Clinical implementation and
application of Monte Carlo methods
in photon and electron dose
calculation
John DeMarco1 and Joanna E. Cygler2,3,4
1UCLA
Radiation Oncology, David Geffen School of Medicine
2The
Ottawa Hospital Cancer Centre, Ottawa, Canada
3Carleton University Dept. of Physics, Ottawa, Canada
4University of Ottawa, Dept. of Radiology. Ottawa, Canada
The Ottawa
L’Hopital
Hospital
d’Ottawa
Regional Cancer Centre
Part I: Photon beams
John DeMarco, Ph.D.
UCLA Department of Radiation Oncology
David Geffen School of Medicine
Los Angeles, CA
Outline
1. Educational review of the physics of the MC method.
2. Factors associated with vendor implementation of
the MC dose calculation, such as statistical
uncertainties, spatial resolution, variance reduction,
CT-number to material density assignments, and
reporting of dose-to-medium versus dose-to-water.
3. Review the vendor transport codes currently used
for clinical treatment planning.
4. Experimental verification of Photon based MC
algorithms.
5. Potential clinical implications of Photon based MC
calculated dose distributions.
General Purpose Monte Carlo Codes
Monte Carlo Codes Optimized for
Treatment Planning
Peregrine (Hartmann-Siantar et. al. 2002)
DPM (Sempau et. al. 2000)
MCDose (Ma et. al. 2002)
VMC/XVMC (Kawrakov and Fippel)
Commercial implementations
CMS Monaco
Brainlab iPlan
I. Kawrakow, M. Fippel, and K. Friedrich, ‘‘3D electron dose calculation using a Voxel
based Monte Carlo algorithm (VMC),’’ Med. Phys. 23, 445–457 (1996).
M. Fippel, “Fast Monte Carlo dose calculation for photon beams based on the VMC
electron algorithm”, Med. Phys., 26, 1466-1475 (1999).
Accuray Multiplan
C-M Ma, J S Li, T Pawlicki, S B Jiang, J Deng, M C Lee,T Koumrian, M Luxton and S
Brain, “A Monte Carlo dose calculation tool for radiotherapy treatment planning”
Phys. Med. Biol. 47 (2002) 1671–1689.
Ma C-M, Li JS, Deng J, Fan J. “Implementation of Monte Carlo dose calculation
for CyberKnife treatment planning. J Phys Conf Ser 2008;102
Spatial
resolution
Statistical
uncertainty
Material
Conversion
MLC Modeling
iPlan/Brainlab
Linear Accelerator Source Modeling
Phase-space
Virtual source
Virtual Energy Fluence Model
Complete Simulation (target to
patient)
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. 34, 4818-4853 (2007).
Virtual Energy Fluence Model
• Primary photon source and multiple
scatter photon sources defined as
two-dimensional Gaussian shapes
• Electron contamination source
• Photon energy spectrum derived
based upon measured depth dose
curves in water
M. Fippel, F. Haryanto, O. Dohm, F. Nusslin, and S. Kriesen,
“A virtual photon energy fluence model for Monte Carlo
dose calculation”, Med. Phys. 30, 301-311, (2003).
Photon Transport
Collide or Cross?
Region 1
• Energy (E)
v
• Direction u = (u, v, w) = (cos θ x , cos θ y , cos θ z )
• Position
L
v
x = (xo , yo , zo )
x=
− ln (ξ )
μ
Region 2
Sampling for the photon
collision type
0.000
Coherent
0.107
Incoherent
Random Number = 0.532
0.788
1.000
PhotoElectric
Update Photon
Direction
φ
θ
(u,v,w)
u = cosθx = sinθ cosφ
y = cosθ y = sinθ sinφ
z = cosθz = cosθ
(0,0,1)
Particle start
CT Voxel
Array
The
transport
process
is
repeated across each voxel of a
3D rectilinear array (based upon
the simulation CT scan).
Appropriate routines for scoring
the energy deposition from
secondary electrons.
Particle end
Appropriate routines to convert
from HU to mass density and
material composition on a voxel by
voxel basis.
Accuracy vs. Precision
1
x = ∑xi
n i=1
N
sx
sr =
x
⎡ ∑ xi2 1 ⎤
− ⎥
sr ≈ ⎢
2
⎢⎣ (∑ xi ) n ⎥⎦
Reproduced from the MCNP users manual
Simulation Efficiency and
Variance Reduction
1
ε= 2
sT
I.
Kawrakow
and
M.
Fippel,
“Investigation of variance reduction
techniques for Monte Carlo photon
dose calculation using XVMC”. Phys.
Med. Biol. 45 (2000) 2163–2183.
• “Variance reduction” techniques seek to increase the efficiency
of the simulation by
• ray-tracing
• photon splitting
• electron history repetition
• electron and photon cut-off energies
Particle start
Primary photon
collision points
Initial ray-tracing can be used to
pre-calculate the collision number
within a voxel for incoming
primary photons.
Particle end
Spatial
resolution
Statistical
uncertainty
Material
Conversion
MLC Modeling
iPlan/Brainlab
Monte Carlo calculation time as a function
of the axial plane voxel size
(iPlan/Brainlab Monte Carlo implementation)
7-Field IMRT plan
RPC Lung & Spine phantom
Mean variance = 2%
Dose-to-medium
Monte Carlo calculation time as a function
of the variance setting
(iPlan/Brainlab Monte Carlo implementation)
7-Field IMRT plan
RPC Lung & Spine phantom
Voxel resolution = 3 mm
Dose-to-medium
Variance Setting and the Qualitative Assessment
of the Absorbed Dose Distribution
5%
2%
7-Field IMRT plan
RPC Lung & Spine phantom
Voxel resolution = 3 mm
Dose-to-medium
1%
Mean Variance = 5%
Mean Variance = 1%
7-Field IMRT plan
RPC Lung & Spine phantom
Voxel resolution = 3 mm
Dose-to-medium
Mean Variance = 5%
Mean Variance = 1%
7-Field IMRT plan
RPC Lung & Spine phantom
Voxel resolution = 3 mm
Dose-to-medium
Dosew vs. Dosemed
J. V. Siebers, P. J. Keall, A. E. Nahum, and R. Mohan,
“Converting absorbed dose to medium to absorbed
dose to water for Monte Carlo based photon beam
dose calculations,” Phys. Med. Biol. 45, 983–995
2000.
7-Field IMRT plan
RPC Lung & Spine phantom
Dmed
Dw
Clinical Planning Comparison
medium vs. water
(γ-setting 3%/3mm)
Dosimetric Validation
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. 34, 4818-4853 (2007).
“Experimental verification of a MC algorithm should include testing to assess
the accuracy of: (a) the beam model be it measurement-driven or based on
treatment head simulation and (b) the radiation transport algorithm in
homogeneous and heterogeneous phantoms. The former is part of routine
commissioning of dose calculation algorithms, whereas the latter is likely to
have significantly more involvement from developers and vendors.”
• Beam Model
• Multileaf collimator and other beam modifying devices
• Output factors and the normalization condition for conversion to absolute dose
B. Fraass, K. Doppke, M. Hunt, G. Kutcher, G. Starkschall, R. Stern, and J. Van Dyke, “American Association
of Physicists in Medicine Radiation Therapy Committee Task Group 53: Quality assurance for clinical
radiotherapy treatment planning,” Med. Phys. 25, 1773–1829 1998.
IAEA-Technical Report Series No. 430: Commissioning and quality assurance of computerized planning
systems for radiation treatment of cancer,” in International Atomic Energy Agency, Vienna, 2004
Dosimetric Validation
CMS Monaco
Grofsmid et al. “Dosimetric validation of a commercial Monte
Carlo based IMRT planning system”, Med. Phys. 37, 540-549,
(2010).
Dosimetric Validation
CMS Monaco
Grofsmid et al. “Dosimetric validation of a commercial Monte
Carlo based IMRT planning system”, Med. Phys. 37, 540-549,
(2010).
Dosimetric Validation
CMS Monaco
Grofsmid et al. “Dosimetric validation of a commercial Monte
Carlo based IMRT planning system”, Med. Phys. 37, 540-549,
(2010).
Retrospective Comparison
Accuray Multiplan
2.1.0
Sharma et al. “Clinical implications of adopting Monte Carlo treatment
planning for Cyberknife”, JACMP, 11, (170-175), 2010.
8-Field IMRT plan
3 x 18 = 54 Gy
Clinical Planning Comparison
Pencil beam algorithm versus Monte Carlo
2.5x2.5x1.5 mm3
Monte Carlo Variance setting = 1%
Dose to Medium
The Monte Carlo recalculated plan predicts a
lower dose (3%-8%) across
the axial slice of the PTV
Monte Carlo
Pencil beam
Clinical Implications for Monte Carlo
based Photon Treatment Planning
N. van der Voort et al., “Clinical introduction of Monte Carlo treatment
planning: A different prescription dose for non-small cell lung cancer
according to tumor location and size”, Radiotherapy and Oncology 96 (2010)
55–60.
• Comparison of conventional treatment
planning algorithms vs. Monte Carlo
• Modification of prescription dose based
upon Monte Carlo recalculation
Clinical Implications for Monte Carlo based
Photon Treatment Planning
A. Fogliata, E. Vanetti, D. Albers, C. Brink, A. Clivio, T. Knoos, G. Nicolini, and
L. Cozzi, “On the dosimetric behaviour of photon dose calculation algorithms
in the presence of simple geometric heterogeneities: comparison with Monte
Carlo calculations” Phys. Med. Biol. 52 (2007) 1363–1385.
Photon energy, field size, and the heterogeneous nature of the treatment
area will determine the dosimetric impact of a Monte Carlo treatment
planning algorithm.
Part II: Electron beams
Joanna E. Cygler, Ph.D., FCCPM, FAAPM
The Ottawa Hospital Cancer Centre, Ottawa, Canada
Carleton University Dept. of Physics, Ottawa, Canada
University of Ottawa, Dept. of Radiology, Ottawa, Canada
Outline
• Rationale for MC dose calculations for electron
beams
• Commercially available Monte Carlo based electron
treatment planning systems
• Clinical implementation of MC-based TPS
• Issues to pay attention to when using MC based
system
• Timing comparisons of major vendor MC codes in
the clinical setting.
Rationale for Monte Carlo dose
calculation for electron beams
• Difficulties of commercial pencil beam based
algorithms
– Monitor unit calculations for arbitrary
SSD values – large errors*
– Dose distribution in inhomogeneous media
has large errors for complex geometries
*
can be circumvented by entering separate virtual
machines for each SSD – labour consuming
Rationale for Monte Carlo dose
calculation for electron beams
6.2 cm
15
Relative Dose
9 MeV
10
Measured
Pencil beam
Monte Carlo
depth = 6.2 cm
depth = 7 cm
5
0
-10
/tex/E TP /abs/X TS K 09S .OR G
-5
0
Horizontal Position /cm
5
10
98-10-21
Ding, G. X., et al, Int. J. Rad. Onc. Biol Phys. (2005) 63:622-633
Commercial implementations
• MDS Nordion (now Nucletron) 2001
- First commercial Monte Carlo treatment planning for electron
beams
– Kawrakow’s VMC++ Monte Carlo dose calculation algorithm (2000)
– Handles electron beams from all clinical linacs
• Varian Eclipse eMC 2004
– Neuenschwander’s MMC dose calculation algorithm (1992)
– Handles electron beams from Varian linacs only (23EX)
– work in progress to include linacs from other vendors
• CMS XiO eMC for electron beams 2010
– Based on XVMC (Kawrakow, Fippel, Friedrich, 1996)
– Handles electron beams from all clinical linacs
Nucletron Electron Monte Carlo
Dose Calculation Module
•Originally released as part of Theraplan Plus
•Currently sold as part of Oncentra Master Plan
•Fixed applicator with optional, arbitrary inserts, or
variable size fields defined by the applicator like
DEVA
•Calculates absolute dose per monitor unit (Gy/MU)
•User can change the number of particle histories
used in calculation (in terms of particle #/cm2)
•Data base of 22 materials
510(k) clearance (June 2002)
•Dose-to-water is calculated in Oncentra
•Dose-to-water or dose-to-medium can be calculated
in Theraplan Plus MC DCM
•Nucletron performs beam modeling
Varian Macro Monte Carlo
transport model in Eclipse
• An implementation of Local-to-Global (LTG) Monte Carlo:
– Local: Conventional MC simulations of electron transport performed
in well defined local geometries (“kugels” or spheres).
• Monte Carlo with EGSnrc Code System - PDF for “kugels”
• 5 sphere sizes (0.5-3.0 mm)
• 5 materials (air, lung, water, Lucite and solid bone)
• 30 incident energy values (0.2-25 MeV)
• PDF table look-up for “kugels”
This step is performed off-line.
– Global: Particle transport through patient modeled as a
series of macroscopic steps, each consisting of one local
geometry (“kugel”)
C. Zankowski et al “Fast Electron Monte Carlo for Eclipse”
Varian Macro Monte Carlo
transport model in Eclipse
• Global geometry calculations
– CT images are pre-processed to
user defined calculation grid
– HU in CT image are converted to
mass density
– The maximum sphere radius and
material at the center of each
voxel is determined
• Homogenous areas → large
spheres
• In/near heterogeneous areas →
small spheres
C. Zankowski et al “Fast Electron Monte Carlo for Eclipse”
Varian Eclipse Monte Carlo
• User can control
– Total number of particles per simulation
– Required statistical uncertainty
– Random number generator seed
– Calculation voxel size
– Isodose smoothing on / off
• Methods: 2-D Median, 3-D Gaussian
• Levels: Low, Medium, Strong
• Dose-to-medium is calculated
CMS XiO Monte Carlo system
• XiO eMC module is based on VMC*
– simulates electron (or photon) transport through voxelized
media
• The beam model and electron air scatter functions
were developed by CMS
• The user can specify
–
–
–
–
–
–
the number of histories
voxel size
dose-to-medium or dose-to-water
random seed
the total number of particle histories
or the goal Mean Relative Statistical Uncertainty (MRSU)
• CMS performs the beam modeling
*Kawrakow, Fippel, Friedrich, Med. Phys. 23 (1996) 445-457
*Fippel, Med. Phys. 26 (1999) 1466–1475
User input data for MC based TPS
Treatment unit specifications:
• Position and thickness of jaw collimators and MLC
• For each applicator scraper layer:
Thickness
Position
Shape (perimeter and edge)
Composition
• For inserts:
Thickness
Shape
Composition
No head geometry details required for Eclipse, since at this time it only
works for Varian linac configuration
User input data for MC TPS cont
Dosimetric data for beam characterization, as
specified in User Manual
• Beam profiles without applicators:
-in-air profiles for various field sizes
–in-water profiles
–central axis depth dose for various field sizes
–some lateral profiles
• Beam profiles with applicators:
– Central axis depth dose and profiles in water
– Absolute dose at the calibration point
Dosimetric data for verification
– Central axis depth doses and profiles for various
field sizes
Clinical implementation of MC
treatment planning software
• Beam data acquisition and fitting
• Software commissioning tests*
• Clinical implementation
– procedures for clinical use
– possible restrictions
– staff training
*should
include tests specific to Monte Carlo
A physicist responsible for TPS implementation should
have a thorough understanding of how the system works.
Software commissioning tests: goals
• Setting user control parameters in the TPS to
achieve optimum results (acceptable statistical
noise, accuracy vs. speed of calculations)
– Number of histories
– Voxel size
– Smoothing
• Understand differences between water tank and
real patient anatomy based monitor unit values
Software commissioning tests
• Criteria for acceptability
– Van Dyk et al, Int. J. Rad. Oncol. Biol. Phys., 26, 261-273,1993;
– Fraass, et al, AAPM TG 53: Quality assurance for clinical radiotherapy
treatment planning,” Med. Phys. 25, 1773–1829 1998
• Homogeneous water phantom
• Inhomogeneous phantoms (1D, 2D, 3D, complex)
– Cygler et al, Phys. Med. Biol., 32, 1073, 1987
– Ding G.X.et al, Med. Phys., 26, 2571-2580, 1999
– Shiu et al, Med.Phys. 19, 623—36, 1992;
– Boyd et al, Med. Phys., 28, 950-8, 2001
• Measurements, especially in heterogeneous phantoms,
should done with a high (1 mm) resolution
Lateral profiles at various depths,
SSD=100cm, Nucletron TPS
20 MeV, 10x10cm2 applicator, SSD=100cm.
Homogeneous water phantom. Cross-plane profiles at
various depths. MC with 10k and 50k/cm2.
110
110
100
100
90
90
80
80
70
meas.@2cm
60
calc.@2cm
50
meas.@3.0cm
calc.@3.0cm
40
meas.@d=3cm
calc.@d=3cm
calc.@d=3cm,50k
meas.@d=7.8cm
calc.@d=7.8cm
70
Dose / cGy
Dose / cGy
9 MeV, 10x10cm2 applicator, SSD=100cm. Homogeneous
water phantom,cross-plane profiles at various depths. MC
with 10k/cm2.
60
50
calc.@d=7.8cm,50k
meas.@d=9cm
calc.@d=9cm
calc.@d=9cm,50k
40
meas.@4.0cm
30
30
calc.@4.0cm
20
20
10
10
0
0
-10
-5
0
Off - axis / cm
5
10
-10
-5
0
Off - axis / cm
5
10
CMS: Cut-out factors
Cutout Output Factors: 17 MeV
Cutout Output Factors: 9 MeV
1.050
1.050
O u tp u t F a c to r (c G y /M U )
SSD=100 cm
O u tp u t F a c to r (c G y /M U )
1.000
0.950
0.950
0.850
SSD=100 cm
0.900
0.750
0.850
0.800
0.650
SSD=115 cm
0.750
0.550
0.700
Experimental
XiO Calculated
0.450
SSD=115 cm
0.650
Experimental
XiO Calculated
0.600
0.350
1
2
3
4
5
6
Square Cutout Length (cm)
7
8
9
1
2
3
4
5
6
7
8
Square Cutout Length (cm)
Vandervoort and Cygler, COMP 56th Annual Scientific Meeting, Ottawa June 2010
9
Eclipse eMC no smoothing
Voxel size = 2 mm
Air
Air
Bone
Bone
120
110
120
depth = 4.7 cm
18 MeV
110
100
90
90
Relative Dose
100
Relative Dose
4.7 cm
80
depth = 6.7 cm
70
60
50
depth = 7.7 cm
40
18 MeV
depth = 4.7 cm
80
70
60
50
40
30
20
Measured
eMC
30
Measured
eMC
20
10
10
0
0
-6
-4
-2
0
2
Off-axis X position /cm
4
6
-6
-4
-2
0
2
Off-axis Y position /cm
Ding, G X., et al (2006). Phys. Med. Biol. 51 (2006) 2781-2799.
4
6
Eclipse eMC
Effect of voxel size and smoothing
Air
Air
Bone
Bone
110
2 mmand no smoothing
18 MeV
110
Relative Dose
100
90
80
70
2 mmand with 3D smoothing
60
5 mm and with 3D smoothing
50
120
Relative Dose
120
4.7 cm
90
80
70
60
50
40
30
30
depth = 4.9 cm
5 mm and with
3D smoothing
100
40
20
2 mm and with 3D smoothing
20
10
depth = 4.9 cm
10
0
2 mmand no smoothing
18 MeV
0
-6
-4
-2
0
Off-axis X position /cm
2
4
6
-6
-4
-2
0
2
Off-axis Y position /cm
Ding, G X., et al (2006). Phys. Med. Biol. 51 (2006) 2781-2799.
4
6
CMS: 9 MeV - Trachea and spine
Air
Bone
Bone
Air
Bone
Bone
Film
Film
Vandervoort and Cygler, COMP 56th Annual Scientific Meeting, Ottawa June 2010
Dose-to-water vs. dose-to-medium
Hard bone cylinder
2cm
1 cm diameter and 1 cm length
1100
Small volume
of water
Bone cylinder is replaced
by water-like medium but
with bone density
100
90
BEAM/dosxyz
simulation
80
70
Dose
Dm - energy absorbed in
a medium voxel divided
by the mass of the
medium element.
60
50
Bone
cylinder
location
40
30
20
10
Voxel of medium
Dw - energy absorbed in
a small cavity of water
divided by the mass of
that cavity.
0
0
3
4
5
1.14
9 MeV
SPR
⎛S⎞
Dw = Dm ⎜ ⎟
⎝ ρ ⎠m
2
Central Axis Depth /cm
1.13
w
1
1.12
Water/Bone stopping-power ratios
1.11
1.10
0
Ding, G X., et al Phys. Med. Biol. 51 (2006) 2781-2799.
1
2
3
depth in water /cm
4
5
Good clinical practice
• Murphy’s Law of computer software (including
Monte Carlo)
“All software contains at least one bug”
• Independent checks
MU MC vs. hand calculations
Monte Carlo
Hand Calculations
Real physical dose
calculated on a patient
anatomy
Rectangular water
tank
Inhomogeneity
correction included
No inhomogeneity
correction
Arbitrary beam angle
Perpendicular beam
incidence only
9 MeV, full scatter phantom
(water tank)
RDR=1 cGy/MU
Lateral
scatter missing
Real contour / Water tank =
=234MU / 200MU=1.17
MU real patient vs.water tank
MC / Water tank= 292 / 256=1.14
MU-real patient vs. water tank
Impact on DVH
120
PTV-MU-MC
100
PTV-MU-WT
%volume
80
LT eye-MU-MC
LT eye-MU-WT
60
RT eye-MU-MC
40
RT eye-MU-WT
20
0
0.0
10.0
20.0
30.0
dose / Gy
40.0
50.0
60.0
Posterior cervical lymph node
irradiation - impact on DVH
45.0
customized
40.0
35.0
30.0
PTV / cm
3
conventional
25.0
20.0
15.0
10.0
Jankowska et al, Radiotherapy & Oncology, 2007
5.0
0.0
0.0
5.0
10.0
15.0
dose / Gy
20.0
25.0
30.0
Internal mammary nodes
MC / Water tank= 210 / 206=1.019
Timing – Pinnacle3
dual processor 1.6 GHz Sun workstation, 16 GB RAM.
Overall uncertainty
2%
1%
0.5%
Patient
#
histories
CPU time
(min)
#
histories
CPU time
(min)
# histories
CPU time
(h)
1(cheek)
3.4x106
4.8
1.4x107
20
1.6x108
3.9
2 (ear)
1.7x106
2.1
6.5x106
8.1
7.1x107
1.5
3 (breast)
3.3x106
7.1
1.4x107
29.9
1.5x108
5.4
4 (face)
1.1x107
32.1
4.7x108
134.5
5.2x108
24.5
Fragoso et al.: Med. Phys. 35, 1028-1038, 2008
Timing – Nucletron TPS
Oncentra 4.0
Anatomy - 201 CT slices
Voxels 3 mm3
10x10 cm2 applicator
50k histories/cm2
4 MeV Timer Results:
Init = 0.321443 seconds
Calc = 42.188 seconds
Fini = 0.00158201 seconds
Sum = 42.5111 seconds
20 MeV Timer Results:
Init = 0.311014 seconds
Calc = 110.492 seconds
Fini = 0.00122603 seconds
Sum = 110.805 seconds
Faster than pencil beam!
Timing – Varian Eclipse
Eclipse MMC, Varian single CPU Pentium IV
XEON, 2.4 GHz
10x10 cm2, applicator, water phantom,
cubic voxels of 5.0 mm sides
6, 12, 18 MeV electrons,
3, 4, 4 minutes, respectively
Chetty et al.: AAPM Task Group Report No. 105: Monte Carlobased treatment planning, Med. Phys. 34, 4818-4853, 2007
Conclusions
• Commercial MC based TP system are available
– fairly easy to implement and use
– MC specific testing required
• Fast and accurate 3-D dose calculations
• Single virtual machine for all SSDs
• Large impact on clinical practice
– Accuracy improved
– More attention to technical issues needed
– Dose-to-medium calculated
– MU based on real patient anatomy (including contour
irregularities and tissue heterogeneities)
• Requirement for well educated physics staff
Acknowledgements
George X. Ding
George Daskalov
Gordon Chan
Robert Zohr
Ekaterina Tchistiakova
Indrin Chetty
Margarida Fragoso
Charlie Ma
Eric Vandervoort
David W.O. Rogers
In the past I have received research support from
Nucletron and Varian
TOHCC has a research agreement with Elekta
Thank You