On the Biaxial Mechanical Properties of the Layers of the Aortic Valve Leaflet

[+] Author and Article Information
John A. Stella

Engineered Tissue Mechanics Laboratory, Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA 15219; McGowan Institute for Regenerative Medicine, University of Pittsburgh, Pittsburgh, PA 15219

Michael S. Sacks1

Engineered Tissue Mechanics Laboratory, Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA 15219; McGowan Institute for Regenerative Medicine, University of Pittsburgh, Pittsburgh, PA 15219msacks@pitt.edu


Corresponding author.

J Biomech Eng 129(5), 757-766 (Feb 22, 2007) (10 pages) doi:10.1115/1.2768111 History: Received December 03, 2005; Revised February 22, 2007

All existing constitutive models for heart valve leaflet tissues either assume a uniform transmural stress distribution or utilize a membrane tension formulation. Both approaches ignore layer specific mechanical contributions and the implicit nonuniformity of the transmural stress distribution. To begin to address these limitations, we conducted novel studies to quantify the biaxial mechanical behavior of the two structurally distinct, load bearing aortic valve (AV) leaflet layers: the fibrosa and ventricularis. Strip biaxial tests, with extremely sensitive force sensing capabilities, were further utilized to determine the mechanical behavior of the separated ventricularis layer at very low stress levels. Results indicated that both layers exhibited very different nonlinear, highly anisotropic mechanical behaviors. While the leaflet tissue mechanical response was dominated by the fibrosa layer, the ventricularis contributed double the amount of the fibrosa to the total radial tension and experienced four times the stress level. The strip biaxial test results further indicated that the ventricularis exhibited substantial anisotropic mechanical properties at very low stress levels. This result suggested that for all strain levels, the ventricularis layer is dominated by circumferentially oriented collagen fibers, and the initial loading phase of this layer cannot be modeled as an isotropic material. Histological-based thickness measurements indicated that the fibrosa and ventricularis constitute 41% and 29% of the total layer thickness, respectively. Moreover, the extensive network of interlayer connections and identical strains under biaxial loading in the intact state suggests that these layers are tightly bonded. In addition to advancing our knowledge of the subtle but important mechanical properties of the AV leaflet, this study provided a comprehensive database required for the development of a true 3D stress constitutive model for the native AV leaflet.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Intact: AV leaflet cross sections parallel to the circumferential and radial cross sections (see inset), demonstrating highly specialized structures and a distinct trilayer arrangement. The fibrosa (F) is comprised primarily of circumferentially oriented collagen (yellow). The spongiosa (S) is a gelatinous layer containing GAGs and interstitial cells. The ventricularis (V) contains a dense elastin population whose fibers are oriented in the radial direction (long black fibers seen lying parallel in the radial cross-sectional image). Separated: The separated fibrosa is shown with its dense collagen fiber population and the remains of the spongiosa layer exposed by separation, indicating that the severed spongiosa remained relatively undamaged. The separated ventricularis sections also showed that the remaining spongiosa displayed no visible damage induced during separation.

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Figure 2

Microdissection of an aortic leaflet specimen. (a) The test specimen was cut from the lower belly region of the leaflet below the nodulus of Arantii. A set of four polypropylene markers was applied to the surface of both the fibrosa and ventricularis layers, which were located in the approximate center of the test specimen. All markers were placed on the specimen prior to the testing-separation-testing protocol. (b) The test specimen is pinned to a cork dissection board such that the ventricularis can be gently lifted to expose the many fibrous structures coupling the fibrosa and ventricularis. (c) A magnified view of a partially separated leaflet showing the numerous connections found throughout the spongiosa. Each fibrous connection is severed manually, enabling us to separate the fibrosa and ventricularis. Note that the blue markers shown were applied to the outer surface of the fibrosa and ventricularis prior to intact testing and the subsequent separation.

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Figure 3

(a) A diagram of the complete three day protocol developed to test the intact and separated layers. After testing or separation, the test specimens were allowed to recover for 24h at 4°C. (b) A diagram depicting the kinematic reconstruction of a bilayer material progressing from the stress-free configuration to the mechanically loaded state. β0 is defined as the separated, unconstrained configuration; β1 corresponds to the native, preloaded configuration; and βt represents the current intact configuration of the experimentally deformed tissue. The deformation gradient tensor associated with the transition from β0 to β1 is F0-1L. Similarly, the deformation gradient tensor associated with the transition from β1 to βt is defined as F1-tL.

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Figure 4

The time course effects on tissue strain due to leaflet separation, wherein internal forces are relieved allowing the layers to attain their stress free (free floating) configurations. When separated the undulated configuration of the fibrosa is removed causing it to extend 28.2% and 4.8% in circumferential and radial directions respectively. The ventricularis, which was in tension in the intact configuration, is seen to gradually contract 10.9% and 8.2% in circumferential and radial directions respectively. Note too that layers demonstrated statistically significant directional layer dimensional changes.

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Figure 5

Mean equibiaxial tissue responses of the intact, separated fibrosa, and ventricularis layers each with respect to their own preconditioned, free floating reference state β0(n=7). I=intact, F=separated fibrosa, and V=separated ventricularis tissue behaviors. Note: All planar biaxial data is referred to its own reference state (i.e., tension=0N∕m at λ=1), but the biaxial testing device necessitates the use of a 0.5g load to be applied to the specimen to ensure test repeatability. As a result, the data reported start from the deformation associated with this preload.

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Figure 6

The equibiaxial responses of the fibrosa and ventricularis computed with respect to both β0 and β1. When referenced to the intact conformation (β0), substantial differences were seen between the radial contributions of each layer. Thickness measurements (Table 1) enabled us to calculate the corresponding first Piola–Kirchoff stresses: P22v=95.74kPa while P22f=26.63kPa at equivalent levels of stretch. These results suggest that the ventricularis layer makes profound contributions to the intact leaflet response in the radial direction.

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Figure 7

(a) The accuracy of the simultaneous imaging system verified by testing of a latex rubber specimen. (b) Mean results of imaging the fibrosa and ventricularis sides simultaneously during equibiaxial tension (n=8); it was shown that the stretches experienced by either layer were not significantly different. This finding suggests that the strain distribution through the thickness of the specimen is homogeneous.

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Figure 8

(a) Experimental test configuration of the modified strip biaxial testing device. (b) From the strip biaxial testing of the separated ventricularis, it can be seen that there is significant mechanical anisotropy even at very low stress levels, with the circumferential direction exhibiting greater stiffness.

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Figure 9

Simulations for the intact native porcine AV leaflet exposed to strip biaxial and equibiaxial loading conditions using the structural constitutive model developed by Billiar and Sacks (16). (a) Model predictions for strip biaxial loading when stretched in the circumferential direction. (b) Similarly, the model predictions for a specimen stretched in the radial direction. (c) The simulated equibiaxial tension response of the intact AV tissue for comparison purposes. Model predictions indicate that strip biaxial loading conditions underestimate the coupling effects exhibited by the AV leaflet.



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