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Research Papers

Transverse Compression of Tendons

[+] Author and Article Information
S. T. Samuel Salisbury

Department of Engineering Science,
University of Oxford,
Parks Road,
Oxford OX1 3PJ, UK
e-mail: sam.salisbury@oxon.org

C. Paul Buckley

Department of Engineering Science,
University of Oxford,
Parks Road,
Oxford OX1 3PJ, UK
e-mail: paul.buckley@eng.ox.ac.uk

Amy B. Zavatsky

Department of Engineering Science,
University of Oxford,
Parks Road,
Oxford OX1 3PJ, UK
e-mail: amy.zavatsky@eng.ox.ac.uk

1Corresponding author.

Manuscript received April 24, 2015; final manuscript received January 18, 2016; published online February 19, 2016. Assoc. Editor: Guy M. Genin.

J Biomech Eng 138(4), 041002 (Feb 19, 2016) (9 pages) Paper No: BIO-15-1191; doi: 10.1115/1.4032627 History: Received April 24, 2015; Revised January 18, 2016

A study was made of the deformation of tendons when compressed transverse to the fiber-aligned axis. Bovine digital extensor tendons were compression tested between flat rigid plates. The methods included: in situ image-based measurement of tendon cross-sectional shapes, after preconditioning but immediately prior to testing; multiple constant-load creep/recovery tests applied to each tendon at increasing loads; and measurements of the resulting tendon displacements in both transverse directions. In these tests, friction resisted axial stretch of the tendon during compression, giving approximately plane-strain conditions. This, together with the assumption of a form of anisotropic hyperelastic constitutive model proposed previously for tendon, justified modeling the isochronal response of tendon as that of an isotropic, slightly compressible, neo-Hookean solid. Inverse analysis, using finite-element (FE) simulations of the experiments and 10 s isochronal creep displacement data, gave values for Young's modulus and Poisson's ratio of this solid of 0.31 MPa and 0.49, respectively, for an idealized tendon shape and averaged data for all the tendons and E = 0.14 and 0.10 MPa for two specific tendons using their actual measured geometry. The compression load versus displacement curves, as measured and as simulated, showed varying degrees of stiffening with increasing load. This can be attributed mostly to geometrical changes in tendon cross section under load, varying according to the initial 3D shape of the tendon.

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Figures

Grahic Jump Location
Fig. 1

Schematic drawing of the tendon compression rig. (a) View in X–Y plane. Distance from paddle pivot to center of the glass window = 175 mm, distance from center of glass window to LVDT = 125 mm, and distance from LVDT to load = 50 mm. (b) View in Y–Z plane. Height of glass plate = 40 mm and height of glass backing = 75 mm.

Grahic Jump Location
Fig. 2

(a) Tendon cross-sectional profiles acquired after preconditioning. Tendon width (ΔX0) ranged from 8.9 to 15.6 mm, and tendon thickness (ΔY0) ranged from 3.7 to 5.8 mm (correctly resolved to within 0.15 mm or less [15]). (b) Race-track approximation (cross-sectional area 36.6 mm2) fitted to the average tendon shape (cross-sectional area 35.1 mm2).

Grahic Jump Location
Fig. 3

Examples of measured displacements in (a) Y-direction and (b) X-direction as functions of time, during each profile of transverse loading. Each curve begins at time zero and is followed by a brief spike, which indicates when the 0.9 N calibration load was applied; the displacement axis is zeroed at the peak of this spike. Following the spike, there is a brief period of recovery followed by the main load applied at 90 s.

Grahic Jump Location
Fig. 4

Load versus 10 s isochronal (a) Y-displacement and (b) X-displacement measured during creep for seven tendons

Grahic Jump Location
Fig. 5

Comparison of the FE simulation of transverse compression of a model tendon with race-track geometry (see Fig.2) (solid lines), with average measured 10 s creep displacements (circles) in (a) the Y-direction and (b) the X-direction. Dashed lines show the range of measured displacements at each load level. The model uses best-fit values E = 0.34 MPa and ν = 0.490.

Grahic Jump Location
Fig. 6

Comparison of the FE simulations (solid lines) of transverse compression of two tendons, using their tendon-specific cross-sectional geometries, with measured 10 s creep displacements (symbols) in the Y-direction. The model uses ν = 0.49, and best-fit values (a) E = 0.14 MPa and (b) E = 0.10 MPa.

Grahic Jump Location
Fig. 7

Example of an FE model of the experiment viewed from the side (Y–Z plane, as defined in Fig. 1). The tendon is being compressed between the glass plate and the glass backing by 19%. Logarithmic (true) tensile strain in the fiber-aligned direction (εZ) is plotted, revealing some axial expansion at the ends of the compression zone.

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