Transcript vs2008 7625
Julien Lenoir
IPAM January 11th, 2008
Classification
Human tissues:
Intestines
Fallopian tubes
Muscles
…
Tools:
Surgical thread
Catheter, Guide wire
Coil
…
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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)
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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)
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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
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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
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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)
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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
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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
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Fallopian tubes
Collision and Self-collision with spheres
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Soft-Tissue Simulation
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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)
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Tool Simulation
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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…
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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
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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
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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)
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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)
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Surgical Thread Simulation
Helpful tool for Suturing
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Surgical Thread Simulation
Helpful tool for knot tying
Lack of DOF in the knot area:
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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
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Surgical Thread Simulation
Helpful tool for knot tying
Results:
Non adaptive dynamic spline
Adaptive dynamic spline
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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
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Tool Simulation
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Catheter/Guidewire navigation
Interventional
neuroradiology
Diagnostic:
Catheter/Guidewire
navigation
Therapeutic:
Coil
Stent
…
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Catheter/Guidewire navigation
Arteries/venous
network reconstruction
Patient specific data
from CT scan or MRI
Vincent Luboz’s
work at CIMIT/MGH
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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)
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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
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Catheter/Guidewire navigation
Arteries 1st test:
Triangulated surface for contact
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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)
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Catheter/Guidewire navigation
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Catheter/Guidewire navigation
Coil deployment:
Using the same technique
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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]
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