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Research Papers

A Methodology for the Derivation of Unloaded Abdominal Aortic Aneurysm Geometry With Experimental Validation

[+] Author and Article Information
Santanu Chandra, Vimalatharmaiyah Gnanaruban

Department of Biomedical Engineering,
University of Texas at San Antonio,
San Antonio, TX 78249

Fabian Riveros

Aragon Institute of Engineering Research,
Universidad de Zaragoza,
Zaragoza 50018, Spain

Jose F. Rodriguez

Aragon Institute of Engineering Research,
Universidad de Zaragoza,
Zaragoza 50018, Spain;
Department of Chemistry, Materials, and
Chemical Engineering “Giulio Natta,”
Politecnico di Milano,
Milano 20133, Italy

Ender A. Finol

Department of Mechanical Engineering,
University of Texas at San Antonio,
EB 3.04.23,
One UTSA Circle,
San Antonio, TX 78249
e-mail: ender.finol@utsa.edu

1Corresponding author.

Manuscript received December 3, 2014; final manuscript received August 1, 2016; published online August 30, 2016. Assoc. Editor: Jonathan Vande Geest.

J Biomech Eng 138(10), 101005 (Aug 30, 2016) (11 pages) Paper No: BIO-14-1602; doi: 10.1115/1.4034425 History: Received December 03, 2014; Revised August 01, 2016

In this work, we present a novel method for the derivation of the unloaded geometry of an abdominal aortic aneurysm (AAA) from a pressurized geometry in turn obtained by 3D reconstruction of computed tomography (CT) images. The approach was experimentally validated with an aneurysm phantom loaded with gauge pressures of 80, 120, and 140 mm Hg. The unloaded phantom geometries estimated from these pressurized states were compared to the actual unloaded phantom geometry, resulting in mean nodal surface distances of up to 3.9% of the maximum aneurysm diameter. An in-silico verification was also performed using a patient-specific AAA mesh, resulting in maximum nodal surface distances of 8 μm after running the algorithm for eight iterations. The methodology was then applied to 12 patient-specific AAA for which their corresponding unloaded geometries were generated in 5–8 iterations. The wall mechanics resulting from finite element analysis of the pressurized (CT image-based) and unloaded geometries were compared to quantify the relative importance of using an unloaded geometry for AAA biomechanics. The pressurized AAA models underestimate peak wall stress (quantified by the first principal stress component) on average by 15% compared to the unloaded AAA models. The validation and application of the method, readily compatible with any finite element solver, underscores the importance of generating the unloaded AAA volume mesh prior to using wall stress as a biomechanical marker for rupture risk assessment.

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Figures

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Fig. 1

Flowchart of the proposed iterative algorithm to generate a predicted unloaded geometry of the solid domain (Sug), i.e., AAA wall and ILT, and the fluid domain (Fug), i.e., AAA lumen, from a CT image-based geometry (Sib)

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Fig. 2

The displacements of a selected node in the principal directions, Dx, Dy, and Dz, are drawn against the pressure, which is normalized to the diastolic pressure. The displacements are extrapolated by second-order quadratic fitting (solid lines) and were found to be nonlinear in varying degrees. Linear extrapolation (dashed lines) is also shown for comparison.

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Fig. 3

Model AAA12 used for the in-silico verification of the algorithm. Wall geometry and ILT distribution are shown.

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Fig. 4

AAA phantom for the experimental validation: (a) phantom representing a 4.7 cm aneurysm and (b) schematic of pressure loading of the phantom for validation of the unloaded geometry algorithm

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Fig. 5

Mesh sensitivity study of the unloaded AAA phantom subject to 120 mm Hg equivalent loading. The mean wall displacement converged within 2% of the 5 × 106 element mesh (5 M) with 150,000 volume elements. However, a mesh size in the range of 250,000–300,000 elements is preferred to execute the unloaded geometry algorithm, since the incremental improvement in mean wall displacement, which is measured as its percentage deviation by a mesh relative to the immediately finer mesh, is highest (1.7%) in this size range.

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Fig. 6

Convergence of the algorithm for the AAA12 model. Maximum and average nodal distances between the estimated and the actual unloaded geometries are depicted. The inset shows the unloaded geometry of the aneurysm at each iteration.

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Fig. 7

Qualitative visualization of the distance distribution between the predicted unloaded geometry (Sug) estimated from the three pressurized states (80 mm Hg (a), 120 mm Hg (b), and 140 mm Hg (c) gauge) and the actual unloaded geometry (UG). The maximum distance was obtained along the distal anterior wall for all three loading conditions (see black arrow), and it is evident that higher pressures lead to larger distances between the surfaces.

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Fig. 8

Comparison of the predicted unloaded geometry (Sug) ((a), (d), and (g)), the actual unloaded geometry (UG) ((b), (e), and (h)), and the μCT image-based geometry (Sib) ((c), (f), and (i)) of the AAA phantom based on the first principal stress distribution. The applied intraluminal pressure was equivalent to 80 mm Hg for (a)–(c); 120 mm Hg for (d)–(f); and 140 mm Hg gauge for (g)–(i).

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Fig. 9

(a) Logarithmic representation and normalized relative L2-norm errors of the nodal distances between the CT image-based geometry (Sib) and the predicted diastolic geometry obtained with the unloaded geometry (Sug) when pressurized to the diastolic pressure, with the number of iterations as a measure of performance of the algorithm for the AAA1, AAA2, and AAA3 meshes. (b) Sib of AAA1 with overlapping Sug demonstrating the differences in the geometries.

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Fig. 10

Predicted peak wall stress with the CT-based (solid blue bars) and the unloaded (striped red bars) geometries at their stress-free reference configurations

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Fig. 11

Views of the CT image-based (Sib) and unloaded (Sug) FE models for aneurysms AAA1 and AAA2 showing the distribution of first principal stress at the normal physiological systolic pressures. For the Sug cases, the unloaded geometries have been estimated with the patient-specific diastolic pressures and the normal physiological systolic pressure.

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