Transcript vs2008 7625

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  Qi  
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
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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)
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)
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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
i2
bi (s )
~
bi ( s)
qi1   id,i qi0  (1   id,i )qi01
 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
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
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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
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)
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Catheter/Guidewire navigation
35
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

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