Calculation algorithms in radiation therapy treatment planning systems

Transcription

1 Calculation algorithms in radiation therapy treatment planning systems Colleen DesRosiers, Ph.D. AAMD Region III annual meeting, Indianapolis, Indiana April 12, 2013

2 Learning Objectives 1. 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:

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4 I am not the expert 1. Khan, FM Gerbi, BJ Treatment Planning in Radiation Oncology, 3 rd edition, Khan, The Physics of Radiation Therapy, 4 th edition, 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: Ahnesjö, Anders, Basic modeling concepts in treatment planning dose dose calculations, fluence, raytracing, kernels, etc- Uppsala University, Sweden, Ahnesjö, Anders Patient dose calculation models in TPS.

5 More references 6. Wiesmeyer MD, Miften MM. A multigrid approach for accelerating threedimensional 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: 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: Mackie TR, Scrimger JW, Battista JJ. A convolution method of calculating dose for 15 MV X-rays. Med Phys 1985;12: 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 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

6 Acknowledgments Vadim Moskvin, Ph.D Indra Das, Ph.D.

7 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:

8 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.)

9 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)

10 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

11 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

12 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

13 Photon interactions or events in Monte Carlo terms 1. Photoelectric effect photon transfers all energy to electron, ejected, increases with Z 3 and decreases with E 3 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 Z 2 and E 2. 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)

14 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 photons crossed this voxel. However, simulation of photons multiplied on field size will take infinite amount of time. According to LLN, we can simulate 10 7 photons for whole field and get results according to CLT with 1% accuracy.

15 Monte Carlo method Direct Monte Carlo method o Particle trajectory is simulated in details on the evenby-even basis with the maximum accuracy in details. o Binary estimator is used. Example: General-purpose code algorithms, PENELOPE, EGSnrc, FLUKA Specialized Monte Carlo method o Variance reduction based simulation or certain simplifications in the transport description o Weighted estimator is used. Example: FLUKA and MCNPX neutron transport module, MMC used in TPS, DPM electron-photon code.

16 Monte Carlo code uses programming subroutines and interaction probabilities to calculate dose

17 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 times If the quarter is flipped 100 times If the quarter is flipped times If only a few photons were needed to deliver dose, the MC method would not be accurate

18 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. Khan, 2010 (1) 2. Since the cost associated with higher performance computing has decreased over the years, more sophisticated algorithms employing MC calculations are clinically available.

19 On the light side 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!"

20 Phase Space Phase space is a 6 dimensional characterization of the particles r ( x, y, z) 6D ( x, y, z,,, E)

21 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?

22 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

23 Monte Carlo Codes EGS4 EGSnrc GEANT PENELOPE MCNP MCNPx FLUKA

24 Different types of calculation algorithms Semi-empirically based Model based Direct Monte Carlo Hybrid

25 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.

26 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

27 Physical Density Material Density (g/cm 3 ) Relative to water Impact Air /800 Attenuation and scattering Lung /5 Attenuation and scattering Water(soft tissue) Bone X (Attenuation and scattering) Titanium X Attenuation Steel X Attenuation

28 Semi Empirical (also called Correction or Factor based) Based on measured data PDD Profile TAR ETAR Batho Power Law Clarkson

29 Model Based Photon dose calculation methods Dose engines Method characteristics Monte Carlo Point kernel methods Convolution/superposition, Collapsed Cone Explicit particle transport simulation + Accurate - Noisy distributions Implicit particle transport + Accurate - Minor systematic errors Remarks Standard research tool, clinical use under development Current workhorse for accurate calculations in lung. Pencil Kernel Methods Heterogeneity impact through corrections The workhorse for many applications Factor Based 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 Ahnesjö, 2013 (4)

30 Calculation algorithms for TPS (photons) Elekta XiO Clarkson FFT Convolution Multigrid Convolution Superposition Fast Superposition Phillips Pinnacle Collapsed Cone Convolution Pencil Beam Varian ECLIPSE AAA Collapsed Cone Convolution Pencil Beam

31 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.

32 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 semiempirical correction)

33 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

34 Homogeneous media Inhomogeneous media High density heterogeneity Pencil beam algorithm predictions Changes in side scatter not modeled Attenuation correction only Low density heterogeneity

35 High density heterogeneity Inhomogeneous media 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

36 Convolution känvəˈlo oshən 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.

37 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

38 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

39 Equations scatter accounts simplistically for ' energy released in the mass total TERMA, ' ' ) ( ' ' 3 3 r A r r T r d r A r r T r d r A r r D r p p distance from the source to the photon site the radiologic is deposition site to the primary photon site and the radiologic distance from the dose is ' where ' ' ) ( ' ' ' 3 ' 3 r r r r d r r A r T r d r A r r D r r r r r r r p Convolution Equation Convolution- Superposition Equation

40 Data and Clinical Examples

41 Treatment Planning and Measurements Experimental geometry for the treatment planning and measurement. The phantom consists of 14.4 cm of lung equivalent material (Cork, =0.25g/cm 3 ) sandwiched between slabs of solid water. Measurements were made at various depth with micro-chamber Das et al., 2008 (11)

42 Charged particle equilibrium (CPE) Pencil beam algorithm does not accurately account for secondary electron production, calculations at the tissue/lung interface are not accurate. medium Region of nonequilibrium From Khan, 2010 (2)

43 Pencil Beam Superposition Monte Carlo C orrection Factor (D i/dh) Pencil Beam Convolution CMS-XiO, 6 MV Depth (cm) 1x1 2x2 3x3 4x4 5x5 6x6 8x8 10x10 C orrection Factor (D i/d h) CMS-XiO, 6 MV Superposition 1x1 2x2 3x3 4x4 5x5 6x6 8x8 10x Depth (cm) C o rrecti o n Facto r ( D i/ D h ) Monte Carlo, 6 MV 1.8 PENELOPE, MC x1 2x x3 4x x3 6x Depth (cm) Plot = Di/Dh Das et al., 2008 (11)

44 Lung Case 1. SBRT case 10 fields 2. 1 cm volume 3. 6 MV 4. AAA and Pencil beam 5. Heterogeneity corrections on

45 AAA 100% White 95% 90% 80% Calculation verification program predicts 11.3% higher dose than AAA with same MUs

46 Pencil Beam 100% White 95% 90% 80% Calculation verification program agrees well with Pencil beam (.01%)

47 Comparison of isodose curves AAA Pencil Beam Max dose = 100.8% Max dose = 102.2% 80% volume = 42.4 cc 80% volume = 57.7 cc The 80% volume generated in PBC is 36% greater than AAA

48 Spine Case High Z APPA spine 6 MV beams High density implanted devices, HU Bone measured density values = HU AAA and Pencil Beam Heterogeneity corrections on

49 AAA MU sum = 206 Pencil Beam MU sum = 208

50 AAA edge of heterogeneity PBC edge of heterogeneity PBC results in 10% higher dose at edge of high Z heterogeneity

51 AAA inside heterogeneity PBC inside heterogeneity PBC results in 10% higher dose inside the high Z heterogeneity

52 APPA Spine case No implant 16 MV photons 200 cgy anterior to vertebral body No difference in MUs between AAA and PBC Heterogeneity corrections on

53 AAA PBC Less than 1% difference in dose calculated to cord

54 AAA PBC Less than 1% difference in calculated dose in bone

55 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

56 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

57 The academic portion of the lecture is now complete.

58 An Irish blessing for the Medical Dosimetrist May your first optimization meet your dose constraint If not, may you meet with a little dose paint May your calc d and your plan MUs always agree May you need not replan for a re-drawn GTV May your MD not change his mind post approval And your user rights never suffer removal May your IMRT QA turn out right And you get to go home while there is still light

59 Questions?