High-resolution spatial mapping of shear properties in cartilage

Abstract

Structural properties of articular cartilage such as proteoglycan content, collagen content and collagen alignment are known to vary over length scales as small as a few microns (Bullough and Goodfellow, 1968; Bi et al., 2006). Characterizing the resulting variation in mechanical properties is critical for understanding how the inhomogeneous architecture of this tissue gives rise to its function. Previous studies have measured the depth-dependent shear modulus of articular cartilage using methods such as particle image velocimetry (PIV) that rely on cells and cell nuclei as fiducial markers to track tissue deformation (Buckley et al., 2008; Wong et al., 2008a). However, such techniques are limited by the density of trackable markers, which may be too low to take full advantage of optical microscopy. This limitation leads to noise in the acquired data, which is often exacerbated when the data is manipulated. In this study, we report on two techniques for increasing the accuracy of tissue deformation measurements. In the first technique, deformations were tracked in a grid that was photobleached on each tissue sample (Bruehlmann et al., 2004). In the second, a numerical technique was implemented that allowed for accurate differentiation of optical displacement measurements by minimizing the propagated experimental error while ensuring that truncation error associated with local averaging of the data remained small. To test their efficacy, we employed these techniques to compare the depth-dependent shear moduli of neonatal bovine and adult human articular cartilage. Using a photobleached grid and numerical optimization to gather and analyze data led to results consistent with those reported previously (Buckley et al., 2008; Wong et al., 2008a), but with increased spatial resolution and characteristic coefficients of variation that were reduced up to a factor of 3. This increased resolution allowed us to determine that the shear modulus of neonatal bovine and adult human tissue both exhibit a global minimum at a depth z of around 100 microm and plateau at large depths. The consistency of the depth dependence of |G*|(Z) for adult human and neonatal bovine tissue suggests a functional advantage resulting from this behavior.

Figure 1

Confocal micrographs of 5-DTAF-stained human articular cartilage with vertical photobleached lines (A) before and (B) during application of shear. The photobleached lines are spaced by 50 μm.

Figure 2

(A) Mean intensity I(x) at depth z for a sheared sample of articular cartilage at time t (blue). Also shown are local parabolic fits near each photobleached line location (black) and the calculated photobleached line locations (red stars). (B) Mean photobleached line location u(z,t) at depth z vs. time t for a sheared sample of articular cartilage (blue circles) and sinusoidal fit (black solid line).

Figure 3

Depth dependence of peak-to-peak displacement amplitudes and complex shear moduli for single representative samples of (A) neonatal bovine and (B) adult human articular cartilage subject to shear at 100 mHz and analyzed using 5PLSQ and WAND.

Figure 4

Depth dependence of complex shear moduli for n=3 samples of (A) neonatal bovine and (B) adult human articular cartilage subject to shear at 100 mHz and analyzed using PIV and GRATE.