Title: Treatment Planning for ImageGuided Robotic Radiosurgery
1Treatment Planning forImage-Guided Robotic
Radiosurgery
- Rhea Tombropoulos,
- John Adler, and Jean-Claude Latombe
- Computer Science Department
- Neurosurgery Department
- Stanford University
2Outline
- Introduction radiosurgical planning problem
- Conventional systems
- The Cyberknife system image-guided robotic
radiosurgery - The CARABEAMER planner
- Conclusion
3Radiosurgery
- 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
4The Problem...
Tumor bad
Critical structures good and sensitive
Brain good
5Cross-firing at the Tumor Decreases Dose to
Normal Brain Tissue
6Treatment 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
7Approaches 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
8Conventional Radiosurgical SystemsLimit
Treatment Alternatives
- Stereotactic frame required
- Isocenter-based treatments
from Luxton et al., 1993
adapted from Winston and Lutz, 1988
9Stereotactic Frame
10Conventional 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
11Typically, 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)
12Most 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
13What 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
14Image-Guided Robotic Radiosurgery
Cyberknife system
15Arbitrarily Shaped Dose Distributions
16The 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
17Basic 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)
18Basic Planning Algorithm in Context
Delineate Regions of Interest
3-D Reconstruction
Assign Constraints
Beam Selection
Beam Weighting
Dosimetry Calculations
Plan Evaluation
Treatment
19Hypotheses in Basic Planner
- Beam diameter is fixed and given
- Radiation energy is constant throughout the beam
- Beam is perfectly cylindrical
20Step 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
21The 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
22Step 2 The system creates a 3-dimensional
reconstruction of the geometry
- Triangulated surface representation of tumor -
Volume representation (3D array of voxels) of
tissue
23Step 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
24Beam Selection Algorithm
- Place points evenly on the surface of the tumor
- Pick beam orientations at random at these points
25Evenly 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
26Pick Beam Orientations at Random at Target Points
27 More Deterministic (Heuristic) Schemes for Beam
Selection are not as Robust
28At the End of Beam Selection the Region of High
Dose Encompasses the Tumor
50 Isodose Surface
80 Isodose Surface
All beams have same weight
29Dose-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
30Step 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
31Establish 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
32Reducing 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
33Results of Beam Weighting
Before Weighting
After Weighting
50 Isodose Curves
80 Isodose Curves
34Dose-Volume Histograms afterBeam Weighting
cubic mm
cubic mm
Percent Dose
Percent Dose
Tumor (Integral 94.03)
Brain Stem (Integral 2.57)
35Histogram Comparison
36Step 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
37Step 6 Plan Evaluation
- Radiation oncologist reviews resulting plan
- If satisfactory, treatment can be delivered
- If not...
- Add new constraints
- Adjust existing constraints
38Extensions 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
39Path 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
40Automatic 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
41Better 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
42Finding 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
43A 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 -
. . .
. . .
44CARABEAMER 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 -
. . .
45Minimizing 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
46Iterative 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
47Objective 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 -
. . .
48Evaluation
- 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
49Evaluation 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
50Evaluation 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
51Evaluation 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
52Evaluation 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
53Sample Case
Linac plan 80 Isodose surface
CARABEAMERs plan 80 Isodose surface
54Sample Case
50 Isodose Surface
80 Isodose Surface
Linac plan
CARABEAMERs plan
55Sample Case
Linac plan 80 Isodose surface
CARABEAMERs plan 80 Isodose surface
56Sample Case
CARABEAMERs plan 80 Isodose surface
Linac plan 80 Isodose surface
57Sample Case
Linac plan 50 Isodose surface
CARABEAMERs plan 50 Isodose surface
58Sample Case
Linac plan 80 Isodose surfaces
CARABEAMERs plan 80 Isodose surfaces
59Sample Case
Linac plan 80 Isodose surface
CARABEAMERs plan 80 Isodose surface
60Sample Case
Linac plan 80 Isodose surface
CARABEAMERs plan 80 Isodose surface
61Evaluation on Synthetic Data
- GOAL Demonstrate CARABEAMERs performance on
increasingly difficult cases - Evaluate performance on 36 different data sets
- Study 2 different iterations algorithms
62Evaluation 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
63Evaluation 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
64Average 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
65Average 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
66Dosimetry 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
67Informal 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?
68Prostate Tumor Case
Bladder
Rectum
Tumor
69Isodose Curves for Prostate Case
50 Isodose Curve
70 Isodose Curve
70Dose-Volume Histograms for Prostate Case
Cubic mm
Rectum
Tumor
15000
12500
Bladder
10000
7500
5000
2500
Percent Dose
71Prostate Dosimetry with Cyberknife
72Conclusion
- 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