11 of February, 2014 Principle of convolution/superposition algorithm for dose calculation for Treatment Planning System Woong Cho tarotblue@gmail.com What is RTP System? Radiation Treatment Planning System Eclipse, Pinnacle, RayStation, Xio …. CorePlan (?) Determining treatment parameters to deliver acceptable radiation dose to the patient Contouring Treatment simulation (planning) Dose calculation Evaluation of plans Architecture of general RTP System Patient DB • Study information • Images(CT, MRI…) • Planning Data • Dose Data RTP Main Module • Patient Data I/O • 3D Visual rendering • Contouring • Planning GUI • Dose calculation • Planning result analysis ETC module • DVH calculator • Isodose generator • NTCP/TCP calculator Beam Data DB • Linac geometry info • Dosimetric Data •PDD data • Profile data • Output factor • Wedge/MLC info • CT HU-density table • ETC… • Kernel table (hidden) Commissioning module • RTP commissioning • Data I/O interface • Spectrum optimization • Source modeling optimization • Determine output factor: value/MU, cGy/MU • Wedge shape… IMRT Module • Beam-let extraction • Make Voxel lists per organ • Constraint I/O • Run optimization • MLC sequencing Dose calc Engine • Photon Dose calculation - ETAR , CCC, AAA… • Electron Dsoe - PBC Hogstrom algorithm Optimization engine • Steepest decent method - for spectrum - for beam source model - for IMRT Dose calculation engines Dose calculation engine Most important to predict dose distribution Consisted of two parts Dose calculation part Interpolation based method: ETAR Semi-analytic model method Superposition/Convolution algorithm FFT, CCC, AAA… LBTE algorithm Acuros XB Monte Carlo based method Beam modeling part Based on measured dosimetric data Directly linked to RTP commissioning module Convolution/superposition method Two step of the process at depositing doses Photon and a media interaction making TERMA Electrons from a interaction point are traversed through the media making excitation and ionization (kernel) TERMA Total energy released per media Temporal energy deposition before electron transport Considering attenuation and divergence effect Kernel Relative energy spread from unit TERMA Energy deposition from electron transport Function of energy and media Dose = TERMA ⓧ kernel D(r ) Tp (r ') ker nel (r r ' ) d 3 r ' Convolution/superposition method TERMA deposition: Pencil beam transfer energy at each voxels in tissue through its traveling way. Assume that directly give potential energy to each volume element Kernel spread: Deposited dose spread to 3D space from TERMA at each voxel. Dose: D(r ) Tp (r ') ker nel (r r ' ) d 3 r ' Superposition: Sun of all kerma map at each voxel. Same as convolution of TERMA and kernel General Process of Dose Calculation • Consider geometric infomations Calculate Photon fluence • Photon beam source • • 2 source model • • 3 source model • Beam aperture • • Collimators • MLC • Horn effects • Beam Divergence • Inverse square law Calculate 3D TERMA Do convolution Poly-energetic kernels Attenuation Beam Kernel(r , , ) hardening/softening all Energy Transmission through Monoker nel(r , , , Energy) MLC /block/collimators • C/S or CCC or AAA • Differential kernels or Accumulative kernels Geometric transformation Source • Geometric definition Beam coordinate yb xb • Freedom of beam directions • • • • zb 0 Block Block 1 • Beam coordinate Transformation between Patient coordinate and Beam coordinate xb CT coordinate yb xg zb zg • Source 0 1 isocenter yg • Gantry angles Collimator angles Couch angles Translations of couch Patient coordinate system • • • • World (global) coordinators Based on CT coordinators Define 3D dose Define contours Beam coordinate system • • • • Origin is beam source Z axis is beam center Fluence. Beam source, TERMA, kernels Defined per beams Geometric transformation • Simple Example • yb zb Source Sb ( 0, 0, 0) Beam coordinate yb • xb zb • yg zg yb zb yb CT Origin Pg (0,0,0) Beam coordinate 5zb xb Isocenter Beam coordinate 5 xb Pb xg Pb at iso-center ( Xb, Yb, Zb) = (0, 0, 100) Assume Iso-center (Pg ) is (0, 5, 5) Converting Pb to Pg? • Rotate based on Xb axis by 90’ counter clock wise • Pb = (0,-100, 0) • Translate Beam coordinate by (0, -100, 0) • Beam coordinate origin shifted to isocenter • Pb = ( 0,0,0) • Translate Beam coordinate by (0, -5, -5) • Beam coordinate is same to patient coordinate • Pb = (0, 5, 5) = Pg x g cos cos cos sin sin sin cos sin sin cos sin cos xb t x y g cos sin cos cos sin sin sin sin cos cos sin sin yb t y z sin z b t z sin cos cos cos g Process of TERMA Calculation • Calculation of Fluence and TERMA distribution in media • Beam source model Calculate Fluence at each voxel • Binary MLC plane • Using Hit test Calculate • Considering Beam divergence partially block Source 0 1 Calculate Horn effect Calculate effective depth for each voxels Calculate beam softening effect Calculate Attenuation Calculation point Beam source Model: 3 source model Gantry head Point source Srcprimary plane Zsp = 4cm Point source: Cp Srcsp plane Srcprimary (r ) C p Disk source Zsf = 12.5 cm Srcsf plane Collimator MLC Primary photon source Annulus source Collimator MLC or or Scattered photon source from primary collimator Annulus shape Srcsp (r ) Csp , ( R01 r R02 ) 0 , otherwise SCD = 100 cm Isocenter Scattered photon source from other structures Point of calculation (xb,yb,zb) Disk shape Intensity function with r A0 Src sf (r ) exp( k r ) r Beam source model: 3 source model Gantry head Point source Srcprimary plane Annulus source Srcsp plane Disk source Srcsf plane Collimator MLC Collimator MLC or or Fluence at an arbitrary point C C Fluence Isocenter Point of calculation (xb,yb,zb) p dAsrc 1 f ISW _ src 1 sp (rsp ) dAsrc 2 f ISW _ src 2 A0 exp(k rsf ) dAsrc 3 f ISW _ src 3 r Implementation of Beam source model Beam Source center (0, 0, 0) Binary Block Plane 1 1 Fluence Voxel (xb, yb, zb) 0 • Define Binary MLC Grid from the position of MLC leaves – Considering partially block – Hit Test algorithm Prepare Binary 2DGrid For all voxels (xb,yb,zb) { Src1_fluence = Calc_OpenRatio(Subboxels) { for (3x3x3 Subvoxels) do HitTest(SubVoxels) } Src2_fluene =Calc_ScatterSource2() Src3_fluene =Calc_ScatterSource3() } Implementation of Beam source model 1 0 Xs Ys 0 Source plane Z = Z_src 5mm resolution 0 Hit_corner_grid: partially block MLC plane Z= 67 cm 0.1mm resolution Sub voxel Blocking ratio= 9/25 = 0.36 (Xb,Yb,Zb) Calculation point: 101 x 101 x 101 Src2_fluene =Calc_ScatterSource(): For all SourceGrid { Hit-test 4 corner bloks at first If not blocked Calculate Radius (Xb,Yb,Zb) Get source value from source functions Src_flue += source_value } Process of TERMA Calculation • Calculation of Fluence and TERMA distribution in media Calculate Fluence at each voxel Calculate Beam divergence Calculate Horn effect Source FluenceDiv FluenceInit Distref ( 100cm) SPD 0 2 1 SPD Distref Calculate effective depth for each voxels Calculate beam softening effect Calculate Attenuation Calculation point Process of TERMA Calculation • Calculation of Fluence and TERMA distribution in media Source Calculate Fluence at each voxel 0 Calculate Beam divergence Calculate Horn effect 1 FluenceHorn HornF(OAD) FluenceDiv OAD 100 Calculate effective depth for each voxels Calculate beam softening effect Calculate Attenuation OAD Calculation point Process of Dose Calculation • Calculation of Fluence and TERMA distribution in media Source Calculate Fluence at each voxel 0 Calculate Beam divergence 1 Calculate Horn effect Calculate effective depth for each voxel d Effective Calculate beam softening effect r r r source r voxel (r ) r ri source Calculate Attenuation (r )d r i Calculation point Process of Dose Calculation • Calculation of Fluence and TERMA distribution in media Source Calculate Fluence at each voxel 0 Calculate Beam divergence 1 Calculate Horn effect Calculate effective depth for each voxels Calculate beam softening effect Calculate Attenuation d soften (OAD) 1 1 f SofteningRatio OAD d Effective Calculation point Process of Dose Calculation • Calculation of Fluence and TERMA distribution in media Source Calculate Fluence at each voxel 0 Calculate Beam divergence 1 Calculate Horn effect Calculate effective depth for each voxels Calculate beam softening effect • Beam hardening effect TERMAmono ( E ) FluenceHorn exp( Calculate Attenuation TERMA ( E ) d soften ) E ( E ) E max TERMA E min mono (E) Implementation of convolution Photon source D(r ) TERMAp (r ') Kernel (r r ' ) d 3 r ' N TERMA (r ' ) Kernel (r r ' ) V r ' 1 p for all r’…(N voxels in volume) { D(r) T(r’) Get TERMA(r’) r r' for all r…. { Get Kernel (r-r’) from Table Accumulate TERMA(r’) x Kernel (r-r’) to the r’ voxel } } Why Collapse Cone Convolution? Limitation of convolution/superposition method Center of kernel has too steep gradient. Discrete kernel data Significant error at the center voxels in dose calculation. Too long calculation time FFT is a good method. But no inhomogeneity correction. Not invariant kernel at inhomogeneous medium Iterative calculation: N6 number of iteration at N x N x N voxels From “Current Concepts in Dose Calculations”, Anders Ahnesjö. Collapsed cone approximation M Number of Cones N N voxels M rays N number of Voxels N No of Iterations: N3 No of Iterations : M x N • Can reduce calculation time because of computing dose to MxN points instead of NxNxN points. • More accurate dose calculation in heterogeneous media by considering effective pathway through cone lines Scatter particle transport directions Near center voxels Spherical voxels are generally smaller than cubic voxels Far away voxels One spherical voxels covers several cubic voxels Only consider the voxels in axial lines Too much energy imparted. But small errors because of small fraction energy at far site. Process of Convolution • Sphere Convolution Process • Total 288 cone rays A Collapsed Cone – 24 divisions of theta Y – 12 divisions of phi angle θ • Extracting voxel lists traversed by each ray vector r. • Heterogeneity correction by effective X pathway through vector r φ A TERMA Voxel • Convolution kernel table with -Z spherical coordinate system. • Consideration of kernel tilting effect • Adaption of accumulative kernel D( x ) D (x r ) 288 1 sub TERMA ( r ) k ( x r ) k ( x r ) ( r )V primary scatter 288 1 Process of convolution Prepare Poyenrgetic_Spherical_Kernel (r, θ, φ) Make Accumulative_Kernel (r, θ, φ) For (all 3D voxels with (Xp,Yp,Zp) ) { for (all r, θ, φ) { Calc_vector() Get_transversed_voxel_Lists() Calculate eff_pathlength(voxel_Lists) for (all Listed voxels) { Calculate θtilt Energy = Accumulative_Kernel(rinner) - Accumulative_Kernel(router) Get_TERMA(voxel) Dose +=TERMA x Energy } } } (r, θ, φ) (Xp, Yp, Zp) Kernel tilting rg rsrc TERMA Voxel rg θbeam Divergent Beam tilt beam cone θcone Dose Voxel riso rsrc (rg rsrc ) (riso rsrc ) arccos( ) cone (rg rsrc ) (riso rsrc ) Considering Beam hardening • Poly-energetic kernel – Photon spectrum is changed according to depths • Solve: – Get changed spectrums at every 10 cm depth – Prepare each kernel tables from the changed spectrum – Calculate interpolate kernel values between two tables using the depth of voxels Discussion & Question

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# Beam source Model