1. Keith Evan Schubert Professor of Computer Science and Engineering California State University, San Bernardino

2. Why Protons? Dose % 100 Photon Proton Depth in Tissue Electron

3. pCT Scanner

4. Problem Flow

5. Discretized Area

6. A Proton Path

7. Problem Size ~10 7 voxels ~ 10 8 proton paths (min) ~ 400 voxels/paths Thus: Size(A) ~ 10 7  10 8 = 1 PB (dense) Computation SVD ~ 10 7  10 7  10 8 = 10 10 Tflops/Cycle

9. Problem Size ~10 7 voxels ~ 10 8 proton paths (min) ~ 400 voxels/paths Thus: Size(A) ~ 10 8  10 3 = 100 GB Computation ART ~ 10 3  10 3  10 8 = 10 2 Tflops/Cycle

10. Problem Flow

11. Convex Hull

17. Simulation No Noise Noise Space CarvingFiltered Back Projection

18. Actual Scans Pediatric Head Phantom Rat Head Space CarvingFiltered Back Projection

19. Calculating Entry and Exit Points

20. Problem Flow

21. The Most Likely Path (1)

22. The Most Likely Path (2) 79 flops / step Redundant calculations (Sigma/R) 1600 possible (20.0 cm depth x 0.125 mm step) 10 8 -10 9 histories Precalculate all Sigma/R terms 7 flops/step

23. Proton Histories vs. Depth

24. Reconstruction Sparse Sequential algorithm ART Sparse Parallel algorithm Fully simultaneous algorithms Cimmino, CAV Block iterative BIP, BICAV, DROP, OS-SART String averaged SAP, CARP

25. ART x0x0 x0x0 x1x1 x2x2 x3x3 x4x4 x5x5 x6x6

26. Cimmino x0x0 x0x0 x1x1

27. Block Iterative Projections x0x0 x0x0 x1x1

28. x0x0 x0x0 x1x1 x2x2

29. String Averaged Projections x0x0 x0x0 x1x1

30. BIP xkxk X k+1 ai

31. Fermi

32. Iteration - b - A x = R Calculate ResidualSync BlocksUpdate x x += c A T R

33. Summing In Inner Product 0123456789101112131415 81012141618 20 22 2428 32 36 5664 120

34. SAP Number of Histories Protons=voxels Protons=10 voxels Protons=5 voxels Protons=20 voxels

35. SAP Relaxation Parameter 0.010.1 0.20.5

36. Conclusions A simple convex hull calculation is fast and precise GPGPU acceleration yields a three order of magnitude increase in speed Pre-calculating and binning yields a two order of magnitude increase in speed SAP gives good convergence and image quality 2D (single machine) 12 hours to a few seconds 3D (cluster) day to under 30 minutes More to do…