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Research Papers

Biaxial Tensile Testing and Constitutive Modeling of Human Supraspinatus Tendon

[+] Author and Article Information
Spencer E. Szczesny, John M. Peloquin, Daniel H. Cortes

 Department of Orthopaedic Surgery, University of Pennsylvania, 424 Stemmler Hall, 36th Street and Hamilton Walk, Philadelphia, PA 19104; Department of Bioengineering, University of Pennsylvania, 240 Skirkanich Hall, 210 South 33rd Street, Philadelphia, PA 19104

Jennifer A. Kadlowec

 Department of Mechanical Engineering, Rowan University, 232 Rowan Hall, 201 Mullica Hill Road, Glassboro, NJ 08028

Louis J. Soslowsky

Department of Orthopaedic Surgery, University of Pennsylvania, 424 Stemmler Hall, 36th Street and Hamilton Walk, Philadelphia, PA 19104; Department of Bioengineering, University of Pennsylvania, 240 Skirkanich Hall, 210 South 33rd Street, Philadelphia, PA 19104

Dawn M. Elliott1 n2

Department of Orthopaedic Surgery, University of Pennsylvania, 424 Stemmler Hall, 36th Street and Hamilton Walk, Philadelphia, PA 19104; Department of Bioengineering, University of Pennsylvania, 240 Skirkanich Hall, 210 South 33rd Street, Philadelphia, PA 19104delliott@udel.edu

1

Corresponding author.

2

Present address: Biomedical Engineering, University of Delaware, 130 Academy St., Rm. 201 Spencer Lab, Newark, DE 19716.

J Biomech Eng 134(2), 021004 (Mar 19, 2012) (9 pages) doi:10.1115/1.4005852 History: Received December 22, 2011; Revised December 28, 2011; Posted January 01, 2012; Published March 14, 2012; Online March 19, 2012

The heterogeneous composition and mechanical properties of the supraspinatus tendon offer an opportunity for studying the structure-function relationships of fibrous musculoskeletal connective tissues. Previous uniaxial testing has demonstrated a correlation between the collagen fiber angle distribution and tendon mechanics in response to tensile loading both parallel and transverse to the tendon longitudinal axis. However, the planar mechanics of the supraspinatus tendon may be more appropriately characterized through biaxial tensile testing, which avoids the limitation of nonphysiologic traction-free boundary conditions present during uniaxial testing. Combined with a structural constitutive model, biaxial testing can help identify the specific structural mechanisms underlying the tendon’s two-dimensional mechanical behavior. Therefore, the objective of this study was to evaluate the contribution of collagen fiber organization to the planar tensile mechanics of the human supraspinatus tendon by fitting biaxial tensile data with a structural constitutive model that incorporates a sample-specific angular distribution of nonlinear fibers. Regional samples were tested under several biaxial boundary conditions while simultaneously measuring the collagen fiber orientations via polarized light imaging. The histograms of fiber angles were fit with a von Mises probability distribution and input into a hyperelastic constitutive model incorporating the contributions of the uncrimped fibers. Samples with a wide fiber angle distribution produced greater transverse stresses than more highly aligned samples. The structural model fit the longitudinal stresses well (median R2 ≥ 0.96) and was validated by successfully predicting the stress response to a mechanical protocol not used for parameter estimation. The transverse stresses were fit less well with greater errors observed for less aligned samples. Sensitivity analyses and relatively affine fiber kinematics suggest that these errors are not due to inaccuracies in measuring the collagen fiber organization. More likely, additional strain energy terms representing fiber-fiber interactions are necessary to provide a closer approximation of the transverse stresses. Nevertheless, this approach demonstrated that the longitudinal tensile mechanics of the supraspinatus tendon are primarily dependent on the moduli, crimp, and angular distribution of its collagen fibers. These results add to the existing knowledge of structure-function relationships in fibrous musculoskeletal tissue, which is valuable for understanding the etiology of degenerative disease, developing effective tissue engineering design strategies, and predicting outcomes of tissue repair.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 8

Representative sensitivity plots for the normalized SSE, given changes in the mean fiber angle and circular variance. Isometric lines indicate fold increases in the SSE compared to the model fits using the experimentally measured fiber angle parameters (•). The majority of plots were kidney-shaped, with the fits of 10/21 samples located (a) near the center of the contours, and those of 8/21 samples (b) at an offset. The plots for three samples had (c) a different shape.

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Figure 7

(a) Fiber modulus was not correlated with circular variance, while positive correlations were observed for both (b) the mean uncrimping stretch (λ¯c), and (c) the standard deviation of uncrimping (λcSD)

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Figure 6

(a) For one-third of the samples, the model fits of the transverse stresses from the 4:1 test produced negative R2 values. (b) Normalizing the model errors for the transverse stress by the maximum longitudinal stress (σ̂error) demonstrates that the errors for the more highly aligned samples are relatively inconsequential in comparison to samples with a wider distribution of fibers.

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Figure 5

An example of the fits of the structural model to the experimental data for the (a),(b) 4:1 test, (c),(d) unloaded test, and (e),(f) 1:0 test. Note that the 1:0 test was not used to determine the model parameters and, therefore, represents a validation of the model.

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Figure 4

Significant correlations were observed between circular variance (where a low variance represents more highly aligned fibers) for (a) the longitudinal linear-region modulus from the unloaded boundary condition test, (b) the ratio of maximum transverse to maximum longitudinal stress (σratio ) from the 4:1 test, and (c) the range (where higher values indicate less affine behavior)

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Figure 3

Representative fit of the empirical histogram of fiber angles with a von Mises probability density function

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Figure 2

Schematic of the custom algorithm used to monitor the slope of the longitudinal stress-strain curve in real-time by fitting the most recent 15 s of data at each time point (t1 ,t2 ,t3 ,…). Once the slope dropped by 0.5% from the maximum value (at t4 ), the test was stopped (t* ) and the final recorded stress was used as the limit for the subsequent mechanical testing. Note spacing between time points is exaggerated for clarity.

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Figure 1

(a) Schematic of regions where supraspinatus tendon samples were harvested. (b) Image of speckle-coated sample in reference configuration with markers (arrow) attached to sandpaper tabs via transparent plastic (dashed line). (c) Biaxial testing device with the crossed linear polarizers above and below the sample loaded in the center of the PBS bath.

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