Calculation algorithms in radiation therapy treatment...
Transcript of Calculation algorithms in radiation therapy treatment...
Calculation algorithms in radiation therapy treatment planning systems
Colleen DesRosiers, Ph.D.AAMD Region III annual meeting, Indianapolis, Indiana
April 12, 2013
Learning Objectives1. The learner will be able to describe the different
types of algorithms used in treatment planning systems
2. The learner will be able to identify strengths and weakness of algorithms used in treatment planning systems
3. The learner will be able to identify reasons for disagreement between monitor unit calculations generated by treatment planning systems and by monitor unit check programs.
Image from: http://oeaeuprrp.blogspot.com/2011/09/workshop-how-to-write-and-assess.html
http://toons.beck-cartoons.info/?section=tooned
I am not the expert …
1. Khan, FM Gerbi, BJ Treatment Planning in Radiation Oncology, 3rd
edition, 20122. Khan, The Physics of Radiation Therapy, 4th edition, 20103. Murlidhar, KR, Murthy, NP, Raju, AK, Sresty, NVNM. Comparative study
of convolution, superposition, and fast superposition algorithms in conventional radiotherapy, three-dimensional conformal radiotherapy, and intensity modulated radiotherapy techniques for various sites, done on CMS XIO planning system J Med Phys [serial online] 2009 [cited 2013 Apr 1];34:12-22.
4. Ahnesjö , Anders, Basic modeling concepts in treatment planning dose dose calculations, fluence, raytracing, kernels, etc- Uppsala University, Sweden, 2013
5. Ahnesjö , Anders Patient dose calculation models in TPS.
More references…6. Wiesmeyer MD, Miften MM. A multigrid approach for accelerating three-
dimensional photon dose calculation Med Phys 1999; 26 :1149 (Abstract)7. Mackie TR, Bielajew AF, Rogers DWO, Battista JJ. Generation of photon energy
deposition kernels using the EGS Monte Carlo code. Phys Med Biol 1988;33:1-20. 8. Sharpe MB, Battista JJ. Dose calculations using convolution and superposition
principles: The orientation of dose spread kernels in divergent X-ray beams. Med Phys 1993;20:1685-94.
9. Mackie TR, Scrimger JW, Battista JJ. A convolution method of calculating dose for 15 MV X-rays. Med Phys 1985;12:188-96
10. Gagné, I, Zavgorodni, S. Evaluation of the analytical anisotropic algorithm in an extreme water–lung interface phantom using Monte Carlo dose calculations. Journal of Applied Clinical Medical Physics, vol. 8, (1), Winter 2007
11. Das, I, Cheng, C.W., Srivastava, S, et al. Variability of Low-Z Inhomogeneity Correction in IMRT/SBRT: A Multi-Institutional Collaborative Study AAPM annual meeting 2008
Acknowledgments
Vadim Moskvin, Ph.DIndra Das, Ph.D.
al·go·rithm \ˈal-gə-ˌri-thəm\
1. a procedure for solving a mathematical problem in a finite number of steps that frequently involves repetition of an operation;
2. a step-by-step procedure for solving a problem or accomplishing some end especially by a computer
From: http://www.merriam-webster.com/dictionary/
Where, in the planning system, do we find algorithms?
• MU calculations• Isodose distributions• DVH generation• IMRT optimization• DRR generation• Brachytherapy calculations• Any process that occurs when the user does not
dictate each step (e.g. generating a 3D image from a series of slices, placing a margin around a structure, etc.)
In the beginning …• Calculations were performed
strictly based on empirical (directly measured) data in tabular format.
• Isodose curves were generated based on PDD and profile data
• Corrections based on patient were very simplistic, depth corrections only (attenuation)
Most advanced …Monte Carlo method
Histories of millions of photons and secondary electrons are traced to calculate dose deposition based on physics interactions in matter
Monte Carlo method is the most accurate method for dose calculation but requires the greatest processing time. Most calculation algorithms use pre-calculated MC kernels.
4. Ahnesjö , Anders
Monte Carlo terms
• Random number generator (RNG)– the random number generator selects a number between 0 and 1 to determine the path of the particle (photon)
• History – the tracking of a single particle (how is the photon losing energy as it passes through the medium)
• Phase space – characterizes position in 6D
• Events – PE, CE, PP, electron interactions
More Monte Carlo terms…• Sampling – the draw of the parameters of events from
the probability distributions using RNG• Scoring – acquiring the value of the parameter of
interest during the simulation• Estimator – mathematical and algorithmical description
of the scoring method• Kernel – Pencil or point; a Monte Carlo simulation that
has been “scored” of a small “pencil” beam which incorporates the events in that path, or that occur at a “point”
Photon interactions… or events in Monte Carlo terms
1. Photoelectric effect – photon transfers all energy to electron, ejected, increases with Z3 and decreases with E3
2. Compton effect – dominant at therapy energies, results in scattered photons and secondary electrons, decreases slowly with E and is independent of Z
3. Pair Production – results in the creation of electron/positron
pair, annihilation, dependent on Z2 and E2.Which lead to Electron interactions – ionization, excitation,
bremsstrahlung, ultimately dose deposition(There are other effects that contribute to dose, such as neutron
production, which may or may not be modeled)
Monte Carlo method• MC method uses known probabilities and probability
distributions in sampling to predict results of interactions (events) (e.g. Compton: Klein-Nishina coefficients)
• MC utilizes the Law of Large Numbers (LLN)Theorem: The average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.
• The convergence of the Monte Carlo method follows the Central Limit Theorem (CLT)
Example: 2 Gy dose in 3x3x3 mm voxel could be delivered by 1011 photons crossed this voxel. However, simulation of 1011 photons multiplied on field size will take infinite amount of time. According to LLN, we can simulate 107 photons for whole field and get results according to CLT with 1% accuracy.
Monte Carlo method• Direct Monte Carlo method
o Particle trajectory is simulated in details on the even-by-even basis with the maximum accuracy in details.
o Binary estimator is used. Example: General-purpose code algorithms, PENELOPE, EGSnrc, FLUKA
• Specialized Monte Carlo methodo Variance reduction based simulation or certain
simplifications in the transport descriptiono Weighted estimator is used.
Example: FLUKA and MCNPX neutron transport module, MMC used in TPS, DPM electron-photon code.
Monte Carlo code uses programming subroutines and interaction
probabilities to calculate dose
Why does MC method work?• As the number of photons required for dose delivery
decreases, dose delivery uncertainty increases• Example: a quarter landed on “heads” or “tails”
Probability = 50%If the quarter is flipped 10 timesIf the quarter is flipped 100 timesIf the quarter is flipped 1011 times
• If only a few photons were needed to deliver dose, the MC method would not be accurate
So, if MC is the most accurate method for calculation, why develop other algorithms?
1. Time! Processing time makes MC calculations impractical for clinic as the TPS engine, but may serve well for treatment plan verification.
2. Since the cost associated with higher performance computing has decreased over the years, more sophisticated algorithmsemploying MC calculations are clinically available.Khan, 2010 (1)
Two atoms are sitting in a field of ionizing radiation.One atom says, "I think I lost an electron."
The other says, "Are you sure?"The first atom says, "I'm positive!"
On the light side …
Phase Space• Phase space is a 6 dimensional
characterization of the particles
),,,,,(6),,(
EzyxDzyxr
Monte Carlo accuracy - Modeling• Highly dependent on
the modeling of the components of the accelerator head
• Where can secondary electrons be produced? Where can scatter occur? Where does the calculation start?
http://health-7.com/imgs/20/7507.jpg
Monte Carlo input • Finite photon source size Open fluence distribution Fluence modulation Head scatter sources flattening filter collimators wedges Monitor back scatter Collimator leakage, including MLC interleaf leakage
shape of MLC leaf ends • Beam spectra • Spectral changes• Electron contamination
Monte Carlo Codes• EGS4• EGSnrc• GEANT• PENELOPE• MCNP• MCNPx• FLUKA
Different types of calculation algorithms
• Semi-empirically based• Model based• Direct Monte Carlo• Hybrid
Give me 30 minutes and I can confuse anyone. I don’t need to prepare.
Lech Papiez, Ph.D.Indiana University
Dr. Papiez’ response to a request to give a talk on algorithms to medical residents on the same day of the request.
Why do we need calculation algorithms?
Measurements are performed under specific conditions:- Fixed square fields- Fixed depths- Homogenous medium (water)- Flat surface
Monte Carlo based algorithms and the simplest of empirically based algorithms reasonably agree in homogeneous media
Physical DensityMaterial Density
(g/cm3)Relative to
waterImpact
Air 0.0012 1/800 Attenuation and scattering
Lung 0.2-0.3 1/5 Attenuation and scattering
Water(soft tissue)
1.000 1.000
Bone 1.600 1.6X (Attenuation and scattering)
Titanium 4.5 4.5X Attenuation
Steel 7.5 7.5X Attenuation
Semi Empirical (also called Correction or Factor based)
• Based on measured dataPDDProfile
• TAR• ETAR• Batho• Power Law• Clarkson
Photon dose calculation methods “Dose engines”
Method characteristics
Remarks
Monte Carlo Explicit particle transport simulation + Accurate - Noisy distributions
Standard research tool, clinical use under development
Point kernel methods Convolution/superposition ,Collapsed Cone
Implicit particle transport + Accurate - Minor systematic errors
Current workhorse for accurate calculations in lung.
Pencil Kernel Methods Heterogeneity impact through corrections
The workhorse for many applications
Scatter dose estimations ”Semi” pencil kernel metods
Often used for factor based calculation schemes
1D heterogeneity corrections Models what happen along the incident beam direction only
Can be used to correct dose calculated with any method for heterogeneities
Model Based
Factor Based
Ahnesjö, 2013 (4)
Calculation algorithms for TPS (photons)Elekta XiO• Clarkson• FFT Convolution• Multigrid Convolution• Superposition• Fast SuperpositionPhillips Pinnacle• Collapsed Cone Convolution• Pencil BeamVarian ECLIPSE• AAA Collapsed Cone Convolution• Pencil Beam
Model based algorithms• Empirically based algorithms rely on measurement,
corrections performed based on patient characteristics
• Model based algorithms rely less on measured data, more on predictions of dose distribution (equations, probabilities)
• No clear distinction!Empirical based algorithms use models for
corrections and model based algorithms use some measured data.
Pencil Beam algorithm (Convolution)• Monte Carlo “kernels”• Spatially invariant (non-divergent)• Scatter not modeled well
- Lateral scatter not considered- Heterogeneity correction largely attenuation
correction only (generally convolved with Batho or other correction)
- Generally a “hybrid” algorithm (modeled with semi-empirical correction)
Monte Carlo kernel Summation of kernels
In the pencil beam algorithm, kernels are spatially invariant, i.e., parallel to surface, non-divergent,
source of some inaccuracy
Homogeneous media Inhomogeneous media
Pencil beam algorithm predictions Changes in side scatter not modeled
Attenuation correction only
High density heterogeneity
Low density heterogeneity
Inhomogeneous media
High density heterogeneity
Low density heterogeneity
Increased areas of scatter not modeled
Will result in higher MUs than is needed
Decreased areas of scatter not modeled
Will result in lower MUs
Convolution känvəˈlo͞oSHən• A coil or twist, esp. one of many• A thing that is complex and difficult to follow• a mathematical operation on two functions f
and g, producing a third function that is typically viewed as a modified version of one of the original functions.
• It is based on theory of Laplace transformation of functions.
http://en.wikipedia.org/wiki/Convolution
Convolution-Superposition method (Collapsed Cone, Superposition)
• Most commonly used and widely accepted algorithm class in radiotherapy planning systems.
• Primary photons are treated separately from scattered photons and electrons set in motion
Convolution-Superposition algorithms• Point kernels (finer resolution than pencil kernels)• Consideration of divergence• Consideration of lateral scatter• Consideration of energy spectrum• Consideration of primary/secondary interactions with
inhomogeneous media• Effects of collimator, flattening filter• Less averaging than pencil beam
Equations
scatter for ally simplistic accounts'
mass in the releasedenergy totalTERMA,
'')(
''
3
3
rrA
rT
rdrrArT
rdrrArrD
p
p
sitephoton the tosource thefrom distanceradiologic theis and sitephoton primary the tosite deposition dose thefrom distance radiologic theis' where
'')(
''
'
3'
3
rrr
rdrrArT
rdrrArrD
r
rr
rrrp
Convolution Equation
Convolution-Superposition
Equation
Data and Clinical Examples
Experimental geometry for the treatment planning and measurement. The phantom consists of 14.4 cm of lung equivalent material (Cork, =0.25g/cm3) sandwiched between slabs of solid water. Measurements were made at various depth with micro-chamber
Treatment Planning and Measurements
Das et al., 2008 (11)
medium
Charged particle equilibrium (CPE)
Pencil beam algorithm does not accurately account for
secondary electron production, calculations at
the tissue/lung interface are not accurate.
Region of non-equilibrium
From Khan, 2010 (2)
Plot = Di/Dh
CMS-XiO, 6 MV
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0 2 4 6 8 10 12 14 16 18 20
Depth (cm)
Cor
rect
ion
Fact
or (D
i/Dh)
1x12x23x34x45x56x68x810x10
Pencil Beam Convolution
Pencil Beam
CMS-XiO, 6 MV
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0 2 4 6 8 10 12 14 16 18 20
Depth (cm)
Cor
rect
ion
Fact
or (D
i/Dh)
1x12x23x34x45x56x68x810x10
Superposition
Monte Carlo, 6 MV
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0 2 4 6 8 10 12 14 16 18 20
Depth (cm)
Cor
rect
ion
Fact
or (D
i/Dh)
1x12x23x34x43x36x6
PENELOPE, MC
Superposition Monte Carlo
Das et al., 2008 (11)
Lung Case
1. SBRT case –10 fields
2. 1 cm volume
3. 6 MV
4. AAA and Pencil beam
5. Heterogeneity corrections “on”
AAA100% White
95%
90%
80%
Calculation verification program predicts 11.3%
higher dose than AAA with same MUs
Pencil Beam100% White
95%
90%
80%
Calculation verification program agrees well with
Pencil beam (.01%)
Comparison of isodose curvesAAA Pencil Beam
Max dose = 100.8%
80% volume = 42.4 cc
Max dose = 102.2%
80% volume = 57.7 cc
The 80% volume generated in PBC is 36% greater than AAA
Spine Case – High ZAPPA spine
6 MV beams
High density implanted devices, 3000+ HU
Bone measured density values = 900-1500 HU
AAA and Pencil Beam
Heterogeneity corrections on
AAA MU sum = 206
Pencil Beam MU
sum = 208
AAA – edge of heterogeneity PBC– edge of heterogeneity
PBC results in 10% higher dose at edge of high Z heterogeneity
AAA – inside heterogeneity PBC – inside heterogeneity
PBC results in 10% higher dose inside the high Z heterogeneity
Spine case
No implant
APPA
16 MV photons
200 cGy anterior to vertebral body
No difference in MUs between AAA and PBC
Heterogeneity corrections on
AAA PBC
Less than 1% difference in dose calculated to cord
AAA PBC
Less than 1% difference in calculated dose in bone
Summary• Algorithms are step by step processes which are used
in planning systems (and otherwise) to complete specific tasks.
• The simplest of algorithms perform as accurately as the most sophisticated algorithms for ideal conditions.
• Time is a critical factor in the development of treatment planning algorithms.
• Heterogeneities pose the greatest challenge to predicting accurate dose distributions in patients
Summary (cont.)• The Monte Carlo method is the most accurate method
for calculating dose in heterogeneities. The most accurate currently available algorithms incorporate Monte Carlo kernels.
• Discrepancies in calculations more likely to arise from low density media than from high density media
• Safer to rely on your “convolution-superposition” algorithm than your verification calculation, since your verification calculation uses a simpler, less accurate algorithm
www.pythian.com
The academic portion of the lecture is now
complete.
An Irish blessing for the Medical Dosimetrist …
May your first optimization meet your dose constraintIf not, may you meet with a little dose paintMay your calc’d and your plan MUs always agreeMay you need not replan for a re-drawn GTVMay your MD not change his mind post approvalAnd your user rights never suffer removalMay your IMRT QA turn out rightAnd you get to go home while there is still light
Questions?
http://crippledcollie.com/wordpress/wp-content/uploads/2012/08/deer-in-headlights.jpg