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Research Papers

Computational Growth and Remodeling of Abdominal Aortic Aneurysms Constrained by the Spine

[+] Author and Article Information
Mehdi Farsad

Department of Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: farsad@msu.edu

Shahrokh Zeinali-Davarani

Department of Mechanical Engineering,
Boston University,
Boston, MA 02215
e-mail: zeinalis@bu.edu

Jongeun Choi

Associate Professor
Department of Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824;
Department of Electrical and
Computer Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: jchoi@egr.msu.edu

Seungik Baek

Associate Professor
Department of Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: sbaek@egr.msu.edu

1Corresponding author.

Manuscript received November 17, 2014; final manuscript received June 27, 2015; published online July 22, 2015. Assoc. Editor: Jonathan Vande Geest.

J Biomech Eng 137(9), 091008 (Jul 22, 2015) Paper No: BIO-14-1568; doi: 10.1115/1.4031019 History: Received November 17, 2014

Abdominal aortic aneurysms (AAAs) evolve over time, and the vertebral column, which acts as an external barrier, affects their biomechanical properties. Mechanical interaction between AAAs and the spine is believed to alter the geometry, wall stress distribution, and blood flow, although the degree of this interaction may depend on AAAs specific configurations. In this study, we use a growth and remodeling (G&R) model, which is able to trace alterations of the geometry, thus allowing us to computationally investigate the effect of the spine for progression of the AAA. Medical image-based geometry of an aorta is constructed along with the spine surface, which is incorporated into the computational model as a cloud of points. The G&R simulation is initiated by local elastin degradation with different spatial distributions. The AAA–spine interaction is accounted for using a penalty method when the AAA surface meets the spine surface. The simulation results show that, while the radial growth of the AAA wall is prevented on the posterior side due to the spine acting as a constraint, the AAA expands faster on the anterior side, leading to higher curvature and asymmetry in the AAA configuration compared to the simulation excluding the spine. Accordingly, the AAA wall stress increases on the lateral, posterolateral, and the shoulder regions of the anterior side due to the AAA–spine contact. In addition, more collagen is deposited on the regions with a maximum diameter. We show that an image-based computational G&R model not only enhances the prediction of the geometry, wall stress, and strength distributions of AAAs but also provides a framework to account for the interactions between an enlarging AAA and the spine for a better rupture potential assessment and management of AAA patients.

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Figures

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Fig. 1

Different domains from reference (ΓR) to current (Γt) and the corresponding natural configurations for a time τ∈[0,t]. x(t) denotes the current position vector on the aortic wall, while in reference configuration the position vector is shown by X

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Fig. 2

Significant interaction of a patient's AAA with the spine: (a) expansion of the patient's AAA during five longitudinal CT scans (taken during 43 months). The 3D images are built using segmentation software. (b) and (c) The CT images of the cross section indicating the AAA and the spine contact in the first (s1) and last (s5) scans, respectively. (d) The changes of AAA's circumferential radius of curvature in the contact section during the five longitudinal scans (from s1 to s5). The significant increase of circumferential radius of curvature, especially in the last scan, shows flattening of the AAA and its significant interaction with the spine. Circumferential parameter refers to a nondimensionalized parameter showing the position of a point on the AAA cross section's perimeter, such that the values of 1 and 9 represent θ= 0 and 360 deg, respectively.

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Fig. 3

(a) The anatomical model of the vertebral column is constructed from the patient's CT image. (b) The computational model of a healthy aorta and probable contact area of the spine as a cloud of points.

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Fig. 4

The schematic view of the AAA penetration into the spine to use in the penalty method. X1,X2, and X3 denote the global principal directions; x and xb represent the position of a node on the AAA penetrated into the spine and the closest point on the spine surface to x, respectively; n is the out-normal unit vector to the AAA surface; g=x-xb is the penetration vector and gn and gt are the components of the penetration vector along the normal and tangential directions to the AAA surface, respectively.

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Fig. 5

The von Mises stress distributions of the AAA wall after 3400 days for case 1 (a)–(c) without the AAA–spine interaction; (d)–(f) with the AAA–spine interaction in the lateral, posterior, and anterior sides, respectively. (g) The elastin distribution for the damage case 1. The arrows and the stress values next to them show the location and the amount of the maximum values, respectively.

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Fig. 6

The von Mises stress distributions of the AAA wall after 3400 days for case 2 (a)–(c) without the AAA–spine interaction; (d)–(f) with the AAA–spine interaction in the lateral, posterior, and anterior sides, respectively. (g) The elastin distribution for the damage case 2. The arrows and the stress values next to them show the location and the amount of the maximum values, respectively.

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Fig. 7

(a) and (b) The changes of simulated AAAs' final asymmetry along the AAA after 3400 days. (c) and (d) The changes of simulated AAAs maximum asymmetry during time. Asymmetry is calculated using the definition represented by Doyle et al. [36] based on the perpendicular distance of any point on the AAA's centerline from the straight line connecting end points of the centerline.

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Fig. 8

The final distribution of simulated AAAs wall stretch for case 1 along longitudinal (a)–(d) and circumferential (e)–(g) directions with and without AAA–spine interaction. λ1 and λ2 are longitudinal and circumferential stretches, respectively, from reference to current configuration. The values shown next to the arrows denote the maximum values.

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Fig. 9

The final distribution of simulated AAAs wall stretch for case 2 along longitudinal (a)–(d) and circumferential (e)–(g) directions with and without AAA–spine interaction. λ1 and λ2 are longitudinal and circumferential stretches, respectively, from reference to current configuration. The values shown next to the arrows denote the maximum values.

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Fig. 10

The collagen fiber content in the AAA wall after 3400 days for case 1. (a) and (b) The posterior and anterior view without the AAA–spine interaction. (c) and (d) The posterior and anterior view with the AAA–spine interaction.

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Fig. 11

The collagen fiber content in the AAA wall after 3400 days for case 2. (a) and (b) The posterior and anterior view without the AAA–spine interaction. (c) and (d) The posterior and anterior view with the AAA–spine interaction.

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Fig. 12

(a) The changes of the simulated AAAs' maximum diameter versus time. (b) Comparison between the computational and clinical rate of maximum diameter versus time. The longitudinal CT data from 14 patients are used in Ref. [47].

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Fig. 13

The ratio of the first principal stress to the tensile strength in the AAA wall after 3400 days for case 1 (a)–(f) and case 2 (g)–(l) for the conditions with and without AAA–spine interaction

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