Contribution of Proteoglycan Osmotic Swelling Pressure to the Compressive Properties of Articular Cartilage

Abstract

The negatively charged proteoglycans (PG) provide compressive resistance to articular cartilage by means of their fixed charge density (FCD) and high osmotic pressure (π_PG), and the collagen network (CN) provides the restraining forces to counterbalance π_PG. Our objectives in this work were to: 1), account for collagen intrafibrillar water when transforming biochemical measurements into a FCD-π_PG relationship; 2), compute π_PG and CN contributions to the compressive behavior of full-thickness cartilage during bovine growth (fetal, calf, and adult) and human adult aging (young and old); and 3), predict the effect of depth from the articular surface on π_PG in human aging. Extrafibrillar FCD (FCD_EF) and π_PG increased with bovine growth due to an increase in CN concentration, whereas PG concentration was steady. This maturation-related increase was amplified by compression. With normal human aging, FCD_EF and π_PG decreased. The π_PG-values were close to equilibrium stress (σ_EQ) in all bovine and young human cartilage, but were only approximately half of σ_EQ in old human cartilage. Depth-related variations in the strain, FCD_EF, π_PG, and CN stress profiles in human cartilage suggested a functional deterioration of the superficial layer with aging. These results suggest the utility of the FCD-π_PG relationship for elucidating the contribution of matrix macromolecules to the biomechanical properties of cartilage.

Introduction

The main extracellular matrix components of articular cartilage, proteoglycans (PG) and collagens (COL), provide biomechanical properties that vary with growth, aging, and depth from the articular surface. The negatively charged PG contribute to compressive resistance and provide a high osmotic pressure (π_PG) within the tissue. In contrast, the collagen network (CN) provides the restraining stress that counterbalances π_PG at rest or during loading (Fig. 1, A and B), and the high resistance of cartilage to tension (1). Nearly 90% of PG is aggrecan, which complexes with hyaluronan (HA) and link protein to form large PG aggregates entrapped within the CN (2). The aggrecan monomers contain many long chains of sulfated glycosaminoglycans (GAG), specifically chondroitin sulfate (CS) and keratan sulfate (KS). CS and KS, in turn, provide a fixed charged density (FCD) to the tissue due to the sulfate and carboxyl groups of CS and sulfate groups of KS. With the electrostatic repulsion of negatively charged GAG moieties, the FCD contributes to the compressive resistance of the tissue by providing π_PG within the tissue (3).

Figure 1.

Multiscale schematic of the effects of FCD and π_PG on the CN. (A and B) At the macroscopic tissue scale, compression (A->B) leads to increased FCD and π_PG. (C–F) At the microscale, both compression (C->E and D->F) and increasing depth (superficial C, E to deep D, and F) lead to higher FCD and π_PG, and a fluid shift from IF space into EF space.

Native cartilage tissue exhibits variations in compressive properties, both with age and with depth from the articular surface, due in part to variations in biochemical content. Even with a steady GAG concentration during bovine growth from fetal to adult stages, cartilage compressive modulus increases ∼2-fold due an increase in COL concentration by two- to threefold (4). On the other hand, human aging is associated with a trend of decreasing cartilage compressive modulus and PG concentration while COL concentration remains steady (5,6). Cartilage also displays compressive properties and biochemical content and organization that vary with depth from the articular surface to the bone. The superficial layers have a relatively low FCD and exhibit larger strains during compression compared with the deeper layers (7–9). The depth-dependent variations in water content, PG content, FCD, and π_PG seen in normal cartilage are altered with osteoarthritic disease in association with aging (7). Such alterations perturb the balance between PG swelling and CN restraining stress, and the normal mechanics of the tissue (1).

Several models have been proposed to describe the relationship between π_PG and PG content, usually expressed via FCD or GAG concentrations (10–13). The π_PG contribution to overall cartilage mechanical properties, such as compressive modulus or aggregate modulus, has been estimated (10,12,14). Using the concept of balance of forces with π_PG, investigators have also estimated the CN contribution to compressive resistance (3,11,15). Such comparisons are affected by the accuracy of FCD and π_PG calculations, and assumptions made in those calculations. Estimates of FCD imply but often do not account explicitly for CS and KS charge differences (z_CS = ∼2, z_KS = ∼1 pr disaccharide) and varying CS/KS ratios, which vary substantially with age and depth from the articular surface (7,16). Additionally, because π_PG models are typically developed from relationships with aggrecan or CS in solution, investigators have not needed to consider the interaction between PG and COL. However, it has been proposed that in articular cartilage, water is distributed between COL fibrils (intrafibrillar (IF)) and PG (extrafibrillar (EF); Fig. 1, C and E), and this water distribution varies with external stress applied to the tissue (11,17). The fluid shift from IF to EF with applied stress has been estimated from the lateral spacing of COL fibrils within cartilage (Fig. 1, D and F) as determined from x-ray scattering experimental data and previously described models (i.e., the Ogston and Hodge-Petruska models) (17,18). Thus, the effective FCD and associated π_PG in cartilage may be higher than apparent values and need to be calculated based on EF water. Such modulation of π_PG by the CN may affect the biomechanical properties of cartilage.

FCD-π_PG models may provide a useful tool for elucidating the relationship between the composition and function of articular cartilage, because they allow estimation of π_PG from a known PG concentration or FCD. Combined with measurements of tissue mechanical properties, these models can also provide insights into the CN's mechanical properties (19). The effect of compression on FCD and π_PG was previously considered for full-thickness cartilage (10) and layers of adult bovine cartilage (20), but has not been characterized with growth and aging. Thus, our objectives in this work were to 1), describe relationships to explicitly account for variations in CS/KS ratios and exclusion of IF water in a FCD-π_PG relationship; 2), predict π_PG and COL contributions to compression using experimentally obtained biochemical data and compressive equilibrium stress (σ_EQ) for full-thickness cartilage at various stages of bovine growth (fetal, calf, and adult) and human aging (young and old); and 3), predict the effect of depth from the articular surface in human young and old cartilage on π_PG using experimentally obtained biochemical data.

Methods

Bovine cartilage biochemical and biomechanical data

For the bovine cartilage studies, we used data from a previous study (4). Briefly, 1000-μm-thick cylindrical slices (d = 4.8 mm) were taken from bovine fetal (2nd and 3rd trimester, n = 6), calf (1–3 months old, n = 8), and adult (1–2 years old, n = 7) cartilage from a site-matched, central region of a femoral condyle. The samples were analyzed for wet weight (WW), equilibrium stress after uniaxial confined compression to compressive strain (ɛ) of 15% and 30%, dry weight (DW), sGAG content by dimethylmethylene blue (DMMB) assay (21), and COL content by hydroxyproline assay (22) (Fig. S1). Samples from the patella-femoral groove cartilage were similarly tested, and the results are presented in the Supporting Material.

Human cartilage biochemical and biomechanical data

For the human cartilage studies, we used data from a previous study (23). Briefly, normal adult human articular cartilage from a site-matched, antero-medial region of femoral condyles from young (30 ± 2 years old, n = 7) and old (69 ± 2 years old, n = 7) cadaveric donors were analyzed. Spanning the majority of the thickness from the surface to the deep zone, ∼250-μm-thick slices of the tissue were each analyzed for WW, DW, sGAG content, and COL content (Fig. S1). Donor-matched hemicylindrical osteochondral samples with full-thickness articular cartilage (d = 4.8 mm) were subjected to uniaxial confined compression to an overall compression of ∼10%, ∼20%, and ∼30% (24,25). At equilibrium, the stress was measured along with the depth-dependent displacement and strain (23).

Incorporation of the CS/KS ratio and exclusion of IF water into the FCD-π_PG relationship

To compute FCD, accounting for variation in the CS/KS ratio, we described a relationship (Eq. 1) using the molecular mass (MW) per disaccharide of CS (MW_CS = 457 g/mol) and KS (MW_KS = 444 g/mol), masses of CS and KS (m_CS and m_KS), mol-charges of CS and KS (z_CS = 2 and z_KS=1 charge/disaccharide), and mass of EF water (m_EF,H2O). We calculated the MW of CS and KS from the molecular structures of each disaccharide found in the repeating portion of a chain. CS and KS content can be determined by several methods, including enzyme-linked immunosorbent assay, selective enzymatic digestion, and assays that take advantage of different hexose compositions of CS and KS (26–29). Details of the FCD_EF calculation from commonly used assays to determine GAG content are provided in the Supporting Material.

$$FC{D}_{EF}=\frac{\left(m_{CS}\times \frac{z_{CS}}{M{W}_{CS}}\right)+\left(m_{KS}\times \frac{z_{KS}}{M{W}_{KS}}\right)}{m_{EF,H2O}}\times \frac{1000\text{mEq}}{1\text{mol}-\text{charge}}.$$ (1)

To describe π_PG based on FCD_EF, we fit a piecewise continuous function of four segments with monotonically increasing, quadratic equations and continuous first derivatives to the FCD-π_PG data by weighted least-squared error fit (Fig. 2). The PG-π_PG data from Fig. 2 of Buschmann and Grodzinsky (10), originally from Williams and Comper (30), and FCD-π_PG data from Fig. 3 of Basser et al. (11), originally from Urban et al. (31), were used for the fit that was made to be continuous to FCD-π_PG points from the Donnan equations at FCD > 0.5 mEq/ml (10). The Donnan model provides a good model at higher FCD or under macro-continuum conditions because the Donnan and Poisson-Boltzmann-cell models converge under those conditions (32), and both fit the high FCD-π_PG data from Basser et al. (11). We converted the PG concentrations from Buschmann and Grodzinsky (10) to FCD using DW/uronic acid = 3.29 (for KS-free rat chondrosarcoma aggrecan used in that study) and the MW of glucuronolactone (MW_{glucuronolactone} = 176.124 g/mol) (33) as described in the Supporting Material.

Figure 2.

(A and B) Four-segment, piecewise curve-fitting to data from Williams and Comper (30) and Basser et al. (11). An inset of A at lower FCD values is shown in B. (C) The nomograms of CS and KS contents (downward tic marks) for the corresponding FCD (upward tic marks) provide the conversion between CS or KS contents to FCD. The FCD contributions from CS and KS can also be summed and used to estimate the π_PG from the curves in A and B.

Figure 3.

FCD (A–C) and π_PG (D–F) for bovine fetal (A and D), calf (B and E), and adult (C and F) femoral condyle cartilage calculated using the total water or EF water content.

The four-segment piecewise continuous equations to describe the FCD-π_PG relationship were of the form

$${\pi }_{\text{PG},\text{i}}={\text{a}}_{\text{i}}{\left({\text{FCD}}_{\text{EF}}-{\text{x}}_{\text{i}}\right)}^2+{\text{b}}_{\text{i}}\left({\text{FCD}}_{\text{EF}}-{\text{x}}_{\text{i}}\right)+{\text{c}}_{\text{i}}\text{for}{\text{x}}_{\text{i}}<{\text{FCD}}_{\text{EF}}\le {\text{x}}_{\text{i}+1}$$ (2)

with the constants in Table 1. This FCD_EF-π_PG relationship provided a good fit, including at low FCD values, which are typical of cartilage in the superficial zone and at low compression (Fig. 2).

Table 1.

Constants for the four-segment quadratic fit to FCD-π_PG data

I	xi [mEq/g]	ai [kPa/(mEq2/g2)]	bi [kPa/(mEq/g)]	ci [kPa]
1	0	587.1	38.79	0
2	0.1035	9255	160.4	10.31
3	0.1726	1199	1438	65.49
4	0.4890	276.3	2197	640.6

For samples of cartilage, where WW, DW, fixed charge mass (i.e., in Eq. 1), and COL mass (m_COL) are given (e.g., determined experimentally), the EF FCD (FCD_EF), and consequently π_PG from Eq. 2, can be calculated (11) as follows:

The total water content (m_H2O) is the difference between WW and DW:

$${\text{m}}_{\text{H}2\text{O}}=\text{wet}\text{weight}-\text{dry}\text{weight}.$$ (3)

The fluid mass, m_H2O, is distributed between EF (m_EF,H2O) and IF (m_IF,H2O) compartments:

$${\text{m}}_{\text{EF},\text{H}2\text{O}}={\text{m}}_{\text{H}2\text{O}}-{\text{m}}_{\text{IF},\text{H}2\text{O}}.$$ (4)

The fluid content of COL, m_IF,H2O, has been determined experimentally to be related to EF stress (π_EF), where π_EF = π_PG, by the following expression (11,34):

$${\text{m}}_{\text{IF},\text{H}2\text{O}}=\left(0.726+0.538\times \text{exp}\left(-0.258\times {\pi }_{\text{EF}}\right)\right)\times {\text{m}}_{\text{COL}}.$$ (5)

Because Eqs. 1, 2, 4, and 5 are coupled and do not have an explicit solution, the four unknowns, m_EF,H2O, m_IF,H2O, FCD_EF, and π_PG, are calculated iteratively until π_EF and π_PG converge (11). Conceptually, when fluid is distributed appropriately between m_EF,H2O, and m_IF,H2O for the charge and COL present, π_PG of Eq. 2 just balances the π_EF of Eq. 5.

π_PG and σ_COL for various stages of growth and aging under compression

We studied the effect of IF water exclusion by calculating FCD normalized by total water content or by EF water content and the resulting π_PG for bovine fetal, calf, and adult femoral condyle cartilage under compression of 0–30%.

Using the FCD-π_PG relationship described above, we estimated π_PG-values during compression for full-thickness cartilage using the experimentally obtained biochemical data for various stages of bovine growth (fetal, calf, and adult) (4) and human aging (young and old; Fig. S1) (23).

For human cartilage, we computed thickness-weighted averages of the biochemical data to obtain biochemical values for the full-thickness tissue. Then, for both bovine and human cartilage, we determined FCD_EF from the total CS-equivalent sGAG content measured using the DMMB assay with CS sodium salt (Sigma, St. Louis, MO) standards, accounting for the presence of impurities such as water and extra sodium salts (∼14–15%). Whereas the CS and KS contents were not separately measured, the measured CS-equivalent sGAG content from the charge-based DMMB assay was directly converted to FCD. Details are provided in the Supporting Material.

To estimate π_PG for each sample under compression, we first calculated FCD_EF at each compression level. With compression, we assumed that matrix m_GAG and m_COL was maintained in the tissue while fluid was expelled as displaced volume (ΔV). The relationship for EF water with compression is

$${\text{m}}_{\text{EF},\text{H}2\text{O}}={\text{m}}_{\text{H}2\text{O}}-{\text{m}}_{\text{IF},\text{H}2\text{O}}-{\rho }_{\text{water}}\times \Delta \text{V}$$ (6)

where ρ_water = 1.0 and ΔV = ε^∗π^∗r² for a cylindrical sample or ΔV = 1/2^∗ε^∗ π^∗r² for a hemicylindrical sample under uniaxial confined compression of ε. Then, we determined FCD_EF, π_PG, m_EF,H2O, and m_IF,H2O using the FCD_EF−π_PG model as described above.

We estimated the CN contribution to compression, CN stress (σ_CN), at each compression level, from the calculated π_PG and experimentally obtained compressive equilibrium stress (σ_EQ) using the balance of forces (3,11):

$${\sigma }_{\text{EQ}}={\pi }_{\text{PG}}+{\sigma }_{\text{CN}.}$$ (7)

In Eq. 7, each component (π_PG and σ_CN) contributes stress to the overall tissue volume. The π_PG is stress that is generated by PG (Eq. 2) but affects the tissue throughout via compaction of CN (Eq. 5). Similarly, the σ_CN is counterbalancing stress of the CN, considering the entire tissue.

We then calculated the CN prestress at 0% compression level and compression level at σ_CN = 0 kPa for both bovine and human cartilage. For compression level at σ_CN = 0 kPa, only samples in which σ_CN transitioned from tension (negative value) to compression (positive value) were considered (bovine: n = 4–6; human: n = 6).

π_PG with depth and age in human cartilage under compression

The ε, FCD_EF, π_PG, and σ_CN were calculated in 10 normalized layers through the thickness of young and old human cartilage. To estimate π_PG,i for ∼250-μm-thick layer i, we first calculated free EF water (m_EF,H2O,i,ε) from Eq. 4 using experimentally obtained strains (ε_i) for each layer at each overall compression levels of ∼10%, ∼20%, and ∼30% (23). We then calculated the FCD_EF,ι based on biochemical data for each layer, and calculated π_PG,i for each layer throughout full-thickness cartilage using the FCD-π_PG fit (Eq. 2). We estimated the σ_CN,i in each layer at each strain from the calculated π_PG,i and σ_EQ using Eq. 7. Then, the weighted averages of ε_i, FCD_EF,ι, π_PG,i, σ_CN,i, total water/WW, and EF water/WW were calculated for each of 10 layers through the depth of human cartilage; layer 1 was the most superficial layer at the articular surface, and layer 10 was the deepest layer next to the subchondral bone.

Statistical analysis

Data are presented as the mean ± standard error. The effect of bovine growth on cartilage biochemical data, and FCD_EF and π_PG at each compression level was assessed by one-way analysis of variance (ANOVA) and Tukey's post-hoc test. The effect of aging in human cartilage was assessed by Student's t-tests. For human cartilage, the effect of aging was assessed by repeated-measures ANOVA with the depth as a repeated factor at each compression level. When the age had a significant (p < 0.05) independent or interactive effect with layer, each layer was analyzed separately. When the depth had a significant effect (p < 0.05), pairwise comparisons of layers for either young or old cartilage were performed with a Sidak correction of the p-value.

Results

Variation of CS/KS ratios and IF water exclusion were incorporated into the calculation of FCD (Eqs. 1–6). Approximately twice the mass of KS relative to CS was equivalent to the same FCD (Fig. 2 C). Also, π_PG increased with an increasing CS/KS ratio, reflecting the charge difference between KS and CS. Considering IF water and using only EF water for calculation of PG-associated properties in (Eqs. 4–6), FCD and, as a result, π_PG were substantially higher than values calculated using total water content for cartilage. With compression, the differences in FCD and π_PG calculated with EF water instead of total water content became even more pronounced (Fig. 3).

Applying the FCD_EF-π_PG relationship to data from full-thickness bovine femoral condyle cartilage revealed that FCD_EF and π_PG changed with growth (ANOVA, p < 0.05 for FCD_EF at 0, 15%, and 30%, and π_PG at 30% compression; Figs. 4 A and 5). Calf and adult femoral condyle cartilage generally had higher FCD_EF and π_PG values than fetal cartilage at each compression level (p < 0.05 for calf versus fetal for FCD_EF at 0–30%, and π_PG at 30% compression). Even with similar GAG/WW at zero strain, the higher FCD_EF in calf and adult cartilage was due to higher COL content (Fig. S1) and increased IF water (Fig. 3). For bovine cartilage, π_PG closely approximated σ_EQ for all growth stages at all compression levels (Fig. 5). The σ_CN were generally low and moved from tension (negative in this convention) at the reference state to compression (positive stress) with increasing applied compression. For full-thickness adult human cartilage, young cartilage had higher FCD_EF and π_PG than old cartilage at all compressive strains (p < 0.01; Figs. 4 B and 6). The π_PG for young cartilage closely approximated σ_EQ at all strains levels, whereas π_PG for old cartilage accounted for only approximately half of σ_EQ (Fig. 6). The low π_PG for old cartilage suggested a larger proportion of σ_CN contribution to σ_EQ than was found in young human cartilage. The σ_CN for both young and old cartilage generally increased with compressive strain, moving from tension toward compression.

Figure 4.

FCD_EF for bovine (A) and human (B) femoral condyle cartilage (^∗p < 0.05 versus fetal; p < 0.01 versus young).

Figure 5.

Values of π_PG, σ_EQ, and σ_CN for bovine fetal (A), calf (B), and adult (C) femoral condyle cartilage (#p < 0.05 versus fetal).

Figure 6.

Values of π_PG, σ_EQ, and σ_CN for human young (A) and old (B) femoral condyle cartilage (# for π_PG and ^∧ for σ_CN, p < 0.01 versus young).

The properties of CN under compression were altered with growth and aging of cartilage. The CN prestress for bovine calf and adult cartilage tended to be higher than that for fetal cartilage (ANOVA p = 0.19; p = 0.20 for adult and p = 0.28 for calf versus fetal; Fig. 7 A). In human cartilage, young cartilage had higher CN prestress than old cartilage (p < 0.01; Fig. 7 B). The compression level at σ_CN = 0, changing from prestressed tension to compression, tended to be higher for bovine calf and adult cartilage than for fetal cartilage (ANOVA p = 0.24; p = 0.38 for adult and p = 0.28 for calf versus fetal; Fig. 7 C) and for human young cartilage than for old cartilage (p = 0.20; Fig. 7 D).

Figure 7.

CN prestress (A and B) and compression level at σ_CN = 0 (C and D) for bovine (A and C) and human (B and D) cartilage (^∗p < 0.01 versus young).

Under compression, the profiles of strain, FCD_EF, π_PG, σ_CN, total water content, and EF water content for human cartilage varied with depth from the articular surface (ANOVA p < 0.001 for strain and EF water at all compressions, and for FCD_EF, π_PG, σ_CN, and total water content at 0, 20%, and 30% compression; Fig. 8, Fig. S4, and Fig. S5). These profiles also were significantly different with the tissue age alone (p < 0.01 for FCD_EF and π_PG at all compressions, and for σ_CN at 0% compression) and interactively with depth (p < 0.01 for FCD_EF, π_PG, and σ_CN at 0% compression and for strain at 10% compression).

Figure 8.

Strain (A–E), π_PG (F–K), and σ_CN (L–Q) for human young (A, F, and L) and old (B, G, and M) cartilage with initial normalized depth of the tissue at each compression level (0%, 10%, 20%, and 30%; ^∗p < 0.05 versus young).

The strain profiles in young and old cartilage were distinct from each other. The highest compressive strains in young cartilage were found only in the most superficial layer and linearly decreased with depth at all compression levels (p < 0.05 for layer 1 versus 5–10 at 20% compression; Fig. 8, A and C–E). However, in old cartilage, the highest strains were more evenly distributed into the middle layer, and strain then decreased through the depth of the cartilage (p = 0.054 for layer 1 versus 9 and 10; p < 0.05 for layer 2 versus 8–10 at 20% compression; Fig. 8, B–E).

The FCD_EF and π_PG profiles differed with depth (p < 0.001 at 0, 20%, and 30% compression) and between old and young cartilage (p < 0.005; Fig. 8, F–K, and Fig. S3). At zero strain, the local FCD_EF and π_PG varied with depth (p < 0.001) and aging (p < 0.001; Fig. 8, F–K). The superficial layers had lower FCD_EF and π_PG than the deeper layers in both young and old cartilage (e.g., p ≤ 0.05 for layer 1 versus 6), with young cartilage having higher FCD_EF and π_PG in deeper layers than old cartilage (p < 0.05 for layers 5–10). With compression, FCD_EF and π_PG profiles for young cartilage increased in the superficial layers, evened out through the depth of the cartilage at 10% and 20% compression (p > 0.2), and peaked in the superficial layers and the upper deep layers at 30% compression (p < 0.05 for layer 5 versus layers 9 and 10). However, FCD_EF and π_PG profiles for old cartilage tended to peak in the middle layer (layer 4) at all compression levels, and showed increasing amplitude with increasing compression.

For both young and old cartilage, the σ_CN profiles at zero compression were generally in tension more in the deep layer than in the superficial layer (p < 0.05 in young and p = 0.056 in old for layer 1 versus 6; Fig. 8, L–Q). The σ_CN profiles shifted toward compression at 10% and 20% compression, with old cartilage tending to shift to slightly higher stresses than young cartilage at corresponding depth layers (Fig. 8, O and P). At 30% compression for young cartilage, superficial and middle-layer CN were back in tension, whereas the deep-layer CN was in compression (Fig. 8 Q). For old cartilage, most of the CN was in compression with just the middle layers in tension.

The FCD_EF, π_PG, and σ_CN profiles for old cartilage generally were similar to the trends in the profiles for young cartilage at a normalized depth of ≥0.2. These variations in FCD_EF, π_PG, and σ_CN with depth of cartilage and aging may play a role in the changes observed with the overall mechanical properties of the tissue.

Discussion

In this work, we applied the FCD_EF-π_PG relationship to predict the contribution of PG to the compressive properties of articular cartilage. By accounting for sGAG content more accurately and for exclusion of IF water to PG, this approach appears to predict π_PG reasonably well for both bovine and human cartilage at various stages of growth and aging, and with depth from the articular surface during compression. Even with similar GAG/WW, more-mature cartilage (bovine calf and adult) had higher FCD_EF and π_PG than less-mature tissue (bovine fetal), and this effect was amplified with compression. With aging, the overall FCD_EF and π_PG were lower in old human cartilage as compared with young cartilage. The π_PG-values were close to σ_EQ in bovine cartilage with growth and in human young cartilage, but only approximately half of σ_EQ in human old cartilage. The strain, FCD_EF, π_PG, and σ_CN profiles revealed depth-related variations in human cartilage that were substantially altered with normal aging, suggesting deterioration of a functional superficial layer. These results demonstrate that the FCD_EF-π_PG relationship elucidated here can provide a useful tool for assessing the contribution of PG and its interaction with the CN to the biomechanical properties of cartilage as they vary with growth, aging, and depth from the articular surface.

For a precise calculation of π_PG, it is important to obtain an accurate estimate of FCD_EF from the total sGAG content. The CS/KS ratio varies across joint surfaces (35), decreases with growth and depth (26), and increases with degeneration of articular cartilage (16), and the charge difference between CS and KS can affect FCD_EF determined from GAG mass by as much as 50%. Nonsulfation or double sulfation of the GAG was not taken into account in the FCD equation presented here, because previous studies indicated that the assumption of normal sulfation gave excellent agreement between calculated and experimentally measured FCDs (35). The accurate accounting of MW in converting the mass of CS and KS into FCD is important because values in literature vary by as much as ∼10% (457 g/mol versus 503 g/mol for CS disaccharide (35)). Here, 457 g/mol disaccharide was chosen with the assumption of CS in a long chain, with loss of a water molecule between 2 disaccharides due to a glycosidic linkage (see Supporting Material for details).

The curve fit of the FCD-π_PG relationship appears to provide good estimates of π_PG, especially at low FCD_EF as found in cartilage in the superficial zone and at low compression. Previous FCD-π_PG fits, such as the quadratic relationships presented in works by Basser et al. (11) and Chahine et al. (12), provide excellent fits for FCD > 0.16 mEq/ml. To extend the FCD-π_PG relationship to the lower FCD range that is important for bovine cartilage and the upper layers of human articular cartilage, we fit a piecewise quadratic relationship to experimental data (10,11), including the low-FCD data from Williams and Comper (30). Although the experimental data were obtained from an extracted aggrecan solution, the measured FCD_EF-π_PG relationships were similar for extracted aggrecan in solution or for an intact tissue from the intervertebral disc (36). The FCD-π_PG data points and the experimental data used here were for samples in a bath solution with isotonic buffer or equivalent to 0.15 M NaCl, which is typical of the environment within a joint. The curve-fitting approach used here may also be useful for describing FCD-π_PG relationships at other salt concentrations from experimental data.

In our analysis of cartilage, we assumed the presence of COL hydration (IF water) and the unavailability of water (while in the IF space) to PG or other surrounding larger molecules, as studied previously (17,18,37). Because aggrecan monomers are impermeable to membranes with pore sizes < 125 nm (38), and the IF space, at least on the outer surface of the COL fibril, is no larger than the gap region on the COL fibril or approximately half of a period (∼34 nm) (39), the large polyanionic PG are unlikely to exchange into the IF space. The deformation of COL fibrils due to π_PG (17,18) implies a molecular-level balance of stresses between the EF and IF spaces. Thus, π_PG represents the swelling tendency of aggrecan in the EF space and, equally, the counterbalancing resilience of the CN compacted in the IF space.

Accounting for exclusion of IF water from PG affects FCD_EF and π_PG values, and how FCD contributes to cartilage properties. The use of EF water instead of total water leads to increased estimates of local FCD by as much as 30% in the samples analyzed here, which in turn leads to increased estimates of π_PG over that due to the nonlinear nature of the FCD-π_PG relationship. This may clarify the role of π_PG in the compressive aggregate modulus of cartilage. Although the slopes of the curves for π_PG, representing its contribution to modulus, were generally less than that for σ_EQ at 0–10% or 0–15% compression, they accounted for nearly all of σ_EQ by π_PG in bovine cartilage and young human cartilage, and nearly half of σ_EQ in old human cartilage at physiological salt concentrations. Previous studies using total water content attributed ∼1/3 of the compressive modulus of cartilage to π_PG (12,40). If the assumption of water partitioning were not true, the π_PG amplification would be only that due to the nonlinear FCD-π_PG relationship. With changes in COL content during growth, aging, and depth, the proportion of EF water available to interact with PG varies, resulting in changes in FCD_EF and π_PG. This highlights the importance of interaction between the extracellular matrix components PG and CN, and the contribution from both components to FCD_EF and π_PG.

Our results can be consistent with previous studies of cartilage compressive modulus at increased salt concentration (40,41). At the physiological salt concentrations considered here, nonelectrostatic contributions to π_PG, such as configurational entropy and mixing entropy, are likely to be small. Mixing entropy is generally considered to be very low at physiological PG concentrations (42), and configurational entropy has been suggested to be negligible at physiological salt concentrations using the Debye-Huckel model with a repulsive Lennard-Jones potential (13). However, at high salt concentrations that shield the electrostatic contribution, configurational entropy likely increases (12,13,42) and is thought to contribute to a larger proportion of the π_PG and the compressive properties, with estimates of ∼40–60% of compressive modulus values from experimental studies (12,40,41). Thus, the determination of electrostatic contribution at physiological condition from studies with increasing salt concentrations (40,41) is complicated by an increasing nonelectrostatic contribution to compressive properties. For the tissues analyzed here, with physiological concentrations of salt and PG, it appears that the electrostatic contribution from the charged GAGs is the major source of the π_PG.

The level of prestress exerted on the CN by π_PG at zero strain appears to have an important impact on the compressive properties of the tissue, as suggested previously (43). The shift of the CN stress-strain curve from zero stress-strain state (i.e., 0, 0) into a prestress in tension at overall tissue zero strain indicates that the CN participates in compression, where the prestress is relieved. The compressive strain where the combined effect from high-sloped tension from the CN and low π_PG from lower FCD_EF likely contributes to the compressive softening previously observed at low strains (25,43,44). In addition, the degree of compression needed to relieve the CN prestress varies with growth, aging, and depth of the tissue. This appears to be related to the maturity of the CN (e.g., the presence of cross-links and COL orientation), because CN in immature cartilage provides much less restraining force than more-mature tissues, resulting in lower FCD_EF with compression and weaker compressive properties. The contribution to compressive properties from both PG and CN, especially at low strains, gives articular cartilage its unique biomechanical properties.

Variations in FCD_EF and π_PG with the depth of adult cartilage appear to affect the overall functional properties of the tissue. The evening out of FCD_EF, π_PG, and σ_CN profiles through the depth in young cartilage at 10% and 20% compression reflects the state of articular cartilage during steady-state loading. The changes in σ_CN of normal young human cartilage from tension at zero strain to compression at lower applied compression (10% and 20%), and to tension in superficial CN while in compression in the deep layer CN at a high applied compression level (30%) are supported by previous studies of the CN under compression. The COL fibrils in superficial and middle layers may dissipate the strain under lower load, whereas COL fibrils in deep layers initially buckle or crimp and then distribute the load to the superficial layer under high load, leading to tension of the superficial COL fibrils and compression of deeper-zone COL fibrils (45). These results also have implications for cartilage function during dynamic loading. FCD is also inversely related to the hydraulic permeability of cartilage (3,4), and the dynamic stiffness and pressurization of cartilage depend on both the equilibrium compressive modulus and hydraulic permeability (46,47). Thus, our analysis of the FCD and π_PG of cartilage provides insight into the function of cartilage during physiological loading.

The FCD_EF, π_PG, and σ_CN profiles for old cartilage generally were similar to the trends observed for young cartilage at a normalized depth of ≥0.2, consistent with a dysfunction of the superficial layer with normal aging (6). With aging in old human cartilage, the highest levels of strains were observed in the middle layers and were not just localized to the superficial layers as in young cartilage, resulting in high local FCD_EF and π_PG in the middle layers. The FCD_EF and π_PG peak in aged cartilage may indicate an abnormal distribution of stress through the depth of the tissue that may be unfavorable to the health of the matrix and chondrocytes in those regions. Although it is unclear whether this peak in π_PG in deeper layers is a result or cause of matrix degradation, these depth-varying compressive properties likely have important implications for the mechanobiology of cartilage and provide insight into the age-related changes that may lead to tissue degeneration.

The application of the FCD_EF-π_PG relationship to experimental biochemical data has the potential to predict π_PG for native cartilage of various sources (including human); depths; and states of growth, aging, and degeneration; as well as for engineered cartilaginous tissues with varying PG and COL contents. This may provide helpful insights into the design of (and possible targets for) tissue-engineered constructs on a macroscale with more uniform matrix composition (48) or on a microscale, at the level of individual cells, with more local, radially varying matrix regions (i.e., pericellular matrix) (49). Because only biochemical and compressive strain data are needed to estimate π_PG, the calculations described above may provide a useful tool for elucidating, predicting, and targeting the biomechanical properties of native and engineered cartilaginous tissues, and relating the composition of a tissue to its function.