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TECHNICAL PAPERS

[+] Author and Article Information
Wei Sun1

Engineered Tissue Mechanics Laboratory, Department of Bioengineering,  University of Pittsburgh, Pittsburgh, PA 15219

Engineered Tissue Mechanics Laboratory, Department of Bioengineering,  University of Pittsburgh, Pittsburgh, PA 15219

Michael S. Sacks2

Engineered Tissue Mechanics Laboratory, Department of Bioengineering,  University of Pittsburgh, Pittsburgh, PA 15219msacks@pitt.edu

1

Present address: Edwards Lifesciences, Irvine, CA.

2

To whom correspondence should be addressed.

J Biomech Eng 127(6), 905-914 (Jul 14, 2005) (10 pages) doi:10.1115/1.2049337 History: Received May 05, 2005; Revised July 14, 2005

## Abstract

For more than $40years$, the replacement of diseased natural heart valves with prosthetic devices has dramatically extended the quality and length of the lives of millions of patients worldwide. However, bioprosthetic heart valves (BHV) continue to fail due to structural failure resulting from poor tissue durability and faulty design. Clearly, an in-depth understanding of the biomechanical behavior of BHV at both the tissue and functional prosthesis levels is essential to improving BHV design and to reduce rates of failure. In this study, we simulated quasi-static BHV leaflet deformation under 40, 80, and $120mmHg$ quasi-static transvalvular pressures. A Fung-elastic material model was used that incorporated material parameters and axes derived from actual leaflet biaxial tests and measured leaflet collagen fiber structure. Rigorous experimental validation of predicted leaflet strain field was used to validate the model results. An overall maximum discrepancy of 2.36% strain between the finite element (FE) results and experiment measurements was obtained, indicating good agreement between computed and measured major principal strains. Parametric studies utilizing the material parameter set from one leaflet for all three leaflets resulted in substantial variations in leaflet stress and strain distributions. This result suggests that utilization of actual leaflet material properties is essential for accurate BHV FE simulations. The present study also underscores the need for rigorous experimentation and accurate constitutive models in simulating BHV function and design.

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## Figures

Figure 1

A schematic of the overall study design, showing the experimental (left side) and computational side (right side), with comparisons performed on the measured and predicted strain fields (center). A novel aspect of the current study is the utilization of actual individual leaflet structural and material parameters, as well as validation using surface strains.

Figure 2

One camera view of valve 1 at 0mmHg transvalvular pressure, showing the marker array used for strain measurements, and the width (in pixels) of the valve

Figure 3

(a) A typical triangular element mesh constructed from the digitized markers positions (e.g., Fig. 2). The number ellipsoidal regions indicate areas used for strain tensor component comparisons (see Tables 3 and 4). (b) Strain calculations were based on the motion of a triangle (ABC) in the reference state and (A′B′C′) in the current state. Each triangle has its own local coordinate system, with the oz axis aligned with its surface normal direction during the motion.

Figure 4

The FE model showing the trileaflet geometric configurations, which are attached to the wireform stent

Figure 5

Representative SALS data for (a) leaflet 1, (b) leaflet 2, and (c) leaflet 3 for valve 1. The vectors represent the local preferred fiber orientations, and the color indicates the degree of collagen fiber orientation (OI), as described in Ref. 35. Most leaflets had a ±45° preferred orientation and relatively uniform degree of orientation throughout the leaflet.

Figure 6

The biaxial mechanical data for the 1MPa equibiaxial Lagrangian stress test protocol for all six leaflets from two valves studied. Unlike our previous study on the biaxial mechanical properties of GLBP (see Ref. 28), test specimens were tested aligned to the leaflet circumferential and radial axes since the collagen fiber orientation were generally ±45°.

Figure 7

(a) Normalized peak strains with keeping the transverse shear stiffness equal to 10kPa unchanged, while varying the coefficient of friction f to value of 0.0, 0.1, 0.3, and 0.5. (b) Normalized peak strains with keeping the coefficient of friction f=0.3 unchanged and varying transverse shear stiffness to values of 1, 10, 30, 50, and 100kPa.

Figure 8

Maximum in-plane principal strain magnitude plotted using the same color fringe scale for pressure levels of 40, 80, and 120mmHg. It is interesting to note that the free edge of one leaflet was slightly higher than that of the other two leaflets and this feature was captured by the FE model (photo of valve at 120mmHg).

Figure 9

Comparison of FE predicted and experimentally measured maximum principal strain magnitude for valve 1 leaflet 2 for each pressure level at each of the six leaflet regions (Fig. 3). Peak strains increased predictably with increasing transvalvular pressure. Overall, most regions demonstrated close agreement with the FE model results, with the best agreement in region 3 (typically 0.5% strain difference) and the worst in region 5 (∼2.5%).

Figure 10

FE results for the simulations with the same material properties of all three leaflets and DA of (a) 0.83, (b) 1.14, and (c) 2.12 on aortic side of leaflet surface and on the ventricular side for the same simulations with the DA of (e) 0.83, (f) 1.14, and (g) 2.12

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