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Woong Cho tarotblue @gmail.com

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 (?).

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Woong Cho tarotblue @gmail.com

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  1. 11 of February, 2014 Principle of convolution/superposition algorithm for dose calculation for Treatment Planning System Woong Cho tarotblue@gmail.com

  2. 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

  3. Architecture of general RTP System RTP Main Module Patient DB ETC module • Patient Data I/O • 3D Visual rendering • Contouring • Planning GUI • Dose calculation • Planning result analysis • Study information • Images(CT, MRI…) • Planning Data • Dose Data • DVH calculator • Isodose generator • NTCP/TCP calculator Beam Data DB Commissioning module • Linac geometry info • Dosimetric Data • PDD data • Profile data • Output factor • Wedge/MLC info • CT HU-density table • ETC… • Kernel table (hidden) • RTP commissioning • Data I/O interface • Spectrum optimization • Source modeling optimization • Determine output factor: value/MU, cGy/MU • Wedge shape… Dose calc Engine • Photon Dose calculation • - ETAR , CCC, AAA… • Electron Dsoe • - PBC Hogstromalgorithm IMRT Module Optimization engine • Beam-let extraction • Make Voxel lists per organ • Constraint I/O • Run optimization • MLC sequencing • Steepest decent method • - for spectrum • - for beam source model • - for IMRT

  4. 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

  5. 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

  6. 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: • Superposition: Sun of all kerma map at each voxel. • Same as convolution of TERMA and kernel Convolution/superposition method

  7. General Process of Dose Calculation • Consider geometric infomations Do convolution Calculate Photon fluence Calculate 3D TERMA • Photon beam source • 2 source model • 3 source model • Beam aperture • Collimators • MLC • Horn effects • Beam Divergence • Inverse square law • Poly-energetic kernels • C/S or CCC or AAA • Differential kernels or Accumulative kernels • Attenuation • Beam hardening/softening • Transmission through MLC /block/collimators

  8. yb yb xb xb zb zb yg zg xg Geometric transformation Source Source • Geometric definition Beam coordinate Beam coordinate • Freedom of beam directions • Gantry angles • Collimator angles • Couch angles • Translations of couch • Patient coordinate system • World (global) coordinators • Based on CT coordinators • Define 3D dose • Define contours isocenter • Beam coordinate system • Origin is beam source • Z axis is beam center • Fluence. Beam source, TERMA, kernels • Defined per beams 0 0 Block Block 1 1 • Transformation between Patient coordinate and Beam coordinate CT coordinate

  9. yb yb yb zb zb zb yb xb xb xb xb zb yg zg xg Geometric transformation • Simple Example Beam coordinate Beam coordinate Beam coordinate Beam coordinate • 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 Source Sb ( 0, 0, 0) 5 IsocenterPb CT Origin Pg (0,0,0) 5

  10. Source 0 1 Process of TERMA Calculation • Calculation of Fluence and TERMA distribution in media • Beam source model • Binary MLC plane • Using Hit test • Considering partially block Calculate Fluence at each voxel Calculate Beam divergence Calculate Horn effect Calculate effective depth for each voxels Calculate beam softening effect Calculation point Calculate Attenuation

  11. Point source Srcprimary plane • Primary photon source • Point source: Cp Zsp = 4cm Annulus source Srcsp plane Disk source Zsf = 12.5 cm Srcsf plane • Scattered photon source from primary collimator • Annulus shape Collimator or MLC Collimator or MLC SCD = 100 cm • Scattered photon source from other structures • Disk shape • Intensity function with r Isocenter Point of calculation (xb,yb,zb) Beam source Model: 3 source model Gantry head

  12. Gantry head Point source Srcprimary plane Annulus source Srcsp plane Disk source Srcsf plane Collimator or MLC Collimator or MLC Isocenter Point of calculation (xb,yb,zb) Beam source model: 3 source model • Fluence at an arbitrary point

  13. Implementation of Beam source model Beam Source center (0, 0, 0) • Define Binary MLC Grid from the position of MLC leaves • Considering partially block • Hit Test algorithm Binary Block Plane 1 • 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() • } 1 0 Fluence Voxel (xb, yb, zb)

  14. 1 0 Xs Ys 0 0 Source plane Z = Z_src 5mm resolution 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 Implementation of Beam source model 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 }

  15. Source 0 1 Process of TERMA Calculation • Calculation of Fluence and TERMA distribution in media Calculate Fluence at each voxel Calculate Beam divergence Calculate Horn effect SPD Distref Calculate effective depth for each voxels Calculate beam softening effect Calculation point Calculate Attenuation

  16. Source 0 1 Process of TERMA Calculation • Calculation of Fluence and TERMA distribution in media Calculate Fluence at each voxel Calculate Beam divergence Calculate Horn effect Calculate effective depth for each voxels OAD Calculate beam softening effect Calculation point Calculate Attenuation

  17. Source 0 1 Process of Dose Calculation • Calculation of Fluence and TERMA distribution in media Calculate Fluence at each voxel Calculate Beam divergence Calculate Horn effect Calculate effective depth for each voxel Calculate beam softening effect Calculation point Calculate Attenuation

  18. Source 0 1 Process of Dose Calculation • Calculation of Fluence and TERMA distribution in media Calculate Fluence at each voxel Calculate Beam divergence Calculate Horn effect Calculate effective depth for each voxels Calculate beam softening effect Calculation point Calculate Attenuation

  19. Source 0 1 Process of Dose Calculation • Calculation of Fluence and TERMA distribution in media Calculate Fluence at each voxel Calculate Beam divergence Calculate Horn effect Calculate effective depth for each voxels • Beam hardening effect Calculate beam softening effect Calculate Attenuation

  20. Implementation of convolution Photon source for all r’…(N voxels in volume) { Get TERMA(r’) for all r…. { Get Kernel (r-r’) from Table Accumulate TERMA(r’) x Kernel (r-r’)to the r’ voxel } } D(r) T(r’) r r'

  21. Why Collapse Cone Convolution? • Limitation of convolution/superposition method • 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 • Center of kernel has too steep gradient. • Discrete kernel data  Significant error at the center voxels in dose calculation. From “Current Concepts in Dose Calculations”, Anders Ahnesjö.

  22. N N voxels M rays N Collapsed cone approximation • 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 M Number of Cones N number of Voxels No of Iterations: N3 No of Iterations : M x N

  23. 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.

  24. A Collapsed Cone Y θ X φ A TERMA Voxel -Z Process of Convolution • Sphere Convolution Process • Total 288 cone rays • 24 divisions of theta • 12 divisions of phi angle • Extracting voxel lists traversed by each ray vector r. • Heterogeneity correction by effective pathway through vector r • Convolution kernel table with spherical coordinate system. • Consideration of kernel tilting effect • Adaption of accumulative kernel

  25. 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)

  26. TERMA Voxel Dose Voxel θcone θbeam Divergent Beam Kernel tilting TERMA Voxel

  27. 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

  28. Discussion & Question

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