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Research Papers

# Viscoelastic Properties of the Aortic Valve Interstitial Cell

[+] Author and Article Information
W. David Merryman1

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

Paul D. Bieniek

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

Farshid Guilak

Orthopaedic Research Laboratories, Department of Surgery, and Department of Biomedical Engineering, Duke University Medical Center, Durham, NC 27710

Michael S. Sacks2

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

1

Current address: Department of Biomedical Engineering, University of Alabama Birmingham, Birmingham, AL 35294.

2

Corresponding author.

J Biomech Eng 131(4), 041005 (Feb 02, 2009) (5 pages) doi:10.1115/1.3049821 History: Received April 19, 2007; Revised October 01, 2008; Published February 02, 2009

## Abstract

There has been growing interest in the mechanobiological function of the aortic valve interstitial cell (AVIC) due to its role in valve tissue homeostasis and remodeling. In a recent study we determined the relation between diastolic loading of the aortic valve (AV) leaflet and the resulting AVIC deformation, which was found to be substantial. However, due to the rapid loading time of the AV leaflets during closure $(∼0.05 s)$, time-dependent effects may play a role in AVIC deformation during physiological function. In the present study, we explored AVIC viscoelastic behavior using the micropipette aspiration technique. We then modeled the resulting time-length data over the 100 s test period using a standard linear solid model, which included Boltzmann superposition. To quantify the degree of creep and stress relaxation during physiological time scales, simulations of micropipette aspiration were preformed with a valve loading time of 0.05 s and a full valve closure time of 0.3 s. The 0.05 s loading simulations suggest that, during valve closure, AVICs act elastically. During diastole, simulations revealed creep (4.65%) and stress relaxation (4.39%) over the 0.3 s physiological time scale. Simulations also indicated that if Boltzmann superposition was not used in parameter estimation, as in much of the micropipette literature, creep and stress relaxation predicted values were nearly doubled (7.92% and 7.35%, respectively). We conclude that while AVIC viscoelastic effects are negligible during valve closure, they likely contribute to the deformation time-history of AVIC deformation during diastole.

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Copyright © 2009 by American Society of Mechanical Engineers
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## Figures

Figure 1

Representative response of an AVIC under micropipette aspiration (circles) with both the BSLS and SLS model fits. Applied pressure history is plotted on the right y-axis. Inset table shows determined parameters from both models for the representative AVIC (n=1) that was used.

Figure 2

(a) Viscous effects due to varying simulation loading times for a single AVIC at 0.05 s, 0.5 s, 2.5 s, and 5.0 s. (b) Percentage increase in simulated aspiration length at the end of the applied pressure ramp versus 0.05 s. As loading time increases, viscous effects are more pronounced. While below 0.5 s viscous effects appear to be negligible, it is interesting to note that over 2.5 s, the time needed to apply pressure during the micropipette aspiration experiment, viscous effects are 40% greater than when applying the load in 0.05 s.

Figure 3

Representative creep simulation response for an AVIC loaded to 500 Pa in 0.05 s and held for 0.3 s using both the BSLS and SLS models

Figure 4

Representative stress relaxation simulation response for an AVIC aspirated to 2.3 μm in 0.05 s and held for an additional 0.3 s using both the BSLS and SLS models. Note that 4.96 μm was the actual aspiration length occurring for that AVIC during the micropipette aspiration experiments.

## Errata

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