Treatment Planning for ImageGuided Robotic Radiosurgery

1
Treatment Planning forImage-Guided Robotic
Radiosurgery

• Rhea Tombropoulos,
• John Adler, and Jean-Claude Latombe
• Computer Science Department
• Neurosurgery Department
• Stanford University

2
Outline

• Introduction radiosurgical planning problem
• Conventional systems
• The Cyberknife system image-guided robotic
  radiosurgery
• The CARABEAMER planner
• Conclusion

3
Radiosurgery

• Procedure that uses an intense, focused beam of
  radiation as an ablative surgical instrument to
  destroy tumors
• The goal
• Deposit a lethal dose of radiation in the tumor
• Avoid irradiation of dose-sensitive/critical
  areas
• Minimize irradiation of other normal tissue

4
The Problem...
Tumor bad
Critical structures good and sensitive
Brain good
5
Cross-firing at the Tumor Decreases Dose to
Normal Brain Tissue
6
Treatment Planning

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

7
Approaches to Treatment PlanningForward
Planning vs. Inverse Planning
Set Planning Parameters
Set Desired Dose Distribution
Calculate Dose Distribution
Calculate Planning Parameters
Review Dose Distribution
Unsatisfactory
Treat
Satisfactory
Treat
8
Conventional Radiosurgical SystemsLimit
Treatment Alternatives

• Stereotactic frame required
• Isocenter-based treatments

from Luxton et al., 1993
adapted from Winston and Lutz, 1988
9
Stereotactic Frame
10
Conventional Systems Rely on 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
• Cold Spots arise where coverage is poor
• Over-irradiation of healthy tissue results due to
  poor shape matching
• Hot Spots arise where the spheres overlap

11
Typically, Forward Planning is used to Adjust the
Treatment-Planning Variables Manually

• Number of isocenters
• Location of each isocenter
• Beam diameter
• Orientation and length of treatment arcs (linac)/
  plug pattern (gamma knife)
• Dose along each arc (linac)
• Shape of beam (linac)

12
Most Inverse Planning is done with Optimization

• Objective Function
• Minimize total dose
• Maximize homogeneity
• Minimize critical dose
• Biological objective

• Starting Point
• Isocenter location
• Beam directions
• Collimator diameters
• Constraint points

• Constraint Function
• Tumor dose
• Critical tissue dose
• Maximum beam weight

• Optimization Method
• Linear programming
• Quadratic programming
• Gradient methods
• Simulated annealing

Beam Weights
13
What do We Want from a New Radiosurgical System?

• Better treatment (more degrees of freedom)
• Better localization method
• Treatment of wide variety of tumors, including
• Large Tumors
• Extracranial tumors
• gtgtgt Cyberknife system

14
Image-Guided Robotic Radiosurgery
Cyberknife system
15
Arbitrarily Shaped Dose Distributions
16
The Cyberknife Raises New Issues in Treatment
Planning

• Very large search space
• Many more possible beam configurations
• More complex interactions between beams
• Robot path planning
• Avoid collisions
• Do not obstruct X-ray cameras
• gtgtgt the CARABEAMER planner

17
Basic Idea of CARABEAMER

• Impossible to search all possible combinations of
  beam configurations
• However, given a set of configurations, we can
  evaluate their effectiveness
• Combine inverse and forward planning
• inverse planning gtgt select beam configurations
  from tissue geometry
• forward planning gtgt adjust beam weights to
  satisfy dose constraints (beam weight
  duration)

18
Basic Planning Algorithm in Context
Delineate Regions of Interest
3-D Reconstruction
Assign Constraints
Beam Selection
Beam Weighting
Dosimetry Calculations
Plan Evaluation
Treatment
19
Hypotheses in Basic Planner

• Beam diameter is fixed and given
• Radiation energy is constant throughout the beam
• Beam is perfectly cylindrical

20
Step 1 The surgeon delineates the regions of
interest and specifies constraints

• tumor dose should be between 2000 and 2200 rads

• critical tissue dose should be under 500 rads

21
The Surgeon can Specify Several Different Kinds
of Dose Constraints
Dose to the Tumor Region
Tumor
Dose to the Critical Region
Critical
Fall-off of Dose Around the Tumor
Fall-off of Dose in the Critical Region
22
Step 2 The system creates a 3-dimensional
reconstruction of the geometry
- Triangulated surface representation of tumor -
Volume representation (3D array of voxels) of
tissue
23
Step 3 Beam Selection

• Infinite set of possible beam directions to
  choose from (4D space)
• Goal is to isolate a relatively small (200-400)
  subset of these beams with that hold promise for
  creating a satisfactory dose distribution
• These beams are selected such that their
  intersections conform to the tumors shape

24
Beam Selection Algorithm

• Place points evenly on the surface of the tumor
• Pick beam orientations at random at these points

25
Evenly Spacing Target Pointson the Surface of
the Tumor

• Distribute n points (called target points) on the
  tumor surface
• Assign each triangle a number of target points
  based on its area
• Even out this distribution with point repulsion
• For each target point Pi
• Map each Pis neighbor onto the plane of the
  triangle containing Pi
• Compute the total repulsive force Fi exerted on
  Pi by its neighbors
• Move each target point Pi along Fi while
  keepingit on the surface of the tumor

26
Pick Beam Orientations at Random at Target Points
27
More Deterministic (Heuristic) Schemes for Beam
Selection are not as Robust
28
At the End of Beam Selection the Region of High
Dose Encompasses the Tumor
50 Isodose Surface
80 Isodose Surface
All beams have same weight
29
Dose-Volume Histogram after Beam Selection
cubic mm
cubic mm
Percent Dose
Percent Dose
Tumor (Integral 71.84)
Brain Stem (Integral 3.74)
Over 300 cubic mm of the tumor receives 80 of
the maximal dose, or more The entire tumor
receives more than 40 of the maximal dose Less
than 1000 cubic mm of the brain stem receives
more than 4 of the maximal dose
30
Step 4 Beam Weighting

• Decompose space into cells based on where
  beamsand tissues intersect

• Impose constraints on the sum of weights of beams
  passing through each region
• Tumor regions
• Critical regions
• Fall-off regions
• Set beams maximum weight

31
Establish Linear Constraint on Sum of Beam
Weights in Each Cell
2000 lt Tumor lt 2200 2000 lt B2 B4 lt 2200 2000
lt B4 lt 2200 2000 lt B3 B4 lt 2200 2000 lt B3 lt
2200 2000 lt B1 B3 B4 lt 2200 2000 lt B1 B4 lt
2200 2000 lt B1 B2 B4 lt 2200 2000 lt B1 lt
2200 2000 lt B1 B2 lt 2200
0 lt Critical lt 500 0 lt B2 lt 500
32
Reducing the Number of Inequalities
2000 lt Tumor lt 2200 2000 lt B2 B4 lt 2200 2000
lt B4 lt 2200 2000 lt B3 B4 lt 2200 2000 lt B3 lt
2200 2000 lt B1 B3 B4 lt 2200 2000 lt B1 B4 lt
2200 2000 lt B1 B2 B4 lt 2200 2000 lt B1 lt
2200 2000 lt B1 B2 lt 2200
2000 lt Tumor lt 2200 2000 lt B4 2000 lt B3 B1
B3 B4 lt 2200 B1 B2 B4 lt 2200 2000 lt B1
0 lt Critical lt 500 0 lt B2 lt 500
0 lt Critical lt 500 B2 lt 500
33
Results of Beam Weighting
Before Weighting
After Weighting
50 Isodose Curves
80 Isodose Curves
34
Dose-Volume Histograms afterBeam Weighting
cubic mm
cubic mm
Percent Dose
Percent Dose
Tumor (Integral 94.03)
Brain Stem (Integral 2.57)
35
Histogram Comparison
36
Step 5 Calculate Resulting Dose Distribution

• Calculate resulting dose distribution using
  direct dosimetry model that considers
• Weight of each beam
• Diameter of the collimator used to shape the beam
• Distance from source
• Distance from the beams central axis

37
Step 6 Plan Evaluation

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

38
Extensions and Improvements

• Path planning and collision avoidance
• Automatic collimator selection
• Improvement of dosimetry model used in planning
• Enhanced target-point selection
• Search for the best possible solution
• Minimization of number of beams in solution

39
Path Planning and Collision Avoidance

• Constraints
• Avoid obstacles within the workspace
• Avoid obstructing X-ray cameras

Principle - Define a fixed dense grid of
feasible source points on a sphere and a
standard path through those points - For
each target point on the tumor, select beam
orientation by picking a source point at
random
40
Automatic Selection of Collimator Diameter

• Weightwide lt Weightmedium lt Weightnarrow

narrow

• Choose the wide collimator if all weights come
  out equal
• Choose the medium collimator if Weightmedium
  Weightnarrow but Weightwide is smaller
• Choose the narrow collimator if both Weightwide
  and Weightmedium are smaller than Weightnarrow

medium
wide
T
T
C
B2
41
Better Dosimetry Model

• Dose to a voxel B1W1 B2W2 . . . BnWn
• With simple dose model, B1 - Bn are 0s and 1s
• If voxel is contained within the cylinder
  representing a given beam i, then Bi 1
• Otherwise Bi 0

• We can represent a more accurate dose model by
  calculating a coefficient that represents the
  percent of a beams dose that will be deposited
  in a given voxel

42
Finding Best Possible Solution

• When the constraints cannot be satisfied, the
  linear program returns that the problem is
  infeasible and does not find the best possible
  solution
• Best possible solution given a set of beams would
  provide information to improve beam set
• Surgeon may find it good enough even though it
  does not satisfy the input constraints

43
A Quick Review of Linear Programming...

• A linear is program is typically specified as
• Minimize c1x1 c2x2 . . . cnxn
• Subject to l1 lt a1,1x1 a1,2x2 . . .
  a1,nxn lt u1
• l2 lt a2,1x1 a2,2x 2 . . . a2, nxn lt
  u2
• lm lt am,1x 1 am,2x 2 . . . am,
  nxn lt um
• Using slack variables, we can rewrite this
• Minimize c1x1 c2x2 . . . cnxn
• Subject to a1,1x1 a1,2x2 . . .
  a1,nxn s1 0, -u1 lt s1 lt -l1
• a2,1x1 a2,2x 2 . . . a2, nxn s2
  0, -u2 lt s2 lt -l2
• am,1x 1 am,2x 2 . . . am, nxn sm
  0, -um lt sm lt -lm

. . .
. . .
44
CARABEAMER Adds Extra Slack Variables to Solve
for the Best Possible Solution

• New slacks ?1 ... ?m
• Minimize 1?1 1?2 . . . 1?m
• Subject to a1,1x1 a1,2x2 . . .
  a1,nxn s1 ????1 0, -u1 lt s1 lt
  -l1
• a2,1x1 a2,2x 2 . . . a2, nxn
  s2 ?2 0, -u2 lt s2 lt -l2
• am,1x 1 am,2x 2 . . . am, nxn
  sm ?m 0, -um lt sm lt -lm
• The idea is to minimize the sum of the
  infeasibilities

. . .
45
Minimizing Number of Beams

• Especially for fractionated treatments, it is
  important to keep number of beams small
• But the more beams we consider, the more likely
  we are to find a solution
• Idea
• Find initial solution with large number of beams
• Iteratively reduce number of beams by eliminating
  beams with small weights
• Use objective function that minimizes the number
  of high-weight beams in the solution

46
Iterative Reduction of Number of Beams

• 1. Find a solution to the constraints with many
  beams
• 2. Set nonzero to the number of beams in this
  solution whose weights are greater than 0
• 3. While (nonzero lt ngoal)
• a. Remove all beams whose weights 0
• b. Remove the ? beams with the smallest weights
• c. Pick ? new beams at random (? lt ? )
• d. Run the linear program
• i. If no solution, add more random beams and
  rerun
• ii. If solution, calculate nonzero

47
Objective Function to Minimize the Number of
Nonzero Variables in the Solution

• Minimize 1x1 1x2 . . . 1xn
• Subject to a1,1x1 a1,2x2 . . .
  a1,nxn s1 0, -u1 lt s1 lt -l1
• a2,1x1 a2,2x 2 . . . a2, nxn
  s2 0, -u2 lt s2 lt -l2
• am,1x 1 am,2x 2 . . . am, nxn
  sm 0, -um lt sm lt -lm

. . .
48
Evaluation

• Phase 1 Analysis of system performance on
  clinical cases
• Phase 2 Analysis of system performance on
  synthetic cases
• Phase 3 Informal analysis of system performance
  on other difficult cases

49
Evaluation on Clinical Data

• GOAL Determine if CARABEAMER meets
  treatment-planning requirements
• Study 12 clinical cases treated at Stanford with
  conventional radiosurgery
• 20 tumorsAcoustic neuromas, angioperictomas,
  hemangioblastomas, metastases, and pituitary
  adenomas
• 17 critical structuresBrain stem, optic nerves,
  optic chiasm, and cornea

50
Evaluation on Clinical Data Methods

• For each case, the neurosurgeon responsible for
  planning defined the treatment-planning problem
• Delineated the regions of interest
• Specified dose constraints
• Tumor target dose 2000 rads 10
• Critical dose lt 800rads
• CARABEAMER was run with this input
• CARABEAMER was evaluated in terms of whether or
  not it was able to satisfy the dose constraints
  of the neurosurgeon

51
Evaluation on Clinical Data Results

• CARABEAMER was able to satisfy the surgeons
  constraints in all 12 cases
• Sample Results

Region of Interest Neurosurgeon CARABEAMER m
in max min max Lesion 1 1800 2200 1800 2
200 Brain Stem 0 800 0 800 R. Optic
Nerve 0 800 155 800 Optic Chiasm 0 800 0
314 External Tissue -- -- 0 2218
52
Evaluation on Clinical Data Discussion

• CARABEAMER met the specified requirements
• CARABEAMER typically did not do better than the
  specified requirements dictated
• These requirements are biased toward current
  treatment capabilities
• Tumors are mostly spherical
• Dose constraints are fairly wide
• Difficult to compare to actual plans that were
  actually used in treatment
• Different radiosurgical devices
• Different treatment goals
• Different dose models

53
Sample Case
Linac plan 80 Isodose surface
CARABEAMERs plan 80 Isodose surface
54
Sample Case
50 Isodose Surface
80 Isodose Surface
Linac plan
CARABEAMERs plan
55
Sample Case
Linac plan 80 Isodose surface
CARABEAMERs plan 80 Isodose surface
56
Sample Case
CARABEAMERs plan 80 Isodose surface
Linac plan 80 Isodose surface
57
Sample Case
Linac plan 50 Isodose surface
CARABEAMERs plan 50 Isodose surface
58
Sample Case
Linac plan 80 Isodose surfaces
CARABEAMERs plan 80 Isodose surfaces
59
Sample Case
Linac plan 80 Isodose surface
CARABEAMERs plan 80 Isodose surface
60
Sample Case
Linac plan 80 Isodose surface
CARABEAMERs plan 80 Isodose surface
61
Evaluation on Synthetic Data

• GOAL Demonstrate CARABEAMERs performance on
  increasingly difficult cases
• Evaluate performance on 36 different data sets
• Study 2 different iterations algorithms

62
Evaluation on Synthetic Data Methods
2000 lt DT lt 2400, DC lt 500
Beam Iteration
n 500 n 250 n 100
10 random seeds
X
2000 lt DT lt 2200, DC lt 500
X
X
X
Constraint Iteration
2000 lt DT lt 2100, DC lt 500
63
Evaluation on Synthetic Data Iteration
Algorithms

• Beam Iteration
• Start with reasonable number of beams
• Increase number of beams until a solution is
  found
• Iteratively reduce number of beams to desired
  number
• Constraint Iteration
• Start with reasonable number of beams
• Keep number of beams constant until a solution is
  found
• Find best possible solution at each iteration
• Use this solution as a starting point for the
  next iteration
• Iteratively reduce number of beams to desired
  number

64
Average Run Time for Synthetic Test Cases
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
• 1000-2100
• n 500
• n 250
• n 100

20 20 35 32 29 43 0134 0128 88022
1
41 40 51 50 59 0102 0141 0131 02
38
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
65
Average Number of Iterations for Synthetic Test
Cases
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
• 1000-2100
• n 500
• n 250
• n 100

1.0 1.0 1.0 1.0 1.0 1.0 1.5 1.4 3.8
1.4 1.3 2.1 1.4 1.8 2.0 2.9 2.6 6.4
2.0 2.0 2.1 2.0 2.0 8.8 2.0 3.2 144.7
2.5 2.5 3.3 2.7 2.8 7.4 3.4 3.9 115.1
2.0 2.0 2.1 2.9 2.8 30.4 5.0 6.0 780.5
2.7 3.0 3.1 3.8 3.5 32.9 12.9 13.7 731.9
2.5 3.1 48.8 4.0 6.0 5.0
3.9 4.0 40.9 8.6 10.4 14364.0 34.5 426.1
66
Dosimetry Results for Evaluation on Synthetic
Data
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
67
Informal Evaluation of Other Cases

• Study performance of planner on real cases that
  cannot be treated with conventional radiosurgery
• Study application of planner to treatment of
  extracranial and large tumors?

68
Prostate Tumor Case
Bladder
Rectum
Tumor
69
Isodose Curves for Prostate Case
50 Isodose Curve
70 Isodose Curve
70
Dose-Volume Histograms for Prostate Case
Cubic mm
Rectum
Tumor
15000
12500
Bladder
10000
7500
5000
2500
Percent Dose
71
Prostate Dosimetry with Cyberknife
72
Conclusion

• New generation of radiosurgical devices is
  emerging
• Automatic treatment planning will be necessary to
  harness the flexibility of these new devices
• CARABEAMER has proven to be an effective planning
  approach
• takes advantage of general kinematics of
  Cyberknife
• creates conformal treatments for arbitrarily
  shaped tumors
• deals with critical structures close to tumors
• has satisfactory computational efficiency
• Parts of CARABEAMER are now in clinical use at
  Stanford
• Lot more work to do...
• Greater efficiency to investigate several
  alternative plans
• Better interaction with surgeon
• Use of multi-leaf collimators
• More accurate dose model