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Research Papers

Effect of Pre-Stress on the Dynamic Tensile Behavior of the TMJ Disc

[+] Author and Article Information
J. Lomakin

Department of Chemical and
Petroleum Engineering,
University of Kansas,
Lawrence, KS 66045

P. A. Sprouse

Bioengineering Program,
University of Kansas,
1530 West 15th Street,
Lawrence, KS 66045

S. H. Gehrke

e-mail: shgehrke@ku.edu
Department of Chemical and
Petroleum Engineering,
University of Kansas,
Lawrence, KS 66045
Bioengineering Program,
University of Kansas,
1530 West 15th Street,
Lawrence, KS 66045

1Present address: Arsenal Medical, 480 Arsenal Street, Watertown, MA 02472.

2Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received February 9, 2013; final manuscript received September 16, 2013; accepted manuscript posted October 19, 2013; published online November 26, 2013. Assoc. Editor: Tammy Haut Donahue.

J Biomech Eng 136(1), 011001 (Nov 26, 2013) (8 pages) Paper No: BIO-13-1069; doi: 10.1115/1.4025775 History: Received February 09, 2013; Revised September 16, 2013; Accepted October 19, 2013

Previous dynamic analyses of the temporomandibular joint (TMJ) disc have not included a true preload, i.e., a step stress or strain beyond the initial tare load. However, due to the highly nonlinear stress-strain response of the TMJ disc, we hypothesized that the dynamic mechanical properties would greatly depend on the preload, which could then, in part, account for the large variation in the tensile stiffnesses reported for the TMJ disc in the literature. This study is the first to report the dynamic mechanical properties as a function of prestress. As hypothesized, the storage modulus (E′) of the disc varied by a factor of 25 in the mediolateral direction and a factor of 200 in the anteroposterior direction, depending on the prestress. Multiple constant strain rate sweeps were extracted and superimposed via strain-rate frequency superposition (SRFS), which demonstrated that the strain rate amplitude and strain rate were both important factors in determining the TMJ disc material properties, which is an effect not typically seen with synthetic materials. The presented analysis demonstrated, for the first time, the applicability of viscoelastic models, previously applied to synthetic polymer materials, to a complex hierarchical biomaterial such as the TMJ disc, providing a uniquely comprehensive way to capture the viscoelastic response of biological materials. Finally, we emphasize that the use of a preload, preferably which falls within the linear region of the stress-strain curve, is critical to provide reproducible results for tensile analysis of musculoskeletal tissues. Therefore, we recommend that future dynamic mechanical analyses of the TMJ disc be performed at a controlled prestress corresponding to a strain range of 5–10%.

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Copyright © 2014 by ASME
Topics: Stress , Disks , Storage
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Figures

Grahic Jump Location
Fig. 1

The nonlinear stress-strain response causes variation in dynamic moduli, depending on the magnitude of the prestress applied before cyclic loading. Dynamic tests using a small prestress measures the properties within the “toe region” of the stress-strain curve, whereas tests using sufficiently larger prestresses measure properties in the linear region. We hypothesized that incorporating larger prestresses up to the linear region would result in larger storage moduli.

Grahic Jump Location
Fig. 2

Representative frequency sweeps of the TMJ disc in the mediolateral direction at 0.1% dynamic strain. (a) The storage modulus increased 2 orders of magnitude with greater prestress and was also a weak function of oscillation frequency. (b) The tan δ decreased as a function of sample prestress. The approximate range of prestrains corresponding to the prestresses was 0–15%.

Grahic Jump Location
Fig. 3

Representative strain sweeps of the TMJ disc in the mediolateral direction at 1 rad/s. (a) The storage modulus was constant, indicating linear viscoelastic behavior, up to 0.1% strain. At greater strains, the storage modulus dipped slightly and then rose. The rise was a consequence of the nonlinear stress-strain response. (b) The tan δ as a function of strain. The approximate range of prestrains corresponding to the prestresses was 0–15%.

Grahic Jump Location
Fig. 4

(a) The storage modulus (E′) at 10 rad/s and 0.1% strain with 95% confidence intervals of the TMJ disc in the mediolateral and anteroposterior directions as a function of the prestress. The modulus appeared directly proportional to the sample prestress. (b) Frequency exponents (n) with 95% confidence intervals. Here, n was calculated from a power law fit of frequency sweeps of the TMJ disc in the mediolateral direction and n appeared to reach a plateau at higher prestresses. The approximate range of prestrains corresponding to the prestresses was 0–15%.

Grahic Jump Location
Fig. 5

Representative frequency sweeps of the TMJ disc in the anteroposterior direction at 0.1% strain. (a) The storage modulus increased 2 orders of magnitude with greater prestress and was also a weak function of the oscillation frequency. (b) The tan δ decreased as a function of the sample prestress. The approximate range of prestrains corresponding to the prestresses was 0–10%.

Grahic Jump Location
Fig. 6

Representative strain sweeps of the TMJ disc in the anteroposterior direction at 10 rad/s. (a) The storage modulus was constant, indicating stable linear viscoelastic behavior, up to 0.1% strain. At greater strains, the storage modulus dipped slightly and then rose. The rise was a consequence of the nonlinear stress-strain response. (b) The tan δ as a function of strain. The approximate range of prestrains corresponding to the prestresses was 0–10%.

Grahic Jump Location
Fig. 7

A representative series of constant rate sweeps at different strain rates for the TMJ disc mediolateral sections at 80 g preload. During each sweep, the applied strain amplitude was inversely proportional to the oscillation frequency.

Grahic Jump Location
Fig. 8

Master curves for the TMJ disc sections. (a) Mediolateral section prestressed with 17.1 Pa. (b) Mediolateral section prestressed with 51.3 Pa. (c) Anteroposterior section prestressed with 308.0 Pa. (d) Anteroposterior section prestressed with 513.3 Pa. The value of the correction factor b was ω−1 and the value of a was experimentally determined to be ω−0.03.

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