Stress–relaxation of human patellar articular cartilage in unconfined compression: Prediction of mechanical response by tissue composition and structure

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Journal of Biomechanics 41 (2008) 1978–1986 www.elsevier.com/locate/jbiomech www.JBiomech.com

Stress–relaxation of human patellar articular cartilage in unconfined compression: Prediction of mechanical response by tissue composition and structure Petro Julkunena,b,, Wouter Wilsonc, Jukka S. Jurvelinb,d, Jarno Rieppoe, Cheng-Juan Que, Mikko J. Lammif, Rami K. Korhonenb,g a

Department of Clinical Neurophysiology, Kuopio University Hospital, POB 1777, FI-70211, Kuopio, Finland b Department of Physics, University of Kuopio, Kuopio, Finland c Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands d Department of Clinical Physiology and Nuclear Medicine, Kuopio University Hospital, Kuopio, Finland e Department of Biomedicine, Anatomy, University of Kuopio, Kuopio, Finland f Department of Biosciences, Applied Biotechnology, University of Kuopio, Kuopio, Finland g Human Performance Laboratory, Faculty of Kinesiology, University of Calgary, Calgary, Alberta, Canada Accepted 28 March 2008

Abstract Mechanical properties of articular cartilage are controlled by tissue composition and structure. Cartilage function is sensitively altered during tissue degeneration, in osteoarthritis (OA). However, mechanical properties of the tissue cannot be determined non-invasively. In the present study, we evaluate the feasibility to predict, without mechanical testing, the stress–relaxation response of human articular cartilage under unconfined compression. This is carried out by combining microscopic and biochemical analyses with composition-based mathematical modeling. Cartilage samples from five cadaver patellae were mechanically tested under unconfined compression. Depth-dependent collagen content and fibril orientation, as well as proteoglycan and water content were derived by combining Fourier transform infrared imaging, biochemical analyses and polarized light microscopy. Finite element models were constructed for each sample in unconfined compression geometry. First, composition-based fibril-reinforced poroviscoelastic swelling models, including composition and structure obtained from microscopical and biochemical analyses were fitted to experimental stress–relaxation responses of three samples. Subsequently, optimized values of model constants, as well as compositional and structural parameters were implemented in the models of two additional samples to validate the optimization. Theoretical stress–relaxation curves agreed with the experimental tests (R ¼ 0.95–0.99). Using the optimized values of mechanical parameters, as well as composition and structure of additional samples, we were able to predict their mechanical behavior in unconfined compression, without mechanical testing (R ¼ 0.98). Our results suggest that specific information on tissue composition and structure might enable assessment of cartilage mechanics without mechanical testing. r 2008 Elsevier Ltd. All rights reserved. Keywords: Articular cartilage; Finite element analysis; Quantitative microscopy; Collagen content; Fixed charge density; Water fraction; Unconfined compression

1. Introduction Corresponding author at: Department of Clinical Neurophysiology,

Kuopio University Hospital, POB 1777, FI-70211, Kuopio, Finland. Tel.: +358 44 7174118; fax: +358 17 173244. E-mail address: petro.julkunen@uku.fi (P. Julkunen). 0021-9290/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2008.03.026

Articular cartilage is a load-bearing, porous tissue covering the articulating surfaces of bones in diarthrodial joints. It consists of a three-dimensional collagen network, proteoglycan (PG) matrix with high fixed charge density

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(FCD), and interstitial water (Buckwalter and Martin, 1995). Abnormal or impact mechanical loading or joint inflammation may lead to degradation of cartilage matrix resulting in impaired functional properties of the tissue (Armstrong and Mow, 1982; Mow et al., 1992). This may further lead to osteoarthrosis (OA) (Buckwalter and Martin, 1995). Changes in the structure and composition of the cartilage matrix can be detected by imaging techniques, such as magnetic resonance imaging (MRI) or quantitative microscopy (Alhadlaq et al., 2004; Bi et al., 2006, 2007; Kiviranta et al., 2007; Nissi et al., 2004; Rieppo et al., 2003a; Wheaton et al., 2005). The function of articular cartilage is controlled by tissue composition and structure (Julkunen et al., 2008a; Kiviranta et al., 2006; Parsons and Black, 1987; Rieppo et al., 2003b; Wayne et al., 2003). The relations between the mechanical properties and microscopically determined composition and structure of articular cartilage have been addressed in previous studies (Julkunen et al., 2007; Kiviranta et al., 2006; Parsons and Black, 1987; Rieppo et al., 2003b). At present, however, cartilage mechanics cannot be reliably assessed non-invasively. As the mechanical properties alter sensitively in OA (Saarakkala et al., 2003), a theoretical model enabling non-invasive estimation of the mechanical properties of cartilage from compositional information would be desirable. Frequently, modeling approaches of articular cartilage have aimed at relating the mechanical parameters with tissue composition and collagen architecture (Garon et al., 2003; Julkunen et al., 2007, 2008a; Korhonen et al., 2003; Lu et al., 2004; Wilson et al., 2005b, 2006). However, the previous models have not been able to predict cartilage mechanics from the compositional and structural analysis, but the mechanical properties were determined by fitting the numerical simulations to the experimental data. Recently, Wilson et al. (2006) presented a theory, which utilized the composition and structure of articular cartilage

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to simulate the mechanical response of the tissue. However, sample-specific composition and structure was not used. In the present study, we further validate this theory for unconfined compression of human patellar tissue. This is done by predicting the mechanical behavior of cartilage using sample-specific depth-dependent microscopic and biochemical tissue information, as emerged into samplespecific mathematical models (Wilson et al., 2006). Further, using the model we investigate the role of water, collagen content and architecture as well as FCD for the mechanical behavior of cartilage in unconfined compression. We hypothesize that by means of tissue structure (collagen architecture) and composition (collagen and PG content, water fraction) it is possible to predict the transient mechanical behavior of articular cartilage under unconfined compression. Therefore, this study could help to go forward towards noninvasive diagnostics of functional properties of cartilage without invasive mechanical testing. 2. Materials and methods A flow-chart for the methods of the present study is presented in Fig. 1, and explained in detail below.

2.1. Sample preparation Samples from five human cadaver knee joints were obtained from Jyva¨skyla¨ Central Hospital, Jyva¨skyla¨, Finland, with permission of National Authority for Medicolegal Affairs, Helsinki, Finland (1781/32/ 200/01). Initially, osteochondral plugs (16 mm in diameter) were drilled and freed from patellae. Then, two adjacent full-thickness cartilage samples were removed from each osteochondral plug (one for microscopical analyses and histological grading, and one for mechanical testing) using a razor blade and a biopsy punch (diameter 4 mm) (Table 1) (Nieminen et al., 2007). Additional cartilage in the plug was used for biochemical analyses. All the samples were graded using Mankin score (Mankin et al., 1971), as described earlier (Kiviranta et al., 2007; Nieminen et al., 2004; To¨yra¨s et al., 2003).

Fig. 1. A flow-chart for the methods of the present study.

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Table 1 Size (thickness, radius) and composition of the cartilage samples Sample

Mankin score

Thickness (mm)

Radius (mm)

Water fraction (%)

Collagen fraction (%)

PG fraction (%)

FCD (mEq/g)

I II III IV V

6 2 3 4 7

3.49 2.32 2.24 2.36 2.22

2.00 2.03 2.08 2.00 2.07

76.5 79.9 75.6 74.0 73.7

61.5 66.9 60.0 59.3 42.8

38.5 33.1 40.0 40.7 57.2

88.9 84.7 113.9 42.5 47.3

PG, proteoglycan; FCD, Fixed charge density. Collagen and PG fractions are presented as a fraction of the total solid mass. I–III are the samples used for optimization of the theoretical model (see Section 2) IV and V are the samples used for validation of the theoretical model

Fig. 2. Composition and structure of the cartilage samples. The depth-wise composition and collagen fibril orientation of three samples, used for optimization of the values of mechanical model parameters, are presented using the black (J) line (mean7S.D.). The red (K) and blue (’) lines represent the composition and structure of the two samples used for model validation.

2.2. Quantitative microscopy and biochemical analyses 2.2.1. Biochemical analyses of water, collagen and PGs Water, PG and collagen content of the samples were determined. Wet weight of the samples was measured after immersion in phosphate buffered saline. Then, the samples were freeze-dried, and the dry weight of the tissue was determined. From the wet and dry tissue weights, the bulk water fraction was derived (Qu et al., 2007; To¨yra¨s et al., 2003) (Table 1). Mass fraction of the solid collagen in the samples was estimated as follows. Spectrophotometric assay for hydroxyproline samples was used after hydrolysis of the freeze-dried tissue (Brown et al., 2001; To¨yra¨s et al., 2003). Each sample was analyzed as three replicates. The yield of hydroxyproline in hydrolysis was estimated using hydrolyzed collagen type I from a rat tail, based on the nominal hydroxyproline content of collagen. This information was then used to correct the total collagen content of the samples. Finally, the hydroxyproline content was normalized against the wet and dry weights of each sample. For the analysis of PG content, the samples were digested for 24 h at 60 1C with 1 mg/ml of papain (Sigma, Germany) in 5 mM cysteine and 5 mM EDTA in 150 mM sodium phosphate buffer (pH 6.5). PG contents of the papain-digested samples were estimated by quantifying their total

uronic acid content using a spectrophotometric assay (Blumenkrantz and Asboe-Hansen, 1973; Qu et al., 2007). 2.2.2. Collagen and PG distribution Analysis of the depth-dependent collagen distribution in samples was performed using Fourier transform infrared imaging spectroscopy (FT-IRIS) (Camacho et al., 2001; Rieppo et al., 2004). The depth-dependent amide I (collagen specific) absorption was converted to depth-wise collagen mass-fraction by using the bulk collagen solid mass fraction from biochemical analyses (Fig. 2), i.e. the average value of the depth-wise amide I absorbance profile was first scaled to match with the measured bulk collagen solid mass fraction and the depth-dependent values were then calculated. The depth-wise PG distribution was determined similarly from the biochemical PG content and the depth-dependent FT-IRIS data (Bi et al., 2006, 2007; Camacho et al., 2001; Potter et al., 2001; Rieppo et al., 2004). Volume fractions for the collagen and PG distributions were similar to their mass fractions, as constant solid tissue density (rS ¼ 1.4338 g/ml) was assumed (Basser et al., 1998; Shapiro et al., 2001; Wilson et al., 2007). 2.2.3. Depth-dependent fixed charge density To estimate total fixed charge density (FCD) of the tissue chemical assays were performed to obtain molar contents of various constituents of

ARTICLE IN PRESS P. Julkunen et al. / Journal of Biomechanics 41 (2008) 1978–1986 cartilage PGs. Uronic (Blumenkrantz and Asboe-Hansen, 1973) and sialic acid (Jourdian et al., 1971) contents of the extracted bovine cartilage PGs were assayed spectrophotometrically. The proportion of chondroitin and keratan sulfate was estimated on the basis of their contents and molar ratio of glucosamine and galactosamine, analyzed by gas chromatography (Sa¨a¨ma¨nen et al., 1987). After converting the mean depth-wise absorbance in FT-IRIS to bulk FCD, the depth-wise FCD was determined from the FT-IRIS-derived PG profile (Fig. 2). 2.2.4. Depth-dependent water distribution Using the chemical analysis of collagen and PG contents, combined with the FT-IRIS analyses of the cartilage solid (collagen+PGs) content, the water fraction profile was estimated as a complement of the solid fraction (Rieppo et al., 2004). The solid distribution was scaled so that the mean of the cartilage solid weight was equal to the bulk solid mass fraction, determined from the biochemical analyses as a complement of bulk water mass fraction (Fig. 2). The total water volume fraction (nf) was derived from the water mass fraction (nf,m) through the assumed solid tissue density (Basser et al., 1998; Shapiro et al., 2001; Wilson et al., 2007): nf ¼

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matrices remain constant during compression. The total stress of the nonfibrillar matrix depends on the solid fraction, swelling and the shear modulus (Gm): " # 1 logðJÞ 3ðJ þ ns;0 Þ 3 logðJÞJns;0 Gm I 1 þ þ snf ¼  6 J ðJ þ ns;0 Þ ðJ þ ns;0 Þ2 þ

Gm ðF  FT  J 2=3 IÞ, J

(3)

where snf is the Cauchy stress of the non-fibrillar matrix and J is the determinant of the deformation tensor F (Wilson et al., 2007). Since we had no swelling experiment to validate the value for shear modulus, it was fixed to a value of 0.903 MPa (Wilson et al., 2006). The distinction of intra- and extra-fibrillar water was made, since part of the interstitial water is absorbed by the collagen fibrils (Maroudas and Bannon, 1981; Maroudas et al., 1991). This way, only the extra-fibrillar water was considered to interact with the osmotic pressure gradient: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2 u nf cF 2 g Dp ¼ fint RT t þ 4 ext2 c2ext  2fext RTcext , (4) next g int

rS nf;m . 1  nf;m þ nf;m rS

(1)

2.2.5. Collagen fibril orientation The depth-dependent collagen fibril orientation was analyzed by using quantitative polarized light microscopy (PLM, Fig. 2). Using a cross polarized light microscope with computer controlled rotating polarizers, seven background corrected images were taken from unstained cartilage sections with 151 intervals using a high-performance CCD camera. Spatial orientation maps were computed for each sample by determining signal intensities in each image pixel. Then, the image-pixels were horizontally averaged to yield depth-wise collagen orientation angles (Kiviranta et al., 2006; Rieppo et al., 2008).

2.3. Mechanical testing Stepwise stress–relaxation experiments in unconfined compression geometry were conducted by using a high-precision mechanical testing instrument (To¨yra¨s et al., 1999). Following a 5% pre-strain, two stress– relaxation steps (each 5% of full thickness) were applied with a ramp velocity of 1 mm/s. Relaxation criterion was set to 39 Pa/min. A protocol with two loading steps (in addition to pre-loading step) was chosen to increase the accuracy of the optimization of the model parameters (see Section 2.5).

2.4. Model theory The model theory of Wilson et al. (2006) was applied. The model is an extension of the biphasic theory (Mow et al., 1980) with the inclusion of osmotic swelling pressure. Further, the influence of the water and solid volume fractions is included in the total stress (including the division of solid to fibrillar and non-fibrillar part): ! ! totf totf X X f i i i (2) 1 rc snf þ rc sf  DpI, stot ¼ m I þ ns;0 i¼1

i¼1

where I is unit tensor, ns,0 the initial volume fraction of the solid matrix, ric is the volume fraction of the collagen fibrils in ith direction with respect to the total volume of the solid matrix, snf is the stress of the non-fibrillar matrix, sf is the fibril stress of each individual fibril, mf is the chemical potential of water and Dp is the osmotic pressure difference between internal and external pressures (Wilson et al., 2005a). The solid matrix substance was assumed incompressible. However, porous structure of the tissue itself was compressible. The amount of compressibility depends on the water fraction, i.e. with a water fraction of zero and one, the matrix is fully incompressible or fully compressible, respectively. The relative solid fractions of fibrillar and non-fibrillar

where fint and fext are osmotic coefficients, gint and gext are activity coefficients, and cext is the external salt concentration (0.15 M) (Huyghe et al., 2003). R and T represent the gas constant (8.3145 J/mol K) and absolute temperature (293 K), respectively. nf is the total water volume fraction (intra- and extra-fibrillar), cF is the FCD, and next is the volume fraction of the extra-fibrillar water as a function of the extra-fibrillar water mass fraction (next,m): next ¼

rs next;m . 1  next;m þ rs next;m

(5)

The fibril tensor was given as follows: sf ¼

l Pf ~ ef ~ ef , J

(6)

where l is the elongation of the fibril, Pf the first Piola Kirchhoff fibril stress, and ~ ef the current fibril direction. Mechanical behavior of the collagen fibrils depends on the total fibril strain (ef), strain of the viscoelastic side spring (ee), their derivatives, and the values of E1, k1, E2, k2 and n0 (Wilson et al., 2006) (Fig. 3): P1 ¼ E 1 ðek1 f 1 Þ,

(7)

P2 ¼ E 2 ðek2 e 1 Þ ¼ n0 ð_f  _e Þ,

(8)

Pf ¼ P1 þ P2 ,

(9)

The fibril structure was implemented according to microscopic analyses, including two primary and seven randomly oriented secondary fibril directions (Wilson et al., 2005b). The density of each collagen fibril was presented as a function of the total collagen density (occupied by both the secondary and primary fibrils, rc,tot): C ðprimary fibrilsÞ, 2C þ 7 1 ðsecondary fibrilsÞ, rc ¼ rc;tot 2C þ 7 rc ¼ rc;tot

(10)

where C was 3.009 (Wilson et al., 2005b). The depth-wise permeability was implemented as follows: k ¼ að1  next Þ1:339 ,

(11)

where a is a positive material constant.

2.5. Simulations For each sample a finite element (FE) model was constructed using a fibril-reinforced poroviscoelastic swelling model with the composition based equations described above (Wilson et al., 2006). The experimentally determined compositional and structural information was implemented into the sample-specific models using user-defined material (UMAT) in

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The mean squared errors between the experimental tests and numerical simulations among three samples were 0.5–8.7%, with correlation coefficient ranging from 0.95 to 0.99. After implementation of the optimized values of mechanical model parameters and experimentally determined tissue composition and structure, we predicted successfully the experimental stress–relaxation response of two additional samples (Fig. 4). The mean squared error between the simulated and experimental reaction forces was 2.5–12.5%, with a correlation coefficient of 0.98. Our model was sensitive to compositional and structural parameters (Table 3, Fig. 5). We observed that the water fraction most sensitively altered reaction forces. Collagen mass fraction had most significant effect on the ramp phase of loading. FCD and fibril orientation were less important. FCD modulated mainly the stress–relaxation response at equilibrium. Fig. 3. (A) Schematic presentation of a single, viscoelastic collagen fibril (Wilson et al., 2006). (B) Axisymmetric finite element mesh for one sample in initial configuration, after free swelling, and at steady state, 20 min after the compression.

ABAQUS 6.4 (Abaqus Inc., Providence, RI). Each model consisted of 288 four-node axisymmetric elements (Fig. 3). Models of three randomly selected samples were simultaneously curvefitted to mechanical test data of the corresponding samples to optimize values of model parameters; E1, E2, k1, k2, n0 (Eqs. (7) and (8), Fig. 3) and a (Eq. (11)). The optimization was done by minimizing the mean squared error between the simulated and experimental reaction forces using Matlab 7.2 (MathWorks Inc., Natick, MA). The free-swelling step and pre-strain steps before the stress–relaxation step were also included. As cartilage thickness and radius are changing during swelling, a free-swelling test was used to predict these changes before actual simulation. Then, the thickness and radius changes during swelling were compensated when creating the mesh for the actual simulation. For validation, the optimized values of mechanical parameters, as well as experimentally determined composition and structure, were implemented into the models of the two additional samples. These samples exhibited different composition as compared to those used for optimization (Table 1). Thereby, mechanical behavior of cartilage was characterized without mechanical unconfined compression tests, by using only tissue structure and composition. Separately, using one validation sample, the sensitivity of the model to variations in composition and structure was analyzed with the optimized set of aforementioned model parameters. The implemented composition and structure was varied and reaction forces were simulated: (1) water volume fraction was increased and decreased by 10%, (2) FCD was increased by 100% and decreased by 50%, (3) collagen solid fraction was increased by 20% and decreased by 50% from the original value, (4) the overall collagen orientation angle was increased and decreased by 201 as compared to the PLM-derived collagen architecture.

3. Results The present composition-based model, equipped with a single value set of optimized mechanical parameters, was able to capture simultaneously the stress–relaxation responses of three human articular cartilage samples under unconfined compression (Fig. 4). The optimized values for the mechanical model parameters are presented in Table 2.

4. Discussion By emerging the depth-dependent composition and structure into a FE model, we predicted successfully the compressive mechanical behavior of human articular cartilage, i.e. no experimental mechanical testing was used. Prior to this study, no successful prediction of timedependent mechanical behavior of articular cartilage, using sample-specific tissue composition only, has been presented. The applied model theory was introduced recently; however, applicability of the theory was demonstrated without sample-specific composition and structure that were implemented from earlier experimental studies on bovine cartilage (Wilson et al., 2006, 2007). Although the model predicted mechanical behavior successfully in several loading geometries, it was not validated with sample-specific compositional data. In addition, different samples were used for all test geometries. These were the major limitations of the previous study that we overcame in the present study. Thus, the optimized values for model parameters presented in the present study are different from the ones presented earlier by Wilson et al. (2006) for bovine cartilage (Table 2). We emphasize that the present results validate the use of the model for intact or degraded (Mankin score p7) human patellar articular cartilage under unconfined compression. Biochemical and microscopical techniques for the analysis of collagen and PG content, water fraction and collagen fibril orientation are well-accepted (Brown et al., 2001; Chen et al., 2001; Lipshitz et al., 1975; Maroudas, 1968; Maroudas and Bannon, 1981; Nissi et al., 2006; Rieppo et al., 2004; Shapiro et al., 2001). The estimation of the depth-dependent FCD was made by combining bulk FCD obtained from biochemical analyses with the PG distribution profile obtained from FT-IRIS. We believe this provides a reasonable estimation of the FCD distribution, even though the PG-to-FCD conversion method has not been thoroughly validated.

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Fig. 4. Experimental and simulated reaction forces in the stress–relaxation tests. The samples (I–III) used for optimization of the mechanical model parameters are presented in the upper panel, and the samples (IV and V) used for the model validation, i.e. not included in the model optimization, are shown in the lower panel. The stress–relaxation curves of the samples IV and V (model validation) were predicted by using only the sample-specific tissue composition and structure.

Table 2 Optimized values for the parameters of the mechanical model

Present study Wilson et al. (2006)

E1 (MPa)

E2 (MPa)

k1

k2

n0 (MPa s)

a (  1017 m4/N s)

6.632 4.316

15.555 19.97

3.825 16.85

72.328 41.49

1197.1 14240

5.127 1.787

Results published by (Wilson et al., 2006) for bovine cartilage are presented for comparison. E1, E2, k1, k2 and n0 are parameters of the collagen network (Eqs. (7) and (8), Fig. 3), and a is a parameter of the tissue permeability (Eq. (11)).

In accordance with earlier reports, we showed that water fraction had a significant role in the stress–relaxation response, with an emphasis in the ramp phase (Evans and Quinn, 2005; Kiviranta et al., 2007; Saarakkala et al., 2003). Collagen mostly influenced the peak forces during the ramp phase. This finding agrees with the previous studies (Kiviranta et al., 2007; Saarakkala et al., 2003). FCD had a minor effect on the entire stress–relaxation response; however, most effect was seen in the end of the relaxation phase. This result agrees with the earlier studies

emphasizing the role of PGs in the equilibrium response (Evans and Quinn, 2005; Kiviranta et al., 2007; Saarakkala et al., 2003; Wayne et al., 2003). Collagen orientation had the least effect on the stress–relaxation response. In contrast, our previous study concluded that the collagen architecture modifies significantly the mechanical response of articular cartilage (Julkunen et al., 2008b). This difference relates to the multilaminar nature (Nissi et al., 2006; Xia et al., 2002) of the collagen architecture, which was not simulated in the present study.

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In cartilage degeneration, collagen content and orientation may be affected by collagenase activation, releasing and clearing of collagen fragments from the cartilage (Otterness et al., 2000). This could decrease the hydroxyproline content, which would be accounted for in the implemented collagen content (La˚ngsjo¨ et al., 2002). Besides decreasing the collagen content, collagenase treatment has been shown to decrease the collagen fibril diameter, pyridinoline content per dry weight and the birefringence (La˚ngsjo¨ et al., 2002). It is likely that our mechanical model would detect functional changes caused by the altered composition and structure, as suggested by our previous analyses (Korhonen et al., 2003). The present model was not highly sensitive to FCD, but the transient mechanical behavior in unconfined compression was mostly explained by the collagen and water. The Table 3 Sensitivity of the theoretical model for cartilage composition and structure Compositional parameter

Change with respect to reference

Mean error (%)

Water fraction

+10% 10%

51.1 52.9

Collagen fraction

+20% 50%

10.3 24.7

Fixed charge density

+100% 50%

12.9 4.3

Collagen orientation

201 more parallel-to-surface 201 less parallel-to-surface

4.2 0.7

The values of each parameter were assumed to indicate the physiological range of that parameter.

FCD may have a higher influence in other loading geometries, especially in confined compression or swelling tests. In the present study, two validation samples exhibited FCD about 50% of that in samples used for optimizing the model parameters. According to our parametric study, this could account for 20% difference in the simulated and experimental reaction forces in equilibrium. The composition of the samples used for optimization and validation was different (Fig. 2). In addition, the Mankin scores, representing the histological integrity of the samples, were different for each sample. The validation samples IV and V were slightly and more severely degraded, respectively (Fig. 2, Table 1). Nevertheless, the agreement of experimental and simulation results was good, implying that the model captured the mechanical behavior of cartilage with different structural integrity. However, intact and severely degraded samples from different joints and joint locations are still needed to further validate the model accuracy. Furthermore, we validated the model only in unconfined compression. Feasibility of the model in other loading geometries, such as swelling, indentation and lateral deformation test, as well as using different test protocols, should be thoroughly determined. The peak-forces after ramp loading exhibited some inaccuracy in the predicted mechanical tissue responses. However, the differences between the experimental and simulated peak forces were not systematic. Uncertainties in our experimental approaches may explain some of the inconsistencies. Further, implementation of depth-wise profiles to an axisymmetric model may not represent ideally the depth-wise cartilage composition and structure. Probably, a three-dimensional model could increase the

Fig. 5. Simulated effect of tissue composition on the stress–relaxation response of articular cartilage (sample IV). The stress–relaxation curves are normalized by the equilibrium value of the experimental test (last point of the stress–relaxation measurement).

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accuracy of the predicted mechanical responses. Naturally, the compositional and structural analyses would then be more challenging. In the future, the present model, when combined with the MRI-derived information on tissue composition and structure, may be used for clinical assessment of cartilage function. Earlier, an association between MRI parameters and water distribution has been reported (Shapiro et al., 2001). Similarly, FCD has been associated with 23Na MRI, Gd-DTPA-enhanced MRI or T1r (Bashir et al., 1996; Lesperance et al., 1992; Miyata et al., 2006; Shapiro et al., 2002; Wheaton et al., 2004). In addition, collagen architecture and content have been estimated using MRI (Alhadlaq and Xia, 2005; Lammentausta et al., 2007; Nissi et al., 2006; Xia et al., 2002). Using quantitative MRI information, implementation of the compositional and structural parameters into a mathematical model could enable indirect estimation of mechanical behavior of articular cartilage. In conclusion, the composition-based model was able to predict the transient mechanical stress–relaxation response of human patellar articular cartilage samples in unconfined compression geometry based only on microscopically determined sample-specific composition and structure. As the mechanical properties of cartilage are sensitively impaired in OA, the present modeling approach could, after further validation, have potential in diagnosing OA in vivo. Conflict of interest statement None of the authors have any conflicts of interest. Acknowledgements Funding from the North Savo Fund of Finnish Cultural Foundation, Finland and the Alberta Heritage Foundation for Medical Research is acknowledged. References Alhadlaq, H.A., Xia, Y., 2005. Modifications of orientational dependence of microscopic magnetic resonance imaging T(2) anisotropy in compressed articular cartilage. Journal of Magnetic Resonance Imaging 22, 665–673. Alhadlaq, H.A., Xia, Y., Moody, J.B., Matyas, J.R., 2004. Detecting structural changes in early experimental osteoarthritis of tibial cartilage by microscopic magnetic resonance imaging and polarised light microscopy. Annals of the Rheumatic Diseases 63, 709–717. Armstrong, C.G., Mow, V.C., 1982. Variations in the intrinsic mechanical properties of human articular cartilage with age, degeneration, and water content. The Journal of Bone and Joint Surgery (Am) 64, 88–94. Bashir, A., Gray, M.L., Burstein, D., 1996. Gd-DTPA2- as a measure of cartilage degradation. Magnetic Resonance in Medicine 36, 665–673. Basser, P.J., Schneiderman, R., Bank, R.A., Wachtel, E., Maroudas, A., 1998. Mechanical properties of the collagen network in human articular cartilage as measured by osmotic stress technique. Archives of Biochemistry and Biophysics 351, 207–219. Bi, X., Yang, X., Bostrom, M.P., Camacho, N.P., 2006. Fourier transform infrared imaging spectroscopy investigations in the pathogenesis and repair of cartilage. Biochimica et Biophysica Acta 1758, 934–941.

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