GPU Based Convolution/Superposition Dose Calculation

Transcription

1 GPU Based Convolution/Superposition Dose Calculation Todd McNutt 1, Robert Jacques 1,2, Stefan Pencea 2, Sharon Dye 2, Michel Moreau 2 1) Johns Hopkins University 2) Elekta Research Funded by and Licensed to Elekta

2 Dose (cm 2 /g) ICCR 2000 Monte-Carlo Photon Benchmark Water-Aluminum-Lung-Water Phantom 18MV 1.5 cm x 1.5 cm Monte Carlo Oncentra Pinnacle3 Depth (cm)

3 Dose JHU GPU Superposition Water-Aluminum-Lung-Water Phantom 18MV 1.5 cm x 1.5 cm Monte Carlo Density Scaled Superposition Heterogeneity Compensated Superposition Depth (cm)

4 Incident Energy Fluence (Ψ) Superposition/Convolution Kernel Dose TERMA = Monte Carlo Simulation Figure courtesy of Michael Sharpe r E t dt r E 1 s D r E,0 r e KE t dt, r, r dr r 2 E r r r TERMA

5 Incident Fluence Generation Primary Source Secondary Scatter Source

6 CPU # Rays = incident fluence pixels Serial processing of each ray Requires post processing to remove sampling noise TERMA GPU # Rays = TERMA voxels Each voxel is its own process Avoids write on write conflicts Cache T/Ψ per energy bin per voxel

7 CPU TERMA GPU Pre-compute lookup table for attenuation to avoid exponential Fixed step length Spectral changes in lookup table Use GPU exponential Voxel boundary stepping Attenuate each energy independently!

8 TERMA CPU Lookup table based attenuation Assumes material above is same as current position GPU Exponential evaluation Enables correct beam hardening through heterogeneous media

9 Relative Energy TERMA Accuracy Stair stepping from lookup table resolution in CPU method Pinnacle GPU Analytical Central Axis Distance (cm)

10 TERMA Performance Size Forward Back-projected Homogenous Approximation Intensity M odulation ms 4ms 2ms <1ms ms 35ms 27ms 1ms ms 438ms 363ms 10ms Rearranged attenuation equation improves backprojection performance s r' EM, s E t dt r' M t t dt Attenuation volume caching for Intensity Modulation: M E A r we r e E r T r r A r 0 M r s E t dt

11 Superposition CPU Source GPU or CPU Source D T T D T D D T D D D Each TERMA voxel is a process Read once From TERMA Write many to Dose Write on Write errors T T Each dose voxel is a separate process Read many from TERMA Write once to Dose No Write on Write errors Compute dose to single point T

12 CPU Superposition Not Tilted Tilted GPU Shared ray-tracing Process single ray direction for all voxels Each voxel is thread Read many write once

13 Multi-resolution Superposition Ideal Standard 50% Azimuth Phase Multi-resolution

14 Heterogeneity Compensation Density Scaled Heterogeneity Compensated D r T r ' K r ' r dedr ' E E E

15 Electron Density (g/cm 3 ) ρ-eff for different locations of dose deposition 2.0 ρ ρeff Left->Right ρeff Right->Left Distance (cm)

16 Effective Distance (cm) Effective Distance for Kernel Lookup ρd Left->Right Deff Left->Right Deff Right->Left ρd Right->Left Distance (cm)

17 Relative # photons Kernel Hardening Energy For each mono-energetic bin there is no hardening Too many calculations Solution is to break spectrum up into parts and compute each part separately in parallel as full computation QUAD = 4 parts DUAL = 2 parts

18 Effect of Spectral Binning

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27 HCS, CS vs MC Dose C/S HCS August 7, % difference

28 Heterogeneity Compensation Dose C/S HCS

29 Heterogeneity Compensation Dose C/S HCS

30 Performance Method Grid^3 # rays spectra tilt kernel t (ms) HCS poly tilted CCK 277 HCS dual tilted CCK 305 Best Balance HCS quad tilted CCK 404 Most Accurate HCS poly tilted CCK 3913 HCS dual tilted CCK 4300 High Res 10x10 field using the ICCR 18 MV spectrum NVIDIA Tesla GPU C2050 with ECC enabled Can achieve interactive rates with 64 3 grid grid under 4 seconds

31 Modeling Tools

32 Modeling Tools

33 Modeling Tools

34 Modeling Tools

35 Modeling Tools

36 Modeling Tools

37 Summary - Algorithm Reworked the C/S method from first principles for the GPU Significant accuracy gains by avoiding performance approximations used in CPU methods Able to obtain Monte Carlo accuracy with improvements in the heterogeneity compensation and kernel hardening methods Obtain performance in the ms range for a typical beam calculation

38 Robert Allan Jacques (July 25, June 18, 2013) Thank you! Robert

39 Arc Therapy: Arc Superposition 39

40 Rays # of 's Δ Tilt Multi-resolution Arc Therapy Arc Superposition 6x12 4x8 4x8 4x8 10x8 6x12 4x8 4x8 4x8 P P P O O P P P O O O P P O O O P P High Dose Region % 0.28% 0.99% 1.12% 0.27% 0.12% 0.28% 0.99% 1.12% % 0.28% 0.99% 1.12% 0.32% 0.18% 0.32% 1.01% 1.14% % 0.28% 0.99% 1.12% 0.40% 0.29% 0.40% 1.05% 1.18% % 0.31% 1.02% 1.16% 2.73% 2.66% 2.69% 3.07% 3.18% % 0.44% 1.12% 1.25% 7.05% 6.95% 6.96% 7.21% 7.30% % 0.92% 1.48% 1.60% 14.05% 13.90% 13.88% 14.07% 14.19% Gradient Region ( D > 0.3D ) Standard Superposition % 0.31% 0.88% 1.12% 0.47% 0.14% 0.31% 0.88% 1.12% % 0.31% 0.88% 1.14% 1.30% 1.07% 1.17% 1.62% 1.81% % 0.32% 0.89% 1.14% 2.16% 1.99% 2.05% 2.40% 2.56% % 0.61% 1.07% 1.25% 7.63% 7.54% 7.53% 7.59% 7.69% % 1.08% 1.42% 1.52% 11.86% 11.77% 11.74% 11.75% 11.83% % 2.25% 2.30% 2.33% 17.08% 16.98% 16.91% 16.92% 17.01% 40