```Clinical Monte Carlo: Photon
Beams
C-M Charlie Ma, Ph.D.
Fox Chase Cancer Center
What is Monte Carlo?
A mathematical method using random sampling
What is Monte Carlo ?
• The originators : Neumann and Ulam 1949
• The method : Random sampling from pdf’s to
construct solutions to problems.
John Von Neumann
Stanislow M. Ulam
(1903-1957)
(1909-1984)
Why call it Monte Carlo?
After the city in the Monaco principality ...
What is Monte Carlo
• Random sampling of particle interactions
a good supply of random numbers
probability distributions governing the physics processes
• Information obtained by simulating large
number of histories
Why Use Monte Carlo for
An accuracy of about 5% in dose
delivery is required to effectively treat
certain types of cancers and to reduce
complications.
ICRU Reports 24 (1976) and 42 (1988)
The Accuracy Requirement for
Treatment Planning Dose Calculation
σ2=σ2calib+σ2dose+σ2setup+σ2motion +…
and
σ ≥ 2σdose=5%
then
σdose=2.5%
CPU time required
1 Gy => 1 billion electrons (1cmx1cm field)
1% uncertainty for 0.3 cm cubes requires a few
million electrons (hours on a PC)
1 Gy => 1000 billion photons (1cmx1cm field)
1% uncertainty for 0.3 cm cubes requires up to
a few billion photons (days on a PC)
•
•
•
•
•
•
Fluence and spectrum calculations
Dosimetric parameters (stopping powers, etc.)
Correction factors (BSF, HS, PS, P/S ratio...)
Dosimeter response simulations
Treatment planning dose calculations
Beam data
Prescription
Plan description
Dose calculation
Display
Plan evaluation
Patient CT scan
Dose algorithms for RTP
• Photon beams
Clarkson
FFT, FSPB, superposition convolution
super MC, XVMC
Monte Carlo
• Electron beams
3D pencil beam
MMC, super MC, VMC
Monte Carlo
Equivalent Pathlength Correction
High-density medium
Low-density medium
Variation of Dose Kernels with Density
High-density medium
Low-density medium
Variation of Dose Kernels with Density
High-density medium
Low-density medium
High-density medium
The accuracy depends on how it is implemented.
Correction factor for
bone
for
Correction
factor for
bone6 MV photons
Cl2300 C/D 6MV
1.20
1.15
calculated by FOCUS
measured with ion chamber
calculated by EGS4/DOSXYZ
water
1.10
bone
1.05
water
1.00
0.95
0.90
0.85
0.80
0.0
2.0
4.0
6.0
8.0
cm
Depth (cm)
10.0
12.0
14.0
16.0
Correction factor for lung for 6 MV photons
Correction Factor for Lung
Varian Cl2300C/D 6MV
Lung
1.20
1.15
1.10
water
1.05
water
1.00
as Calculated by FOCUS
measured
0.95
calculated by EGS4/DOSXYZ
0.90
0.85
0.80
0.0
2.0
4.0
6.0
8.0
10.0
cm
Depth (cm)
12.0
14.0
16.0
18.0
Layered Lung Phantom
1.20
Heterogeneity Correction Factor
1.18
1.16
Water 3cm
1.14
Lung 5cm
1.12
Water 16 cm
1.10
1.08
1.06
1.04
1.02
1.00
Measured 6MV,
10cmx10cm
0.98
Measured15MV,
5cmx5cm
0.96
Monte Carlo 6MV,
10cmx10cm
0.94
Monte Carlo 15MV,
5cmx5cm
0.92
0.90
0
2
4
6
8
10
12
14
16
DEPTH (cm)
Depth (cm)
18
20
22
24
26
Comparisons of Pencil Beam and Monte Carlo
Mohan et al (1997)
Conventional Method (Pencil Beam)
PEREGRINE
70 Gy
70 Gy
Tumor
Dose Verification for IMRT
(Pawlicki et al 2000)
Monte Carlo
Corvus
Gy
16.2
14.4
12.6
9.0
5.4
1.8
DVH Comparison
100
MC
Corvus
Volume (%)
80
60
GTV
RT Lung
40
20
Cord
0
0
5
10
Dose (Gy)
15
20
Monte Carlo Algorithms
• Electron beams reported
VMC
DOSXYZ
MCDOSE/MCSIM
PENELOPE
MCRTP
DPM
• Photon beams reported
XVMC
PEREGRINE
MCNP
DOSXYZ
MCDOSE/MCSIM/MCRS
Current Status of MCTP
Accuray
NOMOS
DOSIGRAY
Varian/BrainLab
FCCC...
NumeriX?
Nucletron
CMS
MCV...
Implementation of MCTP
• Accelerator simulation
• Source modeling
• Beam commissioning
• CT data conversion and phantom setup
• Dose calculation algorithms
• Data processing and plan evaluation
• Plan optimization
Measured vs MC Reconstructed Dose Distributions
18 MV
40cmx40cm
6 MV
40cmx40cm
Yang et al, Phys Med Biol (2004) 49: 2657-73
Combined Dose Distribution: Film vs Monte Carlo
Delivery in film phantom
Patient plan (Corvus)
Monte Carlo dose
calculation
inferior
Lee et al (2001)
312 cm
cm from
from isocenter
isocenter
superior
Calculations vs. Measurements
Energy
4 MV
CORVUS
Meas
M-C
2.177 Gy 2.177 Gy 2.201 Gy
15 MV
2.146 Gy 2.161 Gy 2.276 Gy
M-C Simulation Geometry
Source plane
contours
CT phantom
Beam modifier
CT Number to Medium Conversion
2.5
2000~2.088g/cm3
125~1.101g/cm3
-700~0.302g/cm3
-950~0.044g/cm3
-1000~0.001g/cm3
Mass density (g/cm^3)
teflon
2.0
1.5
Skeleton - Ribs
polycarbonate
Vertebral body
water
polyethylene Alderson Muscle
1.0
0.5
Alderson Lung
air
0.0
0
500
1000
1500
CT Number
2000
2500
Density map
Medium map
Treatment Plan Comparison
Prostate
Corvus
Monte Carlo
Gy
77.2
70.0
56.1
48.9
35.0
27.8
21.1
13.9
Prostate
100
MC
Corvus
Volume (%)
80
Prostate
60
40
20
Rectum
0
0
15
30
45
Dose (Gy)
60
75
90
Dose Verification for Non-coplanar Prostate IMRT
100
Volume (%)
80
Corvus without correction
Corvus(CTV) with correction
Monte Carlo
Non-coplanar plan comparison
rectum
60
target
40
20
0
0
50
100
200
150
Dose (cGy)
250
300
T11-L1 Vertebra
Monte Carlo
Gy
17.6
15.6
13.7
11.7
9.8
7.8
5.9
3.9
2.0
Corvus
T11-L1 Vertebra
100
MC
Corvus
Volume (%)
80
GTV
60
40
Cord
20
0
0
5
10
Dose (Gy)
15
20
Effect of Couch Bar on IMRT Dose Distribution
Attenuation for 18 MV photons
40
d=3.3cm calculated
d=3.3cm measured
d=10cm calculated
d=10cm measured
Relative Dose (%)
30
Without bar
20
10
0
-20
-10
0
Off-axis Distance (cm)
10
20
MC vs film measurement
Yang et al 2005
With bar
Effect of Couch Bar on IMRT Dose Distribution
IMRT using 6 MV photons
IMRT using 18 MV photons
DVH Data
18MV DVH
100
100
rectum-no bar
CTV-no bar
rectum-with bar
CTV-with bar
60
40
20
0
rectum - no bar
CTV - no bar
rectum - with bar
CTV - with bar
80
Volume (%)
Volume (%)
80
60
40
20
0
50
Yang et al 2005
100
150
Dose (cGy)
200
250
300
0
0
50
100
Dose
150
200
Mean Target Dose (BP vs MC)
Mean target dose: Pencil beam vs Monte Carlo
ne
ck
an
d
he
pe
lv
is
bd
.
/a
10.0
th
or
ax
Difference relative to Rx dose (%)
15.0
5.0
0.0
-5.0
-10.0
-15.0
Patient cases
Minimum Target Dose (BP vs MC)
an
d
he
pe
lv
is
ra
x
25.0
/a
bd
.
ne
ck
35.0
th
o
Difference relative to Rx dose (%)
Minimum target dose: Pencil beam vs Monte Carlo
15.0
5.0
-5.0
-15.0
-25.0
-35.0
Patient cases
Max. Critical Structure Dose (BP vs MC)
ck
ne
an
d
lv
is
he
15.0
pe
/a
bd
.
20.0
th
or
ax
Difference relative to Rx dose (%)
Maximum critical structure dose: Pencil beam vs Monte Carlo
10.0
5.0
0.0
-5.0
-10.0
-15.0
-20.0
0
Patient cases
Beamlet Dose Distributions
FSPB
90
70
50
5
Pawlicki and Ma (2001)
Monte Carlo
90
70
50
5
CyberKnife Monte Carlo
CyberKnife Monte Carlo
Summary
• MC dose calculation is becoming a practical
• The accuracy of MC dose calculation
depends on the implementation
• The potential of MC dose calculation
remains to be explored
Acknowledgments
The FCCC/Stanford Monte Carlo Team
Charlie Ma
Bob Price
Lili Chen
Eugene Fourkal
Jinsheng Li
Lu Wang
Yan Chen
James Fan
Teh Lin
Max Jin
Steve Jiang
Todd Pawlicki
Jun Deng
Bilal Shahine
Ajay Kapur
Michael Lee
Qianyi Xu
Iavor Veltchev
Alain Tafo
Ahmed ElDib
Francis Tang
Sotirios Stathakis
Jay Chen
Wei Luo
Jie Yang
Lihong Qin
Meisong Ding
Omar Chibani
Grisel Mora
Thai Bing Nguyen
William Xiong
Antonio Leal
Freek Du Plessis
Thank You
FCCC Monte Carlo courses, April 2010
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