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Research Papers

Advances in Quantification of Meniscus Tensile Mechanics Including Nonlinearity, Yield, and Failure

[+] Author and Article Information
John M. Peloquin

Department of Bioengineering,
University of Pennsylvania,
Philadelphia, PA 19104

Michael H. Santare

Department of Mechanical Engineering,
University of Delaware,
Newark, DE 19716

Dawn M. Elliott

Department of Biomedical Engineering,
University of Delaware,
150 Academy Street,
161 Colburn Lab,
Newark, DE 19716
e-mail: delliott@udel.edu

1Corresponding author.

Manuscript received November 1, 2015; final manuscript received December 19, 2015; published online January 27, 2016. Editor: Beth A. Winkelstein.

J Biomech Eng 138(2), 021002 (Jan 27, 2016) (13 pages) Paper No: BIO-15-1545; doi: 10.1115/1.4032354 History: Received November 01, 2015; Revised December 19, 2015

The meniscus provides crucial knee function and damage to it leads to osteoarthritis of the articular cartilage. Accurate measurement of its mechanical properties is therefore important, but there is uncertainty about how the test procedure affects the results, and some key mechanical properties are reported using ad hoc criteria (modulus) or not reported at all (yield). This study quantifies the meniscus' stress–strain curve in circumferential and radial uniaxial tension. A fiber recruitment model was used to represent the toe region of the stress–strain curve, and new reproducible and objective procedures were implemented for identifying the yield point and measuring the elastic modulus. Patterns of strain heterogeneity were identified using strain field measurements. To resolve uncertainty regarding whether rupture location (i.e., midsubstance rupture versus at-grip rupture) influences the measured mechanical properties, types of rupture were classified in detail and compared. Dogbone (DB)-shaped specimens are often used to promote midsubstance rupture; to determine if this is effective, we compared DB and rectangle (R) specimens in both the radial and circumferential directions. In circumferential testing, we also compared expanded tab (ET) specimens under the hypothesis that this shape would more effectively secure the meniscus' curved fibers and thus produce a stiffer response. The fiber recruitment model produced excellent fits to the data. Full fiber recruitment occurred approximately at the yield point, strongly supporting the model's physical interpretation. The strain fields, especially shear and transverse strain, were extremely heterogeneous. The shear strain field was arranged in pronounced bands of alternating positive and negative strain in a pattern similar to the fascicle structure. The site and extent of failure showed great variation, but did not affect the measured mechanical properties. In circumferential tension, ET specimens underwent earlier and more rapid fiber recruitment, had less stretch at yield, and had greater elastic modulus and peak stress. No significant differences were observed between R and DB specimens in either circumferential or radial tension. Based on these results, ET specimens are recommended for circumferential tests and R specimens for radial tests. In addition to the data obtained, the procedural and modeling advances made in this study are a significant step forward for meniscus research and are applicable to other fibrous soft tissues.

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Figures

Grahic Jump Location
Fig. 1

Meniscus specimen shapes used in this study and their dissection locations. The specimen and meniscus outlines are printed at 1:2 scale. The specimen outlines match the median dimensions used in this study. The gray-shaded regions of the specimen were clamped by the grips. The dashed lines schematically illustrate the curved path of the meniscus' fibers.

Grahic Jump Location
Fig. 2

Mean and standard deviation of yield and peak points for circumferential ET specimens by test environment. The stress–strain response of specimens tested in air and PBS did not differ with respect to these points or any other measured parameter (see Table 1 for other parameters).

Grahic Jump Location
Fig. 3

Classification scheme for types of specimen rupture. Circumferential specimens (a) ruptured in two more ways than the radial specimens (b). Gripped region failures and longitudinal splits were considered invalid and excluded from mechanical analysis.

Grahic Jump Location
Fig. 4

A representative stress–strain curve for circumferential ET specimens with the fiber recruitment range (the 0.025 and 0.975 quantiles of λc), mean fiber recruitment stretch (λ¯c), yield point, and peak point marked. The lower plot shows the pointwise tangent modulus curve (the first derivative of the stress–strain curve), the first local maximum of which was identified as the yield point. Both plots share the same x-axis.

Grahic Jump Location
Fig. 5

Stress–strain curves for the circumferential and radial specimens by rupture type and specimen shape. The yield and peak stress points are marked. (a) Circumferential and (b) radial.

Grahic Jump Location
Fig. 6

Fiber modulus (kf) was strongly correlated with tangent modulus at yield (r [95% CI] = 0.77–0.94 by Pearson correlation). The solid line and shaded region are the best-fit line and its 95% confidence interval. The dotted black line illustrates a 1:1 relationship (slope = 1 and intercept = 0).

Grahic Jump Location
Fig. 7

Fiber recruitment model and stress–strain results for circumferentially stretched ET, R, and DB specimens. Significant differences between specimen shapes are marked with a bar and asterisk. The ET specimens showed differences indicating more complete and rapid fiber recruitment.

Grahic Jump Location
Fig. 8

Stress–strain results for radially stretched R and DB specimens. There were no significant differences between specimen shapes.

Grahic Jump Location
Fig. 9

Representative longitudinal strain (Exx) fields at yield for the circumferentially loaded specimens. In (c), the dashed outline over the DB's strain field indicates the loaded region, which has potential grip-to-grip fiber continuity. The flared margins outside this outline are the shielded region, which has no grip-to-grip continuous fibers and exhibits less longitudinal strain than the loaded region. Color scales are truncated at the 0.05 and 0.95 quantiles. The scale bars are 5 mm long. (a) ET, (b) R, and (c) DB.

Grahic Jump Location
Fig. 10

Representative (a) shear strain (Exy) and (b) transverse strain (Eyy) field at yield for the circumferential specimens with (c) the corresponding camera image of the specimen. An ET specimen is shown. The bands in the Exy field qualitatively match the fascicle boundaries visible in the camera image. The color scales are truncated at the 0.05 and 0.95 quantiles. The scale bars are 5 mm long.

Grahic Jump Location
Fig. 11

Representative plot of the longitudinal strain (Exx) in a DB specimen measured optically (y-axis) and by grip displacement (x-axis). The median optical strain in the central region (the loaded region), which has grip-to-grip fiber continuity, is much greater than in the flared ends of the specimen (the shielded region), which contain severed fibers. See Fig. 9(c) for a diagram of these regions. The line of 1:1 correspondence between optical and grip strain is marked by a solid black line. Optical strain is approximately linearly correlated with grip strain up to and a little past the yield point.

Grahic Jump Location
Fig. 12

Representative longitudinal (Exx), shear (Exy), and transverse (Eyy) strain fields for radially stretched DB specimens at yield. The strain fields for radially stretched R specimens are similar. The scale bars are 5 mm long.

Grahic Jump Location
Fig. 13

Optical longitudinal strain 0.05/0.95 interquartile range (shaded region) compared with grip strain (solid black line). The optical strain range broadens in proportion to the applied grip strain. This is a representative example; in other cases, the optical strain range may broaden nonlinearly. The plot shows data up to the peak point.

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