Wenbo Zhu

Biphasic indentation of articular cartilage-II. A numerical algorithm and an experimental study

Part I (Mak et al., 1987, J. Biomechanics 20, 703-714) presented the theoretical solutions for the biphasic indentation of articular cartilage under creep and stress-relaxation conditions. In this study, using the creep solution, we developed an efficient numerical algorithm to compute all three material coefficients of cartilage in situ on the joint surface from the indentation creep experiment. With this method we determined the average values of the aggregate modulus. Poissons ratio and permeability for young bovine femoral condylar cartilage in situ to be HA = 0.90 MPa, vs = 0.39 and k = 0.44 x 10(-15) m4/Ns respectively, and those for patellar groove cartilage to be HA = 0.47 MPa, vs = 0.24, k = 1.42 x 10(-15) m4/Ns. One surprising finding from this study is that the in situ Poissons ratio of cartilage (0.13-0.45) may be much less than those determined from measurements performed on excised osteochondral plugs (0.40-0.49) reported in the literature. We also found the permeability of patellar groove cartilage to be several times higher than femoral condyle cartilage. These findings may have important implications on understanding the functional behavior of cartilage in situ and on methods used to determine the elastic moduli of cartilage using the indentation experiments.

The biphasic poroviscoelastic behavior of articular cartilage: Role of the surface zone in governing the compressive behavior

Surface fibrillation of articular cartilage is an early sign of degenerative changes in the development of osteoarthritis. To assess the influence of the surface zone on the viscoelastic properties of cartilage under compressive loading, we prepared osteochondral plugs from skeletally mature steers, with and without the surface zone of articular cartilage, for study in the confined compression creep experiment. The relative contributions of two viscoelastic mechanisms, i.e. a flow-independent mechanism [Hayes and Bodine, J. Biomechanics 11, 407-419 (1978)], and a flow-dependent mechanism [Mow et al. J. biomech. Engng 102, 73-84 (1980)], to the compressive creep response of these two types of specimens were determined using the biphasic poroviscoelastic theory proposed by Mak. [J. Biomechanics 20, 703-714 (1986)]. From the experimental results and the biphasic poroviscoelastic theory, we found that frictional drag associated with interstitial fluid flow and fluid pressurization are the dominant mechanisms of load support in the intact specimens, i.e. the flow-dependent mechanisms alone were sufficient to describe normal articular cartilage compressive creep behavior. For specimens with the surface removed, we found an increased creep rate which was derived from an increased tissue permeability, as well as significant changes in the flow-independent parameters of the viscoelastic solid matrix. permeability, as well as significant changes in the flow-independent parameters of the viscoelastic solid matrix. From these tissue properties and the biphasic poroviscoelastic theory, we determined that the flow-dependent mechanisms of load support, i.e. frictional drag and fluid pressurization, were greatly diminished in cartilage without the articular surface. Calculations based upon these material parameters show that for specimens with the surface zone removed, the cartilage solid matrix became more highly loaded during the early stages of creep. This suggests that an important function of the articular surface is to provide for a low fluid permeability, and thereby serve to restrict fluid exudation and increase interstitial fluid pressurization. Thus, it is likely that with increasing severity of damage to the articular surface, load support in cartilage under compression shifts from the flow-dependent modes of fluid drag and pressurization to increased solid matrix stress. This suggests that it is important to maintain the integrity of the articular surface in preserving normal compressive behavior of the tissue and normal load carriage in the joint.

Compressive mechanical properties of the human anulus fibrosus and their relationship to biochemical composition.

To enhance understanding of the biomechanical role of the intervertebral disc, the compressive properties and biochemical composition of nondegenerate samples of anulus fibrosus were determined as a function of radial position, region, and level. Because of the large swelling propensity of this tissue, a method was developed to test excised specimens while maintaining their in situ geometry and hydration. Using an analysis based on linear biphasic theory, the compressive modulus, hydraulic permeability, and isometric swelling pressure of the anulus fibrosus were determined and correlated with the tissue composition. The findings indicate that the anulus fibrosus is inhomogeneous, with regional and radial variations in both material properties and biochemical composition. The results of this study suggest that both structural and compositional factors may determine the mechanical behavior.

Determination of collagen-proteoglycan interactions in vitro.

The objective of this study was to characterize the physical interactions of the molecular networks formed by mixtures of collagen and proteoglycan in vitro. Pure proteoglycan aggrecan solutions, collagen (type II) suspensions and mixtures of these molecules in varying proportions and concentrations were subjected to viscometric flow measurements using a cone-on-plate viscometer. Linear viscoelastic and non-Newtonian flow properties of these solutions and suspensions were described using a second-order statistical network theory for polymeric fluids (Zhu et al., 1991, J. Biomechanics 24, 1007-1018). This theory provides a set of material coefficients which relate the macroscopic flow behavior of the fluid to an idealized molecular network structure. The results indicated distinct differences between the flow properties of pure collagen suspensions and those of pure proteoglycan solutions. The collagen network showed much greater shear stiffness and more effective energy storage capability than the proteoglycan network. The relative proportion of collagen to proteoglycan is the dominant factor in determining the flow behavior of the mixtures. Analysis of the statistical network theory indicated that the collagen in a collagen-proteoglycan mixture enhances molecular interactions by increasing the amount of entanglement interactions and/or the strength of interaction, while aggrecan acts to reduce the number and/or strength of molecular interactions. These results characterize the physical interactions between type II collagen and aggrecan and provide some insight into their potential roles in giving articular cartilage its mechanical behavior.

The influence of link protein stabilization on the viscometric properties of proteoglycan aggregate solutions

The dynamic, steady-shear and transient shear flow properties of precisely prepared link-stable (s0 136, 66% aggregate) and link-free (s0 93, 59% aggregate) proteoglycan aggregate solutions at concentrations ranging from 10 to 50 mg/ml were determined using a cone-on-plate viscometer in a mechanical spectrometer. All proteoglycan solutions tested possessed: (1) linear viscoelastic properties - as measured by the dynamic complex modulus under small amplitude steady oscillatory conditions (1 less than or equal to omega less than or equal to 100 rad/s) - and (2) nonlinear shear-rate dependent apparent viscosities and primary normal stress difference under steady shearing conditions (0.25 less than or equal to gamma less than or equal to 250 s-1). Our transient flow data show that all proteoglycan aggregate solutions exhibited transient stress overshoot effects in shear stress and normal stress. From these steady and transient flow data, we conclude that link protein stabilized aggregates have significant effects on their dynamic and steady-shear properties as well as transient flow properties. The transient stress overshoot data provide a measure of the energy per unit volume of fluid required to overcome the proteoglycan networks in solution from a resting state. Thus we found that link-stable aggregates form much stronger networks than link-free aggregates. This is corroborated by the fact that link-stable aggregates form more elastic (lower than delta) and stiffer (higher [G*]) networks than link-free aggregates. The complete spectrum of viscometric flow data is entirely compatible with the proposed role of link protein in adding structural stability to the proteoglycan-hyaluronate bond. In cartilage, the enhanced strength of the networks formed by link-stable aggregates may play an important role in determining the material properties of the tissue and thereby contribute to the functional capacity of cartilage in diarthrodial joints.

The density and strength of proteoglycan-proteoglycan interaction sites in concentrated solutions

Rheological flow properties of link-stable and link-free proteoglycan (PG) aggregates in concentrated solutions were measured using a cone-on-plate viscometer. A second-order constitutive model, based upon the statistical-network theories of Lodge, [Rheol. Acta 7, 379-392 (1968)] and De Kee and Carreau [J. Non-Newtonian Fluid Mech. 6, 127-143 (1979)], was developed to describe the measured steady and transient flow responses exhibited by the PG solutions. Our measurements confirmed previous experimental findings that the complex shear modulus of PG solutions depends on the frequency of the imposed small-amplitude oscillatory shear, and the apparent viscosity and primary normal-stress difference depend nonlinearly on the shear rate under steady-shear flow conditions [Mow et al., J. Biomechanics 17, 325-338 (1984b); Hardingham et al., J. orthop. Res. 5, 36-46 (1987)]. In the present study, we found that PG solutions exhibit pronounced stress overshoot responses and large hysteresis loop effects. These transient responses were shown to be sensitive to acceleration strain (i.e. the second rate of strain) as well as PG structure (i.e. link-protein stabilization). The model parameters were determined by curvefitting of the second-order constitutive model and experimental data from steady, oscillatory and transient shear flow measurements. Using this network model, we calculated the density of the idealized interaction sites existing in the PG network, and the average strength of these interaction sites. The results indicate that link-protein stabilization of PG aggregates does not change the density of interaction sites formed in the PG network, rather, it increases the average strength of these interaction sites.

Viscometric Properties of Proteoglycan Solutions at Physiological Concentrations

Proteoglycans are important components of the extracellular matrix of articular cartilage and other soft tissues. The structural organization of these macromolecules is believed to be significant for maintaining the cohesion of the extracellular matrix, and thus influences the material properties of the tissue as a whole (Pottenger et al. 1982; Muir 1983). Recent studies have shown that the structure of proteoglycans varies with cartilage age and pathology (Hjertquist and Wasteson 1972; Bayliss and Ali 1979; Muir 1977, 1980, 1983; Roughley and White 1980; Pal et al. 1981; Buckwalter et al. 1983; Buckwalter and Rosenberg 1985). In general, as cartilage ages and degenerates, proteoglycan size decreases (i.e. lower molecular weight) and the percentage of non- aggregated forms increases. The decrease in proteoglycan size and percentage aggregation has been shown to be important factors in increased mobility of the proteoglycan within the collagen meshwork (Pottenger et al. 1982; Muir 1983). Link proteins serve to stabilize proteoglycan aggregates by joining the proteoglycan monomers to a linear hyaluronate chain (Hardingham 1979,1981). Changes in proteoglycan aggregation may involve abnormalities in the hyaluronate binding region of the monomer or the link protein (Muir 1977, 1983; Hardingham 1979,1981; Plaas and Sandy 1984; Poole 1986; Ratcliffe et al. 1986). These changes tend to alter the collagen-proteoglycan and proteoglycan-proteoglycan interactions (Obrink 1973; Myers et al. 1984b; Mow et al. 1989), causing possible migration of proteoglycan fragments through, and loss from, the extracellular matrix (Brandt 1974; Muir 1977; Bayliss and Ali 1979; Ratcliffe et al. 1986).