Transcript Multi-Query Strategies

CS 326 A: Motion Planning
http://robotics.stanford.edu/~latombe/cs326/2002
Radiosurgical Planning
Radiosurgery
Minimally invasive procedure that uses
an intense, focused beam of radiation as
an ablative surgical instrument to
destroy tumors
Tumor = bad
Brain = good
Critical structures
= good and sensitive
The Radiosurgery Problem
Dose from multiple beams is additive
Treatment Planning for
Radiosurgery
• Determine a set of beam
configurations that will
destroy a tumor by crossfiring at it
• Constraints:
– Desired dose distribution
– Physical properties of the
radiation beam
– Constraints of the device
delivering the radiation
– Duration/fractionation of
treatment
Tumor
Critical
Conventional Radiosurgical Systems
• Isocenter-based treatments
• Stereotactic frame required
Gamma Knife
LINAC System
Winston and Lutz, 1988
Luxton et al., 1993
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” where coverage is poor
– “Hot Spots” where the spheres overlap
– Over-irradiation of healthy tissue
Stereotactic Frame for
Localization
• Painful
• Fractionation of
treatments is
difficult
• Treatment of
extracranial tumors
is impossible
Optimization Approach to Planning
• Treatment planning variables:
–
–
–
–
Isocenter locations
Treatment arcs
Collimator diameter
Beam weights
• User specifies most planning variables
• User defines constraints on dose to points and
optimization function
• Optimization technique determines beam
weights
[Bahr, 1968; Langer et al. 1987; Webb, 1992; Carol et al., 1992; Xing et al., 1998, …]
Motion-Planning Approach
Critical Structure
Construction of free space
• Configuration space of
the beam is a unit
sphere
• Construct free space
by projecting critical
structures onto the
sphere
• Search for longest arcs
in free space
[Schweikard, Adler, and Latombe, 1992, 1993]
Conformal Dose Distributions
The CyberKnife
linear accelerator
X-Ray
cameras
robotic gantry
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)
Inputs to CARABEAMER
(1) Regions of Interest:
Surgeon delineates the
regions of interest
CARABEAMER generates
3D regions
Inputs to CARABEAMER
(2) Dose Constraints:
Dose to tumor
Tumor
Dose to critical
structure
Critical
Falloff of dose
around tumor
Falloff of dose
in critical structure
(3) Maximum number of beams
Basic Problem Solved by
CARABEAMER
• Given:
– Spatial arrangement of regions of interest
– Dose constraints for each region: a  D  b
– Maximum number of beams allowed: N (~100400)
• Find:
– N beam configurations (or less) that generate
dose distribution that meets the constraints.
Beam Configuration
• Position and orientation of the radiation
z
beam

y
(x, y)
x

• Amount of radiation or beam weight
• Collimator diameter
 Find 6N parameters that satisfy the constraints
CARABEAMER’s Approach
1.
Initial Sampling:
Generate many (> N) beams at random, with each beam
having a reasonable probability of being part of the
solution.
2. Weighting:
Use linear programming to test whether the beams can
produce a dose distribution that satisfies the input
constraints.
3. Iterative Re-Sampling:
Eliminate beams with small weights and re-sample more
beams around promising beams.
4. Iterative Beam Reduction:
Progressively reduce the number of beams in the
solution.
Initial Beam Sampling
• Generate even distribution of target points on the
surface of the tumor
• Define beams at random orientations through these
points
Evenly Spacing Target Points
on Tumor
• Turk [1992]
• Normally distribute
points on tumor surface
• Use potential field to
better distribute points
Deterministic Beam Selection is
Less Robust
Curvature Bias
• Place more target points in regions of
high curvature
Dose Distribution Before Beam
Weighting
50% Isodose Surface
80% Isodose Surface
CARABEAMER’s Approach
1.
Initial Sampling:
Generate many (> N) beams at random, with each beam
having a reasonable probability of being part of the
solution.
2. Weighting:
Use linear programming to test whether the beams can
produce a dose distribution that satisfies the input
constraints.
3. Iterative Re-Sampling:
Eliminate beams with small weights and re-sample more
beams around promising beams.
4. Iterative Beam Reduction:
Progressively reduce the number of beams in the
solution.
Beam Weighting
• Construct geometric arrangement of regions formed
by the beams and the tissue structures
• Assign constraints to
each cell of the
B1
arrangement:
– Tumor constraints
– Critical
B2
constraints
T
C
B4
B3
Linear Programming Problem
• 2000  Tumor  2200
T
B1
B2
2000
2000
2000
2000
2000
2000
2000
2000
2000
C









B2
B4
B3
B3
B1
B1
B1
B1
B1
+

+

+
+
+

+
B4  2200
2200
B4  2200
2200
B3 + B4  2200
B4  2200
B2 + B4  2200
2200
B2  2200
• 0  Critical  500
B4
B3
0  B2  500
Elimination of Redundant
Constraints
• 2000 < Tumor < 2200
2000
2000
2000
2000
2000
2000
2000
2000
2000
<
<
<
<
<
<
<
<
<
B2
B4
B3
B3
B1
B1
B1
B1
B1
+
<
+
<
+
+
+
<
+
B4 < 2200
2200
B4 < 2200
2200
B3 + B4 < 2200
B4 < 2200
B2 + B4 < 2200
2200
B2 < 2200
• 2000 < Tumor < 2200
2000 < B4
2000 < B3
B1 + B3 + B4 < 2200
B1 + B2 + B4 < 2200
2000 < B1
2000 < B2 + B4
2000 < B4
B2 + B4 < 2200
B1 + B2 + B4 < 2200
Results of Beam Weighting
Before Weighting
50%
Isodose
Curves
80%
Isodose
Curves
After Weighting
CARABEAMER’s Approach
1.
Initial Sampling:
Generate many (> N) beams at random, with each beam
having a reasonable probability of being part of the
solution.
2. Weighting:
Use linear programming to test whether the beams can
produce a dose distribution that satisfies the input
constraints.
3. Iterative Re-Sampling:
Eliminate beams with small weights and re-sample more
beams around promising beams.
4. Iterative Beam Reduction:
Progressively reduce the number of beams in the
solution.
Iterative Re-Sampling
• The initial set of beam may not contain
a solution.
• Find the best possible solution
• Keep beams that are useful
• Remove beams that are not useful
• Re-sample
Reformulating the LP Problem …
A linear program is typically specified as:
Minimize:
c1x1 + c2x2 + . . . + cnxn
Subject to:
l1  a1,1x1 +a. 1,2x2
+ . . . + a1,nxn  u1
..
l2  a2,1x1 +a2,2x 2
+ . . . + a2, nxn  u2
lm  am,1x1 +am,2x 2
+ . . . + am, nxn  um
Reformulating the LP Problem …
Using slack variables, we can rewrite this:
Minimize: c1x1 + c2x2 + . . . + cnxn
Subject to:
a1,1x1 + a1,2x2 +
. . . + a1,nxn + s1 = 0, -u1  s1  -l1
...
a2,1x1 + a2,2x2 + . . . + a2,nxn + s2 = 0, -u2  s2  -l2
am,1x1+ am,2x2 + . . . + am,nxn+ sm= 0, -um  sm  -lm
… to Solve for the Best Possible
Solution
New slacks s1, …, sm :
Minimize: |s1 | + | s2 | + . . . + | sm |
Subject to:
a1,1x1 + a1,2x2 + . . . + a1,nxn + s1 + s1 = 0, -u1  s1  -l1
a2,1x1 + a2,2x.2 + . . . + a2,nxn + s2+ s2 = 0, -u2  s2  -l2
..
am,1x 1 + am,2x 2 + . . . + am,nxn + sm+ sm = 0, -um  sm  -lm
The idea is to minimize the sum of the infeasibilities
Re-Sampling Step
Repeat until the constraints are met:
1. Run linear program to find closest possible
solution
2. If some slack variables s1, …, sm  0
• Eliminate beams with low weights
• Replace them with new beams:
– Randomly generate beams in neighborhood of
highly weighted beams
– Randomly generate beams according to initial
algorithm
CARABEAMER’s Approach
1.
Initial Sampling:
Generate many (> N) beams at random, with each beam
having a reasonable probability of being part of the
solution.
2. Weighting:
Use linear programming to test whether the beams can
produce a dose distribution that satisfies the input
constraints.
3. Iterative Re-Sampling:
Eliminate beams with small weights and re-sample more
beams around promising beams.
4. Iterative Beam Reduction:
Progressively reduce the number of beams in the
solution.
Re-Sampling to Reduce
Total # of Beams
Repeat until dose constraints are met
with specified number N of beams:
1. If too many beams in the solution:
•
•
Eliminate beams with low weights
Generate smaller number of beams
2. If no solution:
•
Add more beams
Plan Review
• Calculate resulting dose distribution
• Radiation oncologist reviews
• If satisfactory, treatment can be
delivered
• If not...
– Add new constraints
– Adjust existing constraints
Treatment Planning: Extensions
• Simple path planning
and collision avoidance
• Automatic collimator
selection
Tumor
Critical
• Better dosimetry
model
Evaluation on Sample Case
Linac plan
80% Isodose surface
CARABEAMER’s
plan
80% Isodose surface
Another Sample Case
50% Isodose
Surface
80% Isodose
Surface
LINAC plan
CARABEAMER’s
plan
Evaluation on Synthetic Data
2000  DT  2400,
DC  500
n = 500
X
2000 
 2200,
DC  500
DT
X
n = 250
n = 100
2000  DT  2100,
DC  500
Constraint
Iteration
X
Beam
Iteratio
n
10
random
seeds
X
Dosimetry Results
Case #1
80% Isodose Curve
90% Isodose Curve
Case #3
80% Isodose Curve
90% Isodose Curve
Case #2
80% Isodose Curve
90% Isodose Curve
Case #4
80% Isodose Curve
90% Isodose Curve
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
:20
:20
:35
:41
:40
:51
:03:30
:03:32
:04:28
:05:23
:05:33
:07:19
:04:36
:04:11
:05:03
:06:45
:07:19
:07:06
3:06:12
3:09:19
3:35:28
1:40:55
1:44:18
1:41:19
:32
:29
:43
:50
:59
:01:02
:05:50
:05:50
:08:53
:08:37
:08:42
:10:43
:23:51
:24:44
:33:02
:13:05 25:38:36 6:33:02
:12:16 27:55:18 7:11:01
:21:06
176:25:02
:01:34
:01:28
:02:21
:01:41
:01:31
:02:38
:48:54
:40:49
1:57:25
:27:39
:24:43
1:02:27
3:26:33
3:22:15
7:44:57
1:03:06 53:58:56 44:11:04
1:07:12
84:21:27
5:06:29
2000-2200
n = 500
n = 250
n = 100
2000-2100
Evaluation on Prostate Case
50% Isodose Curve
70% Isodose Curve
Cyberknife Systems
Stanford Report, July 25, 2001
Contact
Stanford Report
News
Service
/Press
Releases
Patients gather to praise minimally
invasive technique used in treating tumors
By MICHELLE BRANDT
When Jeanie Schmidt, a critical care nurse from Foster City, lost hearing in her left ear and experienced
numbing in her face, she prayed that her first instincts were off. “I said to the doctor, `I think I have an
acoustic neuroma (a brain tumor), but I'm hoping I'm wrong. Tell me it's wax, tell me it's anything,'” Schmidt
recalled.
It wasn't wax, however, and Schmidt – who wound up in the Stanford Hospital emergency room when her
symptoms worsened – was quickly forced to make a decision regarding treatment for her tumor.
On July 13, Schmidt found herself back at Stanford – but this time with a group of patients who were treated
with the same minimally invasive treatment that Schmidt ultimately chose: the CyberKnife. She was one of 40
former patients who met with Stanford faculty and staff to discuss their experiences with the CyberKnife – a
radiosurgery system designed at Stanford by John Adler Jr., MD, in 1994 for performing neurosurgeries without
incisions.
“I wanted the chance to thank everyone again and to share experiences with other patients,” said Schmidt,
who had the procedure on June 20 and will have an MRI in six months to determine its effectiveness. “I feel
really lucky that I came along when this technology was around.”
The CyberKnife is the newest member of the radiosurgery family. Like its ancestor, the 33-year-old Gamma
Knife, the CyberKnife uses 3-D computer targeting to deliver a single, large dose of radiation to the tumor in an
outpatient setting. But unlike the Gamma Knife – which requires patients to wear an external frame to keep
their head completely immobile during the procedure – the CyberKnife can make real-time adjustments to
body movements so that patients aren't required to wear the bulky, uncomfortable head gear.
The procedure provides patients an alternative to both difficult, risky surgery and conventional radiation
therapy, in which small doses of radiation are delivered each day to a large area. The procedure is used to treat
a variety of conditions – including several that can't be treated by any other procedure – but is most commonly
used for metastases (the most common type of brain tumor in adults), meningomas (tumors that develop from
Since January 1999, more than
335 patients have been treated at Stanford with the CyberKnife.
the membranes that cover the brain), and acoustic neuromas.