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Monte Carlo for Radiation Therapy Dose Calculations
Monte Carlo Refresher Course
AAPM 2002
Jeffrey V. Siebers, VCU
Outline
What Monte Carlo is
Why it is useful
„ Use of Monte Carlo
„
„
Monte Carlo and IMRT
Research tool
IMRT plan verification
¾ IMRT plan optimization
J.V. Siebers
Virginia Commonwealth University
Medical College of Virginia Hospitals
Richmond, Virginia USA
¾
¾
Radhe Mohan
M.D. Anderson Cancer Center
Houston, Texas
Monte Carlo Method
„
What is Monte Carlo?
„
„
Follows the path of individual
representative particles through
accelerator, beam modifiers, and patient
to determine dose, fluence, and other
distributions in patients and phantoms
Uses basic physics interaction
probabilities (sampled via selection of
random numbers) to determine the fate of
the representative particles
Sufficient representative particles are
transported to produce a statistically
acceptable results (averages)
e-
Monte Carlo
e-
Bremsstrahlung
Target
Monte Carlo
e-
Target
Collimator
Collimator
Vacuum Win
Flattening Filter
Ion Chamber
Vacuum Win
Flattening Filter
Ion Chamber
e-
Compton
Jaws
Photoelectric
MLC
Jaws
Electron
slowing down
and absorption
MLC
Simulate many
(106-108)
particles
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Monte Carlo for Radiation Therapy Dose Calculations
Monte Carlo Refresher Course
AAPM 2002
Jeffrey V. Siebers, VCU
and of the
radiation
source
(electrons)
Monte Carlo
Target
Collimator
Requires
detailed
knowledge of
geometry
and materials
Monte Carlo Beam
Characterization
Target
Collimator
Does not change for
different beams
Vacuum Win
Flattening Filter
Ion Chamber
„
Jaws
e-
Vacuum Win
Flattening Filter
Ion Chamber
PSD Model
¾
¾
PSD Plane
Jaws
File of particles
Source Model
MLC
MLC
and the
patient
materials
Beam Characterization and Commissioning
is still a major task for MC
implementations. GIGO!
Dosimetric Verification
Dose Verification
6 MV
10×10 cm2
6 MV
4×4 cm2
10×10
cm2
4×4 cm2
600
wedge
10×10 cm2 600 wedge
No Normalization,
No Output Factor Measurements Required
Why Monte Carlo?
Distance (cm)
Effect of Heterogeneities on
Dose
water
water
air
water
water
Monte Carlo is recognized as the most accurate
dose calculation algorithm, it is limited only by
accuracy of inputs.
Arnfield et al., Med. Phys, 27 (6) 2000
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Monte Carlo for Radiation Therapy Dose Calculations
Monte Carlo Refresher Course
AAPM 2002
Jeffrey V. Siebers, VCU
Pencil Beam
Calculation Speed
Why
Dose Calculation Algorithms
use Monte Carlo for IMRT?
Superposition/Convolution
Monte Carlo
Calculation Accuracy
Intensity
Dose
Conventional dose algorithms
can be inaccurate for
Small fields
Regions of dose gradients
(radiation disequilibrium)
„ Heterogeneous conditions
„
3DCRT
„
IMRT
IMRT is typically delivered through a
sequence of small static fields or with a
dynamically moving aperture with a
small width. Dose gradients are
common place in IMRT fields
MLC Effects on IMRT Field
„
Intensity variation
„
MLC scatter
„
Beam hardening
MLC effect on energy
distribution
MLC Leaf
Kim et al., Med Phys 28 2497
3
Monte Carlo for Radiation Therapy Dose Calculations
Monte Carlo Refresher Course
AAPM 2002
Jeffrey V. Siebers, VCU
MLC scatter contribution
changes with window width
Reasons for physical dose
measurement for IMRT QA
„
Verify dose calculation accuracy
¾
Conversion of fluence to MLC motions
(homogeneous phantom checks)
Data transfer to treatment
machine
„ Ability of machine to deliver
treatment
„
Fix et al., PMB 46 3241
How
Particle Transport
Target
Collimator
Vacuum Win
Flattening Filter
Ion Chamber
include IMRT into Monte Carlo
dose calculation?
Jaws
MLC
How transport
particles
through
(moving) MLC?
Full MLC Transport
Full MLC Transport
„
„
„
Transport particles through full
complex MLC geometry
Method
¾
¾
MLC geometry is
complex
¾
¾
„
Efficiency
¾
sMLC = many segments
dMLC = continuous segments
„
Hundreds of surfaces to check
Slow MC
For IMRT, many particles hit
MLC, requires 2-5x MU,
therefore 2-5x source particles
Speed
¾
Tens to hundreds of CPU hours
with standard codes (EGS4 /
MCNP)
4
Monte Carlo for Radiation Therapy Dose Calculations
Monte Carlo Refresher Course
AAPM 2002
Jeffrey V. Siebers, VCU
Intensity Matrix Approximation
Intensity Matrix
Target
Collimator
„
Vacuum Win
Flattening Filter
Ion Chamber
Jaws
„
Intensity Matrix
MLC
„
„
¾
Wf =Wi ×I(x, y)
MC MLC
Y
fast ray-tracing
Z
Similar to method used by other
algorithms
Matrix can be same as used by other
dose algorithms or independently
developed
Ignores beam hardening
Does not include MLC scatter
Can be added with empirical correction
Attenuation from One Sample
wi
X
At random “times”
determine thickness t
Z
t
...
...
wf
w f = wi e − µ ( E )t / cosθ z
Multiple Samples
k=0
k=3
k=6
k=1
k=4
k=7
k=2
k=5
k=8
Compton Scattered Photons
Choose one tk from the k
thicknesses
„ Sample energy and angle of
scattered photon (EGS4 routines)
„
… k=N
Determine mean
weight by sampling
at multiple random w f
“times”.
w
= i
N
N
∑e
k =1
− µ ( E ) tk / cosθ z
(
w'f = wi 1 − e− µ ( E)t / cosθ z
) µµ e
c
− µ ( E ')t ' / cosθ z'
5
Monte Carlo for Radiation Therapy Dose Calculations
Monte Carlo Refresher Course
AAPM 2002
Jeffrey V. Siebers, VCU
MC MLC Model
Tongue and Groove
MC MLC Model
Fence Field
Step and shoot with 50% even leaves blocking, 50% odd
leaves blocking
Even leaves blocking field, Jaws set for 10x10 field
„
90% of points
within ±1%,
±1 mm
„
90% of points
within ±1%,
±1 mm
„
Leaf edge
effects
accurately
predicted
„
Model OK for
tongue-andgroove field
Advantage of Monte Carlo
„
Checkpoint
Accurately transport radiation through
the treatment head and patient
Disadvantages of Monte Carlo
Calculation time
„ Statistical noise
„
But…
„
„
„
Monte Carlo codes are getting faster
Computers are getting faster
Noise reduction methods are improving
IMRT Plan Verification
Application
of Monte Carlo to IMRT
„
Use MC to re-compute IMRT plan
for dose verification
¾
Method of including MC in IMRT
important
6
Monte Carlo for Radiation Therapy Dose Calculations
Monte Carlo Refresher Course
AAPM 2002
Jeffrey V. Siebers, VCU
IMRT Plan
Verification
IMRT Plan Verification
MC compared to PB, same intensity matrix
MC compared to PB,
MC uses independent
intensity matrix with
empirical scatter correction
1.400
Pencil Beam
1.300
D95
V95
100
Target
Volume (%)
80
Monte Carlo
Monte Carlo
Pencil Beam
60
RT Lung
Ratio (MC/Std)
1.200
Dmean
1.100
1.000
0.900
0.800
40
Wang et al.,
Med. Phys.
29 2705
0.700
20
Cord
0.600
#1
0
0
5
10
15
Dose (Gy)
SC
20
#2
#3
#4
#5
#6
#7
#8
#8b
#9
Patient
Pawlicki et al.,
Med Dosim, 26 157
Lung
Head / Neck
IMRT Plan Verification
IMRT Plan Verification
MC compared to SC, MC transport through MLC
MC compared to SC
MCMLC
66 Gy Hot-Spot
57 Gy line not cover PTV
7
Monte Carlo for Radiation Therapy Dose Calculations
Monte Carlo Refresher Course
AAPM 2002
Jeffrey V. Siebers, VCU
VCU IMRT QA
„
Beams on Patient
Phantom
¾
¾
„
Phantom Dose Verification
Beams on Phantom
Measure each beam at 5 cm depth, 95 cm SSD in
phantom using film
Compare with Pinnacle’s calculation under same
conditions
Patient
¾
Use Monte Carlo to compute beams for IMRT.
„
¾
MC uses leaf sequence files sent to accelerator to generate
intensity modulation
Compare patient DVHs for MC and Pinnacle’s
convolution calculation
Film Dosimetry
Results
For each beam
SC to Measurement
Comparison
Measured
Calculated
(b)
Included in patients chart
54% of points have a dose difference <2% or a DTA <2 mm
MC to Measurement
Comparison
Measurement and Monte Carlo using Tx planning
systems Intensity Matrix
Measured
Calculated
Patient Dose Verification
Beams on Patient
•Compute dose with MC
(b)
Measurement and Monte Carlo
•Use MLC leaf sequence files
(c)
97% within 2%,2 mm
•Compare DVH’s
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Monte Carlo for Radiation Therapy Dose Calculations
Monte Carlo Refresher Course
AAPM 2002
Jeffrey V. Siebers, VCU
Monte Carlo IMRT verification
Obtain acceptable IMRT plan
Copy plan and compute with MC
Yes
<3% DVH difference?
No
Print and sign DVHs
and dose differences
Include in chart
Notify planning team
Yes
Differences
acceptable?
What
is included in the patient’s
chart from the Monte Carlo
Monitor Unit Check?
No
Modify plan based on MC
SC and MC DVHs
IMRT Plan Verification
VCU IMRT QA
∆=10%
Superposition
Monte Carlo
9
Monte Carlo for Radiation Therapy Dose Calculations
Monte Carlo Refresher Course
AAPM 2002
Jeffrey V. Siebers, VCU
IMRT Plan Verification
VCU IMRT QA
What
about using Monte Carlo for
IMRT optimization?
IMRT optimization
dose evaluation modes
One-pass dose computation
Pre-compute and store each individual
beamlet/ray
¾ Sum beamlets weighted by the ray intensity
in each iteration
¾
Multi-pass dose computation
¾
Dose from each beam computed at each
iteration
Compute
Dose (DO)
2
Evaluate
Plan Objective
3
No
Converged?
4
Create Leaf Sequence
Compute
Dose (DO)
MC During IMRT
Optimization
1
Intensity Matrix
Method
„ Bixel Method
„ IMCO
No
3
Converged?
4
Yes
Optimized
Intensity (IO(x,y))
and Dose DO
Create Leaf Sequence
9
Typical IMRT Process
7
9
Can account for
heterogeneities
¾ Not include leaf
effects
¾
Initial
Intensity (II(x,y))
1
Compute
Dose (DO)
2
Evaluate
Plan Objective
3
Converged?
4
Optimization
6
No
Leaf Sequencer
Leaf positions
do not exist
Yes
Optimized
Intensity (IO(x,y))
and Dose DO
5
Create Deliverable Intensities
8
(ID(x,y))
“Deliverable” Dose
DD
7
Create Deliverable Intensities
8
(ID(x,y))
„
2
6
Evaluate
Plan Objective
5
Adjust
I(x,y)
Initial
Intensity (II(x,y))
Optimized Intensity for each beam
Yes
Optimized
Intensity (IO(x,y))
and Dose DO
“Deliverable” Dose
DD
Adjust
I(x,y)
„
1
6
Adjust
I(x,y)
„
IMRT Optimization
Initial
Intensity (II(x,y))
Create Leaf Sequence
5
7
Create Deliverable Intensities
8
(ID(x,y))
Delivery
“Deliverable” Dose
Calculation DD
9
10
Monte Carlo for Radiation Therapy Dose Calculations
Monte Carlo Refresher Course
AAPM 2002
Jeffrey V. Siebers, VCU
Segment Weight
Re-optimization
Previous
Initial
Intensity (II(x,y))
1
Compute
Dose (DO)
2
Evaluate
Plan Objective
3
Converged?
4
Segment Weight
re-optimization
for sMLC
Create Leaf Sequence
(segment and weights)
No
Yes
Optimized
Intensity (IO(x,y))
and Dose DO
Create Leaf Sequence
Segment weight
re-optimization
does not
guarantee an
acceptable solution
Compute
Dose (DO)
Adjust
Segment
weights
Adjust
I(x,y)
6
5
Evaluate
Plan Objective
Converged?
No
7
Yes
Optimized Plan for
Segmentation
Used
REPLACE
Limits solution space
Create Deliverable Intensities
8
(ID(x,y))
“Deliverable” Dose
DD
“Deliverable” Dose
DD
9
Optimization Process
Previous
Deliverable Optimization
Initial
Intensity (II(x,y))
1
Compute
Dose (DO)
2
Initial
Intensity (II(x,y))
6
1
Converged?
4
Yes
Optimized
Intensity (IO(x,y))
and Dose DO
Create Leaf Sequence
5
Compute
Dose (DO)
2
Evaluate
Plan Objective
3
Converged?
4
MCMLC
6
7
Create Deliverable Intensities
8
(ID(x,y))
“Deliverable” Dose
DD
Recomputed with MCMLC
Create Deliverable Intensities
8
(ID(x,y))
9
Adjust
I(x,y)
Adjust
I(x,y)
No
3
SC optimized
7
Create Leaf Sequence
Evaluate
Plan Objective
Isodose coverage
No
Yes
Optimized
Intensity (IO(x,y))
and Dose DO = DD
5
Final dose is
deliverable
Deliverable Optimized with MC
66 Gy Hot-Spot
57 Gy line not cover PTV
Deliverable Optimized with MC
(a) Approved plan that did not agree with measurement
Original SCopt
Deliverable
Plan SC
MC of
Deliverable
MCopt
(deliverable)
Deliverable
optimization
can restore
original
optimized plan
(b) MC optimized plan restores target coverage
11
Monte Carlo for Radiation Therapy Dose Calculations
Monte Carlo Refresher Course
AAPM 2002
Jeffrey V. Siebers, VCU
Problem
„
MC dose calculation takes too
long for iterative IMRT dose
computation
MC IMRT Problem
„
Possible Solutions
Faster MC codes
Negative weight particle method
¾ Hybrid dose calculations
¾ Smoothing / Denoising MC distributions
¾
¾
What are the objectives of
using hybrid algorithms?
What is a Hybrid Algorithm?
„
Combining or mixing of different
dose calculation algorithms
„
Useful for iterative IMRT
calculation
„
Decrease (wall clock) time
required to do plan
optimization
„
Final optimized result as
good as if accurate algorithm
used for all iterations
Hybrid Dose Calc Methods
Smoothing / Denoising
Correction Method
Initialize II
Set C=0
Calculate
C = DMC - DPB
Optimize using
DPB+C = DC
No
„
¾
Smoothing via fitting
¾
Wavelets to remove high frequencies
„
Optimized Dose
DC,O
„
Compute DMC
DC,O = DMC
?
Yes
Approaches
„
Kawrakow, Fippel
Deasy
Can reduce #particles by ~8x
Optimized Dose
(DC,O = DMC)
12
Monte Carlo for Radiation Therapy Dose Calculations
Monte Carlo Refresher Course
AAPM 2002
Jeffrey V. Siebers, VCU
Lessons learned /
Future directions
Smoothing / Denoising
„
MC reveals dose discrepancies
cause by
¾
¾
„
Useful for plan verification
¾
„
Heterogeneities
Fluence
Practical
In future will be used for plan
optimization
¾
Requires speeding up
Current
„
Commercial implementations of
MC
¾
¾
Nomos (Peregrine) Photon MC
Nucletron (MDS Nordion) Electron MC
The
End
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