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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 -