2. Topics Covered Introduction and Background Data Flow and Problem Setup Convex Hull Calculation Hardware Acceleration of Integral Relative Electron Density Calculation Calculating Entry and Exit Points The Most Likely Path Formalism Optimization Reconstructions Conclusions

3. Introduction and Background

4. Beginnings of pCT (Cormack) Allan M. Cormack, a South African particle physicist, shared the Nobel prize for pioneering efforts in the development of CT with Godfrey Hounsfield in 1979 The idea of doing imaging with protons was probably born at the HCL under its Director Andy Koehler and Cormack mentioned it in his seminal paper 1963 paper (J. Appl. Phys. 34, 2722-2727) Introduction and Background

5. Beginnings of pCT (Hanson) In the late 1970s, Ken Hanson, a Los Alamos physicist, experimentally explored the advantages of pCT Hanson pointed to the dose reduction with pCT and the problem of limited spatial resolution due to proton scattering Feasibility of pCT system demonstrated Introduction and Background

6. Beginnings of pCT In the late 1990s Piotr Zygmanski, a PhD student, uses the Harvard Cyclotron to test a cone beam CT system with protons Introduction and Background

7. The pCT Collaboration 2003- present Goals Perform basic simulation and experimental studies in pCT Build & test prototype pCT scanners Collaborators (2002 – present) Steve Peggs, Todd Satogata (BNL), Detector Physics Harmut Sadrozinski, University of California Santa Cruz, Detector Physics Mara Bruzzi, Nunzio Randazzo, Pablo Cirrone, INFN Florence & Catania, Detector Physics Anatoly Rozenfeld, University of Wollongong, Australia, Medical Physics Jerome Liang, State University N.Y. Stony Brook (SUNYSB), Image Reconstruction Keith Schubert, California State University San Bernardino (CSUSB), Computer Science Yair Censor, University of Haifa, Mathematics, Reconstruction Bela Erdely, Northern Illinois University, Physics Introduction and Background

8. Advantages of pCT over X-ray CT No conversion for use in proton therapy Images must be converted form Hounsfield units to electron density Lower dose required to image Introduction and Background

9. Problem Setup and Data Flow

10. Proton CT Scanner

11. Problem Setup and Data Flow System Geometry

12. Problem Setup and Data Flow Problem Size 10 6 proton histories, 10 6 image voxels in this example 10 8 proton histories, 10 7 image voxels expected Ax = b A is the vectorized proton path matrix b is the integral relative electron density x is the vectorized image to be reconstructed

13. Problem Setup and Data Flow Individual Proton Path

14. Problem Setup and Data Flow Vectorized Path 2-D matrix representation replaced by 1-D row 000000000000000011000000000000000111111000000000…

15. Problem Setup and Data Flow Linear System and Solution A is very large and sparse and the system is inconsistent Solution must me approximated with an iterative projection method like the algebraic reconstruction technique

16. Problem Setup and Data Flow

17. Convex Hull Calculation

19. Descretized Area

20. Convex Hull Calculation Convex Hull

21. Convex Hull Calculation Convex Hull

22. Convex Hull Calculation Convex Hull

23. Convex Hull Calculation Convex Hull

24. Convex Hull Calculation Convex Hull

25. Convex Hull Calculation Convex Hull

26. Convex Hull Calculation Convex Hull Approximation

27. Convex Hull Calculation Convex Hull Approximation

28. Hardware Acceleration of Integral Relative Electron Density Calculation

29. Convex Hull Calculation

30. Hardware Acceleration of Integral Relative Electron Density Calculation The Bethe-Bloch Equation Simplifies to:

31. Hardware Acceleration of Integral Relative Electron Density Calculation

32. Calculating Entry and Exit Points

36. Data Distribution

37. Most Likely Path Formalism Optimization

38. The Most Likely Path

39. Most Likely Path Formalism Optimization The Most Likely Path y mlp has 79 floating point operations per step with matrix multiplication Sigma/R matrices are calculated every 0.5 mm For 20.0 cm object there are 400 different combinations 400 different combinations for 10 6 histories means there are many redundant calculations

40. Most Likely Path Formalism Optimization Separate Sigma and R From y Distribute P 1

41. Most Likely Path Formalism Optimization Separate Sigma and R From y

42. Most Likely Path Formalism Optimization The Most Likely Path

43. Most Likely Path Formalism Optimization The Most Likely Path Y t now has only 7 floating point operations per step

44. Reconstructions

48. Conclusions

49. A simple convex hull calculation is fast and precise GPGPU acceleration of data parallel computation can give a three order of magnitude increase in speed Precalculating Sigma and R matrix combinations removes 91% of calculations at each step of the MLP leading to a two order of magnitude increase in speed

50. Conclusions Future Work Migrate all data parallel pCT code to GPGPU hardware Improve accuracy of reconstruction GPGPU cluster research