Julien Lenoir IPAM January 11 th, 2008

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

Soft-Tissue Simulation 3

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 4

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) 5

Intestines simulation [FLMC02]  Physical modeling: dynamic spline model Previous work ○ [Qin & Terzopoulos TVCG96] “D-NURBS” ○ [Rémion et al. WSCG99-00] 6 DOFs = Control points position Kinetic and potential energies Basis spline function (C 1, C 2 …) ○ Similar to an 1D FEM using an high order interpolation function (the basis spline functions) Lagrangian equations applied to a geometric spline:

Intestines simulation [FLMC02]  Physical modeling: dynamic spline model Using cubic B-spline (C 2 continuity) Complexity O(n) due to local property of spline 3D DOF => no torsion ! 7 Potential energies (deformations) = springs

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

Intestines simulation [FLMC02] 9  Dynamic model:  Explicit numerical integration (Runge-Kutta 4)  165 control points  72 Hz (14ms computation time for 1ms virtual)  Rendering using convolution surface or implicit surface

Soft-Tissue Simulation 10

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) 11

Fallopian tubes  Choice of a predefine cut (not a dynamic cut): 3 dynamic splines connected to keep the continuity 12 3 dynamic spline models Constraints insuring C 2 continuity Release appropriate constraints to cut

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: 13

Fallopian tubes  Collision and Self-collision with spheres 14

Soft-Tissue Simulation 15

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

Tool Simulation 17

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… 18

Surgical Thread Simulation 19  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

Surgical Thread Simulation Helpful tool for Suturing 20  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 constraintSliding point constraint

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

Surgical Thread Simulation Helpful tool for Suturing 22  Resolution acceleration: by giving a direct relation to compute s(t) P(s,t)

Surgical Thread Simulation Helpful tool for Suturing 23

Surgical Thread Simulation Helpful tool for knot tying 24  Lack of DOF in the knot area:

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

Surgical Thread Simulation Helpful tool for knot tying 26  Results: Non adaptive dynamic splineAdaptive dynamic spline

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

Tool Simulation 28

Catheter/Guidewire navigation 29  Interventional neuroradiology  Diagnostic: Catheter/Guidewire navigation  Therapeutic: Coil Stent …

Catheter/Guidewire navigation 30  Arteries/venous network reconstruction Patient specific data from CT scan or MRI Vincent Luboz’s work at CIMIT/MGH

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

Catheter/Guidewire navigation 32  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

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

Catheter/Guidewire navigation 34  Arteries 2 nd test: Convolution surface for contact f(x)=0 ○ Based on a skeleton which can be animated very easily and quickly ○ Collision detection achieve by evaluating f(x) ○ Collision response along  f(x)

Catheter/Guidewire navigation 35

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

Others 1D model 37

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

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] 39