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PhD Thesis Michael Baumann Supervisors Jocelyne Troccaz Vincent Daanen

A 3D U LTRASOUND-BASED T RACKING S YSTEM FOR P ROSTATE B IOPSY D ISTRIBUTION Q UALITY I NSURANCE AND G UIDANCE. PhD Thesis Michael Baumann Supervisors Jocelyne Troccaz Vincent Daanen. Context of this thesis. Outline. TIMC laboratory

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PhD Thesis Michael Baumann Supervisors Jocelyne Troccaz Vincent Daanen

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  1. A3DULTRASOUND-BASED TRACKING SYSTEM FOR PROSTATE BIOPSY DISTRIBUTION QUALITYINSURANCE AND GUIDANCE. PhD Thesis Michael Baumann Supervisors Jocelyne Troccaz Vincent Daanen

  2. Context of this thesis Outline • TIMC laboratory • specializing in computer-assisted medical interventions for more than twenty years now • many clinical and industrial collaborations • Pitié-Salpétrière hospital, urology department • active support of this work and very inspiring exchanges • clinical data acquisition on more than 70 patients now • Koelis SA • industrial partner • objective: commercialize products based on prostate tracking ¯ Introduction ●○○○ Prostate Tissue Tracking ○○ Registration Framework ○○○○○○○ Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○

  3. Bladder Prostate Rectum Urethra Seminal Vesicles Introduction Outline • Prostate • Prostate Cancer • most frequent cancer in men • ~220.000 new cases in US (2007) • ~345.000 new cases in EU25 (2006) • second cause of cancer death for men • 27.000 deaths in US (2007) • 87.400 deaths in EU25 (2006) • slow growing disease • affects mostly elder men (>50 years) ¯ Introduction ●○○○ Prostate Tissue Tracking ○○ Registration Framework ○○○○○○○ Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○

  4. DRE Introduction Outline • Prostate Specific Antigene (PSA) screening • biological tumor marker • sensitivity for 4ng/ml threshold: 68-83% (clinically significant cancer) • specificity: ~30%  false positives! • Digital Rectal Exams (DRE) • highly varying sensitivity in clinical studies reported: 18% to 68% • specificity: 4% to 33% • complementary to PSA screening • Prostate Biopsies • Sensitivity: 60-80 % (clinically significant cancer) • Specificity: >95% (histological analysis) • invasive  programmed only if DRE/PSA positive • dilemma: false negatives  repeated biopsies ¯ Introduction ●○○○ Prostate Tissue Tracking ○○ Registration Framework ○○○○○○○ Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○

  5. 2D TRUS probe with needle guide corresponding 2D US image with needle trajectory longitudinal cut Introduction Outline • Prostate Biopsies • 2D transrectal ultrasound (TRUS) control • needle guide on probe • guide aligned with longitudinal plane of probe ¯ Introduction ●○○○ Prostate Tissue Tracking ○○ Registration Framework ○○○○○○○ Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○

  6. coronal plane Introduction Outline • Biopsy targets • prostate cancer is isoechogenic • systematic targets • McNeal’s 3-zone model: central zone (CZ), transition zone (TZ), peripheral zone (PZ) • 68% of cancer can be found in peripheral zone • Systematic 12-core protocol • clinical representation in (pseudo-)coronal plane ¯ Introduction ●○○○ Prostate Tissue Tracking ○○ Registration Framework ○○○○○○○ Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○ coronal plane

  7. Prostate Motion Problem Outline • Prostate motion • main challenge for any prostate tissue tracking system • displacements and deformations • Transrectal biopsy specific: probe-related motion • end-fire probe • deformations and displacements due to probe pressure • Neighboring organs (diaphragm motion, rectal and bladder filling) • minor impact during prostate biopsies ¯ Introduction ●●○○ Prostate Tissue Tracking ○○ Registration Framework ○○○○○○○ Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○

  8. Prostate Motion Problem Outline • Patient motion • (small) deformations • displacements with respect to surrounding tissues • displacements with respect to operating room (pelvis movements!) ¯ Introduction ●●○○ Prostate Tissue Tracking ○○ Registration Framework ○○○○○○○ Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○

  9. Introduction Outline • Biopsy and Target Localization Problem • only rudimentary knowledge about biopsy position • at all stages of intervention! • Pre-interventional stage/planning • n-core protocol target definition highly approximate • targets have to be mentally mapped into patient anatomy • During intervention: target localization problem • difficult to aim invisible target under 2D control • ultrasound: few structural information • 2D: no depth information • prostate motion ¯ Introduction ●●●○ Prostate Tissue Tracking ○○ Registration Framework ○○○○○○○ Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○ finding the target : what do we aim exactly?

  10. Introduction Outline • Target localization problem (ctd) • there exist better targets than systematic protocol • high quality cancer distribution atlas available [Shen’01] • simulations: biopsy sensitivity > 96% with only 6 needles (transperineal access) • suspicious lesions identified on IRM • repeated biopsy series • avoid already sampled tissues (negative targets) • how to aim these targets? • After intervention : sample localization problem • where were the samples taken exactly? • quality control? • are there unsampled regions? • difficult to map histological cancer information back to anatomy • difficult to use histological information for focal treatment planning ¯ Introduction ●●●○ Prostate Tissue Tracking ○○ Registration Framework ○○○○○○○ Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○

  11. Existing Solutions Outline • Magnet Resonance imaging-based approaches • objective : target suspicious lesions detected on MR images • biopsy under MRI control • instruments calibrated with MR frame • Beyersdorff [05], Musil, Krieger et al. [04,05,07], Stoianovici [07] • IRM compatible biopsy acquisition instruments/robot • pro: possibility to aim IRM targets • con: cannot detect/compensate patient movements • would require high resolution, real-time MRI • con: diagnosis: cost-benefit ratio unsatisfying • several millions of biopsies/year in US and EU ¯ Introduction ●●●● Prostate Tissue Tracking ○○ Registration Framework ○○○○○○○ Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○

  12. Existing Solutions Outline • Probe tracking + registration based approaches • 2D transrectal ultrasound • track US probe with optical or magnetic tracking system • identifies view cone motion • register 2D tracking images with free-hand reference volume • identifies prostate motion • Xu et al. [07]: Magnetic probe tracking + registration • pro: can compensate smaller rigid prostate-movements • con: free-hand volume with end-fire probe  low accuracy • con: rigid registration • con: registration of lateral biopsy images not robust (partial gland problem) • con: difficult to compensate large pelvis movements ¯ Introduction ●●●● Prostate Tissue Tracking ○○ Registration Framework ○○○○○○○ Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○

  13. Outline of the Presentation Outline • Prostate Tissue Tracking and Guidance • clinical and scientific objectives • soft-tissue tracking • Prostate Image Registration • registration framework • multi-resolution techniques • image distance metric (rigid) • probe movement model • rigid refinement • elastic registration framework • forces for elastic registration • Experiments and Results • registration success rate • accuracy • biopsy maps and targeting accuracy study • Discussion • Conclusion and Potential Applications • clinical and scientific contributions • potential applications ¯ Introduction ●●●● Prostate Tissue Tracking ○○ Registration Framework ○○○○○○○ Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○

  14. Objectives Outline • Scientific objectives • prostate tissue tracking • establish tissue correspondence • with respect to a reference space • goal: establish correspondence between • biopsy site planning • reference space • needle position during intervention • Clinical objectives • more sophisticated targets • MRI, statistical cancer atlas, unsampled zones when repeating biopsies • guide clinician to target • feed-back to clinician about exact sample position • immediately and after intervention • biopsy maps Introduction ●●● ¯ Prostate Tissue Tracking ●○ Registration Framework ○○○○○○○ Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○

  15. Image-based Prostate Tracking Framework Outline • Proposed Solution • 3D ultrasound-based • hybrid registration • image-based • a priori model based • deformation estimation • no probe tracking • miniminal overhead for clinician, no segmentation Introduction ●●● ¯ Prostate Tissue Tracking ●● Registration Framework ○○○○○○○ 3D ultrasound view cone Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○ anchor volume tracking volume tracking volume:  acquired during intervention:  “contains” sample trajectory anchor volume:  acquired before intervention  defines the reference space needle projection:  projection into anchor volume  projection can lead to curbed trajectories biopsy map:  contains projections of all samples guidance:  target projection into tracking volume registration: establishment of correspondences for identical tissues present in both images

  16. Registration Framework Outline • Image Registration • Optimization (minimization) problem • φ = transformation model • T = template/transformed image (R3  R) • R = reference/fixed image • D[.] = cost functional • Problems • registration only efficient with local minimization (downhill search) • successful local minimization requires • locally unimodal cost functional • start point inside the convex region • the more degrees of freedom (DOF) of φ, the more difficult to find unimodal region of D[R,T,φ] ! Introduction ●●● Prostate Tissue Tracking ●● ¯ Registration Framework ●○○○○○○ Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○

  17. Registration Framework Outline • Proposed approach Introduction ●●● 3 DOF 6 DOF ~ 125.000 DOF Probe kinematics based rigid presearch Refinement of rigid estimate Prostate Tissue Tracking ●● Elastic estimation ¯ Registration Framework ●○○○○○○ optimization techniques Experiments and Results ○○○ variational optimization parametric local optimization parametric systematic search Discussion ○ multi-resolution approaches loss-containing multi-resolution techniques Conclusion/Applications ○○ voxel intensity based image distance metrics SSD with local intensity shift multivariate correlation coefficient a priori models linear elasticity bio-mechanical probe insertion endorectal probe kinematics inverse consistency

  18. Multi-Resolution probe kinematics elastic rigid refinement Outline • Multi-resolution approach • Gaussian pyramid • registration performed on different resolution levels • Coarse resolutions and information loss Introduction ●●● Prostate Tissue Tracking ●● ¯ Registration Framework ●●○○○○○ Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○ level n level n+1 US-specific: complex image masks problematic when computing level n+1 from level n ≤ 50% of fine-grid voxel  mask coarse-grid voxel else  use average of available voxel attention: introduces, however, local information shifts

  19. Multi-resolution probe kinematics elastic rigid refinement Outline • 50-percent rule • use it for pyramid construction • for interpolation • for every other computation on multiple voxels • gradient computation (image distance metrics!) • Gaussian smoothing • Conclusion • Makes high-speed volume to volume registration possible • reliable registration on very coarse levels • Disadvantage • introduces small local information shifts Introduction ●●● Prostate Tissue Tracking ●● 50% rule level 5 standard level 5 level 1 ¯ Registration Framework ●●○○○○○ Experiments and Results ○○○ Discussion ○ standard level 5 50% rule level 5 Conclusion/Applications ○○ level 1

  20. Distance metric (rigid) probe kinematics elastic rigid refinement Outline • Image distance metric (Rigid Registration) • correlation coefficient (CC) based • well-proven for monomodal registration • multivariate application • intensity image + gradient magnitude image • more robust results on coarse levels Introduction ●●● Prostate Tissue Tracking ●● ¯ Registration Framework ●●●○○○○ Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○ raw image gradient magnitude

  21. Probe kinematics probe kinematics elastic rigid refinement Outline • Challenge • probe used to guide needle  view cone motion • adds up to prostate motion • motion too large for capture range of image distance metric • direct downhill/local registration only ~30-40% success rate • Observations • probe head always in contact with rectal wall in front of prostate • if not, no prostate image or needle trajectory outside prostate • anal sphincter heavily constrains probe motion • fix point for probe motion • most important rotations occur around probe axis (when switching lobe) Introduction ●●● Prostate Tissue Tracking ●● ¯ Registration Framework ●●●●○○○ Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○

  22. Probe kinematics probe kinematics elastic rigid refinement Outline • Model of endorectal probe kinematics: • approximate prostate capsule with ellipsoid from bounding box • estimate rectal probe fix point • admit only positions for which • the probe axis lies on the fix point • the probe origin lies on the membrane • 3 degrees of freedom only • can be exhaustively explored in reasonable time! • Advantages • Makes solution independent of external tracking system! • Solves patient motion problem! Introduction ●●● Prostate Tissue Tracking ●● ¯ Registration Framework ●●●●○○○ Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○

  23. Rigid Refinement probe kinematics elastic rigid refinement Outline • Refinement of rigid estimate Introduction ●●● rigid registration of 5 best transformations provided by probe kinematics Prostate Tissue Tracking ●● high quality registration of best result ¯ Registration Framework ●●●●●○○ Experiments and Results ○○○ classical local/downhill search algorithm: Powell-Brent Discussion ○ Conclusion/Applications ○○ high quality local search: from coarse to fine high speed: optimize on coarsest level

  24. Elastic Registration probe kinematics elastic rigid refinement Outline • Prostate deformations • relatively small (several millimeters) • strongest near probe head • difficult to estimate: • few image information near probe head • Transformation model: displacement field • Framework • : linear elastic potential • regularizes/smoothes displacement field • minimal when no deformation  strong regularizer • : SSD variant to measure image distance • : bio-mechanical simulation of probe insertion • : inverse consistency constraints Introduction ●●● Prostate Tissue Tracking ●● ¯ Registration Framework ●●●●●●○ Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○

  25. Elastic Registration probe kinematics elastic rigid refinement Outline • Elastic regularization: solution scheme • variational approach • necessary condition for solver u* of cost function: • Gâteaux derivative at u* vanishes for all perturbations ψ • Euler-Lagrange equations for linear elastic regularization: • trick: separate force computation and regularization • accumulate forces • solve Euler-Lagrange equations • then we get an elliptic boundary value problem of the form • trick: introduce artificial time to obtain iterative gradient descent scheme Introduction ●●● Prostate Tissue Tracking ●● ¯ Registration Framework ●●●●●●○ gradients of distance metrics gradient of linear elastic potential Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○

  26. Force terms probe kinematics elastic rigid refinement Outline • Image based forces • correlation coefficient: statistically not robust when locally computed • SSD • assumes identity between R and Tû • does not correspond to reality! • changes in ultrasound gain, probe pressure and ultrasound direction • Local intensity shift model • additive model: • b estimated with Gaussian convolutions on R and T • resulting force term Introduction ●●● Prostate Tissue Tracking ●● ¯ Registration Framework ●●●●●●● Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○

  27. Force terms probe kinematics elastic rigid refinement Outline • Bio-mechanical probe insertion model • model of probe-related tissue displacements • Interpret displacement differences as forces in the estimation process Introduction ●●● Prostate Tissue Tracking ●● ¯ Registration Framework ●●●●●●● Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○

  28. Force terms probe kinematics elastic rigid refinement Outline • Inverse consistency forces • Observation: forward and backward estimation u and v not symmetric: • Zhang’s approach [’06] • estimate u and v simultaneously • enforce inverse consistency by minimizing • alternating optimization process: • resulting force term Introduction ●●● Prostate Tissue Tracking ●● ¯ Registration Framework ●●●●●●● Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○

  29. Registration Framework Outline • Proposed approach Introduction ●●● Probe kinematics based rigid presearch Refinement of rigid estimate Prostate Tissue Tracking ●● Elastic estimation ¯ Registration Framework ●●●●●●● Experiments and Results ○○○ variational optimization parametric local optimization parametric systematic search Discussion ○ loss-containing multi-resolution techniques Conclusion/Applications ○○ SSD with local intensity shift multivariate correlation coefficient linear elasticity bio-mechanical probe insertion endorectal probe kinematics inverse consistency

  30. Experiments and results

  31. Experiments and Results Outline • Experiments • on real patient data • Pitie-Salpétrière Hospital, Paris, urology department • P. Mozer, G. Chevreau, S. Bart, J.-C. Bousquet • 3D ultrasound images (GE Voluson, RIC5-9 probe) • acquired before biopsies and after each sample acquisition • targeting carried out under 2D US control • Registration example Introduction ●●● Prostate Biopsy Tracking ●● Registration Framework ●●●●●●● ¯ Experiments and Results ●○○ Discussion ○ Conclusion/Applications ○○

  32. Experiments and Results Outline • Rigid Registration • Algorithm tested on 785 image pairs from 47 patients • 27 mis-registrations (success-rate 96.5 %) • Conclusion • probe movement model works fine! Introduction ●●● Prostate Biopsy Tracking ●● Registration Framework ●●●●●●● ¯ Experiments and Results ●○○ Discussion ○ Conclusion/Applications ○○ ultrasound depth ultrasound quality partial contact

  33. Experiments and Results Outline • Accuracy study • 208 registrations on data from 14 patients • manual point fiducial segmentation (calcifications, dark spots) • error computed on Euclidean distances of corresponding fiducials • Registration accuracy • rigid optimization performed on resolution levels 5 to 3 • elastic optimization performed on resolution levels 6 to 3 • Conclusion • accuracy sufficient for many clinical applications Introduction ●●● Prostate Biopsy Tracking ●● Registration Framework ●●●●●●● ¯ Experiments and Results ●●○ Discussion ○ Conclusion/Applications ○○

  34. Experiments and Results Outline • First Application: Biopsy maps • show targeting difficulties • P. Mozer, M. Baumann, G. Chevreau, A. Moreau-Gaudry [Mozer’08] • apex and base targets more difficult to reach than central gland • operator learning curve measured Introduction ●●● Prostate Biopsy Tracking ●● Registration Framework ●●●●●●● ¯ Experiments and Results ●●● Discussion ○ Conclusion/Applications ○○

  35. Discussion

  36. Discussion Outline • Automatic registration validation • visual validation time-consuming and operator-dependent • open issue: automatic detection of failures! • necessary for guidance! • Registration and real-time • requires 5 – 15 seconds • stream parallelization: • algorithm mainly consists of image convolutions • can be parallelized on a voxel per voxel basis • well suited for latest graphic card architectures (stream processors) • registration times of 1 second or less should be feasible • Similarity measures • Good performance for intra-series registration • Still to be evaluated for inter-series registration • only one patient with two biopsy series for instance • Intensity shift model • depends strongly on parameter σof Gaussian convolution Introduction ●●● Prostate Biopsy Tracking ●● Registration Framework ●●●●●●● Experiments and Results ●●● ¯ Discussion ● Conclusion/Applications ○○

  37. Discussion Outline • Probe movement model (rigid registration) • very good success rate • no probe tracking necessary • less hardware in OR! Simpler workflow and logistics! • improvements with model to data fitting possible • should further improve success rate • Bio-mechanical probe insertion model (elastic registration) • for about 50% image pairs, the model improves elastic registration • but: sometimes inadequate model of reality Introduction ●●● Prostate Biopsy Tracking ●● Registration Framework ●●●●●●● Experiments and Results ●●● ¯ Discussion ● Conclusion/Applications ○○

  38. Discussion Outline • Clinical acceptability • only slight modification of classical acquisition protocol • bounding box placement • registration validation (probably post-op step) • no additional instruments/hardware in operation room • cost effective: cost similar to current procedure Introduction ●●● Prostate Biopsy Tracking ●● Registration Framework ●●●●●●● Experiments and Results ●●● ¯ Discussion ● Conclusion/Applications ○○

  39. Conclusion and Applications

  40. Conclusion Outline • Scientific contributions • probe movement model • robust • no probe tracking hardware required • completely solves patient movement problem • reusable for many endocavitary US interventions! • loss-containing multi-resolution filtering and interpolation • robust optimization on very sparse resolution levels • hybrid model- and image-based elastic deformation framework • novel voxel similarity measure for elastic registration • remarkably robust • simple • proof of concept on large set of patient data • Medical contributions • biopsy accuracy study on biopsy maps • more difficult to reach apex/base than mid-gland • operator learning curve proven Introduction ●●● Prostate Biopsy Tracking ●● Registration Framework ●●●●●●● Experiments and Results ●●● Discussion ● ¯ Conclusion/Application ●○

  41. Future work/Prospects Outline • Potential Applications : Biopsies • biopsy maps • immediate feed-back, post-interventional quality control • cancer maps • map histological results on 3D biopsy map • guidance • assist clinician during targeting • requires automatic registration validation and real-time registration • guidance  MRI target mapping • reach MRI targets under ultrasound control • requires • MRI to ultrasound registration • guidance  repeated biopsy series • avoid multiple sampling • visualize already sampled tissues • guidance  cancer atlas targets • define targets with cancer probability atlas (Shen’01) • map them onto anchor volume • requires atlas to ultrasound volume registration Introduction ●●● Prostate Biopsy Tracking ●● Registration Framework ●●●●●●● Experiments and Results ●●● Discussion ● ¯ Conclusion/Applications ●●

  42. Future work/Prospects Outline • Potential applications : Therapy • improve accuracy of ultrasound-guided therapy • brachytherapy, HIFU, cryotherapy, … • focal therapy? • currently: two unknowns after positive biopsy findings • shape of the tumor • exact location of the biopsy • not accurate enough for focal therapy • we solve 2! • sufficient for focal therapy? • in combination with statistical tumor atlas? Introduction ●●● Prostate Biopsy Tracking ●● Registration Framework ●●●●●●● Experiments and Results ●●● Discussion ● ¯ Conclusion/Applications ●●

  43. Publications and References • Publications • [Baumann’07] M. Baumann, P. Mozer, V. Daanen, J. Troccaz. Towards 3D Ultrasound Image Based Soft Tissue Tracking: a Transrectal Ultrasound Prostate Image Alignment System. MICCAI'07, Brisbane, Australia, 2007. Springer LNCS 4792. • [Mozer’07] P. Mozer, M.Baumann, G. Chevreau, J. Troccaz. “Fusion d’images : application au contrôle de la distribution des biopsies prostatiques,” Progrès en Urologie (les Cahiers de la Formation Continue), vol. 18 (1), 2008 • [Baumann’08] M. Baumann, P. Mozer, V. Daanen, J. Troccaz. “Fast and robust elastic registration of endorectal 3D ultrasound prostate volumes for transrectal prostate needle puncture tracking,”In proceedings of CARS’08, Barcelona, 2008 • References • [Shen’04] D. Shen, Z. Lao, J. Zeng, W. Zhang, I. A. Sesterhenn, L. Sun, J. W. Moul, E. H. Herskovits, G. Fichtinger, and C. Davatzikos. “Optimization of biopsy strategy by a statistical atlas of prostate cancer distribution,” Medical Image Analysis, vol. 8, no. 2, pp. 139–150, 2004. • [Zhang’05] Z. Zhang, Y. Jiang, and H. Tsui. “Consistent multi-modal non-rigid registration based on a variational approach,” Pattern Recognition Letters, pp. 715–725, 2006.

  44. Acknowledgements • Urology department Pitié-Salpétrière • Pierre Mozer, Grégoire Chevreau, Stéphane Bart • Koelis SA • Antoine Leroy • Vincent Daanen • TIMC • GMCAO group • Jocelyne Troccaz • and everyone else who supported this project during the last three years! • Funding: • 2004-06: ”Programme Hospitalier de Recherche Clinique - Prostate-Echo”, French ministry of research • 2005-07: “Surgétique Minimalement Invasive (SMI)”, Agence Nationale de Recherche (ANR) • 2005-08: Association Nationale de la Recherche Technique, bourse CIFRE

  45. Inadequate probe model • possible explanation

  46. Separate elastic estimation • first step: • estimate deformations caused by probe forces • second step: • estimate deformations caused by image forces • start optimization with probe deformation as initial guess

  47. Elastic Regularization probe kinematics elastic rigid refinement Outline • Elastic regularization: solution scheme (ctd) • von Neumann stability analysis of numerical scheme yields • Stability criterion and elasticity parameters • forces in our framework are not physical • derived from distances • how to calibrate them with the elastic forces? • Young’s modulus E has no physical meaning • interpret it as free parameter • control elasticity parameters with Poisson’s coefficient v and ∆t • seek best balance between smoothness and convergence rate • balance elastic smoothing and maximally admitted deformation Introduction ●●● Prostate Tissue Tracking ●● ¯ Registration Framework ●●●●●●○ Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○ Young’s modulus Poisson’s coefficient

  48. Elastic Registration probe kinematics elastic rigid refinement Outline • Elastic regularization: solution scheme (ctd) • solved with Gauss-Seidel and full multigrid strategy • Boundary conditions • bending side-walls, fixed edges • good model for probe insertion Introduction ●●● Prostate Tissue Tracking ●● ¯ Registration Framework ●●●●●●○ Experiments and Results ○○○ Discussion ○ Conclusion/Applications ○○

  49. Introduction • Biopsy acquisition • patient in dorsal or lateral position • local anesthesia • 12 acquisitions

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