Fluid structure interaction in abdominal aortic aneurysm using

ANSYS Workbench

byFlorentina Ene

Outline

• Objectives• Abdominal aortic aneurysm (AAA)• Computational methods (CM)

Finite Element Analysis (FEA) Computational Fluid Dynamics (CFD) Fluid Structure Interaction (FSI)

• Validation of CM• Comparison of CM• Haemodynamics and mechanical factors

Objectives

• To simulate the interaction between the blood flow and the diseased aneurismal wall by– Computational simulation– Experimental testing

for the study of abdominal aortic aneurysm (AAA)

• To investigate the influence of certain haemodynamics factors

Abdominal Aortic Aneurysm (AAA)

• AAA - a localised abnormal dilatation of the abdominal aorta

• Diameter - 1.5 times larger than the nominal diameter

• Causes - primarily atherosclerosis

• Population - 4:1 ratio male to female, 75% over 60 years old

• Risk - a high risk of sudden rupture

• Rupture - 3:1 female to male risk rupture

http://www.emedicine.com/MED

Physics of AAA

• Rupture of AAA– Surgical criterion: max diameter 5-5.5 cm

– Maximum wall stress (Raghavan, 1996)(Raghavan, 1996)

– Asymmetry influence (Vorp, 1998; Scotti,2005)(Vorp, 1998; Scotti,2005)

– Intraluminal thrombus (ILT) ((Wang, 2002)Wang, 2002)

– Pulsating interaction (DiMartino, 2001)(DiMartino, 2001)

Hemodynamics in AAA

• Low flow

• Recirculation regions

• Secondary flow

• Low mean wall shear stress

• Temporal oscillations in shear

(Moore,1992; Moore, 1994; Taylor,1998; Taylor, 2002; Long,1998; Tang, 2006)(Moore,1992; Moore, 1994; Taylor,1998; Taylor, 2002; Long,1998; Tang, 2006)

ANSYS Workbench

• ANSYS Workbench– ANSYS ICEM

Mesh– ANSYS Simulation (ANSYS Structural) FEA– ANSYS CFX CFD

Computational Methods for AAA

• Structural Pressure Analysis (FEA)– Static (sFEA)– Transient (tFEA)

• Computational Fluid Dynamics (CFD)– Steady flow (sCFD)– Pulsating flow (tCFD)

• Fluid-Structure Interaction (FSI)– Steady FSI (sFSI)– Pulsating FSI (tFSI)

Computational Methods for AAA

• FEA evaluates rupture potential– Deformations – Stresses

• CFD evaluates unfavourable flow conditions– Velocity distribution– Pressure distribution– Wall shear stress

• FSI evaluates rupture potential due to extra loading of unfavourable flow conditions

Steps of Computational Methods

Solver

Post-processor

Pre-processor

• Geometry• Mesh (Elements)• Materials• Boundary conditions

• Convergence• Solution monitor and control

• Independence analysis• Validation• Comparison

2

3

1

Realistic Aorta Model withAneurysm from CT Scan

IdealisedRealistic

Mimics,Materialise

1

AAA Geometry

Realistic AAA model with/without ILT

Idealised AAA model with/without ILT

1

Meshing1

• Multiblocking technique with O-grid strategy

Meshing

• Hexahedral – fluid volume - Blood• Quadratic – shell element - Wall• Tetrahedral – solid volume - ILT

1

Material and Boundary Conditions

Fluid domainCFD simulation

Solid domainFEA simulation

Material properties

Material properties

Simulationparameters

Boundaryconditions

Simulationparameters

Boundaryconditions

Solver

FEA CFD

•Linear elastic•E=2.7 MPa•ν=0.45•ρ=2000 kg/m3

•Newtonian homogenous incompressible laminar•ρ=1055 kg/m3

•µ=0.0035 Pa s•Ui=0,i=x,y,z@Si,So•FSI interface

@wall(Pressure from

CFD)

• Time step 0.01s• 5 pulse cycles

• Time step 0.01s• 5 pulse cycles

Geometry&

Mesh

1

-0.05

0.05

0.15

0.25

0 0.4 0.8 1.2

Time (s)

Vel

oci

ty (

m/s

)

-10

0

10

20

30

40

Pre

ssu

re (

mm

Hg

)

Velocity inlet Pressure outlets

Solver

FLUID governing equations• The continuity equation

• Navier-Stokes momentum equation

SOLID governing equations• The motion equation• The equilibrium equation • The constitutive equation

FSI• Fluid: Force send as load to solid• Solid: Displacement send as BC to fluid

2

)(in Skl tCijklij

)(on S ttn iiij )(in S

, taf iijij

Fluid

Solid

0u

uuuu 2)/(/)(

ffpt

Postprocessor

• Vector/Countours/Streamlines/Animation/GraphsResults for every domain’s element

• Is the solution valid?– Engineering criteria– Compare to analytical solutions– Compare to experimental solutions– Compare to previous studies– Compare to similar applications– Mesh check

3

Independence Tests

Independence tests Determine

Mesh type independence 1 mesh type

Mesh independence 1 mesh density

Convergence criteria 1 convergence value

For time-dependent analysis

Pulse cycle independence No of pulse cycles

Timestep independence 1 timestep size

3

Verification and Optimisation

Analytical solutions

Solution type Wall type Numerical technique

Laplace Pressure in thin wall Elastic CSD (FEA)

Hagen-Poiseuille’s Steady flow Rigid CFD (FVM)

Womersley Pulsatile flow Rigid CFD (FVM)

Womersley Pulsatile flow Elastic FSI (FEA, FVM)

Inlet surface

FLUID DOMAIN

Wall surface

Outlet surface

Inlet edge

SOLID DOMAIN

Wall surface

Outlet edge

Solid domain Fluid domain

Young’s modulus E=2.7MPa Density ρ=1055kg/m3

Poisson ratio υ=0.45 Viscosity µ=0.0034 Pas

Density ρ=2000kg/m3

Thickness (SHELL181) h=0.002m

3

Validation with Analytical Solutions

Steady flow in rigid tube

3

0

0.1

0.2

-0.01 -0.005 0 0.005 0.01

Radial distance (m)

Ve

loc

ity

(m

/s)

Theory CFD

0

0.04

0.08

0.12

-1 -0.5 0 0.5 1

Diameter ratio

Velo

cit

y w

(m

/s)

Theory FSI0.25s

Pulsatile flow in elastic tube

Pulsatile flow in rigid tube

0.25 sec

0

0.04

0.08

0.12

-1 -0.5 0 0.5 1

Diameter Ratio

Ve

loc

ity

(m

/s)

Theory CFD

Validation with Experimental/Published Results

Pulsatile pressure in compliant AAA model

3

Static pressure in compliant AAA model

0.00

0.50

1.00

1.50

0 5 10 15 20 25

Axial length from maximum diameter (mm)

Ra

dia

l de

form

ati

on

(m

m)

10

20

30

Ra

diu

s (

mm

)

FEA w/ILT EXP w/ILT FEA w/outEXP w/out Outer radius Inner radiusILT radius

0

0.4

0.8

1.2

0 0.4 0.8 1.2

Time (s)

Ch

an

ge

in d

iam

ete

r(m

m)

Position 1 FEAPosition 2 FEAPosition 3 FEAPosition 4 FEAPosition 1 EXPPosition 2 EXPPosition 3 EXPPosition 4 EXP

Cp1 - rest

Validation with Experimental/Published Results3

Pulsatile flow in rigid wall bifurcation

(Morris, 2004)Steady flow in rigid wall bifurcation

(Walburn & Stein, 1981)

10 mm

-0.05

0.05

0.15

0.25

0.35

0.45

-1 -0.5 0 0.5 1Diameter ratio

Ve

loc

ity

(m

/s)

Walburn & Stein CFDPosition 2

0

0.02

0.04

0.06

0.08

-1 -0.5 0 0.5 1

Diameter ratio

Ve

loc

ity

(m

/s)

LDA CFD

Ultrasound Flow Visualisation3

Comparison of CM

• 6 numerical methods– sFEA/tFEA– sCFD/tCFD– sFSI/tFSI

• 3 models Idealised Realistic Realistic with ILT

3

Comparison in Realistic AAA3

Comparison in Realistic AAA

1

2

3

4

1 - AAA without ILT

2 - AAA with ILT

POSITIONS

3

Comparison in Realistic AAA

• Deformations & Von Mises Stresses– Max 5% difference between sFEA and tFSI

• Pressure– Max difference 2%

• Velocity– tCFD>tFSI by max 40%

• Wall shear stress– tCFD>tFSI by max 20%

• Computational effort– tFSI - 10 x sFEA sFEA may be used as clinical tool– tFSI – 10 x sCFD

3

Haemodynamics & Mechanical Factors

• Non-planarity effect• Aortic arch• Wall thickness• ILT presence

• ILT properties Exp• Wall curvature

A1

A2

A3

A4

A5

A6

FSI in realistic aorta model with aneurysmA1

FSI in realistic aorta model with aneurysmA1

Aortic Arch Velocity (tCFD)

Max acceleration

T=0.15s

Max velocityT=0.25s

Max deceleration

T=0.35s

A2

Wall Thickness

– AAA – thinning of wall

– 3 models of varying wall thickness

Aorta

H1 & H2: 2 mm

AAA

H1 : 2 mm

H2: 1 mm

Iliac arteries:

H1 & H2: 2 mm

0

0.001

0.002

0.00 0.05 0.10 0.15 0.20

Axial length (m)

Th

ick

ne

ss

(m

)

0

0.02

0.04

Dia

me

ter

(m)Thickness Diameter

Aorta AAA Iliac

arteries

H3

A3

Wall ThicknessD

efo

rma

tio

n (

m)

AAA without ILTH1 H2 H3

Vo

n M

ise

s s

tre

ss

(P

a)

Vo

n M

ise

s s

tre

ss

(P

a)

De

form

ati

on

(m

)

AAA with ILTH1 H2 H3

A3

AAA With and Without ILTV

elo

cit

y (

m/s

)

Wa

ll s

he

ar

str

es

s (

Pa

)

De

form

ati

on

(m

)

Pre

ss

ure

(P

a)

-ILT +ILT -ILT +ILT

A4

Influence of ILT Properties &Wall Curvature

A5

• Wall curvature– ↑ peaks in diametral strains and compliance– ↑ high stress

1: No ILT2: ILT E=0.05 MPa3: ILT E=0.1 MPa4: ILT E=0.2 MPa

Conclusions

• ANSYS was proven to be an efficient and accurate tool to analyse haemodynamics and mechanical factors influencing AAA

• Mesh independence and pulse cycle independence should be optimised

• Validation of FEA/CFD/FSI was obtained with analytical and experimental results

Conclusions

• AAA rupture could be predicted using computational simulation

• Effects of patient specific geometry are important on haemodynamics in AAA

• Wall thickness and ILT presence are essential in evaluating AAA rupture potential

Thank you!