Research Papers

Localization of Viscous Behavior and Shear Energy Dissipation in Articular Cartilage Under Dynamic Shear Loading

[+] Author and Article Information
Mark R. Buckley

Department of Physics,
Clark Hall C7,
Cornell University,
Ithaca, NY 14853
e-mail: mbuck@mail.med.upenn.edu

Lawrence J. Bonassar

Department of Biomedical Engineering and
Sibley School of Mechanical and
Aerospace Engineering,
Weill Hall 149,
Cornell University,
Ithaca, NY 14853
e-mail: lb244@cornell.edu

Itai Cohen

Department of Physics,
Clark Hall 508,
Cornell University,
Ithaca, NY 14853
e-mail: ic64@cornell.edu

1Address for correspondence: Itai Cohen, Department of Physics, Clark Hall 508, Cornell University, Ithaca, NY 14853; e-mail: Itai.Cohen@cornell.edu.

Contributed by the Bioengineering Division of ASME for publication in the Journal of Biomechanical Engineering. Manuscript received April 26, 2012; final manuscript received August 7, 2012; accepted manuscript posted August 27, 2012; published online February 11, 2013. Assoc. Editor: Clark T. Hung.

J Biomech Eng 135(3), 031002 (Feb 11, 2013) (9 pages) Paper No: BIO-12-1160; doi: 10.1115/1.4007454 History: Received April 26, 2012; Revised August 07, 2012; Accepted August 27, 2012

Though remarkably robust, articular cartilage becomes susceptible to damage at high loading rates, particularly under shear. While several studies have measured the local static and steady-state shear properties of cartilage, it is the local viscoelastic properties that determine the tissue's ability to withstand physiological loading regimens. However, measuring local viscoelastic properties requires overcoming technical challenges that include resolving strain fields in both space and time and accurately calculating their phase offsets. This study combined recently developed high-speed confocal imaging techniques with three approaches for analyzing time- and location-dependent mechanical data to measure the depth-dependent dynamic modulus and phase angles of articular cartilage. For sinusoidal shear at frequencies f = 0.01 to 1 Hz with no strain offset, the dynamic shear modulus |G*| and phase angle δ reached their minimum and maximum values (respectively) approximately 100 μm below the articular surface, resulting in a profound focusing of energy dissipation in this narrow band of tissue that increased with frequency. This region, known as the transitional zone, was previously thought to simply connect surface and deeper tissue regions. Within 250 μm of the articular surface, |G*| increased from 0.32 ± 0.08 to 0.42 ± 0.08 MPa across the five frequencies tested, while δ decreased from 12 deg ± 1 deg to 9.1 deg ± 0.5 deg. Deeper into the tissue, |G*| increased from 1.5 ± 0.4 MPa to 2.1 ± 0.6 MPa and δ decreased from 13 deg ± 1 deg to 5.5 deg ± 0.2 deg. Viscoelastic properties were also strain-dependent, with localized energy dissipation suppressed at higher shear strain offsets. These results suggest a critical role for the transitional zone in dissipating energy, representing a possible shift in our understanding of cartilage mechanical function. Further, they give insight into how focal degeneration and mechanical trauma could lead to sustained damage in this tissue.

Copyright © 2013 by ASME
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Grahic Jump Location
Fig. 4

Flow diagram of approach #3 for determination of viscoelastic mechanical parameters from the measured displacement u(z,t). u(t) was fit to a periodic function at all z, and calculations involving derivatives of the fit parameters were used to compute |G*|(z), τ(z), and Ed(z)/ΔV. All plotted data is from a representative sample sheared at f = 1 Hz with γi = 0%.

Grahic Jump Location
Fig. 3

(a) Shear stress τ versus shear strain γ at depths z = 98 μm and z = 2182 μm in a representative sample sheared at 1 Hz with γi = 0% with equilibrium values of τ and γ set to zero. (b) From stress strain curves, such as those shown in (a), |G*|, δ, and Ed/ΔV can be obtained from the slope of the major axis, the positive x-intercept, and the enclosed area, respectively (approach #2).

Grahic Jump Location
Fig. 2

Flow diagram of approaches #1 and #2 for determination of viscoelastic mechanical parameters from the measured displacement u(z,t). Approach #1 involves sinusoidal fitting of the calculated strain γ versus time t at each depth z, while approach #2 involves elliptical fitting of γ versus stress τ for all z. All plotted data is from a representative sample sheared at f = 1 Hz with γi = 0%.

Grahic Jump Location
Fig. 1

Schematic diagram of the tissue deformation imaging stage (TDIS). The sample is sheared between the stationary and moveable plates, while it is imaged from below with an inverted confocal microscope.

Grahic Jump Location
Fig. 5

Comparison of the results of approaches #1, #2, and #3 for calculating the (a) dynamic shear modulus |G*|, (b) phase angle δ, and (c) local fraction of energy-dissipated Ed(z)Edtot as a function of depth z for a representative sample sheared at f = 1 Hz with γi = 0%. All approaches yielded similar |G*| profiles, but approach #2 was much more susceptible to noise in calculating δ(z) and Ed(z)Edtot. Data from approaches #1 and #3 were consistent and accurate for all measured parameters.

Grahic Jump Location
Fig. 6

[(a) and (b)] Complex shear modulus |G*|, [(c) and (d)] phase angle δ, and [(e) and (f)] relative energy dissipated Ed(z)Edtot versus z in articular cartilage sheared at f = 0.01, 0.1, and 1 Hz with γi = 0 μm and εc = 20%. Data are mean ± SD, horizontal bars denote p ≤ 0.05/3, and (*) denotes p ≤ 0.05 versus (*) z > 250 μm. In (a), (c), and (e), only upper or lower error bars for selected points are shown to enhance clarity.

Grahic Jump Location
Fig. 7

[(a) and (b)] Ed(z)Edtotvs. depth z in articular cartilage sheared from initial strains γi = 0% and γi = 12% with f = 1 Hz and εc = 20%. Data are mean ± SD, horizontal bars denote p ≤ 0.05/3, and (*) denotes p ≤ 0.05 versus (*) z > 250 μm. In (a), (c), and (e), only upper or lower error bars for selected points are shown to enhance clarity.

Grahic Jump Location
Fig. 8

(a) Confocal reflectance micrograph of a representative sample of articular cartilage subjected to 20% compression and (b) the corresponding average intensity profile along the long axis. (c)–(f) Confocal reflectance micrographs with corresponding Fourier transforms (contrast enhanced) taken near the surface (50 < z < 150 μm) of a sample of articular cartilage [(c) and (d)] before and [(e) and (f)] after application of a 12% shear strain. The arrow to the left of (e) depicts the direction of shear, while the lines in (d) and (f) denote the angles of maximal alignment. (g) Change in Fourier transform aspect ratio before and after application of a 12% shear strain versus depth z. Error bars in (g) represent the experimental uncertainty for measurements on the specimen shown in (a).



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