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Research Papers

Novel Methodology for Characterizing Regional Variations in the Material Properties of Murine Aortas

[+] Author and Article Information
Matthew R. Bersi, Chiara Bellini, Paolo Di Achille, Jay D. Humphrey

Department of Biomedical Engineering,
Yale University,
New Haven, CT 06520

Katia Genovese

School of Engineering,
University of Basilicata,
Potenza 85100, Italy

Stéphane Avril

INSERM, U1059,
Saint-Etienne 42000, France;
Ecole Nationale Supérieure des
Mines de Saint-Etienne,
CIS-EMSE,
SAINBIOSE,
Saint-Etienne F-42023, France

1Corresponding author.

Manuscript received October 14, 2015; final manuscript received May 10, 2016; published online June 7, 2016. Assoc. Editor: Jonathan Vande Geest.

J Biomech Eng 138(7), 071005 (Jun 07, 2016) (15 pages) Paper No: BIO-15-1515; doi: 10.1115/1.4033674 History: Received October 14, 2015; Revised May 10, 2016

Many vascular disorders, including aortic aneurysms and dissections, are characterized by localized changes in wall composition and structure. Notwithstanding the importance of histopathologic changes that occur at the microstructural level, macroscopic manifestations ultimately dictate the mechanical functionality and structural integrity of the aortic wall. Understanding structure–function relationships locally is thus critical for gaining increased insight into conditions that render a vessel susceptible to disease or failure. Given the scarcity of human data, mouse models are increasingly useful in this regard. In this paper, we present a novel inverse characterization of regional, nonlinear, anisotropic properties of the murine aorta. Full-field biaxial data are collected using a panoramic-digital image correlation (p-DIC) system. An inverse method, based on the principle of virtual power (PVP), is used to estimate values of material parameters regionally for a microstructurally motivated constitutive relation. We validate our experimental–computational approach by comparing results to those from standard biaxial testing. The results for the nondiseased suprarenal abdominal aorta from apolipoprotein-E null mice reveal material heterogeneities, with significant differences between dorsal and ventral as well as between proximal and distal locations, which may arise in part due to differential perivascular support and localized branches. Overall results were validated for both a membrane and a thick-wall model that delineated medial and adventitial properties. Whereas full-field characterization can be useful in the study of normal arteries, we submit that it will be particularly useful for studying complex lesions such as aneurysms, which can now be pursued with confidence given the present validation.

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Figures

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Fig. 1

Overview of the p-DIC system. (a) Components include a syringe pump (1), pressure monitor (2), pressure transducer (3), and tubing (4) for pressure control. A 45 deg conical mirror (5) is located within a specimen bath (6) and mounted atop a small kinematic mount (7) that is attached to a three-axis translational stage (8). An annular light source (9) is used for illumination. The digital camera (10) is mounted vertically above the sample on a rotational stage (11) via a large kinematic mount (12) and custom translational stage (13). Images are acquired and sent to the computer for analysis through a camera link cable (14), and the entire system is placed on a precision optical bench (15). (b) Top-view of 45 deg conical mirror inside of the specimen bath showing the speckle pattern on the measurement surface (1) and the calibration target (2) used for 3D reconstruction. (c) Schematic of the cannulation of a pressure-distended specimen showing different gauge needles, locations of fixed and sliding ends, and methods to pressurize and axially stretch the specimen. (d) Loading protocol used for mechanical testing: for each axial stretch (bold solid line; right scale), the sample underwent two cycles of preconditioning followed by a stepwise increase in pressure from 10 to 140 mmHg in 10 mmHg increments (thin solid line; left scale for pressure).

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Fig. 2

Spatial distribution of the coefficients of determination. Goodness-of-fit for (a) specimen A and (b) specimen B. Both panels show outputs from a modified branch splitting algorithm to highlight regions of influence due to specimen branches (1–4). The results are shown in both a 3D (left) and 2D (right) representation over the entire surface of each sample. Boundaries of both low mean curvature (solid enclosed regions) and regions of branch influence (dashed ellipses) are overlaid in the 2D representation to show localization with regions of low Rn2*.

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Fig. 3

Histogram distributions of identified material parameters. The results from the identification procedure are shown for cne (first row), cnm (second row), cnc (third row), cna (fourth row), and βnc (fifth row) for both sample A (S-A, black bars) and sample B (S-B, white bars). All the identified parameters are spatially varying. The results are also shown by region: ventral-top (first column), dorsal-top (second column), ventral-bottom (third column), and dorsal-bottom (fourth column). The gray bars indicate overlapping results for the two samples.

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Fig. 4

Spatial distribution of strain energy. The strain energy density was computed (Eq. (3)) using the identified material properties over the surface of ((a) and (b)) sample A and ((c) and (d)) sample B. The results are shown for two loaded configurations: ((a) and (c)) P(t) = 80 mmHg at λz(t) = λ0 and ((b) and (d)) P(t) = 140 mmHg at λz(t) = λ0. (e) Histograms show the spatial distributions in each quadrant for both samples (cf. Fig. 3).

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Fig. 5

Spatial distribution of biaxial material stiffness. The biaxial material stiffness was computed using the identified material parameters over the surface of ((a) and (b)) sample A and ((c) and (d)) sample B. The results are shown for ((a) and (c)) circumferential (C1111) and ((b) and (d)) axial (C2222) stiffness evaluated at a loaded configuration of P(t) = 100 mmHg and λz(t) = λ0. Regions of influence due to branches (dashed lines) are overlaid to show localization near regions of high stiffness. (e) Histograms show spatial distributions in each quadrant for both samples (cf. Fig. 3).

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Fig. 6

Comparison of p-DIC and standard biaxial results. The reconstructed pressure–radius (left) and circumferential stress–stretch (right) behaviors for (a) sample A and (b) sample B were compared to standard biaxial testing results (black circles). Local responses are compared for locations with an R2* value above 0.95 (light-gray) and 0.99 (dark-gray). Comparison is shown only for data collected at λz(t) = λ0, for clarity.

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