Monte Carlo Applications
in Radiation Therapy
Outline
• What is Monte Carlo?
• Why is Monte Carlo needed for radiation therapy
C-M Charlie Ma, Ph.D.
Department of Radiation Oncology
Fox Chase Cancer Center
Philadelphia, PA 19111, USA
• Accelerator simulation
• Radiation detector simulation
• Treatment planning dose calculation
• Beam delivery and dosimetry verification
What is Monte Carlo ?
Why call it Monte Carlo?
• The originators : Von Neumann and Ulam 1949
• The method : Random sampling from pdf’
pdf’s to
construct solutions to problems.
John Von Neumann
Stanislow M. Ulam
(1903-1957)
(1909-1984)
After the city in the Monaco principality ...
1
A simple example: Calculation of
Results of computer simulation (I)
Nc/Ns=
Nc/Ns= r2/(2r)2 = /4
=4Nc/Ns
=4Nc/Ns
Statistical uncertainty !
Courtesy: SB Jiang
Results of computer simulation (II)
Calculated
10
100
1,000
10,000
100,000
1,000,000
10,000,000
100,000,000
values (3.1416)
4.0000
2.8000
3.1280
3.1144
3.1431
3.1412
3.1420
3.1416
2
Photons
What is Monte Carlo
Radiation Transport?
• Random sampling of particle interactions
a good supply of random numbers
e-
probability distributions governing the physics processes
e+
• Information obtained by simulating large
number of histories
Applications of M-C in radiotherapy
•
•
•
•
•
•
•
Fluence and spectrum calculations
Dosimetric parameters (stopping powers, etc.)
Correction factors (BSF, HS, PS, P/S ratio...)
Dosimeter response simulations
Treatment head simulations
Treatment planning dose calculations
Beam delivery and dosimetry verification
3
Accelerator Geometry
Accelerator Simulation
Target
C-M Ma and SB Jiang Phys Med Biol (1999)
Flattening
filter
F Verhaegen and J Seuntjens Phys Med Biol (2003)
Wave guide
Bending
magnet
Electron gun
Monitor
chamber
Multileaf
collimator
Jaws
Monte Carlo Linac simulations
Depth Dose Curves (25 x 25 cm2)
( EGS4/BEAM, NRCC, Canada )
6 MeV
9 MeV
12 MeV
16 MeV
20 MeV
VARIAN
THERAC
Relative Dose
1.0
0.8
0.6
0.4
0.2
0.0
0
SCANDITRONIX
2
4
6
8
10
12
Depth [cm]
PHILIPS
MC Lee Ph.D.Thesis (2002)
4
Depth Dose Curves (6 x 6 cm2)
6 MeV
9 MeV
12 MeV
16 MeV
20 MeV
0.8
6x6
0.6
0.4
0.2
0.0
0
2
4
6
8
15x15
25x25
10
12
0.8
0.6
0.4
0.2
0.0
-16
-12
Depth [cm]
-8
-4
0
4
8
12
16
Lateral Position [cm]
MC Lee Ph.D.Thesis (2002)
MC Lee Ph.D.Thesis (2002)
Transverse Profiles (20 MeV)
6x6
10x10
15x15
Summary of Linac Simulation
25x25
• Monte Carlo simulations have been commissioned for
different clinical accelerators for Monte Carlo RTP
1.0
Relative Dose
10x10
1.0
Relative Dose
1.0
Relative Dose
Transverse Profiles (6 MeV)
0.8
• In principle, knowledge of treatment head geometry
and source information allows accurate simulation
0.6
0.4
• In practice, the required data on a clinical accelerator
may not be known in full, so free parameters should
extend to source geometry and head geometry
0.2
0.0
-16
-12
-8
-4
0
4
Lateral Position [cm]
8
12
16
• Measurement-based source models could be a practical
solution!
MC Lee Ph.D.Thesis (2002)
5
Why Detector Simulation
Detector Simulation
A Nahum Phys Med Biol 1998
• Dosimeter design studies
energy response
angular response
geometry design
material selection
• Perturbation effect studies
E/
photon and electron fluence perturbations
energy and angular response corrections
Cavity Theory
Fricke wall effect
(cylindrical glass vessels at NRCC, PTB and NPL)
The BraggBragg-Gray (small) cavity theory
Dw = Dair sw,air
Pu
Dw is dose to water
Dair is dose to the cavity air
sw,air is the stopping power ratio for water to air
Pu is the fluence perturbation correction factor
(difficult to measure or derive theoretically but easy for Monte Carlo)
6
Wall correction factors
(for NRCC glass vessels in highhigh-energy photon beams)
Summary of Fricke wall study
• Up to 2% changes in Frike dosimetry
standards using glassglass-walled vessels
• Good agreement between Monte Carlo
and experiments (within 3%)!
• Correlated sampling is necessary for
efficiency and accuracy
• Good test for electron transport
Ma et al Med Phys (1994)
Waterproofing sleeve effect
Waterproofing sleeve effect
(cylindrical chamber in mediummedium-energy photon beams)
(cylindrical chamber in mediummedium-energy photon beams)
Ma and Seuntjens Med Phys (1997)
7
Summary of Sleeve Study
• A significant effect at low energies for
PMMA, nylon and polystyrene
Monte Carlo Treatment Planning
• Good agreement between Monte Carlo
and experiment (within 0.2%)
• Correlated sampling is necessary for
efficiency
• A good test of photon transport
Pinnacle3
BEAM/DOSXYZ
Isodose Comparison for Lung Cancer:
Clarkson versus Monte Carlo
80%
95%
Clarkson w/ density
correction
95%
Monte Carlo
EGS4/MCDOSE
Achterberg et al (ESTRO 1999)
Courtesy: T Pawlicki
8
Target Dose and Regions of Recurrence
CORVUS
Monte Carlo
PTV
MC
(95%)
Recurrent
tumor
PTV
EPL
(100%)
MC
(100%)
EPL
(95%)
recurrence
Courtesy: Indrin Chetty
Pawlicki and Ma Med Dosimetry (2001)
Dose Volume Histogram (H&N)
100
Target
Volume (%)
80
60
Beam Delivery and Dosimetry
Verification for IMRT
RT Optic nerve
Pencil beam
RT
Eye
Monte Carlo
40
Spinal
cord
20
0
0.0
5.0
10.0
15.0
20.0
25.0
Dose (cGy)
9
DIRECTION OF BEAM
Effect of Beam Delivery Systems
Y2 JAW
Effect of leaf leakage and scatter
Y1 JAW
X1 JAW
X2 JAW
leaf size
leaf shape
collimator jaw position
Effect of leaf sequence
MLC
dynamic vs step-and-shoot
CARRIAGE B
CARRIAGE A
leaf synchronization
x
ISOCENTER
NX = 1
MLC LEAVES SIDE VIEW ROUNDED ENDS
NX = 2
Film vs Monte Carlo
NX = 3
MC Lee Ph.D.Thesis (2002)
LEAF A
LEAF B
X
Z
MLC CARRIAGE FRONT
VIEW - NON DIVERGENT
ENDS
1.2
1
0.8
1
2
3
4
5
6
7 ….
N
0.6
0.4
0.2
0
1.2
1.2
1
0.8
0.6
0.4
0.2
0
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
A Kapur Ph.D. Thesis (1999)
10
One field intensity map comparison
DVH comparison between prostate plans
with and without tongue-and-groove effect considered
100
Lines:
without T&G (plan 1)
• Fuzzy
• T&G
Line-and-symbols:
with T&G (plan 2)
By shifting doses of
plan 2 horizontally
by 1.6%, two plans
matches
80
Seminal Vesicle
Volume (%)
• Sharp
• No T&G
Prostate
60
Bladder
40
Skin
Rectum
20
Lymph Node
0
0
10
20
30
40
50
60
70
80
90
100
Dose (Gy)
J Deng et al PMB (2001)
T&G
J Deng et al PMB (2001)
Quantitative comparison
of EPID images
Calculations vs. Measurements
(a) Measured
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
(b) MC Computed
Courtesy: Jeff Siebers
11
External diodes derived target motion
Fiducial Motion & Correlation Error
• rms motion =
4.72 mm
• residual rms
after robot
feedback =
1.33 mm
Courtesy: T Guerrero
Effect of RealReal-Time Chest Wall Motion
Feedback on Delivered Dose
transaxial view
planned
EGS4/MCDOSE DVH Tumor & Lung
Residual loss of tumor coverage
w/ motion
delivered
12
Conclusions
• Monte Carlo is becoming a practical tool for
radiotherapy dose calculation and treatment
verification (home
(home--grown vs commercial)
commercial)
• Monte Carlo is ideal for designing and validating
new hardware/software and treatment techniques
• Monte Carlo is being widely used in other areas
such as brachytherapy,
brachytherapy, proton therapy, radiology
and outcome studies
Acknowledgments
Alan Nahum
Pedro Andreo
Bruce Faddegon
Frank Verhaegen
Steve B Jiang
Jinsheng Li
Ajay Kapur
Jeff Siebers
Dave Rogers
Alex Bielajew
Jan Seuntjens
Iwan Kawrakow
Todd Pawlicki
Jun Deng
Michael Lee
Indrin Chetty
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