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Julien Lenoir IPAM January 11th, 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] Lagrangian equations applied to a geometric spline: n P( s ) q i bi ( s ) b(s ) Basis spline function (C1, C2…) i 1 E p d Ec E ( ) c Qi dt q i qi qi qi (t ) DOFs = Control points position Ec , E p Kinetic and potential energies ○ Similar to an 1D FEM using an high order interpolation function (the basis spline functions) 6 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 7 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 8 Intestines simulation [FLMC02] 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 9 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 Constraints insuring C2 continuity 3 dynamic spline models Release appropriate constraints to cut 12 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: MA L λ B LA E T MA t B T M A L λ c L( A A ) E t c MA t B 1 T A M L .λ c LM 1LT .λ E LA t 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 Joey Teran’s work FVM model [Teran et al., SCA03] Invertible element [Irving et al., SCA04] Volumetric model for muscles (3D) 16 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 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 19 Surgical Thread Simulation Helpful 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) g ( q, q, t ) P( s A , t ) P0 0 Usual fixed point constraint g ( q, q, s, t ) P( s(t ), t ) P0 0 Sliding point constraint 20 Surgical Thread Simulation Helpful tool for Suturing s becomes a new unknown: a free variable Requires a new equation: Given by the Lagrange multiplier formalism g .λ 0 s T λ P(s,t) = Force ensuring the constraint g g s T s(t) 21 Surgical Thread Simulation Helpful tool for Suturing Resolution acceleration: by giving a direct relation to compute s λ g s .λ 0 s T P(s,t) g s T s(t) 22 Surgical Thread Simulation Helpful tool for Suturing 23 Surgical Thread Simulation Helpful tool for knot tying Lack of DOF in the knot area: 24 Surgical Thread Simulation Helpful tool for knot tying Adaptive resolution of the geometry: Exact insertion algorithm (Oslo algorithm): t NUBS of degree d Knot vectors: ~t ~ b j b d i, j i i ti ti 1 insertion ~t i ~ ti 1 tj ~ t j t j 1 1 si 0 sinon ~ t j r ti r ti r 1 ~ t j r r r 1 i, j ~ i, j i 1, j ti r ti ti r 1 ti 1 0 i, j ~t i2 bi (s ) ~ bi ( s) qi1 id,i qi0 (1 id,i )qi01 Simplification is often an approximation 25 Surgical Thread Simulation Helpful tool for knot tying Results: Non adaptive dynamic spline Adaptive dynamic spline 26 Surgical Thread Simulation Helpful 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 27 Tool Simulation 28 Catheter/Guidewire navigation Interventional neuroradiology Diagnostic: Catheter/Guidewire navigation Therapeutic: Coil Stent … 29 Catheter/Guidewire navigation Arteries/venous network reconstruction Patient specific data from CT scan or MRI Vincent Luboz’s work at CIMIT/MGH 30 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=F 1 Newton iteration = linearization Arteries are not simulated (fixed or animated) 31 Catheter/Guidewire navigation Contact handling: Mechanics of contact: Signorini’s law 0 d . f 0 Fixed compliance C during 1 time step => Delassus operator: W HCH T 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 32 Catheter/Guidewire navigation Arteries 1st test: Triangulated surface for contact 33 Catheter/Guidewire navigation Arteries 2nd 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) 34 Catheter/Guidewire navigation 35 Catheter/Guidewire navigation Coil deployment: Using the same technique 36 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