Technical Briefs

Porohyperelastic Finite Element Modeling of Abdominal Aortic Aneurysms

[+] Author and Article Information
Avinash Ayyalasomayajula

Department of Aerospace and Mechanical Engineering, University of Arizona, P.O. Box 210119, Tucson, AZ 85721-011

Jonathan P. Vande Geest1

Department of Aerospace and Mechanical Engineering, Department of Biomedical Engineering, Biomedical Engineering Interdisciplinary Program, and BIO5 Institute, University of Arizona, Tucson, AZ 85721-011jpv1@email.arizona.edu

Bruce R. Simon

Department of Aerospace and Mechanical Engineering and Biomedical Engineering Interdisciplinary Program, University of Arizona, Tucson, AZ 85721-011


Corresponding author. Present address: Aerospace and Mechanical Engineering, University of Arizona, P.O Box 210119, Tucson, AZ 85721-011.

J Biomech Eng 132(10), 104502 (Sep 27, 2010) (8 pages) doi:10.1115/1.4002370 History: Received July 23, 2009; Revised June 21, 2010; Posted August 16, 2010; Published September 27, 2010; Online September 27, 2010

Abdominal aortic aneurysm (AAA) is the gradual weakening and dilation of the infrarenal aorta. This disease is progressive, asymptomatic, and can eventually lead to rupture—a catastrophic event leading to massive internal bleeding and possibly death. The mechanical environment present in AAA is currently thought to be important in disease initiation, progression, and diagnosis. In this study, we utilize porohyperelastic (PHE) finite element models (FEMs) to investigate how such modeling can be used to better understand the local biomechanical environment in AAA. A 3D hypothetical AAA was constructed with a preferential anterior bulge assuming both the intraluminal thrombus (ILT) and the AAA wall act as porous materials. A parametric study was performed to investigate how physiologically meaningful variations in AAA wall and ILT hydraulic permeabilities affect luminal interstitial fluid velocities and wall stresses within an AAA. A corresponding hyperelastic (HE) simulation was also run in order to be able to compare stress values between PHE and HE simulations. The effect of AAA size on local interstitial fluid velocity was also investigated by simulating maximum diameters (5.5 cm, 4.5 cm, and 3.5 cm) at the baseline values of ILT and AAA wall permeability. Finally, a cyclic PHE simulation was utilized to study the variation in local fluid velocities as a result of a physiologic pulsatile blood pressure. While the ILT hydraulic permeability was found to have minimal affect on interstitial velocities, our simulations demonstrated a 28% increase and a 20% decrease in luminal interstitial fluid velocity as a result of a 1 standard deviation increase and decrease in AAA wall hydraulic permeability, respectively. Peak interstitial velocities in all simulations occurred on the luminal surface adjacent to the region of maximum diameter. These values increased with increasing AAA size. PHE simulations resulted in 19.4%, 40.1%, and 81.0% increases in peak maximum principal wall stresses in comparison to HE simulations for maximum diameters of 35 mm, 45 mm, and 55 mm, respectively. The pulsatile AAA PHE FEM demonstrated a complex interstitial fluid velocity field the direction of which alternated in to and out of the luminal layer of the ILT. The biomechanical environment within both the aneurysmal wall and the ILT is involved in AAA pathogenesis and rupture. Assuming these tissues to be porohyperelastic materials may provide additional insight into the complex solid and fluid forces acting on the cells responsible for aneurysmal remodeling and weakening.

Copyright © 2010 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Normal component of total stress and pore pressures applied on the luminal surface for the cyclic loading simulations

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Figure 2

Influence of ILT and wall permeability on the values of vfr normalized to the value of vfr in the baseline simulation

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Figure 3

Pore pressure gradients increased across the ILT with increase in the maximum AAA diameter (measured at z=H/2 on the anterior side). All models had an abrupt pressure gradient across the wall.

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Figure 4

Pore pressure gradients existed primarily in the radial direction with the largest occurring across the wall

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Figure 5

Top: Variation of vfr along the axial length on posterior and anterior AAA lumen. Bottom: Effect of maximum AAA diameter on vfr along the length of the AAA measured on the anterior luminal surface.

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Figure 6

Contour plot of vfr within a hypothetical AAA in the consolidated state under static loading conditions. Note that the peak vfr occurs at the luminal surface at z=H/2.

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Figure 7

Flow reversal occurring at the luminal surface of the AAA as a result of the applied cardiac cycle. The values were recorded at the inner luminal surface on the anterior side at z=H/2. For easy visualization, only the luminal layer of elements is shown.

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Figure 8

Variation of stresses with maximum AAA diameter in the consolidated state. Effective stresses were plotted for the PHE maximum principal stresses. These stresses were all recorded on the anterior wall at z=H/2.

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Figure 9

Top: Pathline used in the following plots. Bottom: (Left) Variations of stresses and pore pressure shows significant differences between PHE and HE maximum principal stresses. (Right) The strains predicted by the HE models were lower than those from PHE.



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