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Simulation of Surgical Procedures in Virtual Environments

Phantom II. Phantom I. Simulation of Surgical Procedures in Virtual Environments. Cagatay Basdogan, Ph.D . College of Engineering, Koc University. Notes & Equations & Matlab Code are online: http://network.ku.edu.tr/~basdogan. Significance:. VR-based training.

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Simulation of Surgical Procedures in Virtual Environments

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  1. EURON Summer School 2003 Phantom II Phantom I Simulation of Surgical Procedures in Virtual Environments Cagatay Basdogan, Ph.D. College of Engineering, Koc University • Notes & Equations & Matlab Code are online: • http://network.ku.edu.tr/~basdogan

  2. EURON Summer School 2003 Significance: VR-based training • to train and certify medical personnel • to reduce the use of animals in training • to test new surgical devices and procedures

  3. EURON Summer School 2003 Overview: Tissue Mechanics Simulation of MIS procedures Training Transfer Device Design Real-time Interaction

  4. EURON Summer School 2003 System: Laparoscopic Instruments Haptic Displays Visual Display

  5. EURON Summer School 2003 Challenges: Real-time Display Physically-Based Modeling • Graphics (30 Hz) • Haptics (1000 Hz) • 1 msec ! Deformation Tissue/organ model Loading via tool Force on the tool FEM ? . . . F = MU + CU + KU (dynamic analysis) F: force Tissue Characteristics Node (e.g. 100) • nonlinear • anisotropic • hysteresis • non-homogeneous • membrane+bending elements • 6-dof for each node • Stiffness Matrix : K (600x600), diagonal M and C • 600 coupled equations ! complex !

  6. EURON Summer School 2003 Topics: A) Collision detection and computational models of surgical instruments B) Physically-based modeling for simulating soft tissue behavior C) Haptic rendering of deformable objects D) Software and hardware integration

  7. EURON Summer School 2003 Polyhedron Particles Line Segments Case Study: Simulation of Catheter Insertion into the Cyctic Duct Cyctic Duct Catheter Laparoscopic Forceps What you see ... What is really happening ...

  8. EURON Summer School 2003 Principles of Collision Detection(object-object is too expensive !) Line Segment Point-Object - Object Polygons tip Points Line Segments Polygons (e.g. catheter - cyctic duct) (e.g. forceps - cyctic duct)

  9. EURON Summer School 2003 Computational Models of Laparoscopic Instruments Group A Group B Point-based rendering Ray-based rendering

  10. EURON Summer School 2003 Physically-based modeling for simulating soft tissue behavior • Desired properties of deformable models • Modeling of deformable objects • 1) particle-based • 2) FEM-based • Implementing constraints • Problems with particle-based techniques • Problems with FEM techniques

  11. EURON Summer School 2003 Desired properties of force-reflecting deformable models • reflect stable forces • display smooth deformations • handle various boundary conditions and constraints • display “physically-based” behavior in real-time

  12. EURON Summer School 2003 e Y Z X Modeling of Deformable Objects visit my web-site for the details : http://eis.jpl.nasa.gov/~basdogan Particle-based : node1 F = ma a (t + Dt) = F/m v (t + Dt) = v(t) + Dt a (t + Dt) p (t + Dt) = p(t) + Dt v (t + Dt) Fspring node2 Fdamping Fgravity FEM-based : F = KU (static analysis) . . . F = MU + CU + KU (dynamic analysis)

  13. EURON Summer School 2003 Comparison Particle-based FEM-based easy to implement, flexible comprehensive Hybrid Approach

  14. EURON Summer School 2003 Constraints (see my SIGGRAPH’99 Course Notes for details, http://eis.jpl.nasa.gov/~basdogan) • Examples: • a node is fixed in 3D space • a node is constrained to stay on a path • curvature constraint • constant volume Implementation: 1) Particle-based models (Ref: Witkin/Baraff, SIGGRAPH’97 Notes) a) Penalty b) Lagrange multipliers 2) FEM

  15. EURON Summer School 2003 Problems with Particle-Based Techniques A) Adding damping to stabilize oscillations B) Adding constraints C) Too many elements stiffer system # of iterations Dt adaptive step size? D) Too few elements difficult to preserve volume E) Non-homogeneous distribution of elements finer adjustment of spring and damper coefficients

  16. EURON Summer School 2003 Problems with FEM Techniques requires A) Change in topology Re-meshing Modeling approximations B) Dynamic analysis Pre-computation C) Matrix inversion Simplifications in the geometry D) Memory allocation

  17. EURON Summer School 2003 Tnet F2 F1 Fnet Ray-based Point-based Reaction force (c) (a) (b) IHIP HIP

  18. EURON Summer School 2003 Computational Architecture Position Orientation Geometry Collision Detection Physics- Based Deformable Model Force Displacement

  19. EURON Summer School 2003 D) Software and Hardware Integration: tips and tricks • Programming tips to speed up your computations • Modeling tips to speed up your computations • Simulation set-up

  20. EURON Summer School 2003 Programming tips to speed up your computations • Synchronize your haptic and graphic loops through a shared database Haptic Database Visual Thread Shared Database • Construct a multi-layered computing structure if possible Display Images 30 Hz Compute Forces/Disp. 200 Hz Display Forces 1 kHz Extrapolate Forces/Disp. Thread #3 Thread #1 Thread #2 • Construct a hierarchical data structure • Update your geometric coordinates less frequently F Dt haptic = 0.001 sec (display forces) Dt iteration= 0.01 sec (update coordinates)

  21. EURON Summer School 2003 Modeling tips to speed up your computations • consider local deformation • take advantage of single point interactions • condense your matrices in FEM • consider modeling approximations for dynamic FEM analysis • pre-compute (matrices, unit displacements/force) • loosely couple your force and deformation model • take advantage of human perceptual limitations

  22. EURON Summer School 2003 loose coupling of force and displacement models local deformation point-based interactions human perceptual limitations condensation • eliminate internal elements • eliminate rotational dofs

  23. EURON Summer School 2003 Modeling approximations: Modal Analysis . . . F = MU + CU + KU (global coordinates, N COUPLED equations !) U = F X . . . fi = Xi + aiXi + w2iXi i = 1, …, N (modal coordinates, DECOUPLED !) Compute F modal reduction (R << N) U, U, U solve for XR , XR, XR

  24. EURON Summer School 2003 Spectral Lanczos Decomposition (not diagonal !) K’ NxN Lanczos Decomposition (diagonal !) L (M << N) MxM

  25. EURON Summer School 2003 Simulation of Catheter Insertion Real Virtual Simulation Set-Up

  26. EURON Summer School 2003 Virtual Geometric Model

  27. EURON Summer School 2003 • tutorial notes are available online: • Siggraph’99, MMVR’00, MMVR’01 • http://network.ku.edu.tr/~cbasdogan • Acknowledgement: • haptic rendering • Chih-Hao Ho, Mandayam Srinivasan, MIT • design of force reflecting grippers • Ela Ben-Ur, Mark Ottensmeyer, Ken Salisbury, MIT • discussions on finite element modeling • Suvranu De, MIT • discussions on medical procedures, videos, and several OR visits • Steve Small, Steve Dawson, David Rattner, MGH-Harvard Medical School • laparoscopic trainer, several visits to animal facility • Cynthia Barlow (Harvard Medical School) • set-up • Chih-Hao Ho, MIT

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