1. Prostate Registration USEFUL CONCEPTS AND TOOLS C. Antonio Sánchez Dept of Elec & Comp Eng University of British Columbia Vancouver, BC, Canada antonios@ece.ubc.ca Siavash Khallaghi Dept of Elec & Comp Eng University of British Columbia Vancouver, BC, Canada siavashk@ece.ubc.ca

2. Prostate Biopsy

3. Q: Can we determine where the biopsy came from? Target suspicious regions Guarantee adequate coverage We may want to … Relies on doctor intuition Take a large number of samples to increase likelihood of adequate coverage Patients often asked to undergo repeat biopsies if high levels of Prostate-specific antigen (PSA) Current practice:

4. Prostate MRI

5. Prostate Ultrasound

6. Ultrasound Sweep

7. 3D MR-TRUS Registration MRI US

8. Point-Set Registration Set up an “error” (objective) function Minimize w.r.t. transform parameters Differentiate, set derivatives to zero, solve Affine transform + translation x1x1 y1y1 x2x2 y2y2

9. Point-Set Registration Set up an “error” (objective) function Minimize w.r.t. transform parameters Differentiate, set derivatives to zero, solve x1x1 y1y1 x2x2 y2y2

10. Point-Set Registration Correspondences unknown? Missing data?

11. Point-Set Registration Gaussian Mixture Model Treat “complete” set as a probability density of Gaussians Maximize likelihood of “observation” Probability y j belongs to Gaussian x i (adds fuzziness) In practice: iterate between computing probabilities / updating transform

12. Point-Set Registration Gaussian Mixture Model Treat “complete” set as a probability density of Gaussians Maximize likelihood of “observation” In practice: iterate between computing probabilities / updating transform

13. Point-Set Registration

14. Transformations RIGID: AFFINE: INTERPOLATION:

15. Finite Element Method Basics Divide volume into building blocks ('elements') Define interpolation functions inside elements ('shape functions') n1n1 n2n2 n3n3 x Interpolation matrix

16. Finite Element Method Basics Divide volume into building blocks ('elements') Define interpolation functions inside elements ('shape functions') Assign material properties n1n1 n2n2 n3n3 x strain energy:

17. 3D Surface-Based Reg. 3D FEM representation from MRI Gaussian Mixture Model for prostate surface Partial segmentation from US FEM-transformed Gauss centres limits deformation adds 'fuzziness' yjyj xixi

18. 3D Surface-Based Reg. MRI US MRI Registere d

19. Locating a 2D Slice

20. Intensity-Based Reg. 3D volume image maps 2D→3D 2D slice image

21. Trajectory-Based Constraint Probe is tracked!! Tracking alone not sufficient

22. Trajectory-Based Constraint Probe is tracked!! Tracking alone not sufficient

23. Trajectory-Based Constraint Probe is tracked!! Tracking alone not sufficient Trajectory traces rectal wall New image lies on rectal wall

24. Trajectory-Based Constraint Probe is tracked!! Tracking alone not sufficient Trajectory traces rectal wall New image lies on rectal wall

25. Trajectory-Based Constraint Probe is tracked!! Tracking alone not sufficient Trajectory traces rectal wall New image lies on rectal wall s = 0 s = 1 slides along trajectory, rotate x3

26. FEM-Based Deformation Still need to account for:  Non-rigid deformation  Off-trajectory translation maps 2D slice to 3D volume limits deformation loops over all 2D slice pixels

27. Locating a 2D slice Targe t Projectio n Trajector y FEM

28. Summary 3D MRI → 3D TRUS s = 0 s = 1 2D TRUS → 3D TRUS US

29. FIN