julien lenoir ipam january 11 th, 2008. classification human tissues: intestines fallopian tubes...
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Julien Lenoir
IPAM January 11th, 2008
Classification Human tissues:
IntestinesFallopian tubesMuscles…
Tools:Surgical threadCatheter, Guide wireCoil…
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Soft-Tissue Simulation
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Intestines simulation [FLMC02]
Goal:Clear the operation field prior to a laparoscopic
intervention Key points:
Not the main focus of the interventionHigh level of interaction with user
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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 interactivityHigh viscosity (no friction)
Not needed:Torsion (no control due to high viscosity)
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Intestines simulation [FLMC02] Physical modeling: dynamic spline model
Previous work○ [Qin & Terzopoulos TVCG96] “D-NURBS”○ [Rémion et al. WSCG99-00]
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i
i
iiq
EQ
q
E
q
E
dt
d pcc
)(
)(tqi
DOFs = Control points position
pc EE , Kinetic and potential energies
n
ii sbs
1
)()( iqP )(sb Basis spline function (C1, C2…)
○ 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 (C2 continuity)Complexity O(n) due to local property of spline3D DOF => no torsion !
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Potential energies (deformations) = springs
Intestines simulation [FLMC02] Collision and Self-collision model:
Sphere basedBroad phase via a voxel grid
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Extremity of a spline segment
Dynamic distribution (curvilinear distance)
Intestines simulation [FLMC02]
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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
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Fallopian tubes
Avoid intrauterine pregnancy Simulation of salpingectomy Ablation of part/all fallopian tube
Clamp the local areaCut the tissue
Minimally Invasive Surgery (MIS)
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Fallopian tubes
Choice of a predefine cut (not a dynamic cut):3 dynamic splines connected to keep the continuity
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3 dynamic spline models
Constraintsinsuring C2 continuity
Release appropriate constraints to cut
Fallopian tubes
Physical modeling:Dynamic spline modelConstraints handled with Lagrange multipliers +
Baumgarte scheme:○ 3 for each position/tangential/curvature constraint
=> 9 constraints per junction
Fast resolution using a acceleration decomposition:
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EA
BλA
L
LM T
EAA
λA
BA
)( ct
Tc
t
L
LM
M
tT
Tc
t
LLLM
LM
M
AEλ
λA
BA
.
.1
1
Fallopian tubes
Collision and Self-collision with spheres
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Soft-Tissue Simulation
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Muscles
Dinesh Pai’s workMusculoskeletal strandBased on Strands [Pai02]Cosserat formulation1D model for muscles
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Joey Teran’s workFVM model [Teran et al., SCA03]Invertible element [Irving et al., SCA04]Volumetric model for muscles (3D)
Tool Simulation
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Surgical Thread Simulation Complex and complete behavior
StretchingBendingTorsion
Twist control very important for surgeons
Highly deformable & stiff behavior Highly interactive Suturing, knot tying…
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Surgical Thread Simulation
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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 SimulationHelpful tool for Suturing
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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)
0),(),,( 0 PtsPtqqg A Usual fixed point constraint
0)),((),,,( 0 PttsPtsqqg Sliding point constraint
Surgical Thread SimulationHelpful tool for Suturing
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s becomes a new unknown: a free variable
0.
λs
g T
P(s,t)
λ = Force ensuring the constraint g
T
sg
Requires a new equation:Given by the Lagrange multiplier formalism
s(t)
Surgical Thread SimulationHelpful tool for Suturing
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Resolution acceleration:by giving a direct relation to compute
0.
λs
gs
T
s(t)P(s,t)
λT
sg
s
Surgical Thread SimulationHelpful tool for Suturing
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Surgical Thread SimulationHelpful tool for knot tying
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Lack of DOF in the knot area:
Surgical Thread SimulationHelpful tool for knot tying
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Adaptive resolution of the geometry:Exact insertion algorithm (Oslo algorithm):
NUBS of degree d
Knot vectors:
)(sbit it 1it
insertion
)(~sbit~ it
~1~
it 2~
it
i
idjij bb~
,
sinon
~si
0
1 10,
jjjji
ttt
rji
iri
rjrirji
iri
irjrji tt
tt
tt
tt,1
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1,
1,
~
~
~
01,
0,
1 )1( idiii
diii qqq
Simplification is often an approximation
Surgical Thread SimulationHelpful tool for knot tying
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Results:
Non adaptive dynamic spline Adaptive dynamic spline
Surgical Thread SimulationHelpful tool for cutting
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Useful side effect of the adaptive NUBS:Multiple insertion at the same parametric abscissa
decreases the local continuityLocal C-1 continuity => cut
Tool Simulation
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Catheter/Guidewire navigation
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Interventional neuroradiology Diagnostic:
Catheter/Guidewirenavigation
Therapeutic:CoilStent…
Catheter/Guidewire navigation
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Arteries/venous network reconstruction
Patient specific datafrom CT scan or MRI
Vincent Luboz’swork at CIMIT/MGH
Catheter/Guidewire navigation
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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=F1 Newton iteration = linearization
Catheter/Guidewire navigation
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Contact handling:Mechanics of contact: Signorini’s lawFixed compliance C during 1 time step
=> Delassus operator:
0.0 fd
THCHW
Solving the current contact configuration:Detection collisionLoop until no new contact
○ Use status method to eliminate contacts○ Detection collision
If algorithm diverge, use sub-stepping
Catheter/Guidewire navigation
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Arteries 1st test:Triangulated surface for contact
Catheter/Guidewire navigation
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Arteries 2nd test:Convolution surface for
contact f(x)=0○ Based on a skeleton
which can be animatedvery easily and quickly
○ Collision detectionachieve by evaluatingf(x)
○ Collision responsealong f(x)
Catheter/Guidewire navigation
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Catheter/Guidewire navigation
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Coil deployment:Using the same technique
Others 1D model
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Hair simulation
Florence Bertail’s (PhD06 – SIGGRAPH07) L’Oréal
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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
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