Monte Carlo Treatment Planning:
Implementation of Clinical Systems
Richard Popple1 and Joanna E. Cygler2,3,4
1Department
of Radiation Oncology,
The University of Alabama at Birmingham
2The Ottawa Hospital Regional Cancer Centre, Ottawa, Canada
3Carleton
4University
University Dept. of Physics, Ottawa, Canada
of Ottawa, Dept. of Radiology. Ottawa, Canada
L’Hopital
The Ottawa
d’Ottawa
Hospital
Regional Cancer Centre
Outline
1. Educational review of the physics of the MC
method.
2. Factors associated with MC dose calculation
within the patient-specific geometry, such as
statistical uncertainties, approximations of the
underlying physics model, CT-number to material
density assignments, and reporting of dose-tomedium versus dose-to-water.
3. Review the vendor transport codes currently used
for clinical treatment planning.
4. Experimental verification of MC algorithms.
5. Potential clinical implications of MC calculated
dose distributions.
6. Example timing comparisons of the major vendor
MC codes in the clinical setting.
Outline/Objectives Part I
Disclosure and Acknowledgements
• UAB has a RapidArc evaluation
agreement with Varian Medical
Systems
• Author has a research grant with
Varian Medical Systems
• Some slides courtesy of
– Indrin Chetty, Ph.D.
– D.W.O. Rogers, Ph.D.
•
Educational review of the physics of the
MC method
factors associated with MC dose
calculation within the patient-specific
geometry
•
–
–
–
–
statistical uncertainties
approximations of the underlying physics
model
CT-number to material density assignments
dose-to-medium versus dose-to-water
1
TGTG-105
Monte Carlo method overview
Med Phys 34 (2007) 4818-4853
10 MeV photon on lead
along incident
photon
.
“The Monte Carlo technique for the
simulation of the transport of electrons and
photons through bulk media consists of using
knowledge of the probability distributions
governing the individual interactions of
electrons and photons in materials to
simulate the random trajectories of
individual particles. One keeps track of
physical quantities of interest for a large
number of histories to provide the required
information about the average quantities.”
D.W.O. Rogers and A.F. Bielajew
10 MeV electrons on water from
rightelectrons blue
positrons red
electrons blue
photons yellow
photons yellow
incident
incident
Courtesy D.W.O. Rogers
Courtesy D.W.O. Rogers
2
Condensed history method
Condensed history techniques
On the condensed history technique for electron
transport”, Kawrakow and Bielajew,
http://www.irs.inms.nrc.ca/papers/LCA/LCA.html
Process overview
Variance Reduction Techniques (VRT)
target
• Efficiency ε = 1 / s2T
– T∝N
• Variance Reduction Techniques increase ε by
reducing s2 for a given number of particles.
–
–
–
–
Range rejection
Bremsstrahlung splitting
Russian roulette
And more…
• Inappropriate application of VRT can result in
inaccurate results and/or reduced efficiency.
vacuum window
flattening filter
phase space plane 1
jaws
patientdependent
structures
MLC
phase space
plane 2
primary
collimator
ion chamber
patientindependent
components
phase space:
position, energy,
direction, type,
latch (region of
creation,
interaction, etc.)
3
Accelerator beam model
CTCT-number to material density
• Patient tissues (via imaging data)
need to be converted into cross
sections required for MC simulation.
• Direct simulation
• Stored phase space
• Virtual source
model
CTCT-number to material density
Tissue
CT image
(HU)
Convert
to
densities
HU vs. density
conversion ramp
Relative
Electron
Density
air
0.0
lung
0.2 (0.10.5)
Soft
tissue,
water
1.0
spongy
bone
1.2
skull
1.65
compact
bone
1.85
CTCT-number to material density
• Both mass density ( ) and material
compositions (atomic number, Z) are
needed for accurate MC calculation
• Failure to incorporate compositions,
Zeff, can result in notable errors at
higher tissue densities (Verhaegen
and Devic, PMB, 50:937, ‘05)
4
DoseDose-toto-medium versus dosedose-totowater
• Historical clinical experience is based
on dose-to-water, (Dw)
– therapeutic doses and normal tissue
tolerance doses are based on Dw
– possible need for revision, since more
accurate dose calculation available now?
• Dose-to-medium (Dm) is inherently computed
by MC dose algorithms.
– may be of more clinical relevance than Dw
• TG-105 recommends that a method be
available in MC code to convert Dm to Dw
and that both values are reported.
Clinical Examples: Dw and Dm
Dm
Converting Dm to Dw
The conversion can be accomplished using the BraggGray formalism:
S
D =D
w
m ρ
S
ρ
w
m
w Unrestricted wat-to-med mass collision
m
stopping power averaged over the energy
spectrum of electrons at the pt. of
interest
This can be applied either as a post-processing step or
as a multiplication factor to the energy loss step
Clinical Examples: Dw and Dm
Dw
Dogan,
Dogan, Siebers, Keall: Phys Med Biol 51: 496749674980 (2006)
Dogan,
Dogan, Siebers, Keall: Phys Med Biol 51: 496749674980 (2006)
5
Clinical Examples: Dw and Dm
Statistical uncertainty
• Two sources
– Treatment head simulation
– Patient simulation
• Statistical uncertainty in dose will
approach the latent uncertainty
associated with the phase space
Knoos et al: Phys Med Biol 51: 57855785-5807
(2006)
Reporting of statistical uncertainty
Effect on dose prescriptions
• Statistical outliers (max. or min. dose
points) can deviate from the mean
dose by many standard deviations
• MC-based dose prescriptions should
be volume-based
• Do not prescribe to max or min dose
points
6
Statistical uncertainties:
Recommendations
Approximations of the underlying
physics model
• DVHs and dose indices, such as TCP
and NTCP are not highly sensitive to
statistical noise
• Systematic uncertainties can be
introduced by approximations
– Calculations with statistical precision of
<2% are sufficient to accurately predict
these values
–
–
–
–
• For serial organs, where point doses
are important, (e.g. the max. cord
dose) higher statistical precision may
be necessary
Monte Carlo Treatment Planning:
Implementation of Clinical Systems
Part II: Clinical Implementation
Outline Part II
•
•
Joanna E. Cygler, Ph.D., FCCPM, FAAPM
The Ottawa Hospital Regional Cancer Centre, Ottawa, Canada
Carleton University Dept. of Physics, Ottawa, Canada
University of Ottawa, Dept. of Radiology. Ottawa, Canada
The Ottawa
L’Hopital
Hospital
d’Ottawa
Regional Cancer Centre
Source model
Efficiency enhancing techniques
Macro Monte Carlo methods
Etc….
•
Monte Carlo based commercial TP systems
Experimental verification of MC algorithms
-
homogeneous water phantom
-
heterogeneous phantoms
-
setting user control parameters in the TPS to achieve optimum
results (minimum statistical noise, minimum distortion of real
dose distribution
Brief review of potential clinical implications of MC
calculated dose distributions
-
Use of bolus, lead wires etc.
-
Water tank vs. real patient MU
• Timing comparisons of major vendor MC codes in the
clinical setting.
7
Rationale for Monte Carlo based
Treatment Planning Systems
Why do we need Monte Carlo
based Treatment Planning
Systems?
• Traditional dose calculation algorithms fail in
many cases
• MC gives us in general the right answer
• There are no significant approximations
–
–
–
–
no approximate scaling of kernels is needed
electron transport is fully modelled
geometry can be modelled as exactly as we know it
All types of inhomogeneities are properly handled
• There are many experimental benchmarks
showing MC calculations can be very accurate
• 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
9 MeV
Relative Dose
Rationale for Monte Carlo dose
calculation for electron beams
10
Measured
Pencil beam
Monte Carlo
depth = 6.2 cm
depth = 7 cm
5
0
-10
/tex/E TP /abs/X TS K 09S .O R 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
8
Commercial implementations
• MDS Nordion 2001*
Description of Nucletron Electron
Monte Carlo DCM
- First commercial Monte Carlo treatment planning for electron
beams
– Implementation of Kawrakow’s VMC++ Monte Carlo dose
calculation algorithm (2000)
Fixed applicator
with optional,
arbitrary inserts
– Handles electron beams from all clinical linacs
• Varian Eclipse eMC 2004
– Based on Neuenschwander’s MMC dose calculation algorithm
Calculates absolute
dose per monitor
unit (Gy/MU)
(1992)
– Handles electron beams from Varian linacs only
• CMS Monaco for photon beams – IMRT only
*presently Nucletron
Varian Macro Monte Carlo
• PDF table look-up for “kugels” or spheres
instead of analytical and numerical
calculation
• CT images pre-processes
510(k) clearance (June 2002)
User input data for MC based TPS
Treatment unit specifications:
• Position and thickness of jaw collimators and MLC
– Homogenous areas
large spheres
– In/near heterogeneous areas
small spheres
• For each applicator scraper layer:
Thickness
Position
Shape (perimeter and edge)
Composition
– 30 incident energy values (0.2-25 MeV)
– 5 materials (air, lung, water, Lucite and solid
bone)
– 5 sphere sizes (0.5-3.0 mm)
• For inserts:
Thickness
Shape
Composition
• Database with probable outcome for every
combination of:
EGSnrc used to create beam data
No head geometry details required for Eclipse, since at this time it only
works for Varian linac configuration
9
User input data for MC TPS cont
Dosimetric data for beam characterization
• Beam profiles without applicators:
-in-air profiles for various field sizes
–in-water profiles
–Central axis depth dose for various field sizes
–Some off-axis 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
Software commissioning tests: goals
• Setting user control parameters in the TPS to
achieve optimum results (minimum 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
Clinical implementation of
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.
User controlled MC calculation
parameters
• Nucletron
– User can define number of histories used in
calculation (in terms of particle #/cm2)
• Varian
– User can define:
• Maximum number of histories used in
calculation >/=0
• statistical uncertainty (within the high dose
volume)
• Calculation grid size (voxel size)
• Smoothing method and level
• Random number generator seed
10
Software commissioning tests
Typical Experimental setup
• 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
• Homogeneous water phantom
• Inhomogeneous phantoms
– 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
Water tank
•p-type electron
diode
Diode
detector
•Scan resolution =
1mm
• Measurements, especially in heterogeneous phantoms,
should done with a high (1 mm) resolution
In-air or in water beam profiles
Lateral profiles at various depths,
SSD=100 cm, Nucletron TPS
Homogeneous water phantom tests
• Standard SSD 100 cm and extended SSD
9 MeV, 10x10cm2 applicator, SSD=100cm. Homogeneous
water phantom,cross-plane profiles at various depths. MC
with 10k/cm2.
– Open applicators – PDD and profiles
– Square and circular cut-outs
• Oblique incidence
– All open applicators
110
110
100
100
90
90
meas.@2cm
60
calc.@2cm
50
meas.@3.0cm
calc.@3.0cm
40
70
60
meas.@d=7.8cm
calc.@d=7.8cm
50
calc.@d=7.8cm,50k
meas.@d=9cm
calc.@d=9cm
calc.@d=9cm,50k
40
meas.@4.0cm
30
30
– Square, rectangular, circular, some irregular
cutouts
meas.@d=3cm
calc.@d=3cm
calc.@d=3cm,50k
80
70
Dose / cGy
• MU tests – SSD 100 and extended SSD
2
20 MeV, 10x10cm applicator, SSD=100cm.
Homogeneous water phantom. Cross-plane profiles at
2
various depths. MC with 10k and 50k/cm .
80
D os e / cG y
– GA = 150 and 300
•RFA300
(Scanditronix)
Scanditronix)
dosimetry system
Electron applicator
treatment planning,” Med. Phys. 25, 1773–1829 1998
calc.@4.0cm
20
20
10
10
0
0
-10
-5
0
Off - axis / cm
5
10
-10
-5
0
5
10
Off - axis / cm
11
Overall mean and variance of MC/hand
monitor unit deviation, Nucletron TPS
Inhomogeneous phantoms
0.45
0.40
0.35
Mean=-0.003
0.30
Variance=0.0129
fraction
Theory
Our data
• Low and high density inhomogeneities
– 1 D (slab) geometry
0.25
– 2 D (ribs) geometry
0.20
0.15
– 3 D (small cylindrical) geometry
0.10
0.05
• Complex (trachea and spine) geometry
0.00
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
1- MC/hand
Cygler et al. Med. Phys. 31 (2004) 142-153
Air cylinder
900 MHz, CPU time for 50k/cm2
14:01-20 MeV , 9:31 – 9MeV
Voxel size 0.39 cm, 47 slices
cylinder
20 MeV, Air cylinder,10x10cm2 applicator,
SSD=100cm. Cross-plane profiles.
MC with 10k/cm2.
9 MeV, Air cylinder,10x10cm2 applicator,
SSD=100cm. Cross-plane profiles.
MC with 10k/cm2.
140
140
60
40
Dose / cGy
80
80
meas.@d=2.1cm
calc.@d=2.1cm
calc.@d=2.1cm,50k
meas.@d=6cm
60
110
100
90
80
calc.@d=6cm
calc.@d=6cm,50k
40
calc.@d=5cm,50k
-1
0
0
-6
-4
-2
0
2
Off - axis / cm
4
6
8
-8
-6
-4
-2
Meas 0.1 cm
70
60
20
20
-8
120
0.39 cm
dose / cGy
100
meas@d= 2.1cm
calc.@d=2.1cm
calc.@d=2.1cm,50k
meas.@d=4cm
calc.@d=4cm
calc.@d=4cm,50k
meas.@d=5cm
calc.@d=5cm
100
0.19 cm
130
120
120
Dose / cGy
Results MC tests:voxel size
9 MeV
Air
0
2
Off - axis / cm
4
6
8
-0 .5
0
0 .5
1
o f f - a x is / c m
Cygler et al. Med. Phys. 31 (2004) 142-153
12
Eclipse eMC no smoothing
Eclipse eMC
Effect of voxel size and smoothing
Voxel size = 2 mm
Air
Air
Air
Air
4.7 cm
Bone
Bone
depth = 4.7 cm
18 MeV
110
90
Relative Dose
100
90
Relative Dose
100
80
depth = 6.7 cm
70
60
50
depth = 7.7 cm
18 MeV
120
depth = 4.7 cm
30
80
70
60
50
20
20
-6
-4
-2
0
2
4
6
-4
-6
-2
0
2
4
6
Off-axis Y position /cm
Ding, G X., et al (2006). Phys. Med. Biol. 51 (2006) 2781-2799.
DoseDose-toto-water vs. dosedose-toto-medium
2 cm
1 cm diameter and 1 cm length
110
90
80
80
5 mm and with 3D smoothing
50
80
70
60
50
2 mm and with 3D smoothing
40
30
depth = 4.9 cm
20
depth = 4.9 cm
10
0
0
-6
-4
-2
0
2
4
6
-6
Off-axis X position /cm
-4
-2
0
2
4
6
Off-axis Y position /cm
Ding, G X., et al (2006). Phys. Med. Biol. 51 (2006) 2781-2799.
9 MeV – clinical hard bone
Dm vs. Dw
BEAM/dosxyz
simulation
70
Dose
Dose
2 mmand with 3D smoothing
60
5 mm and with
3D smoothing
90
Bone cylinder is replaced
by water-like medium but
with bone density
100
90
70
depth = 2
60
50
40
60
50
20
Bone
cylinder
location
40
Measured
eMC
30
30
20
10
10
-8
-6
-4
-2
0
2
4
6
0
8
0
1
2
3
4
5
Central Axis Depth /cm
Off-axis distance /cm
Ding, G X., et al
Phys. Med. Biol. 51
(2006) 2781-2799.
1.14
100
depth = 3
90
9 MeV
80
1.13
depth = 4
70
60
Measured
eMC
50
40
(b)
(a)
SPR
Dose
70
2 mmand no smoothing
18 MeV
100
110
9 MeV
100
0
80
10
Off-axis X position /cm
Hard bone cylinder
90
20
0
0
110
30
10
10
120
40
Measured
eMC
30
Measured
eMC
2 mmand no smoothing
18 MeV
100
40
40
110
Relative Dose
110
120
Relative Dose
120
4.7 cm
Bone
Bone
1.12
30
Location of
bone
Water/Bone stopping-power ratios
1.11
20
10
0
1.10
-8
-6
-4
-2
0
2
4
Off-axis distance /cm
6
8
0
1
2
3
4
5
depth in water /cm
(c)
13
Results: clinical – soft bone
• The maximum difference in dose is 1.8%, in
agreement with soft bone phantom study
and consistent with stopping power ratio
• The maximum difference in dose is 1.8%,
which is in agreement with the phantom
studies
Dose-to-
% dose
Dose-to-Water
Medium
Results: clinical – soft bone
across patient / cm
Clinical implementation issues
Example of poorly fitting bolus
• Bolus fitting (no air gaps)
• Lead markers (wires, lead shots) used in
simulation
• Monitor unit calculations
– Water tank or real patient anatomy
– Dose to water or dose to medium
• Workload
14
How to correct poorly fitting bolus
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
9 MeV, full scatter phantom
(water tank)
RDR=1 cGy/MU
Perpendicular beam
incidence only
15
Lateral
MU real patient vs.water tank
scatter missing
Real contour / Water tank =
=234MU / 200MU=1.17
MC / Water tank= 292 / 256=1.14
MUMU-real patient vs. water tank
Impact on DVH
Posterior cervical lymph node
irradiation - impact on DVH
120.0
PTV-MUMC
PTV-MUWT
80.0
customized
35.0
30.0
LT eye-MU-WT
60.0
20.0
10.0
RT eye-MU-WT
20.0
25.0
15.0
RT eye-MUMC
40.0
conventional
3
LT eye-MUMC
PTV / cm
%volume
45.0
40.0
100.0
Jankowska et al, Radiotherapy & Oncology, 2007
5.0
0.0
0.0
0.0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
5.0
10.0
15.0
20.0
25.0
30.0
dose / Gy
dose / Gy
16
Timing – Nucletron TPS
Theraplan Plus
•
•
•
•
•
•
Timing – Varian Eclipse
10x10 cm2 applicator
50k histories/cm2
Anatomy - 41 CT slices
Voxels 3 mm3
Pentium 4 Xenon 2.2 GHz
Calculation time
– 1.5 min. for 6 MeV beam
– 8.5 minutes for 20 MeV beam
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
Faster than pencil beam!
Chetty et al.: AAPM Task Group Report No. 105: Monte Carlobased treatment planning, Med. Phys. 34, 4818-4853, 2007
Conclusions
Timing – Pinnacle3
dual processor 1.6 GHz Sun workstation, 16 GB RAM.
Overall uncertainty
2%
1%
Patient
# histories
CPU time
(min)
1(cheek)
3.4x106
4.8
2 (ear)
1.7x106
2.1
3
(breast)
3.3x106
4 (face)
1.1x107
#
histories
0.5%
CPU time
(min)
# histories
CPU time
(h)
1.4x107
20
1.6x108
3.9
6.5x106
8.1
7.1x107
1.5
7.1
1.4x107
29.9
1.5x108
5.4
32.1
4.7x108
134.5
5.2x108
24.5
• Commercial MC based TP system are available
– 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
Fragoso et al.: Med. Phys. 35, 1028-1038, 2008
17
Acknowledgements
George X. Ding
George Daskalov
Gordon Chan
Robert Zohr
Elena Gil
Indrin Chetty
Margarida Fragoso
Richard Popple
Charlie Ma
David W.O. Rogers
In the past I have received research support from
Nucletron and Varian
TOHCC has a research agreement with Elekta
18