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