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Modeling the Pelvic Floor using Shell Elements
1Departamento de Engenharia Civil Instituto Superior Técnico Av. Rovisco Pais 1049-001 Lisboa Portugal
2S. João HospitalPortoPortugal
3IDMECFaculty of EngineeringUniversity of Porto Portugal
D. d'Aulignac(1), J.A.C. Martins(1), T. Mascarenhas(2), R.M. Natal Jorge(3) and E.B. Pires(1)
2
Plan
AnatomyFinite Element
Simulation
Data Geometry
3
Why? Understand working of the pelvic
floor Support of organs
Predict damages during childbirth Stress incontinence Prolapse
Uterine Vaginal Rectal
4
Pelvic Floor
Illust. From Netter
5
MRI Images Sao Joao Hospital, Porto
axial sagittal
6
Visualisation
Rasmussen et al (University of Illinois at Chicago)
Segmented manually from MRI data. Julia R. Fielding et al. (Harvard medical school)
7
Cadaver Measurements
Janda et al 2003
8
Geometry
Point SetNURB
Surfaces(Rhino 3d)
PolygonMesh
9
Mesh Geometry
top
side
Frontal view of the mesh:
3068 triangles
1620 nodes
10
3D Muscle Model
1
1[2 ' ' ] '
''
''
''
I f f J
II C
ff
f
JJ
dev U B U n n U IJU
UI
UU
UU
J
isotropic
fibers
volume
Martins et al. 98
11
Muscle Model
11 12
21 22p
F FF
F F
Tp p pB F F
Tp p pC F F
Deformation gradient
Left Cauchy-Green tensor
Right Cauchy-Green tensor
233 33 33B C F
12
Muscle Model
1 33( )CpI tr C C
Tf p pN CN
p pp
f
F Nn
Fibre strain
Direction of fibres (deformed)
First Invariant
13
Plane Stress
33
33
33
1
1
det( )
0
2 ' ( ) '
p
p I p f f p p
J
FF
U B B I U n n
Since incompressibility is assumed
Since normal stresses are zero the plane stress is given as
14
Passive Behaviour
}1])1({exp[
}1)]3({exp[
)()(
2
1
1
ff
CI
ffC
I
aAU
IbcU
UIUU
Humphrey’s model for
cardiac tissue
isotropic fibres
2
2
3.87 /
23.46
5.84 /
12.43
c g cm
b
A g cm
a
15
Passive Tests
lambda
)/( 2cmgstress
16
Muscle Fibres
17
Active Behaviour
18
Muscle Activation
( ) ( , )f pas f act fU U U
20
1
1 4( 1)
for 0.5 1.5
Mact f
f
U T
Sum of passive and active contributions
19
Total Stress
active
total isotropic
fibers
2( / )g cm
20
Discussion Large quantitative differences between
different models Oomens Martins Bosboom Gielen Kojic Humphrey
Comparison with other models and experimental results is essential
21
Simulation
3068 triangular shell elements
Non-linear simulation performed with ABAQUS
UMAT routine decribing the material
22
Muscle Activation
23
The Future Deformation of pelvic floor during
childbirth Damage, fracture of soft tissues Prolapse of internal organs Geometric models from MRI data 8-node solid FE (de Sousa et al. 03)
24
Muscle Model
11 12
21 2233
33
00
00
0 0
p
F FF
F F FF
F
233 33
0 0
0 0
TpT p pB F F
B FFB F
233 33
0 0
0 0
TpT p pC F F
C F FC F
Deformation gradient
Left Cauchy-Green tensor
Right Cauchy-Green tensor