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Technical Briefs

Comparison of Approaches to Quantify Arterial Damping Capacity From Pressurization Tests on Mouse Conduit Arteries

[+] Author and Article Information
Lian Tian

e-mail: ltian22@wisc.edu

Zhijie Wang

e-mail: zwang48@wisc.edu
Department of Biomedical Engineering,
University of Wisconsin-Madison,
Madison, WI 53706-1609

Roderic S. Lakes

Department of Biomedical Engineering,
Department of Engineering Physics, and Department of Materials Science and Engineering,
University of Wisconsin-Madison,
Madison, WI 53706-1609
e-mail: lakes@engr.wisc.edu

Naomi C. Chesler

Department of Biomedical Engineering,
University of Wisconsin-Madison,
Madison, WI 53706-1609
e-mail: chesler@engr.wisc.edu

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received November 6, 2012; final manuscript received March 21, 2013; accepted manuscript posted April 4, 2013; published online April 24, 2013. Assoc. Editor: Dalin Tang.

J Biomech Eng 135(5), 054504 (Apr 24, 2013) (6 pages) Paper No: BIO-12-1540; doi: 10.1115/1.4024135 History: Received November 06, 2012; Revised March 21, 2013; Accepted April 04, 2013

Large conduit arteries are not purely elastic, but viscoelastic, which affects not only the mechanical behavior but also the ventricular afterload. Different hysteresis loops such as pressure-diameter, pressure-luminal cross-sectional area (LCSA), and stress–strain have been used to estimate damping capacity, which is associated with the ratio of the dissipated energy to the stored energy. Typically, linearized methods are used to calculate the damping capacity of arteries despite the fact that arteries are nonlinearly viscoelastic. The differences in the calculated damping capacity between these hysteresis loops and the most common linear and correct nonlinear methods have not been fully examined. The purpose of this study was thus to examine these differences and to determine a preferred approach for arterial damping capacity estimation. Pressurization tests were performed on mouse extralobar pulmonary and carotid arteries in their physiological pressure ranges with pressure (P) and outer diameter (OD) measured. The P-inner diameter (ID), P-stretch, P-Almansi strain, P-Green strain, P-LCSA, and stress–strain loops (including the Cauchy and Piola-Kirchhoff stresses and Almansi and Green strains) were calculated using the P-OD data and arterial geometry. Then, the damping capacity was calculated from these loops with both linear and nonlinear methods. Our results demonstrate that the linear approach provides a reasonable approximation of damping capacity for all of the loops except the Cauchy stress-Almansi strain, for which the estimate of damping capacity was significantly smaller (22 ± 8% with the nonlinear method and 31 ± 10% with the linear method). Between healthy and diseased extralobar pulmonary arteries, both methods detected significant differences. However, the estimate of damping capacity provided by the linear method was significantly smaller (27 ± 11%) than that of the nonlinear method. We conclude that all loops except the Cauchy stress-Almansi strain loop can be used to estimate artery wall damping capacity in the physiological pressure range and the nonlinear method is recommended over the linear method.

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Figures

Grahic Jump Location
Fig. 1

Illustration of the estimation of the damping capacity (a) with the nonlinear method on a clockwise pressure-luminal cross-sectional area (P-LCSA) loop obtained from a carotid artery at 10 Hz, and (b) with the linear method on an elliptical P-LCSA loop. Points A and B are the points corresponding to the maximum and minimum LCSA in the hysteresis loop, respectively. Point C is the point with the maximum LCSA value and the pressure value at point A. Here, WD is the loop area and WS is the area under the loading (upper) curve AB→ and above the straight line AC. Loading curves are indicated by the arrow. Note that the hysteresis loop in (a) shows a weak nonlinearity in that the loop deviates slightly from an elliptical shape.

Grahic Jump Location
Fig. 2

Linear correlation between the damping capacity (d via the nonlinear method) calculated from the (a) pressure (P)-OD, (b) P-ID, (c) P-stretch (λ), (d) P-Green strain (E), (e) P-Almansi strain (e), (f) Cauchy stress-Almansi strain (σ-e), and (g) the second Piola-Kirchhoff stress-Green strain (S-E) loops and that calculated from the P-LCSA loop at the frequencies of 1, 5, and 10 Hz. (LCCA denotes the left common carotid artery and LPA denotes the left pulmonary artery.)

Grahic Jump Location
Fig. 3

Linear correlation between the damping capacity calculated from the P-LCSA loops at all three frequencies (1, 5, and 10 Hz) with the linear and nonlinear methods. (LCCA denotes the left common carotid artery and LPA denotes the left pulmonary artery.)

Grahic Jump Location
Fig. 4

Representative experimental pressure-LCSA loops that have different damping capacities calculated from the linear method versus the nonlinear method with differences of (a) −0.4% from a left pulmonary artery (LPA) at 10 Hz, (b) −9.7% from a LPA at 10 Hz, (c) −24% from a LPA at 5 Hz, and (d) −43% from a LPA at 1 Hz. Loading curves are indicated by the arrow. Note that the loops in (c) and (d) show a strong nonlinearity.

Grahic Jump Location
Fig. 5

Damping capacity calculated from the nonlinear and linear methods with the P-LCSA at different frequencies (1, 5, and 10 Hz). In the legend, N denotes the nonlinear method; L denotes the linear method; 1 denotes group 1; 2 denotes group 2. The symbol ‘*’ denotes P < 0.05 for group 1 versus group 2 for the same method (nonlinear or linear); the ‘#’ symbol denotes P < 0.05 for the linear versus nonlinear method for the same group.

Grahic Jump Location
Fig. 6

Representative relations between the pressure and two stresses (the Cauchy and the second Piola-Kirchhoff stresses) in one observed dynamic cycle for a carotid artery at 10 Hz. The loading curve is indicated by the arrow. Note that the Cauchy stress-pressure loop is anticlockwise.

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