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1D models in medical simulation

Julien Lenoir IPAM January 11 th , 2008. 1D models in medical simulation. Classification. Human tissues: Intestines Fallopian tubes Muscles … Tools: Surgical thread Catheter, Guide wire Coil …. Soft-Tissue Simulation. 1. Intestines simulation. Intestines simulation [FLMC02].

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1D models in medical simulation

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  1. Julien Lenoir IPAM January 11th, 2008 1D models in medical simulation

  2. Classification • Human tissues: • Intestines • Fallopian tubes • Muscles • … • Tools: • Surgical thread • Catheter, Guide wire • Coil • …

  3. Soft-Tissue Simulation 1. Intestines simulation

  4. Intestines simulation [FLMC02] • Goal: • Clear the operation field prior to a laparoscopic intervention • Key points: • Not the main focus of the intervention • High level of interaction with user

  5. Intestines simulation [FLMC02] Real intestines characteristics: • Small intestines (6 m/20 feet) &Large intestines or colon (1.5 m/5 feet) • Huge viscosity (no friction needed) • Heterogeneous radius (some bulges) • Numerous self contact Simulated intestines characteristics: • Needed: • Dynamic model with high resolution rate for interactivity • High viscosity (no friction) • Not needed: • Torsion (no control due to high viscosity)

  6. Intestines simulation [FLMC02] • Physical modeling: dynamic spline model • Previous work • [Qin & Terzopoulos TVCG96] “D-NURBS” • [Rémion et al. WSCG99-00] • Lagrangian equations applied to a geometric spline: Basis spline function (C1, C2…) DOFs = Control points position Kinetic and potential energies • Similar to an 1D FEM using an high order interpolation function (the basis spline functions)

  7. Intestines simulation [FLMC02] • Physical modeling: dynamic spline model • Using cubic B-spline (C2 continuity) • Complexity O(n) due to local property of spline • 3D DOF => no torsion ! • Potential energies (deformations) = springs Stretching Bending

  8. Intestines simulation [FLMC02] • Collision and Self-collision model: • Sphere based • Broad phase via a voxel grid • Dynamic distribution (curvilinear distance) Extremity of a spline segment

  9. Intestines simulation [FLMC02] • Dynamic model: • Explicit numerical integration (Runge-Kutta 4) • 165 control points • 72 Hz (14ms computationtime for 1ms virtual) • Rendering usingconvolution surface or implicit surface

  10. Soft-Tissue Simulation 2. Fallopian tubes

  11. Fallopian tubes • Avoid intrauterine pregnancy • Simulation of salpingectomy • Ablation of part/all fallopian tube • Clamp the local area • Cut the tissue • Minimally Invasive Surgery (MIS)

  12. Fallopian tubes • Choice of a predefine cut (not a dynamic cut): • 3 dynamic splines connected to keep the continuity Constraints insuring C2 continuity 3 dynamic spline models • Release appropriate constraints to cut

  13. Fallopian tubes • Physical modeling: • Dynamic spline model • Constraints handled with Lagrange multipliers + Baumgarte scheme: • 3 for each position/tangential/curvature constraint => 9 constraints per junction • Fast resolution using a acceleration decomposition:

  14. Fallopian tubes • Collision and Self-collision with spheres

  15. Soft-Tissue Simulation 3. Muscles

  16. Muscles • Dinesh Pai’s work • Musculoskeletal strand • Based on Strands [Pai02] • Cosserat formulation • 1D model for muscles • Joey Teran’s work • FVM model [Teran et al., SCA03] • Invertible element [Irving et al., SCA04] • Volumetric model for muscles (3D)

  17. Tool Simulation 4. Surgical Thread Simulation

  18. Surgical Thread Simulation • Complex and complete behavior • Stretching • Bending • Torsion • Twist control very important for surgeons • Highly deformable & stiff behavior • Highly interactive • Suturing, knot tying…

  19. Surgical Thread Simulation • Dynamic spline • Continuous deformations energies • Continuous stretching [Nocent et al. CAS01] • Green/Lagrange strain tensor (deformation) • Piola Kircchoff stress tensor (force) • Continuous bending (approx. using parametric curvature) • No Torsion • [Theetten et al. JCAD07] 4D dynamic spline with full continuous deformations

  20. Surgical Thread SimulationHelpful tool for Suturing • A new type of constraint for suturing: • Sliding constraint:Allow a 1D model to slide through a specific point (tangent, curvature…can also be controlled) Usual fixed point constraint Sliding point constraint

  21. Surgical Thread SimulationHelpful tool for Suturing • s becomes a new unknown: a free variable • Requires a new equation: • Given by the Lagrange multiplier formalism = Force ensuring the constraint g P(s,t) s(t)

  22. Surgical Thread SimulationHelpful tool for Suturing • Resolution acceleration: • by giving a direct relation to compute P(s,t) s(t)

  23. Surgical Thread SimulationHelpful tool for Suturing

  24. Surgical Thread SimulationHelpful tool for knot tying • Lack of DOF in the knot area:

  25. insertion Surgical Thread SimulationHelpful tool for knot tying • Adaptive resolution of the geometry: • Exact insertion algorithm (Oslo algorithm): NUBS of degree d Knot vectors: • Simplification is often an approximation

  26. Surgical Thread SimulationHelpful tool for knot tying • Results: Non adaptive dynamic spline Adaptive dynamic spline

  27. Surgical Thread SimulationHelpful tool for cutting • Useful side effect of the adaptive NUBS: • Multiple insertion at the same parametric abscissa decreases the local continuity • Local C-1 continuity => cut

  28. Tool Simulation 5. Catheter/Guidewire navigation

  29. Catheter/Guidewire navigation • Interventional neuroradiology • Diagnostic: • Catheter/Guidewirenavigation • Therapeutic: • Coil • Stent • …

  30. Catheter/Guidewire navigation • Arteries/venous network reconstruction • Patient specific datafrom CT scan or MRI • Vincent Luboz’swork at CIMIT/MGH

  31. Catheter/Guidewire navigation • Physical modeling of Catheter/Guidewire/Coil: • 1 mixed deformable object => • Adaptive mechanical properties • Adaptive rest position • Beam element model (~100 nodes) • Non linear model (Co-rotational) • Static resolution:K(U).U=F1 Newton iteration = linearization • Arteries are not simulated (fixed or animated)

  32. Catheter/Guidewire navigation • Contact handling: • Mechanics of contact: Signorini’s law • Fixed compliance C during 1 time step=> Delassus operator: • Solving the current contact configuration: • Detection collision • Loop until no new contact • Use status method to eliminate contacts • Detection collision • If algorithm diverge, use sub-stepping

  33. Catheter/Guidewire navigation • Arteries 1st test: • Triangulated surface for contact

  34. Catheter/Guidewire navigation • Arteries 2nd test: • Convolution surface forcontact f(x)=0 • Based on a skeletonwhich can be animatedvery easily and quickly • Collision detectionachieve by evaluatingf(x) • Collision responsealong f(x)

  35. Catheter/Guidewire navigation

  36. Catheter/Guidewire navigation • Coil deployment: • Using the same technique

  37. Others 1D model 6. Hair simulation

  38. Hair simulation • Florence Bertail’s (PhD06 – SIGGRAPH07) • L’Oréal

  39. Hair simulation • Dynamic model • Animated with Lagrange equations • Kircchoff constitutive law • Physical DOF (curvatures + torsion) • Easy to evaluate the deformations energies • Difficult to reconstruct the geometry:Super-Helices [Bertails et al., SIGGRAPH06]

  40. The END

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