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Technical Brief

Quantification of Material Constants for a Phenomenological Constitutive Model of Porcine Tricuspid Valve Leaflets for Simulation Applications

[+] Author and Article Information
Keyvan Amini Khoiy

Department of Biomedical Engineering,
The University of Akron Olson Research Center,
Room 322/3 260 South Forge Street,
Akron, OH 44325
e-mail: ka67@zips.uakron.edu

Anup D. Pant

Department of Biomedical Engineering,
The University of Akron Olson Research Center,
Room 322/3 260 South Forge Street,
Akron, OH 44325
e-mail: adp63@zips.uakron.edu

Rouzbeh Amini

Mem. ASME
Department of Biomedical Engineering,
The University of Akron Olson Research Center,
Room 301F 260 South Forge Street,
Akron, OH 44325
e-mail: ramini@uakron.edu

1Corresponding author.

Manuscript received September 26, 2017; final manuscript received April 26, 2018; published online May 24, 2018. Assoc. Editor: Keefe B. Manning.

J Biomech Eng 140(9), 094503 (May 24, 2018) (11 pages) Paper No: BIO-17-1432; doi: 10.1115/1.4040126 History: Received September 26, 2017; Revised April 26, 2018

The tricuspid valve is a one-way valve on the pulmonary side of the heart, which prevents backflow of blood during ventricular contractions. Development of computational models of the tricuspid valve is important both in understanding the normal valvular function and in the development/improvement of surgical procedures and medical devices. A key step in the development of such models is quantification of the mechanical properties of the tricuspid valve leaflets. In this study, after examining previously measured five-loading-protocol biaxial stress–strain response of porcine tricuspid valves, a phenomenological constitutive framework was chosen to represent this response. The material constants were quantified for all three leaflets, which were shown to be highly anisotropic with average anisotropy indices of less than 0.5 (an anisotropy index value of 1 indicates a perfectly isotropic response, whereas a smaller value of the anisotropy index indicates an anisotropic response). To obtain mean values of material constants, stress–strain responses of the leaflet samples were averaged and then fitted to the constitutive model (average R2 over 0.9). Since the sample thicknesses were not hugely different, averaging the data using the same tension levels and stress levels produced similar average material constants for each leaflet.

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Figures

Grahic Jump Location
Fig. 1

Comparison between the accuracy of linear interpolation and exponential fit to estimate the original data for averaging

Grahic Jump Location
Fig. 2

The constant stress contours produced using the response functions of Eq. (2) plotted over the strain field for typical leaflets: (a,b) anterior, (c,d) posterior, and (e,f) septal leaflets

Grahic Jump Location
Fig. 3

The result of the five-protocol fit along with the experimentally measured circumferential (Circ) and radial data for typical leaflets: (a) anterior, (b) posterior, and (c) septal. The numbers represent the protocol numbers listed in Table 1.

Grahic Jump Location
Fig. 4

The average stress–strain responses developed based on identical tension states from loading protocols (a) number 1 (equibiaxial), (b) number 2, (c) number 3, (d) number 4, and (e) number 5 of Table 1 for the anterior leaflet. The vertical axis is the second Piola–Kirchhoff stress, and the horizontal axis is the Green strain. These data were used to calculate the average material constants presented in Table 3.

Grahic Jump Location
Fig. 5

The average stress–strain responses developed based on identical first Piola–Kirchhoff stress states from loading protocols (a) number 1 (equibiaxial), (b) number 2, (c) number 3, (d) number 4, and (e) number 5 of Table 1 for the anterior leaflet. The vertical axis is the second Piola–Kirchhoff stress, and the horizontal axis is the Green strain. These data were used to calculate the average material constants presented in Table 4.

Grahic Jump Location
Fig. 6

The average stress–strain responses developed based on identical Cauchy stress states from loading protocols (a) number 1 (equibiaxial), (b) number 2, (c) number 3, (d) number 4, and (e) number 5 of Table 1 for the anterior leaflet. The vertical axis is the second Piola–Kirchhoff stress, and the horizontal axis is the Green strain. These data were used to calculate the average material constants presented in Table 5.

Grahic Jump Location
Fig. 7

The five stress-controlled protocols used to reconstruct the tissue responses based on the developed average models. The horizontal axis is the circumferential second Piola–Kirchhoff stress, and the vertical axis is the radial second Piola–Kirchhoff stress.

Grahic Jump Location
Fig. 8

Tissue response of the anterior leaflet to five stress-controlled loading protocols (Fig. 7) reconstructed using the material constants of the arithmetic average (A–B) from Table 2, the tension-based average model (T–B) from Table 3, the first Piola–Kirchhoff-stress-based average model (P–B) from Table 4, and the Cauchy-stress-based average model (C–B) from Table 5. The vertical axis is the second Piola–Kirchhoff stress, and the horizontal axis is the Green strain. The subscripts cc and rr denote the circumferential and radial directions, respectively.

Grahic Jump Location
Fig. 9

Tissue response of the posterior leaflet to five stress-controlled loading protocols (Fig. 7) reconstructed using the material constants of the arithmetic average (A–B) from Table 2, the tension-based average model (T–B) from Table 3, the first Piola–Kirchhoff-stress-based average model (PB) from Table 4, and the Cauchy-stress-based average model (C–B) from Table 5. The vertical axis is the second Piola–Kirchhoff stress, and the horizontal axis is the Green strain. The subscripts cc and rr denote the circumferential and radial directions, respectively.

Grahic Jump Location
Fig. 10

Tissue response of the septal leaflet to five stress-controlled loading protocols (Fig. 7) reconstructed using the material constants of the arithmetic average (A–B) from Table 2, the tension-based average model (T–B) from Table 3, the first Piola–Kirchhoff-stress-based average model (P–B) from Table 4, and the Cauchy-stress-based average model (C–B) from Table 5. The vertical axis is the second Piola–Kirchhoff stress, and the horizontal axis is the Green strain. The subscripts cc and rr denote the circumferential and radial directions, respectively.

Grahic Jump Location
Fig. 11

Small-angle light-scattering scan of the midsection of a typical tricuspid valve anterior leaflet. Each arrow shows the main direction of the extracellular matrix fibers over a 250μm×250μm region. The color map shows the degree of alignment. The warmest color, corresponding to 1, indicates a network in which all fibers are in the same direction; the coolest color, corresponding to 0, indicates a network in which the probability of a fiber existing in any directions is the same.

Grahic Jump Location
Fig. 12

Constant strain energy contours plotted over the Green strain field for the (a) anterior, (b) posterior, and (c) septal leaflets of a typical tricuspid valve

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Fig. 13

The strain energy contours plotted over the strain field for posterior leaflet of the specimen listed as sample 3 in Table 2. The contours are nonconvex, violating the integrity of the developed constitutive model for this specific leaflet.

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