Copyright © 2007 by ASME 1

INTRODUCTION In previous research abdominal aortic aneurysm (AAA) wall stress

analysis has proven to be more accurate in rupture risk prediction than

the clinically used diameter criterion [1]. Together with Philips

Medical Systems (Best, NL), a clinical software tool is created that

automatically derives the AAA geometry from patient CT data and

performs AAA wall stress analysis (Hemodyn package). Using this

software package, the role of intraluminal thrombus (ILT) in AAA

wall stress analysis is evaluated in this study.

ILT is a 3D fibrin structure containing blood cells and platelets and is

found between the AAA wall and the blood flow in 75% of the AAAs.

Observation of ILT reveals that three types of ILT exist (Fig 1). ESEM

images however, do not show clear distinction between the luminal,

medial and abluminal layers, but do show large local variations.

1mm

1mm

1mm

Fig 1: ILT can be divided into luminal, medial and abluminal ILT. ESEM images of ILT from 3 patients, no large structural

changes can be found throughout the ILT.

In previous wall stress studies including ILT, these local variations

were not incorporated and linear mechanical properties of ILT were

either assumed [2,3] or fitted to tensile test data [4,5]. As in vivo ILT

undergoes large deformations, the non-linear viscoelastic behavior of

ILT is studied here using stress relaxation experiments with a

Rheometrics rotational rheometer (DatapointsLab, Ithaca, NY).

After determination of the material properties of ILT, the results are

used to evaluate the effect of ILT on wall stress by performing patient-

specific wall stress analyses with and without ILT and comparing the

results with the conventional ILT material properties as used in

previous research.

METHODS The constitutive model as proposed is displayed in Eq. 1-4.

In this, the Cauchy stress tensor σ is split in σv ,the volumetric part that

only depends on the hydrostatic pressure and σd, the deviatoric part. σd

is split in a non-linear elastic part (σd0) and into n linear viscoelastic

Proceedings of the ASME 2007 Summer Bioengineering Conference (SBC2007) June 20-24, Keystone Resort & Conference Center, Keystone, Colorado, USA

SBC2007-171415

INTRALUMINAL THROMBUS IN AAA WALL STRESS ANALYSIS

Lambert Speelman (1), Evelyne A. van Dam (1), Gerrit W.M. Peters (2), E. Mariëlle M. Bosboom (1), Marcel C.M. Rutten (1), Geert Willem H. Schurink (3),

Michael J.H.M. Jacobs (3), Frans N. van de Vosse (1)

(1) Department of Biomedical Engineering

Eindhoven University of Technology Eindhoven, the Netherlands

(2) Department of Mechanical Engineering

Eindhoven University of Technology Eindhoven, the Netherlands

Luminal Abluminal

(3) Department of General Surgery

Maastricht University Hospital Maastricht, the Netherlands

Copyright © 2007 by ASME 2

modes (Fig. 3). These modes consist of a linear elastic part (Eq 3) and

a time dependent part (Eq 4). Be and Dp are respectively the elastic

Finger tensor and the inelastic rate of deformation tensor. I1 is the first

invariant of the Finger tensor and G0, G1..n, η1...n, A and C are the

model parameters to be fitted.

Fig 2 The mechanical analog of the constitutive model with G0 a non-linear spring and G1..n and η1..n the linear springs

and dashpots in the viscoelastic modes.

Small and large strain experiments are performed on ILT of 7 patients

and the linear and non-linear viscoelastic response is measured. In case

of small strains, the model becomes linear. In the non-linear case, the

material parameters G0, G1..n, η1...n, A and C were fitted on the data.

RESULTS In case of small strains, the results show a shear modulus of 1.7 ± 1.3

kPa. The mean stress response in the large strain relaxation tests of all

samples has been used to obtain the model parameters (Table 1).

Table 1 Model parameters for the mean response

In van Dam et al. (2006) is already concluded that variations in

material behavior within ILT are of the same magnitude as the

variations between patients. This suggests that the same material

parameters may be used to describe all ILT [6]. As the viscous part

turned out to be small compared to the elastic part, only a shear

modulus (GILT) is currently used in the wall stress analyses.

From the CT datasets of 2 patients, finite element meshes are created

with the Hemodyn package. All wall stress simulations are performed

on a Cray mini super computer. The following settings are used:

- A uniform wall thickness (2 mm)

- A population averaged peak systolic blood pressure (16 kPa)

- Proximal and distal fixation of the AAAs in all directions

- No-slip condition between the AAA wall and the ILT

- Linear elastic isotropic material properties (wall and ILT)

- GWALL = 1·103 kPa

The stress results as well as the computational effort are recorded for

all simulations. Simulations are performed without ILT and with ILT

with GILT of 1·102 (conventional) and 1·101 kPa (current results).

When peak stresses and 99 and 95 percentiles for both patients are

compared with and without ILT, it shows that including ILT in the

simulations leads to decreased stress values. However, the effect

appears to be much lower than is observed with the conventional GILT

of 1·102 kPa (Table 2). Another observation that can be made is that

the computational time is significantly increased when including ILT.

As can be seen in Fig. 4, the wall stress distributions for patient 1 are

not markedly influenced by the presence of ILT in case of a GILT equal

to 1·101 kPa. This was identical for patient 2.

Table 2 Simulation results

Patient 1 No ILT ILT (GILT)

kPa - 1·101 1·102

Peak stress 271 232 (-14%) 203(-25%)

99 percentile 214 190(-11%) 165(-23%)

95 percentile 179 167(-7%) 145(-19%)

Comp. time 3 hours 10 hours 10 hours

Patient 2

Peak stress 592 481(-19%) 310(-48%)

99 percentile 254 229(-10%) 172(-32%)

95 percentile 211 195(-8%) 136(-36%)

Comp. time 3 hours 12 hours 11 hours

Figure 4 Wall stress distributions from patient 1, without ILT, and with ILT (GILT = 1·10

1 kPa and 1·10

2 kPa)

DISCUSSION The multimode viscoelastic model can be used to describe the linear

and non-linear viscoelastic properties of ILT. The parameters can be

obtained successfully by fitting them to the experimental data.

From the patient specific simulations it seems that the role of ILT in

AAA wall stress is smaller than indicated in previous research. This

also indicates that the material behavior of the AAA wall may be

much more important. ILT will most likely have a more biochemical

effect causing hypoxia and inflammation of the AAA wall.

Additionally, computing wall stresses without ILT greatly improves

the computational effort, which is important in diagnostic evaluations.

FUTURE WORK Future work includes implementation of a non-linear (visco) elastic

model for ILT in the simulations. To be able to compare the wall stress

distributions, a quantitative measure for wall stress distribution will be

developed. Finally, to be able to draw concrete conclusions from this

research, the study will be extended with a larger patient group.

REFERENCES 1. Fillinger, M.F. et al., J Vasc Surg 2003;37(4):724-32

2. Inzoli, F. et al., Eur J Vasc Endovasc Surg 1999;7:667-674

3. Mower, W. et al., J Vasc Surg 1997;26(4):602-8

4. Di Martino, E. et al., Eur J Vasc Endovasc Surg 1998;15:290-299

5. Wang, D. et al., J Vasc Surg 2002; 36:590-604

6. van Dam, E.A. et al., Biorheology 2006;43(6):695-707

Mode G [Pa] Lambda [s]

1 5.7·102 9.5·10-3

2 2.7·102 9.6·10-2

3 2.6·102 9.1·10-1

4 1.7·102 2.8·101

G0 [Pa] 1.3·103 -

A [-] 5.7·10-1 -

C [-] 5.8·100 -