Research Papers

Recruitment Viscoelasticity of the Tendon

[+] Author and Article Information
Yoram Lanir

e-mail: yoram@bm.technion.ac.il
Faculty of Biomedical Engineering,
Technion-lsrael Institute of Technology,
Haifa 32000, Israel

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the JOURNALOF BIOMECHANICAL ENGINEERING. Manuscript received January 15, 2009; final manuscript received April 15, 2009; published online October 21, 2009. Review conducted by Michael Sacks.

J Biomech Eng 131(11), 111008 (Oct 21, 2009) (8 pages) doi:10.1115/1.3212107 History: Received January 15, 2009; Revised April 15, 2009

There is still no agreement on the nature of tissues' viscoelasticity and on its reliable modeling. We speculate that disagreements between previous observations stem from difficulties of separating between viscoelastic and preconditioning effects, since both are manifested by similar response features. Here, this and related issues were studied in the tendon as a prototype for other soft tissues. Sheep digital tendons were preconditioned under strain that was higher by 1% than the one used in subsequent testing. Each specimen was then subjected to stress relaxation, and quick release or creep. A stochastic microstructural viscoelastic theory was developed based on the collagen fibers' properties and on their gradual recruitment with stretch. Model parameters were estimated from stress relaxation data and predictions were compared with the creep data. Following its validation, the new recruitment viscoelasticity (RVE) model was compared, both theoretically and experimentally, with the quasilinear viscoelastic (QLV) theory. The applied preconditioning protocol produced subsequent pure viscoelastic response. The proposed RVE model provided excellent fit to both stress relaxation and creep data. Both analytical and numerical comparisons showed that the new RVE theory and the popular QLV one are equivalent under deformation schemes at which no fibers buckle. Otherwise, the equivalence breaks down; QLV may predict negative stress, in contrast to data of the quick release tests, while RVE predicts no such negative stress. The results are consistent with the following conclusions: (1) fully preconditioned tendon exhibits pure viscoelastic response, (2) nonlinearity of the tendon viscoelasticity is induced by gradual recruitment of its fibers, (3) a new structure-based RVE theory is a reliable representation of the tendon viscoelastic properties under both stress relaxation and creep tests, and (4) the QLV theory is equivalent to the RVE one (and valid) only under deformations in which no fibers buckle. The results also suggest that the collagen fibers themselves are linear viscoelastic.

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Fig. 2

Stress relaxation and creep protocols. The signals are the imposed and the response strain versus time (a) and the corresponding stress versus time (b) (Sample No. 070325).

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Fig. 3

Stress relaxation and quick release protocols and the measured responses. The imposed strain protocol during the quick release (a) consisted of rapid reductions of the strain level to decreasing lower levels of constant strain. A typical sample response is depicted in (b) (Sample No. 070508).

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Fig. 1

The relaxation loading protocol. The protocol consists of three consecutive sets at 6%, 5%, and 4% strain, respectively. Inset: expanded scheme of the strain protocol for each set consisting of a long (10 min duration) relaxation test, followed by ten cycles of short Clmin duration each) relaxation tests, then a rest period of 10 min, and finally a second long (10 min) relaxation test.

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Fig. 4

RVE descriptive testing. Model prediction of stress relaxation (black line) versus data (grey line) (Sample No. 070325).

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Fig. 5

RVE predictive testing. Stress relaxation and creep data (grey line) and model prediction (black line), (a) All creep cycles are within the pure viscoelastic region (Sample No. 070325) and(b) one creep cycle is above the pure viscoelastic region (Sample No. 070619).

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Fig. 6

Simulated loading protocol for nonbuckling fibers. The RVE and QLV predicted responses are identical, (a) Strain protocol and (b) simulated stress response. x0: straightening strain of the wavy fiber.

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Fig. 7

Simulated loading protocol for buckling fibers. The RVE and QLV predicted responses are different. QLV predicts negative stress and RVE stress is non-negative, (a) Strain and (b) simulated stress.



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