future mc applicationsindico.ictp.it/event/a06223/session/28/contribution/15/material/0/0.pdf ·...
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UNIVERSITY OF WISCONSINSCHOOL OF MEDICINEAND PUBLIC HEALTH
Robert JerajUW Paul P. Carbone Comprehensive Cancer Center,
Departments of Medical Physics, Human Oncology and Biomedical Engineering, University of Wisconsin, Madison, Wisconsin, USA
Jozef Stefan Institute, Ljubljana, Slovenia
JOZEF STEFAN INSTITUTE
Future Monte Carlo Applications in Medicine
Future Monte Carlo applicationsPast:– MC-based radiation dosimetry – had a profound effect on
dosimetry standards (Rogers)– MC-based treatment planning – most likely will become a
standard in the future (Kawrakow, Rogers)– MC proton and heavy ion simulations – more and more
widespread (Jones, Qaim, Paganetti, Wambersi)
Present and Future:– MC-based intensity modulated radiotherapy (IMRT)– MC-based image-guided radiotherapy (IGRT)– Continuous MC simulations (spatial and temporal)– MC-based adaptive radiotherapy– MC-based non-transport applications
Monte Carlo-based Intensity Modulated Radiation Therapy
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Intensity modulated radiation therapy
All commercial IMRT systems use non-Monte Carlo-based dose calculations (pencil beam or convolution/superposition)Questions:– Is inclusion of Monte Carlo calculated dose
into inverse treatment planning trivial?– How does MC-based IMRT compare to the
non-MC-based IMRT?– Can we speed up Monte Carlo-based IMRT?
Correction vs model-based dose calculation
Dose calculation for treatment planning has to be fast and accurate
Inverse treatment planning for IMRT requires calculation of multiple dose beamlets many times…Is Monte Carlo dose calculation feasible at all?
Speed
Accuracy
Correction-based Model-based
Pencil beam C/S Monte Carlo
Monte Carlo-based IMRT
If Monte Carlo-based dose calculation is used we face two errors:– Statistical error because of the
statistical noise itself – Noise convergence error because
optimisation converges to the optimal solution for the noisy beamlets, which is not optimal for the noise-free beamlets
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Statistical error
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σstat ≈ 0.5% σstat ≈ 1%
σstat ≈ 2% σstat ≈ 4%
Jeraj and Keall, Phys Med Biol 45, 2000, 3601
Noise convergence error
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σstat ≈ 0.5% σstat ≈ 1%
σstat ≈ 2% σstat ≈ 4%
Jeraj and Keall, Phys Med Biol 45, 2000, 3601
Dependence of errors
104 105 1060123456789
101112
Statistical Noise convergence
Erro
r [%
]
Number of particles/beamlet
Jeraj and Keall, Phys Med Biol 45, 2000, 3601
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Non-Monte Carlo-based IMRT
If non-Monte Carlo-based dose calculation is used we face two errors:– Systematic error because of the
inaccurate dose calculation – Convergence error because optimisation
converges to the optimal solution for the inaccurate beamlets, which is not optimal for the accurate beamlets
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ErrorsC/S Pencil beam
Convergenceerror
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Systematicerror
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Jeraj et al, Phys Med Biol 47, 2002, 391
Errors for lung case
C/S dose calculation
Pencil beam dose calculation
Error [% Dmax] Tumour Lung
Systematic − 0.1 ± 2 − 1 ± 1
Convergence 0.1-0.8 ± 2-5 0.5-1 ± 1-4
Error [% Dmax] Tumour Lung
Systematic + 8 ± 3 + 6 ± 5
Convergence 7-10 ± 3-5 7-8 ± 6-7
Jeraj et al, Phys Med Biol 47, 2002, 391
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When is Monte Carlodose calculation of advantage?
Monte Carlo dose calculation can be of advantage in IMRT only if the statistical error is <2%
If the statistical error is >2% than the statistical errors and noise convergence errors are higher/comparable to systematic errors and convergence errors of the plans calculated with C/S dose calculation
Note that Monte Carlo dose calculation includes some fraction of the systematic error due to inaccurate commissioning
Hybrid optimization
Siebers et al, Med Phys 34(7), 2007, 2853
Fast convergence –no compromise in accuracy
Siebers et al, Med Phys 34(7), 2007, 2853
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Summary: MC-based IMRT
Clinically significant in heterogeneous regions (e.g., head and neck, lung)Not clinically significant in homogeneous regions (e.g., prostate)If you have it, why not use itUnderlying uncertainties due to inaccurately known sourceNoise
Monte Carlo-based Image-guided Radiation Therapy
Intra-fractional time scale
Inter-fractional time scale
1 second 1 minute 1 hour 1 day 1 week
time ->
respiratorycardiac motion
digestivesystemmotion
bowel/bladder filling
random/systematic
setup errors
tumor growth andshrinkage
weight gain and
loss
AdaptiveSetup VerificationMotion
Management
Radiotherapy time-scales
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Residual errors for image-guidance
0 10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70
80
% E
rror
occ
urs
% Image guidance
Error > 3 mm Error > 5 mm Error > 10 mm
Zeidan et al, Int J Rad Oncol Biol Phys 67, 2007, 670
Every day
Every second day
Weekly
Never
Image-guided radiation therapy
Image-guidance can clearly improve the accuracy of therapy, the question is whether Monte Carlo has anything to add thereQuestions:– Can Monte Carlo simulations be used for
optimization of imaging systems– Can Monte Carlo simulations be useful for
characterization of kV and MV imaging sources
– Can Monte Carlo simulations help with the imaging scatter
Simulations of a kV CBCT source
Ding et al, Phys Med Biol 52, 2007, 1595
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Spectral effects
Ding et al, Phys Med Biol 52, 2007, 1595
Monte Carlo planar imaging
Jarry et al, Med Phys 33(11), 2006, 4320
Experiment
Monte Carlo
Monte Carlo CBCTNo correction MC scatter corr.
Jarry et al, Med Phys 33(11), 2006, 4320
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MV imaging on helical tomotherapy
0 1 2 3 4 5 60.0
2.0x10-6
4.0x10-6
6.0x10-6
8.0x10-6
1.0x10-5
1.2x10-5
1.4x10-5
1.6x10-5
1.8x10-5
Phot
on s
pect
rum
[1/M
eV c
m2 /s
.p.]
Energy [MeV]
Treatment MVCT Imaging
Eave = 6 MV
Eave = 3.5 MV
Helical tomotherapyno patient
-20 -10 0 10 200.0
5.0x10-7
1.0x10-6
1.5x10-6
2.0x10-6
2.5x10-6
3.0x10-6
3.5x10-6
Phot
on fl
uenc
e [1
/s.p
.]
Off axis distance [cm]
Total Primary 1st scatter 2nd scatter
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0.2
0.4
0.6
0.8
1.0
Rel
ativ
e co
ntrib
utio
n
Off axis distance [cm]
Total Primary 1st scatter 2nd scatter
No object in the beam - only 10% of scattered photons– very clean beam
Helical tomotherapyhead and neck patient
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5.0x10-7
1.0x10-6
1.5x10-6
2.0x10-6
2.5x10-6
3.0x10-6
3.5x10-6
Phot
on fl
uenc
e [1
/s.p
.]
Off axis distance [cm]
Total Primary 1st scatter 2nd scatter
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0.2
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0.8
1.0
Rel
ativ
e co
ntrib
utio
n
Off axis distance [cm]
Total Primary 1st scatter 2nd scatter
Patient in the beam – scatter does not increase significantly – excellent for imaging
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Summary: MC-based IGRT
Monte Carlo simulations of imaging systems can reveal many useful details that can be used in their characterization and optimization
Particular important application is estimation of the scatter, which can be used to improve the imaging quality
Continuous Monte Carlo Simulations
Continuous therapy –continuous simulations
Radiotherapy treatment is a dynamic process:– Source motion– Collimator motion (MLC)– Patient motion
Time and position are continuous variables - Monte Carlo sampling is a natural choiceQuestions:– Can Monte Carlo transport help in continuous
environment?– How much improvement can we expect if we include
Monte Carlo dose calculation?
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Continuous vs. discrete simulations
Phase space of discrete vs. continuous time-dependent helical tomotherapy simulations
Tomotherapy delivery errorsDiscrete Continuous Difference
Arc therapy
Chow et al, Med Phys 30(10), 2003, 2686
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Motion effects
Rosu et al, Med Phys 34(4), 2007, 1462
Homogenous vs heterogenousdose calculation
AP/PA, 6MV CRT, 6MV CRT, 15MV
heterogenous > homogeneousheterogenous < homogeneous
Rosu et al, Med Phys 34(4), 2007, 1462
Motion effects
Patien
t A
Patien
t B
Heterogeneity Motion Combined
Rosu et al, Med Phys 34(4), 2007, 1462
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Summary: Continuous MC simulations
Monte Carlo simulations are ideal for continues simulations, both spatial and temporalMonte Carlo simulations not only account for continuous motion, but also properly for heterogeneities (need 4D-CT)Not much yet, but it will become very important in the future
Monte Carlo-based Adaptive Radiotherapy
Adaptive Radiotherapy3-D Imaging
OptimizedPlanning
CT+ Image Fusionor Registration
TreatmentWith DeliveryVerification
DoseReconstruction
DeliveryModification
DeformableDose
Registration
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Adaptive radiotherapy
IGRT enables treatment adaptationTreatment adaptation is yet to happenQuestions:– Can Monte Carlo transport help in adaptive
process?– Can Monte Carlo transport help in re-
optimization convergence?
Φ+(r,Ω,E)
Φ(r,Ω,E)
R
RDose ,Φ= SDose ,+Φ=
Forward vs. adjoint method
S
Forward vs. adjoint method
• Forward transport of the “source” function
• Φ (r,Ω,E)
• Q =
• 1 source → many voxels(source view)
• Prior knowledge of the response function is unnecessary
R,Φ
Forward Method
• Backward transport of the “response” function
• Φ+(r,Ω,E)
• Q =
• 1 voxel → many sources (voxel view)
• Prior knowledge of the source function is unnecessary
S,+Φ
Adjoint Method
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Forward vs. adjoint problem
ψ +
Typically:• few source positions• many voxel scoring positionsSolution:• variance reduction techniques
Use of adjoint information for initial guess and (re)optimization
51 source positions
39 directions/position
left parotid
right parotid
Tumor Regional field
Spinal cord Parotids
ROI adjoint functions
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• Determine relative importance of nonzero beams:
• Assign initial weights according to beam importance
• Reset zero-valued beams to value of least important beam
∑ ∗∗j jj TGTTGT DD
Initial guess: beam weights
Adjoint Analysis:TU* and SS*
Constraints met?
Use of adjoint information in re-optimization
Initial Weights:Wj = TUj* - SSj*
Forward Analysis:Compute dose with Wj > 0
Identify ROIs:TU_under TU_overSS_over NT_over
Adjoint Analysis:TU_under* TU_over*SS_over* NT over*
Amplify ROI AdjointsROI* = ROI* • f(Δ dose)
Update Weights:Wj = Wj +/- ROI*
X
Iterative (re)optimization
Initial guess Optimized
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Convergence
(dosePre - doseDel)2
Adaptive radiotherapy
Adaptive radiotherapy has yet to become clinical reality – many issues to overcomeAdjoint Monte Carlo transport can:– Provide extremely valuable sensitivity
information for adaptation – Help constructing initial guess– Improve optimization convergence– Can speed-up re-optimization
Monte Carlo-basednon-Transport Applications
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Do Monte Carlo simulations stop here
Monte Carlo transport simulations are only a small part of Monte Carlo simulationsQuestions:– Is there a way to combine Monte Carlo
transport with biological information available from functional/molecular imaging?
– Is there a room for Monte Carlo non-transport applications?
Tumor biological heterogeneityFDG FLT CuATSM
Treatment assessment - radiotherapy
Pre-
trea
tmen
tM
id-tr
eatm
ent
(1 w
k of
XR
T)
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Treatment assessment - radiotherapy
Pre-
trea
tmen
tM
id-tr
eatm
ent
(1 w
k of
XR
T)
Final geometry
Simulations on microscopic scale:
Use biological data to complement the given anatomical voxel information.
Assume an average of 106 cells/voxel
and run simulations for each voxel based
on first biological principles.
Pass on changes of each voxel as input
values for tissue level calculations.
CT
PET
PET
Initial anatomy
Biological activity
Hypoxia
Proliferation
Hypoxia map
Proliferation map
Δ cells/voxel
Altered density, same geometry
Imaging level Cellular level Tissue level (voxel space)
Hypoxia
Proliferation
Calculate new tumor morphology by using COMSOLTM based onresults of stochastic
simulations performed on the cellular level.
Extract vector fieldfrom geometric change and apply to transform simulation results into new biol. distributions.
Simulation input parameters from imaging
MC simulation of tumor growth and response to therapy
MC simulations of tumor growthTumor growth
Tumor response to radiation therapy
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MC simulations of vasculature growth
t=1 t=2 t=3
t=4 t=5 t=6
Conclusions
Monte Carlo simulations will continue to play important role in the futureMany new challenges and opportunities:– Characterization and optimization of (new) delivery
systems – lots of opportunities, limitations– Imaging systems for IGRT – detectors, improved
image quality (scatter)– Continuous treatments – underutilized right now – Adaptation – fast corrections/re-optimization– Non-transport/hybrid Monte Carlo applications –
how far can we push the limit?
Thank you for your attention