT

• Intensity Modulated Radiotherapy (IMRT) provides
  a shaped array of 3mm beamlets using a Multi-Leaf
  Collimator (MLC), which is a specialized,
  computer-controlled device with many tungsten
  fingers, or leaves, inside the linear
  accelerator.
• Allows a finer shaped distribution of the dose to
  avoid unsustainable damage to the surrounding
  structures (OARs)
• Implemented via a Multi-Leaf Collimator (MLC)
  creating a time-varying opening (leaves can be
  vertical or horizontal).

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Classical vs. IMRT
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IMRT machine
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IMRT Planning- intensity map

• There is an intensity map for each angle
• 0 means no radiation
• 100 means maximum dosage of radiation
• Multiple beam angles spread a healthy dose
• A collection of shape matrices are created to
  satisfy each intensity map.

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Intensity map to shape matrices
Original Intensity Matrix
Shape Matrix 1
Shape Matrix 3
Shape Matrix 2
Shape Matrix 4
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Program Input/Output

• Input
• An mxn intensity matrix A(ai,j) comprised of
  nonnegative integers
• Output
• T aperture shape matrices dtij such that zK of
  the matrices are used where K lt T
• Non-negative integers ?t (tI..T) giving
  corresponding beam-on times for the apertures
• Apertures obey the delivery constraints of the
  MLC and the weight-shape pairs satisfying
• K is the total number of
• required shape matrices

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Mechanical Constraints

• After receiving the intensity maps, machine
  specific shape matrices must be created for
  treatment
• There are numerous types of IMRT machines
  currently in clinical use, with slightly
  different physical constraints that determine the
  leaf positions (hence the shape matrices)
  possible for the device
• Each machine has varying setup times which can
  dominate the radiation delivery time (beam-on
  time)
• To limit patient discomfort and subtle movement
  from initial placing limit the time the patient
  is on the table
• Goals
• Minimize beam-on time
• Minimize number of different shapes

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Approach Langer, et. al.

• Mixed integer program (MIP) with Branch and Bound
  by Langer, et. al. (AMPL solver)
• MIP linear program with all linear constraints
  using binary variables
• Langer suggests a two-phase method where
• First minimized beam-on time
• T is the upper bound on the
• number of required shape matrices
• Second minimize the number of segments (subject
  to a minimum beam-on time constraint)
• gt 1 if an element switches from
• covered to uncovered (vice versa)
• 0 otherwise

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In Practice

• While Langer, et. al. reports that solving both
  minimizations takes a reasonable amount of time,
  he does not report numbers and we have found that
  the time demands are impractical for real
  application.
• To obtain a balance between the need for a small
  number of shape matrices and a low beam-on time
  we have found that
• numShapeMatricies7 beam-on time
• Initializing T close to the optimal number of
  matrices 1 required reduces the solution space
  and solution time

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Constraint Leaves cannot overlap from right and
left

• To satisfy the requirement that leaves of a row
  cannot override each other implies that one beam
  element cannot be covered by the left and right
  leaf at the same time

ptij 1 if beam element in row i,
column j is covered by the right leaf
when the tth monitor unit
is delivered 0 otherwise ltij is similar
for the right leaf dtij contains the final tth
monitor unit
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Constraint Full leaves and intensity matrix
requirements

• Every element between the leaf and the side of
  the collimator to which the leaf is connected is
  also covered (no holes in leaves).

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Constraint No leaf collisions

• Due to mechanical requirements, leaves can move
  in only one direction (i.e. the right leaf to the
  right). On one row, the right and left leaves
  cannot overlap

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Constraint Shape matrices reqs

• The total number of shape matrices expended it
  tallied
• z 1 when at least one beam element
  reamins exposed
• when the tth monitor unit in
• the sequence is delivered
• 0 otherwise
• I is the number of rows
• J is the number of columns

• Must satisfy the intensity matrix for each
  monitor unit.
• I is the intensity assigned to
• beam element ij

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Constraint Monoshape

• The IMRT delivery is required to contain only one
  shape matrix per monitor unit, a monoshape
• First determine which rows in each monitor unit
  are open to deliver radiation

deliveryit1 if the ith row is being used
a time t 0 otherwise

• Determine if the preceding row in the monitor
  unit delivers radiation

dropit1 if the preceding row (i-1)
in a shape is non-zero and the
current row (i) is 0 0 otherwise
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Constraint Monoshape

• Determine when the monoshape ends

jumpit1 if the preceding row (i-1)
in a shape is zero and the current
row (i) is nonzero 0 otherwise

• There can be only one row where the monoshape
  begins and one row to end

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Complexity of problem

• To account for all of the constraints there is a
  large number of variables and constraints.

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Comparison of results

• Corvus version 4.0

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Comparison of results

• Corvus version 5.0

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Referenced Papers

• N. Boland, H. W. Hamacher, and F. Lenzen.
  Minimizing beam-on time in cancer radiation
  treatment using multileaf collimators. Neworks,
  2002.
• Mark Langer, Van Thai, and Lech Papiez, Improved
  leaf sequencing reduces segments or monitor units
  needed to deliver IMRT using multileaf
  collimators, Medical Physics, 28(12), 2001.
• Ping Xia, Lynn J. Verhey, Multileaf collimator
  leaf sequencing algorithm for intensity modulated
  beams with multiple static segments, Med. Phys.
  25 (8), 1998.
• T.R. Bortfield, D.L. Kahler, T.J Waldron and
  A.L.Boyer, X-ray field compensation with
  multileaf collimators. Int. J. Radiat. Oncol.
  Biol. 28 (1994), pp. 723-730.
• Bortfield, Thomas, et. al. Current IMRT
  optimization algorithms principles, potential
  and limitations Presentation 2000.
• Dink, Delal, S.Orcun, M. P. Langer, J. F. Pekny,
  G. V. Reklaitis, R. L. Rardin, Importance of
  sensitivity analysis in intensity modulated
  radiation therapy (IMRT) 2003.