Radiosurgical Planning

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• Radiosurgical Planning

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Radiosurgery

• Minimally invasive procedure that uses an
  intense, focused beam of radiation as an ablative
  surgical instrument to destroy tumors

Tumor bad
Critical structures good and sensitive
Brain good
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The Radiosurgery Problem
Dose from multiple beams is additive
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Treatment Planning for Radiosurgery

• Determine a set of beam configurations that will
  destroy a tumor by cross-firing at it
• Constraints
• Desired dose distribution
• Physical properties of the radiation beam
• Constraints of the device delivering the
  radiation
• Duration/fractionation of treatment

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After 16 weeks
Prior
After 10 weeks
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Conventional Radiosurgical Systems

• Isocenter-based treatments
• Stereotactic frame required

Gamma Knife
LINAC System
Luxton et al., 1993
Winston and Lutz, 1988
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Isocenter-Based Treatments

• All beams converge at the isocenter
• The resulting region of high dose is spherical

• Nonspherically shaped tumors are approximated by
  multiple spheres

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Stereotactic Frame for Localization

• Painful
• Fractionation of treatments is difficult
• Treatment of extracranial tumors is impossible

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The CyberKnife
linear accelerator
robotic gantry
X-Ray cameras
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CyberKnife (Accuray)
http//accuray.com/
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Treatment Planning Becomes More Difficult

• Much larger solution space
• Beam configuration space has greater
  dimensionality
• Number of beams can be much larger
• More complex interactions between beams
• Path planning
• Avoid collisions
• Do not obstruct X-ray cameras
• ? Automatic planning required (CARABEAMER)

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Inputs to CARABEAMER

• (1) Regions of Interest

Surgeon delineates the regions of interest
CARABEAMER creates 3D regions
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Inputs to CARABEAMER

• (2) Dose Constraints
• (3) Maximum number of beams

Dose to tumor
Falloff of dose around tumor
Dose to critical structure
Falloff of dose in critical structure
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Basic Problem Solved by CARABEAMER

• Given
• Spatial arrangement of regions of interest
• Dose constraints for each region a ? D ? b
• Max number of beams allowed N (100-400)
• Find
• N beam configurations (or less) that generate
  dose distribution that meets the constraints.

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Beam Configuration

• Position and orientation of the radiation beam
• Amount of radiation or beam weight
• Collimator diameter

? Find 6N parameters that satisfy the constraints
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CARABEAMERs Approach

• Initial Sampling Generate many (gt N) beams at
  random, with each beam having a reasonable
  probability of being part of the solution.
• Weighting Use linear programming to test
  whether the beams can produce a dose distribution
  that satisfies the input constraints.
• Iterative Re-Sampling Eliminate beams with
  small weights and re-sample more beams around
  promising beams.
• Iterative Beam Reduction Progressively reduce
  the number of beams in the solution.

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Initial Beam Sampling

• Generate even distribution of target points on
  the surface of the tumor
• Define beams at random orientations through these
  points

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Deterministic Beam Selection is Less Robust
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Curvature Bias

• Place more target points in regions of high
  curvature

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Dose Distribution Before Beam Weighting
50 Isodose Surface
80 Isodose Surface
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CARABEAMERs Approach

• Initial Sampling Generate many (gt N) beams at
  random, with each beam having a reasonable
  probability of being part of the solution.
• Weighting Use linear programming to test
  whether the beams can produce a dose distribution
  that satisfies the input constraints.
• Iterative Re-Sampling Eliminate beams with
  small weights and re-sample more beams around
  promising beams.
• Iterative Beam Reduction Progressively reduce
  the number of beams in the solution.

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Beam Weighting

• Construct geometric arrangement of regions formed
  by the beams and the tissue structures

• Assign constraints to each cell of the
  arrangement
• Tumor constraints
• Critical constraints

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Linear Programming Problem
2000 ? Tumor ? 2200 2000 ? B2 B4 ? 2200 2000
? B4 ? 2200 2000 ? B3 B4 ? 2200 2000 ? B3 ?
2200 2000 ? B1 B3 B4 ? 2200 2000 ? B1 B4 ?
2200 2000 ? B1 B2 B4 ? 2200 2000 ? B1 ?
2200 2000 ? B1 B2 ? 2200
0 ? Critical ? 500 0 ? B2 ? 500
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Results of Beam Weighting
Before Weighting
After Weighting
50 Isodose Curves
80 Isodose Curves
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CARABEAMERs Approach

• Initial Sampling Generate many (gt N) beams at
  random, with each beam having a reasonable
  probability of being part of the solution.
• Weighting Use linear programming to test
  whether the beams can produce a dose distribution
  that satisfies the input constraints.
• Iterative Re-Sampling Eliminate beams with
  small weights and re-sample more beams around
  promising beams.
• Iterative Beam Reduction Progressively reduce
  the number of beams in the solution.

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CARABEAMERs Approach

• Initial Sampling Generate many (gt N) beams at
  random, with each beam having a reasonable
  probability of being part of the solution.
• Weighting Use linear programming to test
  whether the beams can produce a dose distribution
  that satisfies the input constraints.
• Iterative Re-Sampling Eliminate beams with
  small weights and re-sample more beams around
  promising beams.
• Iterative Beam Reduction Progressively reduce
  the number of beams in the solution.

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Plan Review

• Calculate resulting dose distribution
• Radiation oncologist reviews
• If satisfactory, treatment can be delivered
• If not...
• Add new constraints
• Adjust existing constraints

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Evaluation on Sample Case
Linac plan 80 Isodose surface
CARABEAMERs plan 80 Isodose surface
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Another Sample Case
50 Isodose Surface
80 Isodose Surface
LINAC plan
CARABEAMERs plan
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Evaluation on Synthetic Data
2000 ? DT ? 2400, DC ? 500
n 500 n 250 n 100
Constraint Iteration
10 random seeds
X
X
X
2000 ? DT ? 2200, DC ? 500
X
Beam Iteration
2000 ? DT ? 2100, DC ? 500
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Dosimetry Results
Case 1
Case 2
80 Isodose Curve
90 Isodose Curve
80 Isodose Curve
90 Isodose Curve
Case 3
Case 4
80 Isodose Curve
90 Isodose Curve
80 Isodose Curve
90 Isodose Curve
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Average Run Times
Case 1 Beam Constr
Case 2 Beam Constr
Case 3 Beam Constr
Case 4 Beam Constr

• 2000-2400
• n 500
• n 250
• n 100
• 2000-2200
• n 500
• n 250
• n 100
• 2000-2100

20 20 35 32 29 43 0134 0128 0221
41 40 51 50 59 0102 0141 0131 02
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0330 0332 0428 0550 0550 0853 48
54 4049 15725
0523 0533 0719 0837 0842 1043 27
39 2443 10227
0436 0411 0503 2351 2444 3302 32
633 32215 74457
0645 0719 0706 1305 1216 2106 10
306 10712 50629
30612 30919 33528 253836 275518 53
5856
14055 14418 14119 63302 71101 17625
02 441104 842127
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Evaluation on Prostate Case
50 Isodose Curve
70 Isodose Curve
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Cyberknife Systems
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Meningioma affecting vision
After 2 months
208 beam positions. The patient was treated with
5 fractions over 5 days at 40 minutes per
fraction.
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Prostate
Spine
Kidney
Pancreas
Lung
http//accuray.com/