Journal of Medical Engineering & Technology, Vol. 32, No. 2, March/April 2008, 167 170 Short Communication Finite element modeling of the thoracic aorta: including aortic root motion to evaluate the risk of aortic dissection C. J. BELLER*{, M. R. LABROSSE{, M. J. THUBRIKARx and F. ROBICSEK{ {Department of Cardiac Surgery, University Hospital Heidelberg, INF 326, 69120, Heidelberg, Germany {University of Ottawa, Department of Mechanical Engineering, Ottawa, Ontario, K1N 6N5, Canada xedwards Life Sciences, Irvine, California, 92614, USA {Carolinas Medical Center, Charlotte, North Carolina, 28203, USA Objective: We propose that the aortic root motion plays an important role in aortic dissection. Methods and results: A finite element model of the aortic root, arch and branches of the arch was built to assess the influence of aortic root displacement and pressure on the aortic wall stress. The largest stress increase due to aortic root displacement was found at approximately 2 cm above the top of the aortic valve. There, the longitudinal stress increased by 50% to 0.32 MPa when 8.9 mm axial displacement was applied in addition to 120 mmhg luminal pressure. A similar result was observed when the pressure load was increased to 180 mmhg without axial displacement. Conclusions: Both aortic root displacement and hypertension significantly increase the longitudinal stress in the ascending aorta, which could play a decisive role in the development of various aortic pathologies, including aortic dissection. Keywords: Aortic root motion; Mechanical stress; Aortic dissection 1. Introduction Hypertension and aortic dilatation are known key players that can augment the mechanical stress in the aortic wall. While both conditions and aortic wall abnormalities are the most common risk factors for aortic dissection and rupture, cardiac contractions have been suspected as well [1]. Although the stresses associated with cardiac contractions are not known, they may play a role not only in aortic dissection, but also in atherosclerotic plaque dislodgment, and they may affect the longevity of aortic valve replacements. A finite element model was built to evaluate the influence of aortic root movement on the aortic wall stress, using measurements of the aortic root motion reported in the literature. 2. Methods A finite element model of an average adult human aortic root, aortic arch and supra-aortic vessels was built for stress analysis using ANSYS 5.7 software. 2.1. Geometry The distance between the root base and the brachiocephalic trunk was 70 mm, and the aortic root angle to the horizontal plane in the frontal view was 308 [2]. The dimensions of the aortic arch and proximal areas of the arch branches were measured at the Carolinas Medical Center from a silicone mould of a normal human aorta [S. Rao, *Corresponding author. Email: carsten.beller@urz.uni-heidelberg.de Journal of Medical Engineering & Technology ISSN 0309-1902 print/issn 1464-522X online ª 2008 Informa UK Ltd. http://www.tandf.co.uk/journals DOI: 10.1080/03091900600687672
168 C. J. Beller et al. unpublished data, 1994]. The radii of the arch and the aorta were found to be 37 mm and 12.2 mm, respectively. The local aortic wall thickness (mean of 1.2 mm), the branches radii, and the local curvature radius and thickness at the bifurcations were implemented as determined from the mould. Using a 3D magnetic resonance imaging (MRI) in a healthy volunteer, the aortic arch was found to lie approximately in a vertical plane oriented 208 anteroposteriorly, and was modelled accordingly. The aortic root and the ascending aorta were modelled as curved cylinders by prolongation of the arch geometry. The actual shape of the sinuses of Valsalva was not represented, as the aim of the study was to examine the effect of aortic root motion on aortic wall stress. 2.2. Finite elements The model was discretized into 14 707 20-node tetrahedral elements (figure 1). The material of the aortic wall was represented as homogeneous, quasi-incompressible, linear elastic and isotropic, with a Young s modulus of 3 MPa and a Poisson s ratio of 0.49. In order for the aorta to deform physiologically, the distal ends of the supra-aortic vessels and the aorta were fixed in all directions, and stiffer material properties (Young s modulus of 12 MPa) were used to increase the influence of the anchors. Geometric nonlinearities were included in the analysis due to the potentially large deflections experienced by the aorta. 2.3. Loading A luminal pressure of 120 mmhg was the only load in the control model. Then, additionally, 8.9 mm axial displacement and 68 twist were applied to the aortic root base [3,4] (figure 1). To compare the effect of root motion versus hypertension on the stress in the aortic wall, the analysis was also carried out for a luminal pressure of 180 mmhg. Other loading conditions were implemented to investigate how increased axial displacement (15 mm), twist (148) and aortic wall stiffness (Young s modulus of 6 MPa) may influence the aortic wall stress. 3. Results 3.1. Deformed shape Pressurization alone did not appreciably deform the model, but adding 8.9 mm axial displacement and 68 twist at the root base caused significant deformation, especially in the ascending aorta and the brachiocephalic trunk. In the vertically downward direction, this loading resulted in displacements of 7.5 mm at the root base and about 3 mm at the brachiocephalic trunk origin. In the direction perpendicular to the plane of the transverse arch, the loading induced displacements of 4 mm at the root base and about 2 mm at the brachiocephalic trunk level. 3.2. Stresses with pressure load, without aortic root motion Stress concentrations were present at the ostia of the supraaortic vessels as expected. Between the brachiocephalic trunk and the left common carotid artery (LCCA), the circumferential stress was approximately 0.40 MPa and the longitudinal stress 0.25 MPa. Above the sinotubular junction (STJ), the circumferential and longitudinal stresses in the aortic wall were 0.32 and 0.21 MPa respectively. At 180 mmhg pressure, the stress between the origin of the brachiocephalic trunk and the LCCA was approximately 0.68 MPa in the circumferential direction, and 0.27 MPa in the longitudinal direction. Above the STJ, the circumferential and longitudinal stresses were 0.49 and 0.34 MPa, respectively. 3.3. Stresses with pressure load and aortic root motion Figure 1. Front view of the finite element model of the aortic root, arch and branches. The undeformed mesh is shown along with the deformed shape outline when 8.9 mm axial displacement and 68 twist were applied to the aortic root base in addition to the 120 mmhg pressure. At 120 mmhg luminal pressure, the circumferential and longitudinal stresses did not change markedly between the brachiocephalic trunk and the LCCA when aortic root motion was applied. The area where the most significant changes occurred was about 2 cm above the STJ: while the
Aortic root motion and dissection 169 circumferential stress was unchanged, the longitudinal stress increased by 50% up to 0.32 MPa with 8.9 mm axial displacement (figure 2). At the highest value of axial displacement (15 mm), the longitudinal stress was further increased to 0.47 MPa. It ultimately reached 0.64 MPa when the stiffness of the aorta was doubled to simulate the rigidity one may encounter in older subjects. Similar findings were observed with a pressure of 180 mmhg. Adding 8.9 mm axial displacement increased the longitudinal stress above the STJ from 0.34 to 0.41 MPa, while the circumferential stress stayed at approximately 0.49 MPa. The longitudinal stress rose further to 0.56 MPa with 15 mm axial displacement, or to 0.57 MPa when the stiffness of the aorta was doubled without increasing the displacement. The mechanical influence of twist was found to be negligible in all cases. 4. Discussion The geometry of the model was comparable to a 3D-MRI reconstruction, and included the details of the ostia of the aortic arch vessels and changes in aortic wall thickness of a human sample. With aortic root motion enforced as found in the literature, and proper tethering of the model, it was Figure 2. Distribution of stress (MPa) in the longitudinal direction of the deformed shape. The longitudinal stress in the ascending aorta rose by about 50% in the region highlighted by the box, compared to the control model. The stresses are displayed in the toroidal coordinate system attached to the aortic arch. possible to mimic physiological deformations throughout the model. This indicates that the simplified model and the material properties used were reasonable. It is important to realize that, as the initial geometry of the model was based on physiological dimensions (say under diastolic pressure, or about 80 mmhg), the stresses and deformations presented herein are representative of what happens to the aorta between diastole and systole. The ostia of the aortic branches benefit from a reinforced vascular architecture and are not typical locations where mechanical failures occur, in spite of the observed stress concentrations. By contrast, the ascending aorta a few centimetres above the STJ appeared as the region most uniquely affected by the aortic root motion (see box in figure 2). In this location, the longitudinal stress increased significantly and could play a decisive role in the development of various aortic pathologies. It is indeed where more than 60% of aortic dissections are observed [5]. Although the longitudinal stress only reached approximately half the known yield stress of the thoracic aorta in the longitudinal direction and did not present an imminent threat, the damage associated with cyclic loading was not considered. As the ratio of longitudinal to circumferential stress increases, there may be an increased risk for a circumferential tear to develop, as observed in most aortic dissections [5]. It is important to note that aortic root motion alone is only an indicator of the force that the heart exerts on the aorta. Thus, a large aortic root displacement may be well tolerated in a compliant aorta, or may cause a disaster in a subject with stiffer aortic tissue. A mesh sensitivity analysis showed that doubling the number of elements in the model changed the stress results of the analysis by less than 7%. The specific stress values found may be affected by the simplified material properties used, but it is believed the overall findings of the study are not. Note that only average transmural stresses were reported since their gradient cannot be determined using the homogeneous wall hypothesis. Finally, this study shows that finite element models could be an invaluable complement to medical investigation tools such as magnetic resonance or computerized tomography imaging in order to identify patients at high risk of aortic dissection. Although the actual mechanical properties of the patient s aortic wall are not usually known, generic simplified properties may be used in combination with the correct value of aortic root displacement, blood pressure and geometry of the patient s aorta. This would represent a considerable improvement in diagnostic capabilities over the current criteria based mainly on aortic diameter and blood pressure. References [1] Wheat Jr, M.W., 1983, Pathogenesis of aortic dissection. In R.M. Doroghazi and E.E. Slater (Eds) Aortic dissection (New York: McGraw-Hill), pp. 55 60.
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