PhD Thesis Michael Baumann Supervisors Jocelyne Troccaz Vincent Daanen

PhD Thesis Michael Baumann Supervisors Jocelyne Troccaz Vincent Daanen
A 3D ULTRASOUND-BASED TRACKING SYSTEM FOR PROSTATE BIOPSY DISTRIBUTION QUALITY INSURANCE AND GUIDANCE. PhD Thesis Michael Baumann Supervisors Jocelyne Troccaz Vincent Daanen

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 ○○

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

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: % (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 ○○ (DRE) (PSA) mettre accent sur la problématique sensibilité biopsies  biopsies de répétition DRE

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

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 coronal plane

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 ○○ avant problèmes biopsie

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 ○○

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?

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 ○○

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 ○○ fusionner les trois approches dire le nombre de biopsies > aux States

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 ○○ éliminer Marek réduire cons chez Xu à volume free-hand rigid biopsies latérales

Outline of the Presentation
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 ○○ Je vais tout d’abord introduire la problématique du suivi des tissues et du guidage, pour vous présenter ensuite notre méthode. On enchaine avec les expérimentations et les résultats avant de passer à la discussion. Nous allons conclure avec nos contributions techniques et les applications potentielles de notre méthode.

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 ○○

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 ○○ no segmentation! anchor volume tracking volume guidance:  target projection into tracking volume anchor volume:  acquired before intervention  defines the reference space tracking volume:  acquired during intervention:  “contains” sample trajectory biopsy map:  contains projections of all samples needle projection:  projection into anchor volume  projection can lead to curbed trajectories registration: establishment of correspondences for identical tissues present in both images

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 ○○

Outline Proposed approach Introduction ●●● 3 DOF 6 DOF ~ DOF Probe kinematics based rigid presearch Refinement of rigid estimate Prostate Tissue Tracking ●● Elastic estimation Registration Framework ●○○○○○○ optimization techniques Experiments and Results ○○○ parametric systematic search parametric local optimization variational optimization Discussion ○ multi-resolution approaches Conclusion/Applications ○○ loss-containing multi-resolution techniques voxel intensity based image distance metrics SSD with local intensity shift multivariate correlation coefficient 3-step registration framework start with low DOF transformation models find points inside unimodal region of D on more complex models a priori models linear elasticity bio-mechanical probe insertion endorectal probe kinematics inverse consistency

Multi-Resolution Outline Multi-resolution approach Gaussian pyramid
probe kinematics rigid refinement elastic 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 expliquer masque pas clair du tout 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

Multi-resolution Outline 50-percent rule
probe kinematics rigid refinement elastic 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 ●● standard level 5 50% rule level 5 level 1 Registration Framework ●●○○○○○ Experiments and Results ○○○ Discussion ○ standard level 5 50% rule level 5 Conclusion/Applications ○○ level 1

Distance metric (rigid)
probe kinematics rigid refinement elastic 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 ○○ éliminer les corrélations positives raw image gradient magnitude

Probe kinematics Outline Challenge
rigid refinement elastic 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 ○○ diagramme de Pierre bougés sonde?

Probe kinematics Outline Model of endorectal probe kinematics:
rigid refinement elastic 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 ○○ Expliuer pourquoi indépendant

Rigid Refinement Outline Refinement of rigid estimate
probe kinematics rigid refinement elastic 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 speed: optimize on coarsest level high quality local search: from coarse to fine

Elastic Registration Outline Prostate deformations
probe kinematics rigid refinement elastic 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 ○○

Elastic Registration Outline Elastic regularization: solution scheme
probe kinematics rigid refinement elastic 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 ●●●●●●○ Experiments and Results ○○○ gradient of linear elastic potential gradients of distance metrics Discussion ○ Conclusion/Applications ○○ Expliquer Fi Expliquer concurrence des forces Expliquer que poisson+young physiquement Introduire L

Force terms Outline Image based forces
probe kinematics rigid refinement elastic 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 ○○ Pq pas CC?

Force terms Outline Bio-mechanical probe insertion model
probe kinematics rigid refinement elastic 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 ○○ Boire un coup d’eau

Force terms Outline Inverse consistency forces
probe kinematics rigid refinement elastic 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 ○○

Outline Proposed approach Introduction ●●● Probe kinematics based rigid presearch Refinement of rigid estimate Prostate Tissue Tracking ●● Elastic estimation Registration Framework ●●●●●●● Experiments and Results ○○○ parametric systematic search parametric local optimization variational optimization Discussion ○ Conclusion/Applications ○○ loss-containing multi-resolution techniques SSD with local intensity shift multivariate correlation coefficient 3-step registration framework start with low DOF transformation models find points inside unimodal region of D on more complex models linear elasticity bio-mechanical probe insertion endorectal probe kinematics inverse consistency

Experiments and results

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 ○○ Expliquer protocole clinique Expliquer un peu l’anatomie Schéma pierre Il y a pas de guidage pour l’instant

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 ○○ Rigid registration+dire que grand part succes issue cinematic model ultrasound depth ultrasound quality partial contact

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 ○○ Tableau résultats?

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 ○○ Avant discussion, fin Expérimentation Publi: Cahier info continu… Expliquer ce qu’on voit: expert, débutant, zones non-biopsiées, possibilité accrue de rater un cancer

Discussion

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 σ of Gaussian convolution Introduction ●●● Prostate Biopsy Tracking ●● Registration Framework ●●●●●●● Experiments and Results ●●● Discussion ● Conclusion/Applications ○○ no modification of clinical protocol

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 ○○ Recalage élastique améliore recalage Modèle d’insertion de la sondd n’améliore pas la qualité du rec élastique pour l’instant

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 ○○

Conclusion and Applications

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 ●○

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 ●● rester brèf!!!!

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 ●●

Publications and References
[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, 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.

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: : ”Programme Hospitalier de Recherche Clinique - Prostate-Echo”, French ministry of research : “Surgétique Minimalement Invasive (SMI)”, Agence Nationale de Recherche (ANR) : Association Nationale de la Recherche Technique, bourse CIFRE

Inadequate probe model
possible explanation

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

Elastic Regularization
probe kinematics rigid refinement elastic 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 ○○ Virer? Motiver chaque étape Young’s modulus Poisson’s coefficient

Elastic Registration Outline
probe kinematics rigid refinement elastic 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 ○○ arêtes <-> pts

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

PhD Thesis Michael Baumann Supervisors Jocelyne Troccaz Vincent Daanen

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