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Indentation testing of human articular cartilage: Effects of probe tip geometry and indentation depth on intra-tissue strain
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Indentation testing of human articular cartilage: Effects of probe tip geometry and indentation depth on intra-tissue strain Won C. Baea, Chad W. Lewisc, Marc E. Levenstond, Robert L. Saha,b, a
Department of Bioengineering, 9500 Gilman Dr., Mail Code 0412, University of California-San Diego, La Jolla, CA 92093-0412, USA b Department of Whitaker Institute of Biomedical Engineering, University of California-San Diego, La Jolla, CA, USA c Mechanical Engineering Department, Colorado State University, Fort Collins, CO, USA d George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA Accepted 17 February 2005
Abstract Experimental determination of intra-tissue deformation during clinically applicable rapid indentation testing would be useful for understanding indentation biomechanics and for designing safe indentation probes and protocols. The objectives of this study were to perform two-dimensional (2-D) indentation tests, using indenters and protocols that are analogous to those in clinically oriented probes, of normal adult-human articular cartilage in order to determine: (1) intra-tissue strain maps and regions of high strain magnitude, and (2) the effects on strain of indenter geometry (rectangular prismatic and cylindrical) and indentation depth (40–190 mm). Epifluorescence microscopy of samples undergoing indentation and subsequent video image correlation analysis allowed determination of strain maps. Regions of peak strain were near the ‘‘edges’’ of indenter contact with the cartilage surface, and the strain magnitude in these regions ranged from 0.05 to 0.30 in compression and shear, a range with known biological consequences. With increasing indentation displacement, strain magnitudes generally increased in all regions of the tissue. Compared to indentation using a rectangular prismatic tip, indentation with a cylindrical tip resulted in slightly higher peak strain magnitudes while influencing a smaller region of cartilage. These results may be used to refine clinical indenters and indentation protocols. r 2005 Elsevier Ltd. All rights reserved. Keywords: Cartilage; Biomechanics; Indentation; Strain; Clinical; Diagnosis
1. Introduction Short-duration indentation testing has shown potential as a diagnostic tool for assessing the health and function of human articular cartilage. Such indentation testing allows for non-destructive, quick, and quantitative assessment of cartilage function and biomechanical properties, and has been used in a number of studies (Kempson et al., 1971a, b; Lyyra et al., 1995; Swann and Seedhom, 1993). Rapid indentation testing has also been Corresponding author. Department of Bioengineering, 9500 Gilman Dr., Mail Code 0412, University of California-San Diego, La Jolla, CA 92093-0412, USA. Tel.: +858 534 0821; fax: +858 822 1614. E-mail address: [email protected] (R.L. Sah).
0021-9290/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2005.02.018
used to gauge the extent of cartilage degeneration (Bae et al., 2003; Franz et al., 2001; Roberts et al., 1986) and repair (Peterson et al., 2002) after surgical procedures, complementing in vitro equilibrium indentation tests (Mak et al., 1987; Mow et al., 1989; Hale et al., 1993). Recently, clinical arthroscopic probes utilizing shortduration indentation protocols have been developed (Lyyra et al., 1995; Lyyra-Laitinen et al., 1999; Niederauer et al., 1998), and used to test human articular cartilage of the knee. Such arthroscopic probes are typically fitted with a plane-ended (Lyyra et al., 1995) or a sphere-ended (Bae et al., 2003; LyyraLaitinen et al., 1999) indenter tip with a diameter in the order of 0.5–1.0 mm (Lyyra et al., 1995; LyyraLaitinen et al., 1999). This indenter dimension is
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somewhat less than the cartilage thickness of the femoral condyle, which is in the order of 2 mm (Bae et al., 2003). Typical loading protocols for these probes induce an indentation displacement (depth from the indented surface) of 100–300 mm (Bae et al., 2003; Lyyra et al., 1995; Lyyra-Laitinen et al., 1999). However, it is unclear how the choices of indenter design and indentation protocols affect indentation biomechanics. Classical biomechanical experiments on cartilage have relied on controlling or measuring sample surface displacement, and inferring material properties based on models that often employ simplifying assumptions such as homogeneity. For example, from experiments such as confined and unconfined compression testing, material properties were obtained using homogeneous biphasic/poroelastic models (Armstrong et al., 1984; Frank and Grodzinsky, 1987; Mow et al., 1980). Efforts have been made to incorporate the inhomogeneous nature of cartilage into these models (Chen et al., 2001a; Grodzinsky and Frank, 1990). Depth-varying biomechanical properties of cartilage under these testing configurations were elucidated by two-dimensional (2-D) measurements of intra-tissue cartilage deformation (Chen et al., 2001b; Schinagl et al., 1997, 1996; Wang et al., 2002). Complex cartilage material properties such as inhomogeneity (Schinagl et al., 1996, 1997) and tension–compression non-linearity (Soltz and Ateshian, 2000) are likely to influence indentation mechanics as well. Determination of intra-tissue strain would be useful for characterizing the actual behavior of cartilage during indentation, as well as for refining theoretical models. In order to elucidate intra-tissue deformation, 2-D biomechanical testing configurations, analogous to their three-dimensional (3-D) counter-parts, may be utilized. For example, intra-tissue deformation during confined compression testing has been assessed by bisecting the sample vertically and examining the cut-plane (Wang et al., 2002; Chen et al., 2001b; Schinagl et al., 1996, 1997). Similar approaches may be taken for indentation testing. For example, a vertical bisection during a 3-D indentation of cartilage surface using a plane-ended cylinder would reveal rectangular cut-planes for both the indenter and the sample. Therefore, an indentation test using simpler geometry of rectangular prismatic tip compressing a rectangular sample, with a constrained side to prevent out-of-plane motion (i.e., sample and indenter placed on a smooth glass surface), would exhibit the main features of intra-tissue deformation that occurs in the 3-D counter-part. For 3-D indentation with a sphere-ended tip, an analogous but simpler configuration would be an indentation with the roundedge of a cylindrical indenter (Fig. 1). A number of methods exist for determining in-plane strain based on images representing the structures of the
Fig. 1. Two-dimensional indentation testing setup using a cylindrical tip.
undeformed and deformed tissue. Early approaches utilized computer-assisted identification and tracking of discrete features (markers) of samples in reference and deformed states (Narmoneva et al., 1999; Schinagl et al., 1997, 1996). More recently, video image correlation (VIC) method was introduced for non-contact 2-D strain analysis (Peters and Ranson, 1981) of nonbiological materials (Chu et al., 1985). The VIC method numerically compares reference and deformed images and determines sample displacement and strain maps. VIC has also been used for biological tissues such as bone (Bay, 1995; McKinley and Bay, 2003; Verhulp et al., 2004), retina (Wu et al., 1987), and cartilage in unconfined compression testing (Wang et al., 2002; Chahine et al., 2004). The magnitude of intra-tissue strain has implications for cartilage biology, including metabolism and injury. Relatively low strain magnitudes of 5%, applied dynamically in compression (Kim et al., 1994; Sah et al., 1989) or shear (Jin et al., 2001) stimulate chondrocyte biosynthesis. However, higher strain magnitudes can be injurious to cartilage and cells. With axial compression of 25%, matrix damage occurs at molecular level (Thibault et al., 2002). With 30% axial compression, cell death occurs (D’Lima et al., 2001; Kurz et al., 2001; Patwari et al., 2004). At 40% compression, physical disruption such as fissuring occurs (Quinn et al., 2001). While an indentation compression theoretically results in stress and strain concentrations in cartilage near certain areas of indenter contact (Ciavarella et al., 1998), direct experimental determination of such strains have not been reported. Since an indentation test induces strain in cartilage, and the magnitude and location of intra-tissue strain have a number of biological and clinical implications, intra-tissue strain would be useful to characterize in human articular cartilage in a clinical indentation test scenario. The objectives of this study were to perform 2-D indentation tests, analogous to clinically applicable 3-D indentation tests, on normal human articular cartilage, and to determine (1) intra-tissue strain maps
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and locations of high strain magnitudes, and (2) the effect on strain of indenter geometry and indentation depth.
2. Materials and methods 2.1. Samples Ten millimeter diameter osteochondral cores were harvested from the anterior region of the lateral and medial femoral condyles of three young cadaveric human donors (21 years old, mean age), using a surgical coring device (OATSTM, Arthrex, Naples, FL). The cores had a normal articular surface appearance without erosion or roughening, as described previously (Bae et al., 2003). Briefly, each core was immersed in a solution (Frank et al., 1987) of phosphate-buffered saline and proteinase inhibitors (PBS+PI) at 4 1C for 1 h, and then stored at 70 1C until testing. On the day of testing, the cores were thawed, trimmed to a rectangular block (10 10 2.5 mm3, W L H, with the articular surface parallel to the Y–Z plane, Fig. 1), and immersed for 12 h at 4 1C in a solution of PBS+PI and propidium iodide (0.02 mg/ml) to stain nuclei. Although previously frozen samples were used, past studies found short-duration indentation stiffness measurements are not affected by a freeze-thaw cycle (Black et al., 1979; Kempson et al., 1971a, b; Kiefer et al., 1989; Swann and Seedhom, 1993).
Fig. 2. Video image correlation was performed on (A) reference and (B) indented images, each magnified in (C) and (D), respectively to show detail, by comparing (E, F) smaller patches, known as subsets. Bars ¼ 200 mm.
2.2. Indentation testing and epifluorescence imaging Each sample was mounted in a glass-bottomed chamber (Fig. 1) filled with PBS+PI such that a cartilage/bone surface was in contact with the glass, and the articular surface oriented perpendicular to the direction of indentation (+Z, Fig. 1). The articular surface of each block was indented at the centerline (Y ¼ 0, Fig. 1) using both a 1-mm wide rectangular prismatic indenter (with a rectangular cross-section) and a 1-mm diameter cylindrical indenter (with a circular cross-section), each fabricated from impermeable stainless steel. In this configuration, the intra-tissue deformation would theoretically be symmetric about the centerline and would be exhibited on the bottom of the chamber. Dynamic indentation protocol consisted of a single application of an indentation displacement up to 200 mm at 130 mm/s. Digital epifluorescence microscopic images (768 512 pixels in a field of view, FOV, of a 2.9 2.1 mm2 area, at 8-bit grayscale) were acquired before (Figs. 2A, C, and E) and during (Figs. 2B, D, and F) indentation, at indentation depths of 3573, 8574, 14176, and 190713 mm (1.9, 4.9, 7.7, and 10.4% of the 1.8370.15 mm average cartilage thickness) and denoted as 40, 90, 140, and 190 mm, respectively, in the
text. A pilot study confirmed that visible focus was maintained +20 mm (in the x-direction) from the initial focal plane during indentation. The duration between indentation tests with the tips of different geometry was 30 min, which was sufficient to allow nearly full recovery (average change in thickness between testing was 715 mm, oro71% of average sample thickness). The order of testing between different tip geometries was randomized. 2.3. VIC and determination of strain maps A commercial program (VIC2D, Correlated Solutions, Inc., West Columbia, SC) was used to implement VIC analysis, whose theoretical foundation has been described previously (Sutton et al., 2000). Briefly, the software compares digital images of the reference (Figs. 2A and C) and deformed (Figs. 2B and D) samples in small patches, known as subsets (Figs. 2E and F), which contain unique patterns of pixel intensities. Assuming that there exists a one-to-one correspondence between the pixels in the reference and the deformed subsets, and that the subset region deforms linearly, the displacement of the reference
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subset can be determined computationally, using normalized cross-correlation (Sutton et al., 2000) optimized with the Newton–Raphson method (Chu et al., 1985; Sutton et al., 1983, 1986) and quintic B-spline interpolation (Unser, 1993a, b). Multiple discrete subsets are analyzed in this way to determine the displacement of the center point of each subset, and collectively, a displacement map relative to the reference image. In the present study, incremental displacement maps were determined by comparing pairs of successive images (taken at indentation depths of 0, 40, 90, and 140 mm). A binomial low-pass filter was applied to reduce interpolation bias, typically present for fluorescence images with a bimodal gray intensity distribution (Schreier et al., 2000). Overlapping subsets (41 41 pixels), spaced 5 pixels center-to-center (i.e., ‘‘step-size’’ in both Y- and Z-directions), were analyzed for a total of 15 000 subsets per image set. (Larger subset-size generally increases displacement accuracy until the large size begins to invalidate linearity assumption, while smaller step-size increases both noise and computation time.) In the present study, subset- and step-sizes were chosen such that displacement maps for simulated data sets (rigid body motion) gave accurate (within 0.5% of expected results) and smooth (standard deviation of o1 mm) results. Displacement maps relative to the reference state were determine by adding up the incremental displacement maps, while interpolating (i.e., re-mapping) the displacement maps to the reference to reference coordinates (Gonzalez and Knauss, 1998). Subsequently, strain maps were determined from the displacement maps. Using Matlab 6.5 software (MathWorks, Natick, MA), the displacement gradient at a point was determined as a bilinear least-squares fit of the displacements in a local neighborhood of 45 45 pixels (or 170 170 mm2) centered about the point. Assuming that out-of-plane shear strains were negligible, partial derivatives of the bilinear fit were used to determine in-plane, 2-D Lagrangian principal strain components (Eringen, 1967, Fung, 1977) of Emin (minimum in-plane principal strain), Emax (maximum in-plane principal strain), and Eshear (maximum in-plane shear) at each indentation depth relative to the reference state (i.e., strains at indentation depths of 40, 90, 140, and 190 mm, each relative to 0 mm depth). The maximum and minimum in-plane principal directions (Eringen, 1967) were then determined as ymin and ymax. The method of strain calculation was validated using digitally deformed cartilage images reflecting prescribed axial, lateral and shear strains of 2–10%, as well as rigid body translation (in Y- and Z-directions) of 100–200 mm. The strain values calculated from these digitally deformed and translated images were accurate to within 0.4% of the expected values.
2.4. Statistics For each in-plane principal strain magnitude (Emin, Emax, and Eshear) and direction (ymin and ymax), indentation depth (40, 90, 140, and 190 mm), and indenter geometry (rectangular prismatic and cylindrical), an average strain map for the three samples was determined. To achieve this, the strain maps were aligned about a point along the articular surface intersecting the centerline of the indenter (Y ¼ 0, Fig. 3), and then averaged at all overlapping image pixel coordinates. While the strain maps were not normalized to cartilage thickness, inter-sample thickness variation was small (CV ¼ 0.08) and normalized maps would not be much different since the strain near the bone was negligibly small. The in-plane principal directions of ymin and ymax were shown as arrows, respectively overlaid onto the average maps of Emin and Emax (Figs. 3A, B, D, and E). In addition, the effects of indentation depth (4 levels) and indenter geometry on the strain values were assessed at certain regions of the maps using a two-way repeated measures analysis of variance (ANOVA). The regions of interest were near and along the superficial (at Y ¼ 0, 0.25, 0.5, and 1.0 mm and Z ¼ 0:1 mm), middle (at Y ¼ 0, 0.5, and 1.0 mm and Z ¼ 0:75 mm), and deep (at Y ¼ 0 mm and Z ¼ 1:5 mm) layers of cartilage, assuming an axial symmetry about the centerline (Y ¼ 0 mm). Data are presented as mean7SEM unless noted otherwise.
Fig. 3. Strain magnitude maps from indentation tests using (A–C) rectangular prismatic and (D–F) cylindrical indenters. Lagrangian strain components of (A, D) Emin, (B, E) Emax, and (C, F) Eshear, were plotted for indentation displacements of (i) 40, (ii) 90, (iii) 140, and (iv) 190 mm. Specific regions, a–f, on the maps are referred to in the text.
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3. Results 3.1. Spatial map of strain Strain profiles varied greatly as a function of position relative to the indenter (Fig. 3) and the geometry of the indenter. For indentation with the rectangular prismatic tip, Emin was compressive, generally high in magnitude in the areas of cartilage under and near the indenter (areas a and b, Fig. 3A-iv), and the greatest in area a directly under the indenter edges (0.1870.02 at [Y ¼ 0:5 mm, Z ¼ 0:1 mm], Fig. 3A-iv). For the same samples, Emin values diminished with cartilage depth, being in the range of 0.05 to 0 in area c near the bone (0.0370.01 at [0 mm, 1.5 mm], Fig. 3A-iv), and in area d, far away from the centerline (0.0570.01 at [0.75 mm, 0.75 mm], Fig. 3A-iv). In addition, Emax was tensile and high in magnitude (0.07–0.10) in areas a and b (Fig. 3B-iv) while being relatively low (0.03) in areas c and d (Fig. 3B-iv), with a magnitude profile similar to that of Emin. However, the range of strain values was not as large as that seen in the Emin profile. The spatial variations in Eshear was also similar to that of Emin, with the maximum values found in area a (0.1470.01 at [0.5 mm, 0.1 mm], Fig. 3C-iv) and diminishing with distance away from the indenter and centerline. For indentation with the round-edged cylindrical tip (Figs. 3D–F), the general profile of each strain component was similar to that for indentation with the rectangular prismatic tip, with a few notable differences. Whereas the indentation with the rectangular prismatic tip produced two fixed areas of high strain magnitude near the edge of the indenter at area a, those produced by indentation with the cylindrical tip were more central, indicated by area e at [0 mm, 0.1 mm] and f at [0.25 mm, 0.1 mm] (Figs. 3D-, E-, and F-iv). In addition, the cylindrical indenter qualitatively deformed both a narrower (smaller range of |Y|) and shallower (smaller range of Z) region of cartilage compared to the indentation using a rectangular prismatic indenter. The in-plane principal directions (arrows in Figs. 3A, B, D, and E) indicated that Emin, compressive strain, was mainly in the axial direction, while Emax, tensile strain, was mainly in the lateral direction. The profiles of intra-tissue strain along with the in-plane principal directions suggested that as the indenter tips compressed the cartilage surface, the bulk tissue compressed vertically and expanded laterally while also undergoing a shear deformation. 3.2. Effects of indentation displacement and indenter geometry Indentation depth and indenter geometry had significant effects on strain components in various parts of the cartilage.
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Near the Surface. At central areas near the surface (at [jY j ¼ 0; 0:25, and 0.5 mm, Z ¼ 0:1 mm], Fig. 3), for strain components of Emin, Emax, and Eshear, increasing indentation depth generally increased (all po0:051) strain magnitudes in these areas, in a geometrydependent manner (po0:01 to p ¼ 0:1). Strain magnitudes beneath the indenter center (at [jY j ¼ 0 mm, Z ¼ 0:1 mm], Fig. 3) tended to be higher for the cylindrical indenter (po0:13), while the magnitudes at jY j ¼ 0:5 mm and Z ¼ 0:1 mm, Fig. 3, were significantly higher for the rectangular prismatic indenter (all po0:05). Middle Layer. At areas in the middle layer of cartilage (at [jY j ¼ 0, 0.5 and 0.75 mm, Z ¼ 0:75 mm], Fig. 3), increasing indentation depth significantly increased (all po0.01) the magnitude of all strain components. Strain magnitudes resulting from the rectangular prismatic tip were generally higher than those from the cylindrical tip, especially at [jY j ¼ 0:5, and 0.75 mm, Z ¼ 0:1 mm] (p ¼ 0:010:1). Deep Layer. At deep regions of cartilage (at [jY j ¼ 0 mm, Z ¼ 1:5 mm], Fig. 3), the strain magnitudes of Emin, Emax, and Eshear increased with indentation depth and were generally higher for the rectangular prismatic tip (all po0:05), without significant interactive effects.
4. Discussion In the present study, intra-tissue deformation in human articular cartilage was investigated during short-duration indentation testing. The profiles of intra-tissue strain components were determined (Fig. 3) and the effects of indentation depth and indenter geometry, important parameters in the design of clinical indentation probes and protocols, on strain magnitude were assessed. At a given indentation depth, strain magnitudes were generally high near the ‘‘edge’’ of the indenter (i.e., where it separates from the cartilage surface, at [0.5 mm, 0.1 mm] for the rectangular prismatic indenter, Fig. 4B, and at [Y ¼ 00:25 mm, Z ¼ 0:1 mm] for the cylindrical indenter, Fig. 4E) and low in areas far from either the centerline (at Y ¼ 0 mm) or cartilage surface (at Z ¼ 0 mm). Strain magnitudes generally increased with depth of indentation in all areas (Figs. 3 and 4). Use of the cylindrical tip (relative to rectangular prismatic tip) resulted in slightly higher strain magnitudes near the surface, but lower values in many other areas of the tissue (Fig. 3). Epifluorescence video microscopy and VIC analysis were effective for obtaining information about rapid cartilage deformation in 2-D. The present optical technique allowed for imaging resolution sufficiently high (i.e., 4 mm/pixel) and rate that was adequate (i.e., 5 frames per second), compared to other biomedical
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Fig. 4. Strain profiles resulting from indentation test with (A–C) rectangular prismatic and (D–F) cylindrical indenters. The profiles were taken (A, D) along the cartilage surface, (B, E) with depth along the centerline, and (C, F) with depth along the approximate contacting edge of indenter with cartilage surface, which was approximately at Y ¼ 0:5 and 0.25 mm for rectangular prismatic and cylindrical indenters, respectively.
imaging techniques (e.g., magnetic resonance imaging with a slower scan time (Frank et al., 1999) and ultrasound with lower spatial resolution (Johnson et al., 2002)). VIC analysis of optical images, while not as direct as the methods that track fiducial markers (Chen et al., 2001b; Schinagl et al., 1996), enables rapid determination of 2-D maps of deformation and strain. In addition, the accuracy of the VIC method, with error in strain values of 0.1% or less, found in this study was in agreement with past studies (Sutton et al., 2000; Wang et al., 2002). The present study utilized a particular compression rate and the results from using other compression rates would likely be different. Due to the biphasic/poroelastic nature of cartilage (Frank and Grodzinsky, 1987; Mow et al., 1980), stress-relaxation occurs while the fluid in the tissue flows within and out of the tissue. The extent of stress-relaxation during the indentation may be elucidated by dimensional analysis of a characteristic equation (Frank and Grodzinsky, 1987; Mow et al., 1980) of a2 ¼ tH A kp , where a, t, H A , and kp represent the characteristic distance, characteristic time, aggregate modulus, and hydraulic permeability, respectively. Assuming reasonable values (Athanasiou et al., 1991) of H A and kp of 1 MPa and 1015 m4/N s, respectively, and using a of 0.5 mm (current indenter radius), t is computed to be 250 s. The present protocol used a compression rate of 130 mm/s to reach the maximum indentation depth of 190 mm in 1.5 s, much shorter than the characteristic time of 250 s. Thus, the majority of the tissue is likely to reflect an ‘‘instantaneous’’ type of loading response. In comparison, if a much lower compression rate of 0.1 mm/s were to be used to attain the same indentation depth, it would take 1900 s, and the bulk of tissue would have experienced stressrelaxation, and less strain concentration would be apparent (Spilker et al., 1992). In contrast, if a relatively
fast compression rate of 105 mm/s is used, it would take 0.02 s, and the tissue would exhibit very little fluid loss but greater localized strain near the superficial region. Such an effect may be responsible for greater physical disruption of the cartilage surface when the sample is compressed to a particular depth at increasing rate (Ewers et al., 2001). The current method of strain determination depended on a number of factors. VIC method introduces slight variability in displacement calculation due to subsetand step-size selection. Subsequently, strain determination from displacement can be affected by filtering (linear-fitting of neighboring displacement values). While necessary to suppress noise, filtering underestimates the strain magnitude should a sharp displacement gradient exist, as it may near the articular surface undergoing indentation. Nonetheless, the present methods were reasonably accurate (as determined using validation images with known deformation) when the displacement gradient was not severe. Other smoothing methods, such as thin-plate spline smoothing (Wang et al., 2002), could improve further the accuracy of strain determination in the future. The strain profiles observed in this study are generally consistent with those predicted by analytical and computational analyses of cartilage indentation. The major findings of strains that are compressive axially and tensile laterally (Figs. 3A, B, D, and E) are consistent with theoretical predictions (Haider and Holmes 1995, 1997; Spilker et al., 1992). In addition, the areas of strain concentrations found experimentally are also consistent with predictions of the past studies. For 3-D indentation using a plane-ended cylinder (analogous to rectangular prismatic indenter here), the peak axial strain (similar to Emin here) was predicted to occur along the cartilage surface near the edge of the indenter (Spilker et al., 1992), similar to the present
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experimental findings (Fig. 4B). For indentation using a sphere-ended indenter (analogous to cylindrical indenter used here), largest axial stresses (proportional to Emin here) were predicted to occur along the cartilage surface directly under the indenter (Hayes et al., 1972). This prediction is also similar to the present results (Fig. 4E). In contrast, the experimentally determined strain profiles along the depth of cartilage were somewhat different from those predicted by certain theoretical analyses. For indentation with a plane-ended cylinder of a homogeneous, isotropic, and linearly elastic material (Haider and Holmes, 1997), the theoretical axial strain values along the centerline (at Y ¼ 0 mm) was constant with depth. For a computational simulation of rapid indentation (with a plane-ended cylindrical indenter) of a homogeneous, isotropic and biphasic material (Spilker et al., 1992), the magnitude of axial solid stress (proportional to strain) near the centerline is the highest at the surface, decreases to a somewhat constant value in the middle, then decreases to the minimum in the deep layers of cartilage. This suggests that indentation testing may be affected by complex features of articular cartilage such as depth-dependent inhomogeneity (Kempson, 1982; Schinagl et al., 1996, 1997; Akizuki et al., 1986) and anisotropy (Woo et al., 1976), as well as indentation protocol (i.e., indentation depth, indenter size and geometry, and indentation rate). It would be useful to expand on the current study both experimentally, by testing the effect (Hayes et al., 1972) of aspect ratio (indenter radius/cartilage thickness) using different sizes of indenters, and theoretically, by comparing the present results to analytical and computational models of indentation that may allow estimation of depthvarying material parameters. Experimentally, the present configuration of an unconstrained 2-D indentation, while being similar to that of a 3-D indentation, does not model it exactly. With indentation to a particular depth, the resulting strain magnitude in the 3-D geometry would be greater than that in the 2-D geometry, since a greater applied stress is required for the 3-D case (Haider and Holmes, 1997). 3-D indentation is would be expected to induce hoop stress, which does not occur in the 2-D configuration. In addition, sample preparation for the 2-D geometry may affect the cartilage biomechanical behavior, due, for example, to severing of superficial tangential collagen network. The dependence of strain magnitude profiles on indentation depth and indenter geometry may be useful for assessing the biological effects of indentation compression on cartilage. At 40 mm indentation depth, the magnitudes of strain are on the order of 5%, a level that is likely to stimulate chondrocyte biosynthesis when applied dynamically (Jin et al., 2001; Kim et al., 1994; Sah et al., 1989). Using mild dynamic indentation protocol, applied with different indenter tips that result
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in different strain profiles (Fig. 4), it may be possible to target certain regions of cartilage for physical stimulation in vitro, for tissue engineering purposes for instance. In contrast, with a 190 mm indentation depth, strain profiles exhibited relatively large peak strain magnitudes of 25% or greater, above which may be injurious to chondrocytes (D’Lima et al., 2001; Kurz et al., 2001; Patwari et al., 2004) and extracellular matrix (Quinn et al., 2001; Thibault et al., 2002). The results of this study may also be useful for understanding to what factors indentation testing is sensitive. Past studies suggested that indentation stiffness of cartilage is highly sensitive to the structure (Bae et al., 2003) and material properties (Korhonen et al., 2002) of the superficial layer of cartilage. Such results are consistent with the spatial variations of strain found in this study, with strain concentration at and near the surface for the given sample and indenter geometry and size. Since mechanical integrity of the superficial layer deteriorates with osteoarthritis (Roberts et al., 1986), indentation testing is likely to be sensitive for such conditions as well. The present study has implications for development of effective clinical indentation probes and protocols. Parameters for an indenter design may include tip geometry and size, indentation depth, and compression rate. An ‘‘optimal’’ probe design would require consideration of how each parameter affects certain characteristics of the probe, and the combined effects of the parameters. Visualization of cartilage deformation during indentation allows for direct assessment of mechanical effects of such design parameters. Safety is another important consideration in clinical use of indentation probes, and the present method of strain determination could help reduce the risk of mechanical damage due to poor design or protocol.
Acknowledgments This work was supported by grants from Arthritis Foundation. We thank Drs. M.K. Lotz (Scripps Research Institute), K. Yamada, and K. Kobayashi for providing cartilage samples. References Akizuki, S., Mow, V.C., Muller, F., Pita, J.C., Howell, D.S., Manicourt, D.H., 1986. Tensile properties of human knee joint cartilage: I. influence of ionic conditions, weight bearing, and fibrillation on the tensile modulus. Journal of Orthopaedic Research 4, 379–392. Armstrong, C.G., Lai, W.M., Mow, V.C., 1984. An analysis of the unconfined compression of articular cartilage. Journal of Biomechanical Engineering 106, 165–173. Athanasiou, K.A., Rosenwasser, M.P., Buckwalter, J.A., Malinin, T.I., Mow, V.C., 1991. Interspecies comparisons of in situ intrinsic
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mechanical properties of distal femoral cartilage. Journal of Orthopaedic Research 9, 330–340. Bae, W.C., Temple, M.M., Amiel, D., Coutts, R.D., Niederauer, G.G., Sah, R.L., 2003. Indentation testing of human cartilage: Sensitivity to articular surface degeneration. Arthritis and Rheumatism 48, 3382–3394. Bay, B.K., 1995. Texture correlation: a method for the measurement of detailed strain distributions within trabecular bone. Journal of Orthopaedic Research 13, 258–267. Black, J., Shadle, C.A., Parsons, J.R., Brighton, C.T., 1979. Articular cartilage preservation and storage. II. Mechanical indentation testing of viable, stored articular cartilage. Arthritis and Rheumatism 22, 1102–1108. Chahine, N.O., Wang, C.C., Hung, C.T., Ateshian, G.A., 2004. Anisotropic strain-dependent material properties of bovine articular cartilage in the transitional range from tension to compression. Journal of Biomechanics 37, 1251–1261. Chen, A.C., Bae, W.C., Schinagl, R.M., Sah, R.L., 2001a. Depth- and strain-dependent mechanical and electromechanical properties of full-thickness bovine articular cartilage in confined compression. Journal of Biomechanics 34, 1–12. Chen, S.S., Falcovitz, Y.H., Schneiderman, R., Maroudas, A., Sah, R.L., 2001b. Depth-dependent compressive properties of normal aged human femoral head articular cartilage. Osteoarthritis and Cartilage 9, 561–569. Chu, T.C., Ranson, W.F., Sutton, M.A., Peters, W.H., 1985. Applications of digital image correlation techniques to experimental mechanics. Experimental Mechanics 25, 232–244. Ciavarella, M., Hills, D.A., Monno, G., 1998. The influence of rounded edges on indentation by a flat punch. Proceedings of the Institute for Mechanical Engineers 212 (Part C), 319–328. D’Lima, D.D., Hashimoto, S., Chen, P.C., Lotz, M.K., Colwell Jr., C.W., 2001. Cartilage injury induces chondrocyte apoptosis. Journal of Bone and Joint Surgery-American 83A (Suppl. 2), 19–21. Eringen, A.C., 1967. Mechanics of Continua. Wiley, New York. Ewers, B.J., Dvoracek-Driksna, D., Orth, M.W., Haut, R.C., 2001. The extent of matrix damage and chondrocyte death in mechanically traumatized articular cartilage explants depends on rate of loading. Journal of Orthopaedic Research 19, 779–784. Frank, E.H., Grodzinsky, A.J., 1987. Cartilage electromechanics-I. Electrokinetic transduction and the effects of electrolyte pH and ionic strength. Journal of Biomechanics 20, 615–627. Frank, E.H., Grodzinsky, A.J., Koob, T.J., Eyre, D.R., 1987. Streaming potentials: a sensitive index of enzymatic degradation in articular cartilage. Journal of Orthopaedic Research 5, 497–508. Frank, R.L., Wong, E.C., Luh, W., Ahn, J.M., Resnick, D., 1999. Articular cartilage in the knee: mapping of the physiologic parameters at MR imaging with a local gradient coil-preliminary results. Radiology 210, 241–246. Franz, T., Hasler, E.M., Hagg, R., Weiler, C., Jakob, R.P., MainilVarlet, P., 2001. In situ compressive stiffness, biochemical composition, and structural integrity of articular cartilage of the human knee joint. Osteoarthritis and Cartilage 9, 582–592. Fung, Y.C., 1977. A first course in continuum mechanics. PrenticeHall, Englewood Cliffs p 340. Gonzalez, J., Knauss, W.G., 1998. Strain inhomogeneity and discontinuous crack growth in a particulate composite. Journal of Mechanics and Physics of Solids 46, 1981–1995. Grodzinsky, A.J., Frank, E.H., 1990. Electromechanical and physicochemical regulation of cartilage strength and metabolism. In: Hukins, D.W.L. (Ed.), Connective tissue matrix volume II. Topics in molecular and structural biology. CRC Press, Boca Raton, pp. 91–126. Haider, M.A., Holmes, M.H., 1995. Indentation of a thin compressible elastic layer-approximate analytic and numerical solutions for rigid
flat indenters. Journal of Mechanics and Physics of Solids 43, 1199–1219. Haider, M.A., Holmes, M.H., 1997. A mathematical approximation for the solution of a static indentation test. Journal of Biomechanics 30, 747–751. Hale, J.E., Rudert, M.J., Brown, T.D., 1993. Indentation assessment of biphasic mechanical property deficits in size-dependent osteochondral defect repair. Journal of Biomechanics 26, 1319–1325. Hayes, W.C., Keer, L.M., Herrmann, K.G., Mockros, L.F., 1972. A mathematical analysis for indentation tests of articular cartilage. Journal of Biomechanics 5, 541–551. Jin, M., Frank, E.H., Quinn, T.M., Hunziker, E.B., Grodzinsky, A.J., 2001. Tissue shear deformation stimulates proteoglycan and protein biosynthesis in bovine cartilage explants. Archives of Biochemistry and Biophysics 395, 41–48. Johnson, S., McNally, D., Halliwell, M., 2002. High-frequency ultrasound imaging of the intervertebral disc. Ultrasound in Medicine and Biology 28, 939–947. Kempson, G.E., 1982. Relationship between the tensile properties of articular cartilage from the human knee and age. Annals of the Rheumatic Diseases 41, 508–511. Kempson, G.E., Freeman, M.A.R., Swanson, S.A.V., 1971a. The determination of a creep modulus for articular cartilage by indentation tests of the human femoral head. Journal of Biomechanics 4, 239–250. Kempson, G.E., Spivey, C.J., Swanson, S.A., Freeman, M.A.R., 1971b. Patterns of cartilage stiffness on normal and degenerate human femoral heads. Journal of Biomechanics 4, 597–609. Kiefer, G.N., Sunbdy, K., McAllister, D., Shrive, N.G., Frank, C.B., Lam, T., Schachar, N.S., 1989. The effect of cryopreservation on the biomechanical behavior of bovine articular cartilage. Journal of Orthopaedic Research 7, 494–501. Kim, Y.J., Sah, R.L., Grodzinsky, A.J., Plaas, A.H.K., Sandy, J.D., 1994. Mechanical regulation of cartilage biosynthetic behavior: physical stimuli. Archives of Biochemistry Biophysics 311, 1–12. Korhonen, R.K., Wong, M., Arokoski, J., Lindgren, R., Helminen, H.J., Hunziker, E.B., Jurvelin, J.S., 2002. Importance of the superficial tissue layer for the indentation stiffness of articular cartilage. Medical Engineering and Physics 24, 99–108. Kurz, B., Jin, M., Patwari, P., Cheng, D.M., Lark, M.W., Grodzinsky, A.J., 2001. Biosynthetic response and mechanical properties of articular cartilage after injurious compression. Journal of Orthopaedic Research 19, 1140–1146. Lyyra, T., Jurvelin, J., Pitkanen, P., Vaatainen, U., Kiviranta, I., 1995. Indentation instrument for the measurement of cartilage stiffness under arthroscopic control. Medical Engineering and Physics 17, 395–399. Lyyra-Laitinen, T., Niinimaki, M., Toyras, J., Lindgren, R., Kiviranta, I., Jurvelin, J.S., 1999. Optimization of the arthroscopic indentation instrument for the measurement of thin cartilage stiffness. Physics in Medicine and Biology 44, 2511–2524. Mak, A.F., Lai, W.M., Mow, V.C., 1987. Biphasic indentation of articular cartilage—I. Theoretical analysis. Journal of Biomechanics, 20, 703–714. McKinley, T.O., Bay, B.K., 2003. Trabecular bone strain changes associated with subchondral stiffening of the proximal tibia. Journal of Biomechanics 36, 155–163. Mow, V.C., Kuei, S.C., Lai, W.M., Armstrong, C.G., 1980. Biphasic creep and stress relaxation of articular cartilage in compression: theory and experiment. Journal of Biomechanical Engineering 102, 73–84. Mow, V.C., Gibbs, M.C., Lai, W.M., Zhu, W.B., Athanasiou, K.A., 1989. Biphasic indentation of articular cartilage-II. A numerical algorithm and an experimental study. Journal of Biomechanics 22, 853–861.
ARTICLE IN PRESS W.C. Bae et al. / Journal of Biomechanics 39 (2006) 1039–1047 Narmoneva, D.A., Wang, J.Y., Setton, L.A., 1999. Nonuniform swelling-induced residual strains in articular cartilage. Journal of Biomechanics 32, 401–408. Niederauer, M.Q., Cristante, S., Niederauer, G.M., Wilkes, R.P., Singh, S.M., Messina, D.F., Walter, M.A., Boyan, B.D., 1998. A novel instrument for quantitatively measuring the stiffness of articular cartilage. Transactions of the Orthopaedic Research Society 23, 905. Patwari, P., Gaschen, V., James, I.E., Berger, E., Blake, S.M., Lark, M.W., Grodzinsky, A.J., Hunziker, E.B., 2004. Ultrastructural quantification of cell death after injurious compression of bovine calf articular cartilage. Osteoarthritis and Cartilage 12, 245–252. Peters, W.H., Ranson, W.F., 1981. Digital imaging techniques in experimental stress analysis. Optical Engineering 21, 427–431. Peterson, L., Brittberg, M., Kiviranta, I., Akerlund, E.L., Lindahl, A., 2002. Autologous chondrocyte transplantation Biomechanics and long-term durability. American Journal of Sports Medicine 30, 2–12. Quinn, T.M., Allen, R.G., Schalet, B.J., Perumbuli, P., Hunziker, E.B., 2001. Matrix and cell injury due to sub-impact loading of adult bovine articular cartilage explants: effects of strain rate and peak stress. Journal of Orthopaedic Research 19, 242–249. Roberts, S., Weightman, B., Urban, J., Chappell, D., 1986. Mechanical and biochemical properties of human articular cartilage in osteoarthritic femoral heads and in autopsy specimens. Journal of Bone and Joint Surgery-British 68-B, 278–288. Sah, R.L., Kim, Y.J., Doong, J.H., Grodzinsky, A.J., Plaas, A.H.K., Sandy, J.D., 1989. Biosynthetic response of cartilage explants to dynamic compression. Journal of Orthopaedic Research 7, 619–636. Schinagl, R.M., Ting, M.K., Price, J.H., Sah, R.L., 1996. Video microscopy to quantitate the inhomogeneous equilibrium strain within articular cartilage during confined compression. Annals of Biomedical Engineering 24, 500–512. Schinagl, R.M., Gurskis, D., Chen, A.C., Sah, R.L., 1997. Depthdependent confined compression modulus of full-thickness bovine articular cartilage. Journal of Orthopaedic Research 15, 499–506. Schreier, H.W., Braasch, J.R., Sutton, M.A., 2000. Systematic errors in digital image correlation caused by intensity interpolation. Optical Engineering 39, 2915–2921. Soltz, M.A., Ateshian, G.A., 2000. A conewise linear elasticity mixture model for the analysis of tension-compression nonlinearity in articular cartilage. Journal of Biomechanical Engineering 122, 576–586.
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Journal of Biomechanics 39 (2006) 1039–1047 www.elsevier.com/locate/jbiomech www.JBiomech.com
Indentation testing of human articular cartilage: Effects of probe tip geometry and indentation depth on intra-tissue strain Won C. Baea, Chad W. Lewisc, Marc E. Levenstond, Robert L. Saha,b, a
Department of Bioengineering, 9500 Gilman Dr., Mail Code 0412, University of California-San Diego, La Jolla, CA 92093-0412, USA b Department of Whitaker Institute of Biomedical Engineering, University of California-San Diego, La Jolla, CA, USA c Mechanical Engineering Department, Colorado State University, Fort Collins, CO, USA d George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA Accepted 17 February 2005
Abstract Experimental determination of intra-tissue deformation during clinically applicable rapid indentation testing would be useful for understanding indentation biomechanics and for designing safe indentation probes and protocols. The objectives of this study were to perform two-dimensional (2-D) indentation tests, using indenters and protocols that are analogous to those in clinically oriented probes, of normal adult-human articular cartilage in order to determine: (1) intra-tissue strain maps and regions of high strain magnitude, and (2) the effects on strain of indenter geometry (rectangular prismatic and cylindrical) and indentation depth (40–190 mm). Epifluorescence microscopy of samples undergoing indentation and subsequent video image correlation analysis allowed determination of strain maps. Regions of peak strain were near the ‘‘edges’’ of indenter contact with the cartilage surface, and the strain magnitude in these regions ranged from 0.05 to 0.30 in compression and shear, a range with known biological consequences. With increasing indentation displacement, strain magnitudes generally increased in all regions of the tissue. Compared to indentation using a rectangular prismatic tip, indentation with a cylindrical tip resulted in slightly higher peak strain magnitudes while influencing a smaller region of cartilage. These results may be used to refine clinical indenters and indentation protocols. r 2005 Elsevier Ltd. All rights reserved. Keywords: Cartilage; Biomechanics; Indentation; Strain; Clinical; Diagnosis
1. Introduction Short-duration indentation testing has shown potential as a diagnostic tool for assessing the health and function of human articular cartilage. Such indentation testing allows for non-destructive, quick, and quantitative assessment of cartilage function and biomechanical properties, and has been used in a number of studies (Kempson et al., 1971a, b; Lyyra et al., 1995; Swann and Seedhom, 1993). Rapid indentation testing has also been Corresponding author. Department of Bioengineering, 9500 Gilman Dr., Mail Code 0412, University of California-San Diego, La Jolla, CA 92093-0412, USA. Tel.: +858 534 0821; fax: +858 822 1614. E-mail address: [email protected] (R.L. Sah).
0021-9290/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2005.02.018
used to gauge the extent of cartilage degeneration (Bae et al., 2003; Franz et al., 2001; Roberts et al., 1986) and repair (Peterson et al., 2002) after surgical procedures, complementing in vitro equilibrium indentation tests (Mak et al., 1987; Mow et al., 1989; Hale et al., 1993). Recently, clinical arthroscopic probes utilizing shortduration indentation protocols have been developed (Lyyra et al., 1995; Lyyra-Laitinen et al., 1999; Niederauer et al., 1998), and used to test human articular cartilage of the knee. Such arthroscopic probes are typically fitted with a plane-ended (Lyyra et al., 1995) or a sphere-ended (Bae et al., 2003; LyyraLaitinen et al., 1999) indenter tip with a diameter in the order of 0.5–1.0 mm (Lyyra et al., 1995; LyyraLaitinen et al., 1999). This indenter dimension is
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somewhat less than the cartilage thickness of the femoral condyle, which is in the order of 2 mm (Bae et al., 2003). Typical loading protocols for these probes induce an indentation displacement (depth from the indented surface) of 100–300 mm (Bae et al., 2003; Lyyra et al., 1995; Lyyra-Laitinen et al., 1999). However, it is unclear how the choices of indenter design and indentation protocols affect indentation biomechanics. Classical biomechanical experiments on cartilage have relied on controlling or measuring sample surface displacement, and inferring material properties based on models that often employ simplifying assumptions such as homogeneity. For example, from experiments such as confined and unconfined compression testing, material properties were obtained using homogeneous biphasic/poroelastic models (Armstrong et al., 1984; Frank and Grodzinsky, 1987; Mow et al., 1980). Efforts have been made to incorporate the inhomogeneous nature of cartilage into these models (Chen et al., 2001a; Grodzinsky and Frank, 1990). Depth-varying biomechanical properties of cartilage under these testing configurations were elucidated by two-dimensional (2-D) measurements of intra-tissue cartilage deformation (Chen et al., 2001b; Schinagl et al., 1997, 1996; Wang et al., 2002). Complex cartilage material properties such as inhomogeneity (Schinagl et al., 1996, 1997) and tension–compression non-linearity (Soltz and Ateshian, 2000) are likely to influence indentation mechanics as well. Determination of intra-tissue strain would be useful for characterizing the actual behavior of cartilage during indentation, as well as for refining theoretical models. In order to elucidate intra-tissue deformation, 2-D biomechanical testing configurations, analogous to their three-dimensional (3-D) counter-parts, may be utilized. For example, intra-tissue deformation during confined compression testing has been assessed by bisecting the sample vertically and examining the cut-plane (Wang et al., 2002; Chen et al., 2001b; Schinagl et al., 1996, 1997). Similar approaches may be taken for indentation testing. For example, a vertical bisection during a 3-D indentation of cartilage surface using a plane-ended cylinder would reveal rectangular cut-planes for both the indenter and the sample. Therefore, an indentation test using simpler geometry of rectangular prismatic tip compressing a rectangular sample, with a constrained side to prevent out-of-plane motion (i.e., sample and indenter placed on a smooth glass surface), would exhibit the main features of intra-tissue deformation that occurs in the 3-D counter-part. For 3-D indentation with a sphere-ended tip, an analogous but simpler configuration would be an indentation with the roundedge of a cylindrical indenter (Fig. 1). A number of methods exist for determining in-plane strain based on images representing the structures of the
Fig. 1. Two-dimensional indentation testing setup using a cylindrical tip.
undeformed and deformed tissue. Early approaches utilized computer-assisted identification and tracking of discrete features (markers) of samples in reference and deformed states (Narmoneva et al., 1999; Schinagl et al., 1997, 1996). More recently, video image correlation (VIC) method was introduced for non-contact 2-D strain analysis (Peters and Ranson, 1981) of nonbiological materials (Chu et al., 1985). The VIC method numerically compares reference and deformed images and determines sample displacement and strain maps. VIC has also been used for biological tissues such as bone (Bay, 1995; McKinley and Bay, 2003; Verhulp et al., 2004), retina (Wu et al., 1987), and cartilage in unconfined compression testing (Wang et al., 2002; Chahine et al., 2004). The magnitude of intra-tissue strain has implications for cartilage biology, including metabolism and injury. Relatively low strain magnitudes of 5%, applied dynamically in compression (Kim et al., 1994; Sah et al., 1989) or shear (Jin et al., 2001) stimulate chondrocyte biosynthesis. However, higher strain magnitudes can be injurious to cartilage and cells. With axial compression of 25%, matrix damage occurs at molecular level (Thibault et al., 2002). With 30% axial compression, cell death occurs (D’Lima et al., 2001; Kurz et al., 2001; Patwari et al., 2004). At 40% compression, physical disruption such as fissuring occurs (Quinn et al., 2001). While an indentation compression theoretically results in stress and strain concentrations in cartilage near certain areas of indenter contact (Ciavarella et al., 1998), direct experimental determination of such strains have not been reported. Since an indentation test induces strain in cartilage, and the magnitude and location of intra-tissue strain have a number of biological and clinical implications, intra-tissue strain would be useful to characterize in human articular cartilage in a clinical indentation test scenario. The objectives of this study were to perform 2-D indentation tests, analogous to clinically applicable 3-D indentation tests, on normal human articular cartilage, and to determine (1) intra-tissue strain maps
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and locations of high strain magnitudes, and (2) the effect on strain of indenter geometry and indentation depth.
2. Materials and methods 2.1. Samples Ten millimeter diameter osteochondral cores were harvested from the anterior region of the lateral and medial femoral condyles of three young cadaveric human donors (21 years old, mean age), using a surgical coring device (OATSTM, Arthrex, Naples, FL). The cores had a normal articular surface appearance without erosion or roughening, as described previously (Bae et al., 2003). Briefly, each core was immersed in a solution (Frank et al., 1987) of phosphate-buffered saline and proteinase inhibitors (PBS+PI) at 4 1C for 1 h, and then stored at 70 1C until testing. On the day of testing, the cores were thawed, trimmed to a rectangular block (10 10 2.5 mm3, W L H, with the articular surface parallel to the Y–Z plane, Fig. 1), and immersed for 12 h at 4 1C in a solution of PBS+PI and propidium iodide (0.02 mg/ml) to stain nuclei. Although previously frozen samples were used, past studies found short-duration indentation stiffness measurements are not affected by a freeze-thaw cycle (Black et al., 1979; Kempson et al., 1971a, b; Kiefer et al., 1989; Swann and Seedhom, 1993).
Fig. 2. Video image correlation was performed on (A) reference and (B) indented images, each magnified in (C) and (D), respectively to show detail, by comparing (E, F) smaller patches, known as subsets. Bars ¼ 200 mm.
2.2. Indentation testing and epifluorescence imaging Each sample was mounted in a glass-bottomed chamber (Fig. 1) filled with PBS+PI such that a cartilage/bone surface was in contact with the glass, and the articular surface oriented perpendicular to the direction of indentation (+Z, Fig. 1). The articular surface of each block was indented at the centerline (Y ¼ 0, Fig. 1) using both a 1-mm wide rectangular prismatic indenter (with a rectangular cross-section) and a 1-mm diameter cylindrical indenter (with a circular cross-section), each fabricated from impermeable stainless steel. In this configuration, the intra-tissue deformation would theoretically be symmetric about the centerline and would be exhibited on the bottom of the chamber. Dynamic indentation protocol consisted of a single application of an indentation displacement up to 200 mm at 130 mm/s. Digital epifluorescence microscopic images (768 512 pixels in a field of view, FOV, of a 2.9 2.1 mm2 area, at 8-bit grayscale) were acquired before (Figs. 2A, C, and E) and during (Figs. 2B, D, and F) indentation, at indentation depths of 3573, 8574, 14176, and 190713 mm (1.9, 4.9, 7.7, and 10.4% of the 1.8370.15 mm average cartilage thickness) and denoted as 40, 90, 140, and 190 mm, respectively, in the
text. A pilot study confirmed that visible focus was maintained +20 mm (in the x-direction) from the initial focal plane during indentation. The duration between indentation tests with the tips of different geometry was 30 min, which was sufficient to allow nearly full recovery (average change in thickness between testing was 715 mm, oro71% of average sample thickness). The order of testing between different tip geometries was randomized. 2.3. VIC and determination of strain maps A commercial program (VIC2D, Correlated Solutions, Inc., West Columbia, SC) was used to implement VIC analysis, whose theoretical foundation has been described previously (Sutton et al., 2000). Briefly, the software compares digital images of the reference (Figs. 2A and C) and deformed (Figs. 2B and D) samples in small patches, known as subsets (Figs. 2E and F), which contain unique patterns of pixel intensities. Assuming that there exists a one-to-one correspondence between the pixels in the reference and the deformed subsets, and that the subset region deforms linearly, the displacement of the reference
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subset can be determined computationally, using normalized cross-correlation (Sutton et al., 2000) optimized with the Newton–Raphson method (Chu et al., 1985; Sutton et al., 1983, 1986) and quintic B-spline interpolation (Unser, 1993a, b). Multiple discrete subsets are analyzed in this way to determine the displacement of the center point of each subset, and collectively, a displacement map relative to the reference image. In the present study, incremental displacement maps were determined by comparing pairs of successive images (taken at indentation depths of 0, 40, 90, and 140 mm). A binomial low-pass filter was applied to reduce interpolation bias, typically present for fluorescence images with a bimodal gray intensity distribution (Schreier et al., 2000). Overlapping subsets (41 41 pixels), spaced 5 pixels center-to-center (i.e., ‘‘step-size’’ in both Y- and Z-directions), were analyzed for a total of 15 000 subsets per image set. (Larger subset-size generally increases displacement accuracy until the large size begins to invalidate linearity assumption, while smaller step-size increases both noise and computation time.) In the present study, subset- and step-sizes were chosen such that displacement maps for simulated data sets (rigid body motion) gave accurate (within 0.5% of expected results) and smooth (standard deviation of o1 mm) results. Displacement maps relative to the reference state were determine by adding up the incremental displacement maps, while interpolating (i.e., re-mapping) the displacement maps to the reference to reference coordinates (Gonzalez and Knauss, 1998). Subsequently, strain maps were determined from the displacement maps. Using Matlab 6.5 software (MathWorks, Natick, MA), the displacement gradient at a point was determined as a bilinear least-squares fit of the displacements in a local neighborhood of 45 45 pixels (or 170 170 mm2) centered about the point. Assuming that out-of-plane shear strains were negligible, partial derivatives of the bilinear fit were used to determine in-plane, 2-D Lagrangian principal strain components (Eringen, 1967, Fung, 1977) of Emin (minimum in-plane principal strain), Emax (maximum in-plane principal strain), and Eshear (maximum in-plane shear) at each indentation depth relative to the reference state (i.e., strains at indentation depths of 40, 90, 140, and 190 mm, each relative to 0 mm depth). The maximum and minimum in-plane principal directions (Eringen, 1967) were then determined as ymin and ymax. The method of strain calculation was validated using digitally deformed cartilage images reflecting prescribed axial, lateral and shear strains of 2–10%, as well as rigid body translation (in Y- and Z-directions) of 100–200 mm. The strain values calculated from these digitally deformed and translated images were accurate to within 0.4% of the expected values.
2.4. Statistics For each in-plane principal strain magnitude (Emin, Emax, and Eshear) and direction (ymin and ymax), indentation depth (40, 90, 140, and 190 mm), and indenter geometry (rectangular prismatic and cylindrical), an average strain map for the three samples was determined. To achieve this, the strain maps were aligned about a point along the articular surface intersecting the centerline of the indenter (Y ¼ 0, Fig. 3), and then averaged at all overlapping image pixel coordinates. While the strain maps were not normalized to cartilage thickness, inter-sample thickness variation was small (CV ¼ 0.08) and normalized maps would not be much different since the strain near the bone was negligibly small. The in-plane principal directions of ymin and ymax were shown as arrows, respectively overlaid onto the average maps of Emin and Emax (Figs. 3A, B, D, and E). In addition, the effects of indentation depth (4 levels) and indenter geometry on the strain values were assessed at certain regions of the maps using a two-way repeated measures analysis of variance (ANOVA). The regions of interest were near and along the superficial (at Y ¼ 0, 0.25, 0.5, and 1.0 mm and Z ¼ 0:1 mm), middle (at Y ¼ 0, 0.5, and 1.0 mm and Z ¼ 0:75 mm), and deep (at Y ¼ 0 mm and Z ¼ 1:5 mm) layers of cartilage, assuming an axial symmetry about the centerline (Y ¼ 0 mm). Data are presented as mean7SEM unless noted otherwise.
Fig. 3. Strain magnitude maps from indentation tests using (A–C) rectangular prismatic and (D–F) cylindrical indenters. Lagrangian strain components of (A, D) Emin, (B, E) Emax, and (C, F) Eshear, were plotted for indentation displacements of (i) 40, (ii) 90, (iii) 140, and (iv) 190 mm. Specific regions, a–f, on the maps are referred to in the text.
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3. Results 3.1. Spatial map of strain Strain profiles varied greatly as a function of position relative to the indenter (Fig. 3) and the geometry of the indenter. For indentation with the rectangular prismatic tip, Emin was compressive, generally high in magnitude in the areas of cartilage under and near the indenter (areas a and b, Fig. 3A-iv), and the greatest in area a directly under the indenter edges (0.1870.02 at [Y ¼ 0:5 mm, Z ¼ 0:1 mm], Fig. 3A-iv). For the same samples, Emin values diminished with cartilage depth, being in the range of 0.05 to 0 in area c near the bone (0.0370.01 at [0 mm, 1.5 mm], Fig. 3A-iv), and in area d, far away from the centerline (0.0570.01 at [0.75 mm, 0.75 mm], Fig. 3A-iv). In addition, Emax was tensile and high in magnitude (0.07–0.10) in areas a and b (Fig. 3B-iv) while being relatively low (0.03) in areas c and d (Fig. 3B-iv), with a magnitude profile similar to that of Emin. However, the range of strain values was not as large as that seen in the Emin profile. The spatial variations in Eshear was also similar to that of Emin, with the maximum values found in area a (0.1470.01 at [0.5 mm, 0.1 mm], Fig. 3C-iv) and diminishing with distance away from the indenter and centerline. For indentation with the round-edged cylindrical tip (Figs. 3D–F), the general profile of each strain component was similar to that for indentation with the rectangular prismatic tip, with a few notable differences. Whereas the indentation with the rectangular prismatic tip produced two fixed areas of high strain magnitude near the edge of the indenter at area a, those produced by indentation with the cylindrical tip were more central, indicated by area e at [0 mm, 0.1 mm] and f at [0.25 mm, 0.1 mm] (Figs. 3D-, E-, and F-iv). In addition, the cylindrical indenter qualitatively deformed both a narrower (smaller range of |Y|) and shallower (smaller range of Z) region of cartilage compared to the indentation using a rectangular prismatic indenter. The in-plane principal directions (arrows in Figs. 3A, B, D, and E) indicated that Emin, compressive strain, was mainly in the axial direction, while Emax, tensile strain, was mainly in the lateral direction. The profiles of intra-tissue strain along with the in-plane principal directions suggested that as the indenter tips compressed the cartilage surface, the bulk tissue compressed vertically and expanded laterally while also undergoing a shear deformation. 3.2. Effects of indentation displacement and indenter geometry Indentation depth and indenter geometry had significant effects on strain components in various parts of the cartilage.
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Near the Surface. At central areas near the surface (at [jY j ¼ 0; 0:25, and 0.5 mm, Z ¼ 0:1 mm], Fig. 3), for strain components of Emin, Emax, and Eshear, increasing indentation depth generally increased (all po0:051) strain magnitudes in these areas, in a geometrydependent manner (po0:01 to p ¼ 0:1). Strain magnitudes beneath the indenter center (at [jY j ¼ 0 mm, Z ¼ 0:1 mm], Fig. 3) tended to be higher for the cylindrical indenter (po0:13), while the magnitudes at jY j ¼ 0:5 mm and Z ¼ 0:1 mm, Fig. 3, were significantly higher for the rectangular prismatic indenter (all po0:05). Middle Layer. At areas in the middle layer of cartilage (at [jY j ¼ 0, 0.5 and 0.75 mm, Z ¼ 0:75 mm], Fig. 3), increasing indentation depth significantly increased (all po0.01) the magnitude of all strain components. Strain magnitudes resulting from the rectangular prismatic tip were generally higher than those from the cylindrical tip, especially at [jY j ¼ 0:5, and 0.75 mm, Z ¼ 0:1 mm] (p ¼ 0:010:1). Deep Layer. At deep regions of cartilage (at [jY j ¼ 0 mm, Z ¼ 1:5 mm], Fig. 3), the strain magnitudes of Emin, Emax, and Eshear increased with indentation depth and were generally higher for the rectangular prismatic tip (all po0:05), without significant interactive effects.
4. Discussion In the present study, intra-tissue deformation in human articular cartilage was investigated during short-duration indentation testing. The profiles of intra-tissue strain components were determined (Fig. 3) and the effects of indentation depth and indenter geometry, important parameters in the design of clinical indentation probes and protocols, on strain magnitude were assessed. At a given indentation depth, strain magnitudes were generally high near the ‘‘edge’’ of the indenter (i.e., where it separates from the cartilage surface, at [0.5 mm, 0.1 mm] for the rectangular prismatic indenter, Fig. 4B, and at [Y ¼ 00:25 mm, Z ¼ 0:1 mm] for the cylindrical indenter, Fig. 4E) and low in areas far from either the centerline (at Y ¼ 0 mm) or cartilage surface (at Z ¼ 0 mm). Strain magnitudes generally increased with depth of indentation in all areas (Figs. 3 and 4). Use of the cylindrical tip (relative to rectangular prismatic tip) resulted in slightly higher strain magnitudes near the surface, but lower values in many other areas of the tissue (Fig. 3). Epifluorescence video microscopy and VIC analysis were effective for obtaining information about rapid cartilage deformation in 2-D. The present optical technique allowed for imaging resolution sufficiently high (i.e., 4 mm/pixel) and rate that was adequate (i.e., 5 frames per second), compared to other biomedical
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Fig. 4. Strain profiles resulting from indentation test with (A–C) rectangular prismatic and (D–F) cylindrical indenters. The profiles were taken (A, D) along the cartilage surface, (B, E) with depth along the centerline, and (C, F) with depth along the approximate contacting edge of indenter with cartilage surface, which was approximately at Y ¼ 0:5 and 0.25 mm for rectangular prismatic and cylindrical indenters, respectively.
imaging techniques (e.g., magnetic resonance imaging with a slower scan time (Frank et al., 1999) and ultrasound with lower spatial resolution (Johnson et al., 2002)). VIC analysis of optical images, while not as direct as the methods that track fiducial markers (Chen et al., 2001b; Schinagl et al., 1996), enables rapid determination of 2-D maps of deformation and strain. In addition, the accuracy of the VIC method, with error in strain values of 0.1% or less, found in this study was in agreement with past studies (Sutton et al., 2000; Wang et al., 2002). The present study utilized a particular compression rate and the results from using other compression rates would likely be different. Due to the biphasic/poroelastic nature of cartilage (Frank and Grodzinsky, 1987; Mow et al., 1980), stress-relaxation occurs while the fluid in the tissue flows within and out of the tissue. The extent of stress-relaxation during the indentation may be elucidated by dimensional analysis of a characteristic equation (Frank and Grodzinsky, 1987; Mow et al., 1980) of a2 ¼ tH A kp , where a, t, H A , and kp represent the characteristic distance, characteristic time, aggregate modulus, and hydraulic permeability, respectively. Assuming reasonable values (Athanasiou et al., 1991) of H A and kp of 1 MPa and 1015 m4/N s, respectively, and using a of 0.5 mm (current indenter radius), t is computed to be 250 s. The present protocol used a compression rate of 130 mm/s to reach the maximum indentation depth of 190 mm in 1.5 s, much shorter than the characteristic time of 250 s. Thus, the majority of the tissue is likely to reflect an ‘‘instantaneous’’ type of loading response. In comparison, if a much lower compression rate of 0.1 mm/s were to be used to attain the same indentation depth, it would take 1900 s, and the bulk of tissue would have experienced stressrelaxation, and less strain concentration would be apparent (Spilker et al., 1992). In contrast, if a relatively
fast compression rate of 105 mm/s is used, it would take 0.02 s, and the tissue would exhibit very little fluid loss but greater localized strain near the superficial region. Such an effect may be responsible for greater physical disruption of the cartilage surface when the sample is compressed to a particular depth at increasing rate (Ewers et al., 2001). The current method of strain determination depended on a number of factors. VIC method introduces slight variability in displacement calculation due to subsetand step-size selection. Subsequently, strain determination from displacement can be affected by filtering (linear-fitting of neighboring displacement values). While necessary to suppress noise, filtering underestimates the strain magnitude should a sharp displacement gradient exist, as it may near the articular surface undergoing indentation. Nonetheless, the present methods were reasonably accurate (as determined using validation images with known deformation) when the displacement gradient was not severe. Other smoothing methods, such as thin-plate spline smoothing (Wang et al., 2002), could improve further the accuracy of strain determination in the future. The strain profiles observed in this study are generally consistent with those predicted by analytical and computational analyses of cartilage indentation. The major findings of strains that are compressive axially and tensile laterally (Figs. 3A, B, D, and E) are consistent with theoretical predictions (Haider and Holmes 1995, 1997; Spilker et al., 1992). In addition, the areas of strain concentrations found experimentally are also consistent with predictions of the past studies. For 3-D indentation using a plane-ended cylinder (analogous to rectangular prismatic indenter here), the peak axial strain (similar to Emin here) was predicted to occur along the cartilage surface near the edge of the indenter (Spilker et al., 1992), similar to the present
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experimental findings (Fig. 4B). For indentation using a sphere-ended indenter (analogous to cylindrical indenter used here), largest axial stresses (proportional to Emin here) were predicted to occur along the cartilage surface directly under the indenter (Hayes et al., 1972). This prediction is also similar to the present results (Fig. 4E). In contrast, the experimentally determined strain profiles along the depth of cartilage were somewhat different from those predicted by certain theoretical analyses. For indentation with a plane-ended cylinder of a homogeneous, isotropic, and linearly elastic material (Haider and Holmes, 1997), the theoretical axial strain values along the centerline (at Y ¼ 0 mm) was constant with depth. For a computational simulation of rapid indentation (with a plane-ended cylindrical indenter) of a homogeneous, isotropic and biphasic material (Spilker et al., 1992), the magnitude of axial solid stress (proportional to strain) near the centerline is the highest at the surface, decreases to a somewhat constant value in the middle, then decreases to the minimum in the deep layers of cartilage. This suggests that indentation testing may be affected by complex features of articular cartilage such as depth-dependent inhomogeneity (Kempson, 1982; Schinagl et al., 1996, 1997; Akizuki et al., 1986) and anisotropy (Woo et al., 1976), as well as indentation protocol (i.e., indentation depth, indenter size and geometry, and indentation rate). It would be useful to expand on the current study both experimentally, by testing the effect (Hayes et al., 1972) of aspect ratio (indenter radius/cartilage thickness) using different sizes of indenters, and theoretically, by comparing the present results to analytical and computational models of indentation that may allow estimation of depthvarying material parameters. Experimentally, the present configuration of an unconstrained 2-D indentation, while being similar to that of a 3-D indentation, does not model it exactly. With indentation to a particular depth, the resulting strain magnitude in the 3-D geometry would be greater than that in the 2-D geometry, since a greater applied stress is required for the 3-D case (Haider and Holmes, 1997). 3-D indentation is would be expected to induce hoop stress, which does not occur in the 2-D configuration. In addition, sample preparation for the 2-D geometry may affect the cartilage biomechanical behavior, due, for example, to severing of superficial tangential collagen network. The dependence of strain magnitude profiles on indentation depth and indenter geometry may be useful for assessing the biological effects of indentation compression on cartilage. At 40 mm indentation depth, the magnitudes of strain are on the order of 5%, a level that is likely to stimulate chondrocyte biosynthesis when applied dynamically (Jin et al., 2001; Kim et al., 1994; Sah et al., 1989). Using mild dynamic indentation protocol, applied with different indenter tips that result
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in different strain profiles (Fig. 4), it may be possible to target certain regions of cartilage for physical stimulation in vitro, for tissue engineering purposes for instance. In contrast, with a 190 mm indentation depth, strain profiles exhibited relatively large peak strain magnitudes of 25% or greater, above which may be injurious to chondrocytes (D’Lima et al., 2001; Kurz et al., 2001; Patwari et al., 2004) and extracellular matrix (Quinn et al., 2001; Thibault et al., 2002). The results of this study may also be useful for understanding to what factors indentation testing is sensitive. Past studies suggested that indentation stiffness of cartilage is highly sensitive to the structure (Bae et al., 2003) and material properties (Korhonen et al., 2002) of the superficial layer of cartilage. Such results are consistent with the spatial variations of strain found in this study, with strain concentration at and near the surface for the given sample and indenter geometry and size. Since mechanical integrity of the superficial layer deteriorates with osteoarthritis (Roberts et al., 1986), indentation testing is likely to be sensitive for such conditions as well. The present study has implications for development of effective clinical indentation probes and protocols. Parameters for an indenter design may include tip geometry and size, indentation depth, and compression rate. An ‘‘optimal’’ probe design would require consideration of how each parameter affects certain characteristics of the probe, and the combined effects of the parameters. Visualization of cartilage deformation during indentation allows for direct assessment of mechanical effects of such design parameters. Safety is another important consideration in clinical use of indentation probes, and the present method of strain determination could help reduce the risk of mechanical damage due to poor design or protocol.
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