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Research Papers

Prefailure and Failure Mechanics of the Porcine Ascending Thoracic Aorta: Experiments and a Multiscale Model

[+] Author and Article Information
Sachin B. Shah

Department of Biomedical Engineering,
University of Minnesota,
Minneapolis, MN 55455
e-mail: Shah0394@umn.edu

Colleen Witzenburg

Department of Mechanical Engineering,
University of Minnesota,
Minneapolis, MN 55455
e-mail: Obri0319@umn.edu

Mohammad F. Hadi

Department of Biomedical Engineering,
University of Minnesota,
Minneapolis, MN 55455
e-mail: Hadix004@umn.edu

Hallie P. Wagner

Department of Biomedical Engineering,
University of Minnesota,
Minneapolis, MN 55455
e-mail: wagnerh@umn.edu

Janna M. Goodrich

Department of Biomedical Engineering,
University of Minnesota,
Minneapolis, MN 55455
e-mail: Goodr101@umn.edu

Patrick W. Alford

Department of Biomedical Engineering,
University of Minnesota,
Minneapolis, MN 55455
e-mail: pwalford@umn.edu

Victor H. Barocas

Department of Biomedical Engineering,
University of Minnesota,
Minneapolis, MN 55455
e-mail: Baroc001@umn.edu

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the Journal of Biomechanical Engineering. Manuscript received September 15, 2013; final manuscript received January 1, 2014; accepted manuscript posted January 8, 2014; published online February 5, 2014. Editor: Beth Winkelstein.

J Biomech Eng 136(2), 021028 (Feb 05, 2014) (7 pages) Paper No: BIO-13-1428; doi: 10.1115/1.4026443 History: Received September 15, 2013; Revised January 01, 2014; Accepted January 08, 2014

Ascending thoracic aortic aneurysms (ATAA) have a high propensity for dissection, which occurs when the hemodynamic load exceeds the mechanical strength of the aortic media. Despite our recognition of this essential fact, the complex architecture of the media has made a predictive model of medial failure—even in the relatively simple case of the healthy vessel—difficult to achieve. As a first step towards a general model of ATAA failure, we characterized the mechanical behavior of healthy ascending thoracic aorta (ATA) media using uniaxial stretch-to-failure in both circumferential (n = 11) and axial (n = 11) orientations and equibiaxial extensions (n = 9). Both experiments demonstrated anisotropy, with higher tensile strength in the circumferential direction (2510 ± 439.3 kPa) compared to the axial direction (750 ± 102.6 kPa) for the uniaxial tests, and a ratio of 1.44 between the peak circumferential and axial loads in equibiaxial extension. Uniaxial tests for both orientations showed macroscopic tissue failure at a stretch of 1.9. A multiscale computational model, consisting of a realistically aligned interconnected fiber network in parallel with a neo-Hookean solid, was used to describe the data; failure was modeled at the fiber level, with an individual fiber failing when stretched beyond a critical threshold. The best-fit model results were within the 95% confidence intervals for uniaxial and biaxial experiments, including both prefailure and failure, and were consistent with properties of the components of the ATA media.

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Figures

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Fig. 1

(a) Porcine aortic arch. Black dotted lines demarcate ascending aortic ring. White star symbolizes a marker used to keep track of tissue sample orientation. (b) Ascending aortic ring with intima, adventitia, adipose, and loose connective tissue removed. Axial and circumferential directions shown with white arrows. (c) Undeformed, typical uniaxial sample in CIRC orientation with speckling prior to loading. Arrow indicates orientation and direction of pull. (d) Undeformed, typical biaxial sample with speckling prior to loading. Arrows indicate orientation and direction of pull.

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Fig. 2

Synopsis of multiscale model. Uniaxial or biaxial geometries are developed into millimeter sized finite element meshes. Each element consists of eight Gauss points that dictate its stress-strain response. Each Gauss point consists of representative volume elements (RVE) that consist of a nanoscale fiber network in parallel with a nearly incompressible neo-Hookean matrix. Deformation of the macroscale structure causes the fiber network to stretch and reorient to reach force equilibrium. Fibers that stretch beyond a critical value are considered failed and their modulus of elasticity is reset to a near-zero value.

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Fig. 3

(a) Typical measured uniaxial grip stress versus grip strain response in the CIRC orientation. (b) Typical measured equibiaxial grip stresses versus grip strain.

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Fig. 4

(a) Peak tensile strength of ascending aortic samples for both uniaxial experiment (solid, n = 11) and model (diagonal lines, n = 10). (b) Peak stretch of ascending aortic samples for both uniaxial experiment (solid, n = 11) and model (diagonal lines, n = 10).

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Fig. 5

First Piola–Kirchhoff stress as a function of stretch ratio for the experiment (dots with 95% confidence interval) and model (solid blue line). Colored dots represent the mean experimental stress and error bars depict the 95% confidence interval. The red square indicates the mean peak tensile strength and stretch, and the surrounding dotted black box indicates the 95% confidence interval for the peak experimental stress and stretch with (a) being experimental and model results in the AXI orientation and (b) being experimental and model results in the CIRC orientation.

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Fig. 6

(a) Model circumferential Green strain Eθθ along the axis of pull plotted over the deformed model mesh at given sample stretches (λ). A representative neck region RVE network is shown and its corresponding fiber orientation tensor. (b) Model axial Green strain Ezz along the axis of pull plotted over the deformed model mesh at a given sample stretch (λ). A representative neck region RVE network is shown and its corresponding fiber orientation tensor.

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Fig. 7

(a) Mean first Piola–Kirchhoff stress as a function of grip strain for the biaxial experiment (dashed purple line for AXI and dashed green line for CIRC, n = 9) with 95% confidence interval (purple and green shaded areas, respectively). The striped shaded area represents overlap of the 95% confidence interval of the two orientations (p < 0.05). (b) Mean biaxial model first Piola–Kirchhoff stress as a function of grip strain (solid purple line for AXI and solid green line for CIRC, n = 10) compared to mean experimental results (dashed purple and green lines, respectively, n = 9).

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Fig. 8

(a) Model equibiaxial Green strain Eθθ plotted over the deformed model mesh at various sample stretches (λ). (b) Model equibiaxial Green strain Ezz plotted over the deformed model mesh at various sample stretches (λ). (c) A sample center region RVE network is shown and its corresponding fiber orientation tensors for the stretches depicted in (a) and (b).

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