Prostate Registration USEFUL CONCEPTS AND TOOLS C. Antonio Sánchez Dept of Elec & Comp Eng University of British Columbia Vancouver, BC, Canada Siavash Khallaghi Dept of Elec & Comp Eng University of British Columbia Vancouver, BC, Canada

Prostate Biopsy

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:

Prostate MRI

Prostate Ultrasound

Ultrasound Sweep

3D MR-TRUS Registration MRI US

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

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

Point-Set Registration Correspondences unknown? Missing data?

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

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

Point-Set Registration

Transformations RIGID: AFFINE: INTERPOLATION:

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

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:

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

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

Locating a 2D Slice

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

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

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

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

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

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

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

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

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

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