Model Based Dose Calculation Algorithms In External .

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WE-B-AUD C CE-TherapyJuly 30, 2008Model Based Dose CalculationAlgorithms for Photons inExternal Radiation TherapyTom Knöös, Lund, Sweden2Objectives1.To provide an educational review of the physicsand techniques behind model based algorithmse.g. convolution/superpositioning models.2.To review the methods used to improve thesimulation efficiency i.e. pencil beam andcollapsed cone convolutions.3.To briefly review the vendor codes currently usedfor clinical treatment planning.4.To briefly review the potential clinical implicationsof accurate calculated dose distributions.AAPM 2009Knöös1

13The Probleme- Modelling the linac Energy fluence Source models Monte Carlo Modelling of dose in patients Interpolation and correction ofmeasured data Fluence to dose modelling Monte CarloAAPM 2009Knöös4Remember Photons are indirect ionizing radiation Produces electrons through interaction Pair production, Compton and photo Electrons deposit energy by ionization Thus keeping track of electrons ishighly important for accurate dosecalculationsAAPM 2009Knöös2

5Photon Fluence via TERMA toAbsorbed Dose using ConvolutionD – Dose distributionT – TERMA distributionK – dose deposition kernel D( x)D (r ) T ( x )T (r )[1D convolution]K ( x x )dx K (r )This idea was explored by several papers at the ICCR 1984AAPM 2009Knöös6What is TERMA?Source Ray-tracing Total EnergyReleased in Mass (TERMA) Similar to determiningeffective or radiological depthT (E, z) zeq E ( E , z ) E E 0 ( E ,0 ) e 1 waterAAPM 2009z ( z ' ) dz 'E z eq EFan ray lines0Knöös3

7Dose deposition kernel - K5 MeV0.5 cmPrimary10 cmFirst scatter15 MV10 cmTotal1.25 MeVCourtesy A AhnesjöAAPM 2009Knöös8The fraction of energy deposited within radialbins as function of radius Mackie et al 1988, PMBMax range1.25 MeVMax range10.0 MeVAAPM 2009Knöös4

9Convolve! Apply the dose kernel to each TERMApoint Integrate over the whole volume i.e. aconvolution D( x ) D (r ) T ( x ) T (r )[1D convolution]K ( x x )dx K (r )AAPM 2009Knöös10Convolution in 2D TERMA DoseDepositionKernel[ Absorbed Dose]Convolution is efficiently solved by Fast Fourier Transform techniquesAAPM 2009Knöös5

11Example: Point kernelconvolution - CMS Re-sampling of Mackie’s kernels toCartesian coordinates Fast Fourier Transform (FFT) solution Two separate calculations: A primary kernel for which the calculation isperformed at high-resolution but over a smallregion – high gradient – short range A scatter kernel, where the calculation isperformed at a lower resolution but over a largerarea – low gradient – long range Time saving of about 65 % by this techniqueAAPM 2009Knöös12Limitations of convolution Kernels are not invariant in space Energy distribution varies with position in beam Beam softening laterally Beam hardening longitudinally Kernels vary with densityDivergence leading to tilted kernelsPre-calculated kernels won’t make it!!!FFT not suitable – analytical methods mustbe used – time consuming Approximate methods requiredAAPM 2009Knöös6

131stapproximationPencil Beam Reduce the dimensionality of the problem by pre-convolving in the depthRelative fluencedimension1.00.90.80.70.60.50.40.30.20.10.0 010203040 50Depth (cm) Pencil beams (PB) Superposition of pencil beams in 2D Faster Creation by: De-convolution or differentiation from measurements or byMonte Carlo methodsAAPM 2009Knöös14Illustration of Pencil Beamsuperpositioning (convolution) Energy fluenceAAPM 2009 DoseDepositionKernel Absorbed DoseKnöös7

15Example: Pencil beam model– Nucletron OMP Pencil beams based on MC calculatedpoint kernels, integrated and fitted to alimited number of depth doses Separates “primary” and “scatter” dose Heterogeneities handled via effectivepath length – only longitudinal scaling Extensive beam modellingNucletron (former MDS Nordion and Helax-TMS)AAPM 2009Knöös16Example: Pencil beamsmodel - Eclipse Uses pencil beams extractedfrom measurements (SPB) orfrom Monte Carlo calculation(AAA) Heterogeneities handled viaeffective path length –longitudinal AAA adds a scaling of thespread of the pencil based ondensity – lateral AAA also have an extensivebeam modellingAnalytical Anisotropic AlgorithmAAPM 2009Knöös8

172ndapproximationCollapsed cone convolutionContinuous Dose SpreadDiscrete Dose SpreadKernelDirectionsQuantization in conesCollapsed ConesKernels are discretisedAAPM 2009Collapsing removes the inversesquare law – only exponentialattenuation is leftKnöösBest Med Phys paper 198918Number of collapsed cones ordirections Sufficient density of cones to distribute energy toall voxels Not possible but at least while the energy issignificant 100 (Mackie et al, 1996 Summer school) Voxels will be missed at large distances – very lowenergy contribution 128 CC are used in CMS (48 for the fastversion) 106 CC are standard in OMPAAPM 2009Knöös9

19Implementation issuesAccounts for-HeterogeneitiesKernels scaled for different tissues-Lateral energy transport-Beam Hardening and Off-axis spectrumsofteningIncluded in Ray Trace process- Tilt of kernelsIncluded in TransportPolyenergetic Spectrum accounted for byweighted sum of monoenergetic kernelscalculated by Monte Carlo HVL(0)/HVL1.20Lund / Dublin group, 2008Regular beam Monte Carlo dataRegular beam Tailor et al.Regular beamMeasurementsFFF - MonteCarlo dataFFF Measurements1.151.101.05Weights determined by comparisonwith measured data1.000.950.0AAPM 20092.55.07.510.012.5Angle (deg.)Knöös20Examples: Collapsed cone Philips - Pinnacle Polyenergetic weighted kernels, total energy Off-axis/tilting considered during TERMA Collecting dose or dose point of view CMS - XiO Two kernels, Primary electron dose and scatteredphoton dose No Off-axis/tilting Collecting dose or dose point of view Nucletron – Oncentra MasterPlan Two Kernels are used: One for Collision Kerma into Primary Dose One for ‘Scerma’ into Phantom Scatter DoseThese are‘iso-scatter’lines.They linkpointsproducingequal scatterto here.Primaryinteractionpoint Kernels parameterised and fitting parameters storedfor run timeThese are Off-axis/tilting‘isodose’ Recursive dose collect/deposit model along parallellineslinesFrom Deshpande, PhilipsAAPM 2009Knöös10

21Further approximation Multigrid solution (CMS - XiO) Only calculate dose using superposition at points where it is necessary,and at all other points use interpolation to get a reasonable estimate ofdose Adaptive CCC (Philips - Pinnacle) Only performs convolution at every 4th point in the TERMA array Gradient search performed on TERMA array Dose in between is interpolated if gradient low (i.e TERMA doesn’t changemuch) Convolution performed at every point if TERMA gradient highAAPM 2009Example from CMSKnöös22Summary of Models/Algorithms Inhomogeneities are handled by scaling thekernels rectilinearly with electron densityaccording to the theorem by O’Connor 1957 Type a – Models primarily based on EPLscaling for inhomogeneity corrections. Eclipse/SPB, OMP/PB, PPLAN, XiO/Convolution LONGITUDINAL scaling Type b – Models that in an approximate wayconsider changes in lateral electron transport Pinnacle/CC, Eclipse/AAA, OMP/CC,XiO/Superpositioning. LONGITUDINAL and LATERAL scalingAAPM 2009Knöös11

Performance ofConvolution Models24AAA-PB model in EcpliseElektaSiemensCarefully implementedalgorithms together withaccurate beam modelsworks for most linacs Gamma-analysis, calc-meas Inside field after buildup Less than 0.5 % of pointsoutside 3 mm/1 % One implementation 0.7 %Cozzi et al, 2008, Z Med PhysikVarianAAPM 2009Knöös12

Pencil beamcalculations in ablocked fields25From van’t Weld, 1997,Radioth OncolFrom Storchi and Woudstra, 1996, PMBAAPM 2009From Van Esch et al, 2006, Med PhysKnöös26A problem using pencil beamsIrregular geometriesThe same dose to in all geometries since the PB ispre-integrated to a certain depth/lengthAAPM 2009See also Hurkmans et al, 1986, ROKnöös13

27Convolution methods inhomogeneous water Differences in beam modelling (not part ofthis SAM) Head scatterElectron contaminationWedges/BlocksMLC May lead to slightly different accuracy Basically all models perform well in water Point, pencil or collapsed cone implementationsAAPM 2009KnöösSingle beam28Comparison ininhomogeneous phantoms6 MV6 MVAAPM 2009From Fogliata et al 2007, PMB15 MV15 MVKnöösDensity 0.2 g/cm314

Multiple beams29Common implementation vs MCSmall solid lesion in low density lung tissue e.g. stereotactic treatment1.00.21.00.20.40.10.40.16 MVAAPM 200918 MVFrom Lasse Rye Aarup et al, RO, 2009KnöösKnöös et al, 2006, PMBTangential treatment of CCOMP/PBXiO/SuperAAPM 200930Knöös15

Tangential treatment of breastKnöös et al, 2006, PMBXiO/ConvEclipse/AAA6 MVEclipse/ModBathoOMP/PBDXXAAPM 200931Averagevalues fortype aAveragevalues fortype bPinnacle/CCPTV Mean10099.3PTV D9591.090.4PTV D5108.8108.9PTV D5-D9517.818.5Pulm sin D592.683.1Pulm sin D503.34.0XiO/SuperHigh dose areais the dose level that encompasses XX % of the Knöösvolume32Knöös et al, 2006, PMB5 field 18 MV – lungXiO/ConvEclipse/AAAOMP/PBPinnacle/CCAAPM 2009Knöös16

335 field 18 MV – lungKnöös et al, 2006, PMBXiO/ConvEclipse/AAA6 MVAveragevalues fortype bAveragevalues fortype a18 MVAveragevalues fortype bAveragevalues fortype aPTV Mean10097.510096.3PTV D95 max92.791.395.291.5106.2102.8104.499.89.28.3PTV D5 minOMP/PBPTV D5-D9513.5Pinnacle/CC11.6Pulm Sin D5014.219.715.720.6Pulm Sin D5103.796.3101.391.9Pulm Sin D1107.9100.0104.395.9AAPM 2009Knöös34Results from RPC thoraxphantom 15 cases planned withtype a 84% 16% of the pixelsmet the criteria (5%/5mm) 30 cases planned withtype b 99% 4% of the pixelsmet the criteria (5%/5mm)AAPM 2008 TU-C-AUD B-3 P Alvarez et alAAPM 2009Knöös17

35Conclusions – Dose changes Lung - PTV Prostate non-significant 2-4 % lower average dose Wider penumbra H&N none (depending onaccuracy of scatterintegration) and air cavities(air or low dense water) Breast slightly lower dose to breastand especially in lung inproximity to the targethowever larger irradiatedlung volumeAAPM 2009 Lung (treated side) 10 % lower dose to thehighest irradiated parts ofthe lung 5 % higher dose (15 20%) to the lung (D50) Lung (healthy side) Average dose identical(9.8-10.7 %)Knöös et al, 2006, PMBKnöös36Implications of introducing newand more accurate algorithms Significant changes indose to target volumesand surroundingtissues especially whenlung is involved Consequences forassessment of doseeffect relationshipsAAPM 2009 Careful analysis ofchanges is requiredbefore adopting newalgorithms Retrospectively recalculate plans whenclinical outcome isknown? Construct new planswith older algorithmsand re-calculate? New plans with oldprescriptions and newalgorithms? Optimize plans to thesame biological effect onPTV and/or OAR?Morgan et al 2008Knöös18

37Implications of introducing newand more accurate algorithms Significant changes indose to target volumesand surroundingtissues especially whenlung is involved Careful analysis ofchanges is requiredbefore adoptingen lynewealgorithmsltwlbe to fu nre Retrospectivelytiadesecalculateplanst whenist outcomepoeedlogclinicalisdnnoConsequences for reknown?acs a d onfec tsConstructassessment ofndosenew planscesolder algorithmsonfinaswitheeffect relationshipsecus ists the qu and re-calculate?Dis ysic and onse New plans with oldcph erstprescriptions and newdalgorithms?un Optimize plans to thesame biological effect onPTV and/or OAR?AAPM 2009Morgan et al 2008Knöös38Conclusion Convolution methods are accurate For low density regions – use models withlateral scaling Verification Also Vendor’s responsibility! Be careful when transferring to moreaccurate models but Important to do this!AAPM 2009Knöös19

Model Based Dose Calculation Algorithms for Photons in External Radiation Therapy Tom Knöös, Lund, Sweden WE-B-AUD C CE-Therapy July 30, 2008 AAPM 2009 Knöös 2 Objectives 1. To provide an educational review of the physics and techniques behind model based algorithms

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