optical and mechanical determination of …optical and mechanical determination of poisson’s ratio...

PII: ~21-92~(96~13~9

OPTICAL AND MECHANICAL DETERMINATION OF POISSON’S RATIO OF ADULT BOVINE HUMERAL ARTICULAR CARTILAGE

J. S. Jurvelin,*t M. D. Buschmannf and E. B. Hunziker*

* M. E. Miller Institute for Biomechanics, University of Bern, P.O. Box 30, CH-3010 Bern, Switzerland; i Department of Clinical Physiology and Nuclear Medicine, Kuopio University Hospital, Kuopio, Finland; and

$ Biomedical Engineering Institute, Ecole Polytechnique and Faculty of Medicine, University of Montreal, Montreal, PQ, Canada

Abstract-The equilibrium stiffness of articular cartilage is controlled by flow-independent elastic properties (Young’s modulus, Es, and Poisson’s ratio. us) of the hydrated tissue matrix. In the current study, an optical (microscopic) method has been developed for the visualization of the boundaries of cylindrical bovine humeral head articular cartilage disks (n = 9) immersed in physiological solution. and compressed in unconfined geometry. This method allowed a direct, model-independent estimation of Poisson’s ratio of the tissue at equilibrium, as well as characterization of the shape changes of the sample during the nonequilibrium dynamic phase. In addition to optical analyses, the equilibrium behavior of cartilage disks in unconfined and confined ramp-stress relaxation tests provided a direct estimation of the aggregate modulus, Ha, and Young’s modulus and, indirectly, Poisson’s ratio for the articular cartilage. The mean value for Poisson’s ratio obtained from the optical analysis was 0.185 f 0.065 (mean If: SD., n = 9). Values of elastic parameters obtained from the mechanical tests were 0.754 & 0.198 MPa, 0.677 k 0.223 MPa, and 0.174 f 0.106 for Ha, Es. and zis, respectively (mean k S.D., n = 7). The similar us-values obtained with optical and mechanical techniques imply that, at equilibrium, for these two tests, the isotropic model is acceptable for mechanical analysis. However, the microscopic technique revealed that the lateral expansion, especially during the initial phase of relaxation. was inhomogeneous through the tissue depth. The superficial cartilage zone expanded less than the radial zone. The zonal differences in expansion were attributed to the known zonal differences in the fibrillar collagen architecture and proteoglycan concentrati~~n. -i’ 1997 Elsevier Science Ltd. All rights reserved.

k’eyn~ds: Articular cartilage: Cartilage mechanics: Cartiiage material properties; Mechanical testing: Video

microscopy

INTRODUCTION

Adult articular cartilage is a structurally inhomogeneous and anisotropic tissue. The main constituents of the cartilage matrix, i.e. proteoglycans (PCs) and fibrillar collagens show zonal differences with respect to their concentration and structural arrangement. The concentration of PG (mainly aggrecan) is lowest in the superficial cartilage zone and increases in deeper zones of the cartilage (Jones et ul., 1977; Poole, 1993). Moreover, at any given depth from the articular surface, PG concentration can change as a function of the distance from the chondrocytes (Hunziker, 1992).

The content of collagen (mainly type II) within mature articular cartilage may vary less (Lipschitz et al., 1975; Muir et al., 1970), but the three-dimensional architecture of collagen shows an arcade-like organization consisting of tangential/horizontal fibril network in the superficial zone, a more randomly arranged fibrillar organization within the transitional zone and larger diameter fibres running principally in a vertical direction within the radial zone, through the calcified cartilage to the subchondral bone (Benninghof, 1922; Speer and Dahners, 1979). Due to this complex structure, mature articular cartilage is inhomogeneous and mechanically anisotropic. A significant compression-tension nonlinearity is also well known where the equilibrium stiffness can be

5-10 times larger in tension than in compression (Mow et al., 1992).

In mechanical studies, cartilage is typically modeled as homogeneous and isotropic tissue in order to reduce computational complexity. Elastic (Hayes er ul,, 1972), viscoelastic (Parsons and Black, 19773, and poroelastic (Biot, 1941) or biphasic (Mow et trf., 1980) models have been introduced for the theoretical analysis of dynamic cartilage mechanical behavior. The homogeneous isotropic biphasic model has been used successfully in the analysis of confined compression behavior of cartilage (Frank and Grodzinsky, 1987; Mow et al., 1980). In contrast, model predictions for dynamic tests in unconfined geometry were seen to be unsuccessful initially (Armstrong et al., 1984; Brown and Singermann, 1986). The source of disagreement has been ascribed to both experimental difficulties (Kim et L&, 1995; Spilker et at., 1990) as well as structural mechanisms, such as matrix viscoelasticity (Mak, 1987) or the tension~ompression nonlinearity (Cohen et ni., 1992) of the matrix. The lack of agreement between experiment and theory has limited the application of the unconfined test for the determination of Poisson’s ratio. The confined test, on the other hand, is inherently one-dimensional and, therefore, can- not be used alone for estimation of Poisson’s ratio.

The biphasic indentation technique (Mak et al., 1987: Mow et al., 1989) has provided a means for the evalu- ation of Poisson’s ratio. Although the indentation problem of a homogeneous isotropic model of articular cartilage does not completely agree with the high experimental dynamic stiffness of articular cartilage (Cohen

235

‘36 .I. S. Jurvelin rt ~11

LJ~ 111.; 1993) the technique has recently been applied extensively to determine, from a single indentation measurement, all three material parameters of the model, i.e. shear modulus, /cs, Poisson’s ratio, ls, and permeabil- ity, k, for in situ articular cartilage (Athanasiou et al., 199 1, 1994; Hale et al.. 1993; Schenck et ul., 1994: Setton ct LII., 1994). In general, the values of Poisson’s ratio derived from these analyses have been small and they vary with species, type of joint and the joint area analyzed. For example, the values of 0.098 & 0.069, 0.074 -t 0.084 and 0.00 + 0.00 (mean f S.D., II = 446) were determined for human knee articular cartilage of the lateral condyle, medial condyle and patellar groove of femur (Athanasiou et a/., 1991). Earlier, most values for Poisson’s ratio of articular cartilage were in the range 0.37-0.50, either experimentally determined or assumed for indentation analysis (Altman et al., 1984; Hayes and Mockros, 1971; Hori and Mockros, 1976; Hock et al., 1983; Jurvelin et al., 1987; Kempson et ul., 1971).

In this study, we present an optical method for record- ing the shape changes of bovine humeral head articular cartilage disks loaded in unconfined geometry. By applying constant axial strain for loading, the quantification of lateral strain at equilibrium makes possible a direct and essentially model-independent calculation of Poisson’s ratio for the cartilage matrix. In addition, we measure the stress relaxation behavior of humeral cartilage in confined and unconfined compression. By assum- ing material isotropy, we indirectly calculate Poisson’s ratio for the cartilage matrix from the equilibrium compression data. Comparison of the values of Poisson’s ratio obtained from optical and mechanical analyses thereby allows us to test the validity of a basic assumption of most mechanical models, i.e. isotropy of the cartilage matrix in compression. The optical measurement may also offer new information concerning depth-dependent inhomogeneities of intrinsic material properties.

MATERIALS AND METHODS

Intact shoulder joints of l-2 yr old cows (n = 12) were obtained within 24 h of slaughter from a local abattoir. The joint was opened, and a cylindrical cartilage disk from the central area of the humeral head was cut perpendicularly to the articular surface using a dermal biopsy punch (diameter: 6 mm). Subsequently, the full-thickness disk was removed from the subchondral bone by slicing horizontally with a razor blade and then punched to either 3.7 mm (mechanical analysis) or 1.8 mm diameter (microscopic analysis). During these procedures the cartilage was kept moistened with phos- phate-buffered saline (PBS). In total, 16 disks were pre- pared for immediate microscopic analyses (n = 9) or mechanical tests (n = 7). In addition, three 3.7 mm disks were frozen for the later microscopic analyses. The original thickness of the uncompressed disks was measured using a stereomicroscope (Jurvelin et al., 1987).

Microscopic analysis An image analysis method was developed for the

visualization of the boundaries of the cylindrical cartilage disks which were immersed in PBS and compressed in

unconfined geometry. The compression device consisted of a nonrotating micrometer and a stainless-steel immersion chamber with two glass windows (Fig. 1). The device was fixed to the stage of a light microscope (Olympus Vanox-S AH-2, Olympus Optical Co. Ltd. Tokyo, Japan). The optical path of the microscope was adjusted through the immersion chamber and. using a 4 x objective (Olympus SPlanApo4, numerical aperture = 0.16). the projection of the cartilage disk between the smooth, impermeable compression platens was visualized. The cartilage-platen interfaces were lubricated with synovial fluid. The disk was first compressed to a 5% offset strain. after which a waiting period of 1 h was used to guarantee the mechanical equilibrium. For further compression, steps of 5% strain (manually controlled strain rate - 0.05 s- ‘) were applied up to a total offset of 20%. Using the imaging system, consisting of a microscope, videocamera (Sony DXC-930P, Sony Co., Tokyo, Japan). frame grabber (RasterOps 24XLTV. RasterOps Co., Santa Clara, CA, U.S.A.) and computer (Macintosh 11x), the shape of the sample projected perpendicular to the sample axis was recorded during a complete stress relaxation (< 30 min) by capturing a total number of 15--20 images over this period of time. Image capture and analysis were performed using commercial software (IP-Lab Spectrum, Signal Analytics Co., Vienna, Virginia, U.S.A.). The final magnification of the captured images was 80 x, with a corresponding pixel size of 4 llrn.

Using automatic segmentation (thresholding) of the images, the edges of the disk were recognized and the program then calculated the projected area of the disk. With the projected area and the known thickness (obtained from the micrometer) the mean diameter of the disk was calculated and plotted as a function of time. This automatic procedure for area determination allowed an accurate detection of small dimensional changes of the mean disk diameter. By comparing the diameter of the disk before and after compression, we were able to determine quantitatively the average lateral strain as a function of time. At equilibrium the ratio of average-lateral to average-axial strain yields the value of Poisson’s ratio of articular cartilage. The lateral- to-axial strain ratios were calculated systematically at two time points, i.e. 3 s after the onset of the strain (first image) and after obtaining equilibrium (typically within 30 min), as judged by the constant lateral strain for 10 min.

Fig. 1. Schematic presentation of the device used for optical determination of Poisson’s ratio of articular cartilage. The device is fixed to the stage of the light microscope and the lateral expansion of the sample under unconfined compression is recorded with the microscooevideo- camera&computer system. See text for the operational details: (I) nonrotating micrometer; (2) immersion chamber with two glass windows:

(3) compression platens: (4) seal; (5) cartilage sample.

Optical and mechanical determination of Poisson’s ratio 231

The microscopic imaging and analysis were carried out for each sample in two mutually perpendicular projections, each of which was also perpendicular to the axis of the cartilage disk. Since bovine humeral cartilage shows no or only a weak split line formation after puncturing the articular surface with a round needle, these two mutually perpendicular directions are not necessarily related to collagen fibril orientation in the superficial layer. We chose the first direction of projection randomly and the second at 90” from the first. The depth-averaged lateral strains for these two projections were quantified in the whole uncalcified cartilage, as well as separately in the superficial and radial zones. These zones were defined as the most superficial (super~cial zone) or the deepest (radial zone) cartilage layer with a thickness of 10% that of the entire uncalcified cartilage layer.*

To investigate the possible dependence of our Poisson’s ratio results on the size (diameter) of the disk, three 3.7 mm disks were measured using the technique described above (2 x objective, Olympus Splan Fl-1, numerical aperture = 0.08). Subsequently, the disks were then punched to 1.X mm and measured again using a 4 x objective. In both cases, a 5% step after a 10% offset strain was utilized. Reduction of the diameter increased the thickness/radius aspect ratio of the disk typically by 2.1 x . In this way we wanted to test if the measured Poisson’s ratio is an intrinsic parameter of the tissue, independent of the sample dimensions and consequently not affected by the possible friction between sample and platen surfaces.

The optical technique was calibrated by measuring the diameter of small cylindrical metal rods first with the mechanical micrometer (1 pm resolution) and then, after placing the rod between compression platens in the same measurement geometry as for cartilage samples, with the microscope.

A custom-built material testing device (Buschmann et ni., 1995) was used to conduct confined and unconfined compression measurements on the same specimen. The confined compression measurement was performed initially. We used a confining stainless-steel chamber and a stainless-steel porous platen (5 flrn pores, 50% poros- ity). A series of stress relaxation tests (step 10 jirn, velocity 1 /m s - ” ) was executed up to a 20% offset under automatic computer control. When the slope of the load relaxation curve was less than 9.8 mN min- ’ (3.0 g min- ‘) the next step was automatically started. For each step the complete time-position-load data was col- lected using the sampling frequency of 1 Hz. During nleasurement the disk was kept immersed in PBS. After termination of the confined test the sample was allowed to reswell back to equilibrium. To minimize the friction between compression platens and cartilage surfaces in unconfined compression measurements, the interfaces were lubricated with synovial fluid, harvested from the same joint as the disk. The unconfined compression test

* While we found no systematic differences between two perpendicular projections, tbe measured lateral strains were averaged over projections to yield one mean value for each sample.

followed the same testing protocol used for the confined test. Both confined and uncon~ned compression testing took a total time of 2.5-3 h, Aggregate modulus (Ha), and Young’s modulus (Es), were determined from confined and unconfined tests, respectively, using the equilibrium stress-strain data in the most linear range (typically 520% strain).

Analysis of the rne~s~re~e~z~s At equilibrium, the predictions of biphasic model

necessarily reduce to those of the elastic matrix alone. Using the equilibrium moduli obtained from the confined and unconfined measurements, the (isotropic) Pois- son ratio, os, was determined. For an isotropic linearly elastic material H,, Es and L’~ and are related through the following formula:

1 -I;,

Ha = (1 + z&)(1 -2L$.

The positive root of Equation (1) was used to yield us.

RESULTS

The test measurements with metal rods showed a high accuracy and good linearity (r = 0.99992, vl = 10) of the optical technique for the determination of the diameter of a small, cylindrical object (data not shown).

The optical analyses of cartilage disks revealed that the maximal lateral strain of the disk occurred immediately after the 5% ramp. During the ensuing stress relaxation the expansion partially recoiled and stabilized to a constant value. A typical time-dependent change in the lateral strain of cartilage and the measured stress relaxation (5% offset, 5% strain) are presented in Fig. 2. For comparison, the lateral strain vs time behavior of a single-phase elastic material, rubber (cylindrical rod, thickness = 1.5 mm, diameter = 1.8 mm), is also shown in Fig. 2. The observed shape changes of the cartilage disk under compression systematically revealed that the superficial cartilage layer undergoes a smaller dimensional expansion than the deeper layers immediately after ramp straining (Figs 2 and 3; Table 1). The depth- averaged Poisson’s ratio for the complete hyaline articular cartilage layer (without the calcified zone), determined from the equilibrium response, was 0.185 -I- 0.065 (mean I S.D., n = 9). For the disks measured inigally at a diameter of 3.7 mm and then after coring to 1.8 mm diameter, Poisson ratio values were 0.131 4 0.062 and 0.135 &.0.064, respectively (mean i: SD,, n = 3). The mean difference of these paired measurements was 0.005 (3.76%). No significant changes in the values of Poisson’s ratio measured at different offset strains (5, 10 and 15%) were observed (Table 1, p > 0.05, Friedman two-way ANOVA). The mean lateral strain of uncalcified cartilage, measured in the beginning phase of the relaxation (3 s after 1 s ramp) and normalized to the axial strain (SOh), was 0.380 rf: 0.065. When the expansion results of the superficial and radial cartilage zones were analyzed separately, then the ‘short time’ and the equilibrium values for lateral strains were 0.129 4 0.057 and 0.068 4 0.040 for the superficial zone, and 0.593 & 0.129

J. S. Jurvelin er (I/.

. Uncalclfied carillage, v=O 165 -v- Superhcialzane

A Radlalzane A -.-Rubber.v=0500

8.

Cartilage, ES = 0.55 MPa

d 160 260 360 ” 12bOldOO

TIME (set)

Fig. 2. Typical lateral strain (top; normalized with the axial strain) and the stress relaxation (below; strain .5%, load normalized with the equilibrium load) of bovine humeral head cartilage disk (diameter 1.8 mm). Lateral strain of superficial zone (defined as the most superficial cartilage layer with the thickness of l/10 of the total uncalcified cartilage), radial zone (defined as the deepest cartilage layer with the thickness of l/l0 of the toal uncalcified cartilage) and whole uncalcified cartilage are plotted separately. Equilibrium lateral strain for uncalcified cartilage indicates the value of Poisson’s ratio. The lateral strain

data of a single-phase elastic material, rubber, is also shown.

ORIGINAL n 10% COMPRESSED

Fig. 3. Shape change of the cylindrical cartilage sample 3 s after a 10% compression. The lateral expansion is nonuniform. The superficial zone

is expanded less than the deeper zones.

and 0.225 f 0.099 for the radial zone (Table l), respectively. In statistical comparison, the superficial zone expanded instantaneously and at equilibrium less than the radial zone (p < 0.01, Wilcoxon matched-pairs, Signed- ranks test).

For mechanical tests, a typical load-time response for both unconfined and confined measurements is presented in Fig. 4. For both tests and any given sample the equilibrium responses were typically similar during the first 5% applied strain. Upon increasing the strain (5-20%), the equilibrium stress-strain behavior was highly linear and the samples tested in (complete) confinement systemat-

ically showed a higher stiffness (Fig. 5). The aggregate modulus, H,, obtained from the confined compression tests was 0.754 + 0.198 MPa (mean f S.D., rr = 7) while Es = 0.677 -t 0.223 MPa (mean + S.D.. II = 7) was derived for Young’s modulus from the unconfined compression measurements. Using the mathematical relation of H,, Es and us [Equation (I)], the value for the isotropic Poisson’s ratio was found to be 0.174 Ifl 0.106 (Table 2). Values of Poisson’s ratio obtained from the optical and mechanical analyses showed no statistical difference (p > 0.05, Mann-Whitney [j-test).

DISCUSSION

In the present study we measured Poisson’s ratio of bovine humeral head articular cartilage by microscopic visualization and quantification of the lateral expansion of cylindrical cartilage disks in unconfined compression (Table 1). We also investigated the stress relaxation response of humeral articular cartilage in confined and unconfined compression in order to evaluate the elastic properties (E,, us) of the tissue (Table 2). Dynamic visualization revealed a very fundamental difference between single-phase elastic material (rubber, c - 0.50) and biphasic cartilage (Fig. 2): the former displays a constant, time-independent, lateral expansion during the stress relaxation while the maximal lateral strain of the latter is found immediately after the ramp displacement and is followed by a subsequent partial recoil and stabilization to a constant value, as expected according to biphasic theory (Armstrong et al., 1984). The biphasic model inter- prets the recoil as entirely due to water flow out of the tissue. Due to the time needed for manual compression and to additional time for the computer to capture the first image we were not able to record the lateral displacement during the very first seconds after the onset of compression. Relatively high values of 0.380 + 0.065 (mean f SD., n = 9) were obtained for normalized lateral strain of cartilage at 3 s after the compression. It is thus possible that, under an ideal step input, cartilage tissue behaves like an incompressible (r = 0.50) elastic material (Armstrong et al., 1984). The value of 0.380 is also in harmony with the experimental values for apparent Poisson’s ratio, v = 0.42, determined previously from short-term mechanical tests (Hayes and Mockros, 1971).

The values obtained for Poisson’s ratio from mechanical (0.174 IfI 0.106) or microscopic (0.185 2 0.065) analyses were comparable and thus suggest that, ut equilibrium, for these two test geometries, the isotropy of the matrix is a reasonable assumption for compression studies. However, due to the relatively high standard devi- ations in Poisson’s ratio values it is not possible to precisely distinguish between anisotropic and isotropic behavior. We are not aware of any previous studies describing the equilibrium modulus or Poisson’s ratio for mature bovine humeral head cartilage with which we could compare our results. Based on biphasic indentation analyses aggregate modulus values of 0.472 ir 0.147, 0.899 + 0.427, 0.894 + 0.293 MPa (mean + S.D., n = 10) and Poisson’s ratio values of 0.245 k 0.065, 0.383 -f 0.047, 0.396 + 0.023 (mean + S.D., n = 10) have been derived in situ for the cartilage of bovine patellar groove


Table 1. Lateral strain vatues (normalized with axial strain, 5%) of the bovine humeral articular cartilage determined with increasing offset strains (5,lO and 15%) using the microscopic analysis. Values (mean & SD.) were

derived for the (total) uncalcified cartilage and separately for the superficial and radial zones

Lateral strain

5-100/u IO-15% 1520% Mean

L~ncu/c$d cartilap (n = 9)

Short term* 0.386 + 0.074 0.382 k 0.062 0.373 + 0.064 0.380 & 0.065 Equilibrium 0.186 ‘i 0.086 0.190 & 0.061 0.180 i. 0.051 0.185 & 0.065t

S~~~~~~i~~ mze$ (n = 9)

Short term 0.153 & 0.085 0.118 * 0.051 0.138 f 0.049 0.129 f 0.057 Equilibrium 0.087 * 0.050 0.067 + 0.041 0.054 + 0.042 0.068 + 0.040

Rudiul .xm?$ (n = 9) Short term 0.547 * 0.157 0.579 * 0.112 0.622 $- 0.167 0.593 + 0.129 Equilibrium 0.177 + 0.095 0.218 4 0.104 0.23 1 + 0.098 0.225 -f 0.099

*Determined 3 s after the strain application. ’ Indicates the value of Poisson’s ratio. t Defined as the most superficial cartilage layer with the thickness of l/l0 of the total uncalcified cartilage *Defined as the deepest cartilage layer with the thickness of l/10 of the total uncalcified cartilage.

TIME (see)

0

Fig. 4. A series of confined and unconfined ramp stress relaxation test (step 10 iun, velocity 1 pm s-l) up to a 20% offset strain for cartilage disk (thickness 0.90 mm, diameter 3.7 mm). When the slope of the load relaxation curve was less than 9.8 mNmin-’ (1.0 gmin-‘) the next step

was automatically started.

0 Confined

ff,=O.521 MPa

0 Unconfined

Es=0.479 MPa

b 5 1’0 13 20

EQUILIBRIUM STRAIN (x)

Fig. 5. An example of the equilibrium Ioad-compression behavior of bovine humeral head cartilage in confined and unconfined compression. The aggregate and Young’s moduli were determined using the confined and unconfined compression data, respectively, in the linear

strain range (lines).

as well as for the medial and lateral condyles (Athanasion et al., 1991). Our value for the aggregate modulus, H, = 0.754 + 0.198 MPa, is comparable, but the value of Poisson’s ratio, rs = 0.185 + 0.065, is slightly lower than those obtained for the bovme knee joint articular cartilage. However, our value of Poisson’s ratio is within the range of values found for human or canine articular cartilage in situ using biphasic indentation measurements (Athanasiou et al., 1991, 1994; Hale et al., X993; Setton et al., 1994). Therefore, our results indicate that Poisson’s ratio of the articular cartilage, when measured using excised cartilage cylinders, is relatively small and comparable to that derived for intact articular cartilage.

Microscopic visualization of adult bovine humeral cartilage under compression showed a highly depth-dependent inhomogeneous lateral expansion. The observed expansion 3 s after the application of a fast ramp strain was less in the superficial zone than in the radial cartilage zone. This differential response in the degree of lateral expansion was most pronounced during the short time period just after the onset of the stress relaxation. The similar values of Poisson’s ratio obtained for 1.8 and 3.7 mm disks, as well as the transient shape change of the disk (Fig. 4), indicating free relative motion of the cartilage surface along the platen surface, proposes that the friction between these two interfaces may not significantly restrict the lateral expansion of the cartilage disk. A major factor generating differences in the recorded lateral expansion of the cartilage zones may be related to patterns of collagen arrangement and proteoglycan den- sity in the different zones. Since the collagen fibrils of the superficial zone are arranged parallel to the articular surface, this structural organization may produce the highest resistance to lateral expansion, a hypothesis supported by a high lateral tensile stiffness measured in this zone of human weight-bearing patellar groove cartilage, 6.22 i- 1.64 MPa (Akizuki et al., 1986). In the transitional zone collagen fibrils are organized more randomly in relation to both vertical and parallel planes to the

740 J. S. Jurvelin et al.

Table 2. Thickness, h, and the elastic parameters (confined compression aggregate modulus. H,; Young’s modulus, Es; Poisson’s ratio, us) for the bovine humeral cartilage derived from the equilibrium response of the mechanical measurements (confined and unconfined compression.

IT = 7) or from the microscopic analyses (n = 9)

h (mm) H, (MPa) Es (MPa) ‘5

Mechanical analysis 0.95 * 0.33* 0.754 * 0.198 0.677 i 0.223 0.174 i 0.106 Microscopic analysis 1.20 + - 0.23 0.185 i- 0.065

surface, whereas in the radial zone, the collagen fibrils are organized perpendicularly to the subchondral bone- cartilage interface, adhering the matrix to subchondral bone (Meachim and Stockwell 1979). The axial arrangement of the fibrils in the radial zone may create a relatively low resistance to lateral shape change, consistent with a relatively low lateral tensile stiffness measured in this zone 0.93 + 0.42 MPa (Akizuki et al., 1986). In the normal, functioning joint, bonding of the cartilage layer to subchondral bone provides a mechanism, which effec- tively restricts the lateral expansion. Therefore, the degree of lateral expansion in different zones seems to be inversely related to tensile stiffness of the layer. As sug- gested earlier (Kim et al., 1995; McCutchen, 1987; Miz- rahi et al., 1986), the role of collagen as a restrictor of shape change may be enhanced when high loading rates are used and cartilage starts to behave like an incompressible (u = 0.50) elastic material.

Another important depth-dependent structural in- homogeneity is the concentration of proteoglycan. An approximately monotonic increase of PG concentration from the articular surface to the radial zone has been described for mature articular cartilage (Jones et al., 1977; Kiviranta et al., 1985). While the concentration and orientation of collagen fibrils may primarily dominate (lateral) tensile stiffness, PG concentration can strongly influence both the hydraulic premeability, and the (axial) compressive stiffness through the generation of repulsive electrostatic swelling forces between glycosaminoglycan chains (Maroudas and Bannon, 1981; Buschmann and Grodzinsky, 1995). Hence, under fast loads, the high, essentially volume conserving lateral expansion of the cartilage zones may be a consequence of both axial compressive stiffness, controlled by the PGs, and lateral tensile stiffness, controlled by the collagen in that region.

In summary, our novel optical measurement of Poisson’s ratio for mature bovine humeral articular cartilage has provided a model-independent estimation of this important material parameter. The resulting values agree well with those found indirectly by comparing equilibrium confined and unconfined compression responses of the same disk. The optical method provides new information for the characterization of tissue mechanical behavior. It can provide a quantitative measure of the expansion and recoil of this biphasic material as well as precise information regarding the depth dependence of this response. Our experimental results on early time response highlight a significant role of depth-dependent structure and composition in this mature tissue in con- trolling its mechanical behavior and potentially influenc- ing the distribution of intratissue deformation and stress under physiological dynamic loading conditions.

Acknowledgements-The skillful technical assistance of Mr Urs Rohrer. Mr Erland Miihlheim and Mr Oliver Kaupp is acknowledged. This work was supported by grants from the Swiss National Science Foun- dation, the M. E. Miiller Foundation. Switzerland. The Medical Re- search Council of Canada, and the Finnish Research Council for Physical Education and Sports, Ministry of Education. Finland.

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optical and mechanical determination of …optical and mechanical determination of poisson’s ratio...

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