Monte Carlo methods in
proton beam radiation therapy
Harald Paganetti
p
p
e
–Ionization
• Distal distribution
–Excitation
120
Interaction probability
is proportional to
proton energy
100
80
Dose [%]
Introduction: Proton Physics
Electromagnetic energy loss of protons
60
40
20
0
0
50
100
150
200
250
300
depth [mm]
Peak broadening due to range straggling
Introduction: Proton Physics
Electromagnetic energy loss of protons
• Lateral distribution
p’
θ
p
Multiple Coulomb scattering (small angles)
160 MeV
200 MeV
Introduction: Proton Physics
Nuclear interactions of protons
p’
p’
p
γ, n
Elastic nuclear collision (large θ)
Inelastic int.
p
Nuclear interactions cause a decrease in fluence
Nuclear interactions lead to secondary particles and
thus to
• local dose deposition (secondary protons)
• non-local dose deposition (secondary neutrons)
Introduction: Monte Carlo
Monte Carlo
Probability Density Function
expresses the relative likelihood that a variable will have a
certain value
b
f ( x) ≥ 0 on [a, b]
f (x)dx = 1
a
p
p’
p
p
e
p’
p
p’
θ
p
γ, n
Introduction: Monte Carlo
Introduction: Monte Carlo
step size definition
Condensed history algorithms
group many charged particles track segments into one
single ‘condensed’ step
grouped interactions
discrete interactions
• elastic scattering on nucleus • ‘hard’ d-ray production
energy > cut
multiple Coulomb
• ‘hard’ bremstrahlung
scattering
emission
• soft inelastic collisions
energy > cut
collision stopping
• etc
power
• etc
Monte Carlo applications to proton
radiation therapy
Quality assurance
Treatment head simulation
Patient dose calculations
Treatment head simulation
Phase space calculations
Patient (CT) simulations
Clinical implementation
Neutron dose calculations
Treatment head simulation
Patient simulations
Target
Volume
Beam
Critical
Structure
Double scattering
system
Body
Surface
Aperture
120
Modulator
Dose [%]
Treatment Head Simulation
High-Density
Structure
100
80
60
40
20
0
0
50
100
Depth [mm]
150
200
Treatment Head Simulation
Monte Carlo model of the nozzle (~1000 objects)
Treatment Head Simulation
Monte Carlo model
of the nozzle at the
FHBPTC
Treatment Head Simulation
Monte Carlo model
of the nozzle at the
FHBPTC
Treatment Head Simulation
4D Monte Carlo: Geometry changes during the simulation
via C++ class architecture
Low Z
High Z
1. Beam Gating
Dose [%]
120
100
80
60
40
Beam range: 17.19 cm
Modulation: 6.78 cm
20
0
0
50
100
150
200
150
200
Depth [mm]
2. Beam Current Modulation
120
Dose [%]
Treatment Head Simulation
Range Modulator Wheel Issues
100
80
60
40
Beam range: 17.19 cm
Modulation: 6.78 cm
20
0
0
50
100
Depth [mm]
Treatment Head Simulation
Parameters to characterize the beam
at nozzle entrance
1. Beam size and spread
2. Beam angular spread
3. Beam energy (range!)
4. Beam energy spread
•
(IC measurement)
(manufacturer info)
(control system)
(manufacturer info,
measured)
Are these parameters correlated ?
60
100
55
50
45
80
Dose [%]
40
100
35
60
30
20
40
40
60
80
100
80
N
0
20
40
60
60
80
100
120
N
D e p th [m m ]
0.02
0.02
0.01
0.01
0.00
0.4
am
Be
5
10
Si z
0.0
0.5
1.0
1.5
2.0
2.5
0.01
0.01
0.00
-0.00
-0.01
-0.02
15-0.2
0.0
e
ma
Sig
0.2
0.4
-0.2
-0.02
-0.4
am
Be
Siz
]
[cm
0.02
0.02
-0.02
-0.4
0.0
d]
0
a
igm
eS
0.4
0.2
-0.01
[ra
d]
[ ra
0
0.0
-0.2
-0.4
]
[cm
0.2
Beam Size Sigma [cm]
Depth [cm]
20
0.4
Angular Spread [rad]
ad
-0.02
0.02
20
0.2
-0.01
0.00
ad
re
Sp
re
Sp
40
Angular Spread [rad]
0
l ar
gu
An
Dose [%]
20
l ar
gu
An
Treatment Head Simulation
“Commissioning” of the Monte Carlo
0.02
0.01
0.01
0.00
-0.00
-0.01
-0.02
25-0.2
-0.02
-0.4
0.0
Beam Size Sigma [cm]
30
Dose [%]
Dose [%]
2
4
6
8
10
120
100
80
60
40
20
0
Dose [%]
2
120
100
80
60
40
20
0
Dose [%]
Treatment Head Simulation
120
100
80
60
40
20
0
120
100
80
60
40
20
0
4
2
2
4
4
6
6
6
8
8
8
10
10
12
12
14
depth [cm]
10
14
16
12
16
18
20
14
18
22
20
24
Treatment Head Simulation
Aperture and Compensator
Treatment Head Simulation
Aperture and Compensator
Monte Carlo simulation based
on milling machine files
Example: Quality Assurance / Tolerance Studies
Alignment of second scatterer
100
100
Dose [%]
Dose [%]
80
60
40
20
80
60
40
20
second scatterer aligned
0
0
0
20
40
60
80
100
120
140
-80
160
-60
-40
-20
0
20
40
60
80
Lateral distance to isocenter [mm]
Depth [mm]
120
100
100
Dose [%]
80
Dose [%]
Quality Assurance
120
60
40
20
80
60
40
20
second scatterer tilted by 5o
0
0
0
20
40
60
80
100
Depth [mm]
120
140
160
-80
-60
-40
-20
0
20
40
60
Lateral distance to isocenter [mm]
80
Treatment Head Simulation
Phase Space plane
Phase Space Format Example: (part, x, y, px, py, pz, flags …)
by simulating the ionization chamber output charge
Output − Factor
e ⋅ ε ic
iic =
×
Wair
≅
D cal cGy
MU
iic
dE
dx
Volume for absolute dosimetry
2.2
2.2
12 cm < SOBPr < 15 cm
2.0
20 cm < SOBPr < 24 cm
2.0
Output Factor [cGy / MU]
Output Factor [cGy / MU]
Treatment Head Simulation
Absolute dosimetry (output factor prediction)
1.8
1.6
1.4
1.2
1.0
0.8
1.8
1.6
1.4
1.2
1.0
0.8
0.1
1
10
(SOBPr - SOBPm) / SOBPm
0.1
1
10
(SOBPr - SOBPm) / SOBPm
p ⋅ dξdF
air
Patient Simulation
Monte Carlo dose calculation
• Simulate a large number of particle histories until all
primary and secondary particles are absorbed or
have left the calculation grid
• Calculate and store the amount of absorbed energy
of each particle in each region (voxel)
• The statistical accuracy of the dose is determined by
the number of particle histories
HP1
Patient information
Patient Simulation
Example:
CT scan:
134 CT slices, 512 × 512 voxels/slice
0.488 mm × 0.488 mm × 1.25/2.5 mm
Treatment planning grid:
2.0 mm × 2.0 mm × 2.5 mm
Challenges:
- Memory Consumption
- Many boundary crossings
Slide 24
HP1
Harald Paganetti, 3/14/2008
CT conversion
Patient Simulation
Hounsfield Units (HU)
0
500
1000
1500
2000
2500
3000
HU
Photon Planning System
HU versus electron density
→ Dose-to-water
Density; Material comp.
Proton Planning System
HU versus rel. stopping power
→ Dose-to-water
Density; Material comp.
Monte Carlo
HU versus mass density
HU versus material
→ Dose-to-medium (tissue)
– HU conversion –
Patient Simulation
Group
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
HU range
[ ; -951 ]
[ -950 ; -121 ]
[ -120 ; -83 ]
[ -82 ; -53 ]
[ -52 ; -23]
[ -22 ; 7 ]
[ 8 ; 18 ]
[19 ; 79 ]
[ 80 ; 119 ]
[ 120 ; 199 ]
[ 200 ; 299 ]
[ 300 ; 399 ]
[ 400 ; 499 ]
[ 500 ; 599 ]
[ 600 ; 699 ]
[ 700 ; 799 ]
[ 800 ; 899 ]
[ 900 ; 999 ]
[ 1000 ;1099 ]
[ 1100 ; 1199 ]
[ 1200 ; 1299 ]
[ 1300 ; 1399 ]
[ 1400 ; 1499 ]
[ 1500 ; 1599 ]
[ 1600 ; 1999 ]
[ 2000 ; 3060 ]
[ 3061 ; ]
Density
Density
[g/cm3]
correction
(center of HU bin)
0.0270
1.051
0.4800
0.977
0.9264
0.948
0.9577
0.958
0.9845
0.968
1.0113
0.976
1.0296
0.983
1.0609
0.993
1.1199
0.971
1.1117
1.002
1.1650
1.005
1.2244
1.010
1.2834
1.014
1.3426
1.018
1.4018
1.021
1.4610
1.025
1.5202
1.030
1.5794
1.033
1.6386
1.035
1.6978
1.038
1.7570
1.041
1.8162
1.043
1.8754
1.046
1.9346
1.048
2.0826
1.042
2.4655
1.049
4.5400
1.000
H
C
10.3
11.6
11.3
11.0
10.8
10.6
10.3
9.4
9.5
8.9
8.2
7.6
7.1
6.6
6.1
5.6
5.2
4.9
4.5
4.2
3.9
3.6
3.4
3.4
3.4
10.5
68.1
56.7
45.8
35.6
28.4
13.4
20.7
45.5
42.3
39.1
36.1
33.5
31.0
28.7
26.5
24.6
22.7
21.0
19.4
17.9
16.5
15.5
15.5
15.5
N
75.5
3.1
0.2
0.9
1.5
2.2
2.6
3.0
6.2
2.5
2.7
2.9
3.0
3.2
3.3
3.5
3.6
3.7
3.8
3.9
4.0
4.1
4.2
4.2
4.2
4.2
O
23.2
74.9
19.8
30.8
41.1
50.9
57.8
72.3
62.2
35.5
36.3
37.2
38.0
38.7
39.4
40.0
40.5
41.1
41.6
42.0
42.5
42.9
43.2
43.5
43.5
43.5
Na
0.2
0.1
0.1
0.1
0.2
0.6
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
Material
composition weights [%]
Mg P
S
Cl Ar
1.3
0.2 0.3 0.3
0.1 0.1
0.1 0.1
0.1 0.2 0.2
0.1 0.2 0.2
0.1 0.2 0.2
0.2 0.2 0.2
0.6 0.3
2.1 0.1 0.1
3.0 0.1 0.1
3.9 0.1 0.1
0.1 4.7 0.2 0.1
0.1 5.4 0.2
0.1 6.1 0.2
0.1 6.7 0.2
0.2 7.3 0.3
0.2 7.8 0.3
0.2 8.3 0.3
0.2 8.8 0.3
0.2 9.2 0.3
0.2 9.6 0.3
0.2 10.0 0.3
0.2 10.3 0.3
0.2 10.3 0.3
0.2 10.3 0.3
K
Ca
Ti
0.2
0.1
0.2
0.1
0.1
0.1
4.5
6.4
8.3
0.1
11.7
13.2
14.6
15.9
17.0
18.1
19.2
20.1
21.0
21.9
22.5
22.5
22.5
HU space is divided into 27 groups with members of
each group sharing the same element composition but
differ in mass density (4000 densities)
100.0
Gantry Angle
Patient Simulation
Position XYZ
Rotation
Pitch
Roll
Air Gap
Gantry Couch
AP1A
AS1A
RS1A
RA1A
RS2A
AS2B
0º
65º
305º
295º
300º
90º
0º
270º
50º
0º
60º
270º
ISO
1
1
1
2
2
3
Treatment
Planning
FOCUS/XiO
Clinical Implementation
Patient
Database
Treatment
Control
System
Treatment Head
Geometry
Patient
Geometry
Beam
Setup
Patient
Setup
Phase Space Calculation
Dose Calculation
Monte Carlo
Dose Cube
Monte Carlo
Dose Cube
FOCUS/XiO format
FOCUS and XiO: © Computerized Medical Systems Inc.
Clinical Examples
Example 1
Case 1:
Para-spinal tumor
176 x 147 x 126 slices
voxels: 0.932 x 0.932 x 2.5-3.75 mm3
Clinical Examples
Proton dose in the presence of
range uncertainty
Clinical Examples
Proton dose in the presence of
range uncertainty
Pencil Beam
Monte Carlo
Clinical Examples
1 Gy(RBE)
3 Gy(RBE)
5 Gy(RBE)
7 Gy(RBE)
9 Gy(RBE)
11 Gy(RBE)
13 Gy(RBE)
15 Gy(RBE)
17 Gy(RBE)
Range
Clinical Examples
1 Gy(RBE)
2 Gy(RBE)
3 Gy(RBE)
4 Gy(RBE)
Range
10 Gy(RBE)
20 Gy(RBE)
30 Gy(RBE)
35 Gy(RBE)
40 Gy(RBE)
42 Gy(RBE)
44 Gy(RBE)
46 Gy(RBE)
48 Gy(RBE)
Penumbra
Dose homogeneity
Dose-to-water
Dose-to-tissue
Planned SOBP versus delivered SOBP
1.2
0.8
0.6
0.4
0.2
0.0
0
2
4
6
8
10
12
14
16
Depth [cm]
18
1.2
1.0
Dose [relative]
Dose [relative]
Clinical Examples
1.0
0.8
0.6
0.4
0.2
0.0
0
2
4
6
8
10
Depth [cm]
12
14
16
18
Clinical Examples
MC
Total DVH
XiO
Clinical Examples
Example 2
Case 3:
Maxillary sinus
121x121x101 slices
voxels: 0.656 x 0.656 x 1.25-3.75 mm3
PTV
50
50
Critical
Structure
B
C
A
PTV
50
50
Critical
Structure
B
Pencil Beam
Monte Carlo
Clinical Examples
C
2 Gy(RBE)
6 Gy(RBE)
10 Gy(RBE)
14 Gy(RBE)
18 Gy(RBE)
20 Gy(RBE)
22 Gy(RBE)
24 Gy(RBE)
26 Gy(RBE)
A
Clinical Examples
5 Gy(RBE)
10 Gy(RBE)
15 Gy(RBE)
20 Gy(RBE)
22 Gy(RBE)
24 Gy(RBE)
26 Gy(RBE)
28 Gy(RBE)
30 Gy(RBE)
1 Gy(RBE)
1.5 Gy(RBE)
2 Gy(RBE)
2.5 Gy(RBE)
3 Gy(RBE)
Clinical Examples
10 Gy(RBE)
20 Gy(RBE)
30 Gy(RBE)
40 Gy(RBE)
50 Gy(RBE)
60 Gy(RBE)
65 Gy(RBE)
70 Gy(RBE)
75 Gy(RBE)
2 Gy(RBE)
4 Gy(RBE)
6 Gy(RBE)
8 Gy(RBE)
MC
XiO
Neutron Dose Simulation
Scattered dose as a function of lateral distance
Neutron Dose Simulation
Simulation of the radiation field entering the patient
“External”
Output:
Neutrons leaving the treatment head
Protons leaving the treatment head
“Internal”
Neutron Dose Simulation
Pediatric phantoms
phantom
9 month old
4 year old
8 year old
11 year old
14 year old
Adult
Lee, Lee, Williams, et al. Whole-body voxel
phantoms of paediatric patients - UF Series B.
Phys Med Biol. 51, 4649-4661 (2006)
number of voxels
X
Y
Z
289
180
241
351
207
211
322
171
220
398
242
252
349
193
252
147
86
470
voxel dim (mm)
X
Y
Z
0.9
0.9
3
0.9
0.9
5
1.1
1.1
6
0.9
0.9
6
1.2
1.2
7
4
4
4
Neutron Dose Simulation
From: Annals of the ICRP; ICRP Publication 92; Relative Biological Effectiveness
(RBE), QualityFactor (Q), and Radiation Weighting Factor (wR)
Neutron Dose Simulation
Neutron Dose Simulation
Organ equivalent dose
thyroid (circles)
lung (squares)
liver (triangles)
References
Proton Therapy
Paganetti and Bortfeld: Proton Therapy. In: New Technologies in
Radiation Oncology (Series: Medical Radiology; Subseries: Radiation
Oncology); Eds. Schlegel, W.; Bortfeld, T.; Grosu, A.L.; ISBN 3-54000321-5; Springer Verlag, Heidelberg 2005: 345-63
Monte Carlo dose calculation
Chetty et al., Report of the AAPM Task Group No. 105: issues associated
with clinical implementation of Monte Carlo-based photon and electron
external beam treatment planning. Med Phys 2007: 34, 4818-53
Proton treatment head simulation
Paganetti et al: Accurate Monte Carlo simulations for nozzle design,
commissioning, and quality assurance in proton radiation therapy. Med
Phys 2004: 31, 2107-18
Simulation of neutron doses in proton therapy
Zacharatou Jarlskog et al: Assessment of organ specific neutron
equivalent doses in proton therapy using computational whole-body agedependent voxel phantoms. Phys Med Biol 2008: 53, 693-717
Monte Carlo code Geant4
http://geant4.web.cern.ch/geant4/