Cartilage Biomechanics

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Biphasic Nature

Synovial joints have high loads applied to them statically, cyclically, and repetitively over a lifetime. The solid matrix, the collagens, proteoglycans, and other molecules is arranged in such a way to to sustain these loads. It must be strong, fatigue-resistant, and tough.

What we find regarding the material properties of cartilage is that it is porous, permeable, and very soft. Water makes up a large percentage of the total weight, and can flow through the porous-permeable solid matrix by pressure gradients or compaction of the matrix. The term biphasic means that cartilage can be viewed as having both a solid phase (principally from the solid matrix) and a fluid phase (principally from the water).

Permeability

Water can flow through the cartilage with applied pressure gradients across the tissue. It has a very large frictional drag coefficient and so any interstitial fluid flow causes large drag forces to be generated. Therefore very high pressure gradients are needed to move water through cartilage. Therefore fluid pressure provides significant total load support, minimising the stress on the solid matrix.

Also, with compression water can flow through the porous-permeable solid matrix. The compressive stress leads to the solid matrix being compacted, which raises the pressure in the interstitium, and forces the fluid out of the tissue.

There is a direct relationship between permeability and water content, and an inverse relationship between permeability and proteoglycan content.

Viscoelasticity

Articular cartilage is viscoelastic, meaning it exhibits a time dependent behaviour when subjected to constant load or deformation.

It displays creep, in that with constant compression stress, deformation increases will time, until an equilibrium is reached. Similarly, with a constant strain, the stress rises to a peak, and then slowly relaxes until an equilibrium is reached.

There are two mechanisms that provide articular cartilage with viscoelastic properties: flow-dependent, and flow-independent mechanisms.

Flow-dependent: depends on interstitial fluid flow and pressurisation. The drag that comes about from interstitial fluid flow is the main contributor to the compressive viscoelastic behaviour.
Flow-independent: depends intermolecular friction due to the intrinsic viscoelastic behaviour of the collagen-proteoglycan matrix.

The compressive resilience between proteoglycan aggregates and interstitial fluid is provided by negative electrostatic repulsion forces. In an aqueous solution, the negative charges would cause aggregated proteoglycans to spread out. Under compression the negatively charged sites are pushed together, which increases their repulsive force, and thereby increases the compressive stiffness of the tissue.

Flow Dependent Properties with Compression

Cartilage behaves like a sponge that does not allow fluid to flow through it easily. With the application of a compressive force there is an immediate increase in interstitial fluid pressure, leading to fluid to efflux out of the matrix. With removal of the load, the fluid flows back in from the inner joint space to the tissue.

Under constant load, with creep occurring, the load supported is slowly transferred from the fluid phase to the solid phase as the fluid pressure reduces. In normal cartilage it takes 2.5 to 6 hours to reach this equilibrium, at which point the load is supported entirely by the compressed collagen-proteoglycan solid matrix.

In vivo, this equilibrium doesn't ever occur because the joints tend to always move even with sleep. Therefore there is almost always fluid pressurisation within the tissue. In normal states, fluid pressurisation is the dominant physiologic load-supporting mechanism. The solid matrix is very soft, and has a low permeability, and so allows for this. The ratio of load supported by fluid pressure to that supported by solid matrix is greater than 20 to 1 in normal tissue.

In early osteoarthritic change, there is increased water content and decreased proteoglycan content. This leads to increased tissue permeability, which in turn reduces the fluid pressurisation mechanism of load support in cartilage. In this setting, the solid matrix is called upon to bear more of the load, which is detrimental to the long term viability of cartilage.

Flow Independent Properties with Shear

Collagen is organised randomly with entrapped proteoglycan molecules in the middle zones of cartilage . This contributes to its shear stress-strain curve.

There is a nonlinear response with increasing compression leading to increased resistance to shear stresses.

With pure shear forces, there is no interstitial fluid flow because there is no pressure gradient or volume change.

The stiffness and energy dissipation of cartilage in shear is provided by the proteoglycan-collagen structure, not by the proteoglycan-proteoglycan network. The proteoglycans function to maintain the inflated spatial form of the collagen network, rather than providing any significant resistance to shear.

Tensile Properties

With stretching or compression of a material there is always a change in volume, and so both flow-dependent and flow-independent viscoelastic processes occur with tension stresses.

The tensile modulus is the proportionality constant in the linear phase of the stress-strain curve, and it varies from 5 to 50 MPa. The tensile modulus depends on the many variable such as location, depth, and composition. Superficial zone cartilage is stiffer than middle and deep zone cartilage due to higher concentration and higher degree of collagen fibrils. There is a reduction in tensile stiffness with osteoarthritic changes.

Cartilage Swelling

Swelling is the increase in size or weight with a material being soaked in solution. Articular cartilage swells because of physicochemical forces. Physicochemical refers to the force deriving from the charged nature of the proteoglycans. Proteoglycans have 1 or 2 negative charges on each dimeric hexosamine. In osteoarthritis, the fixed charge density dramatically reduces due to loss of proteoglycans.

The negative charges need opposing positive charges for electroneutrality, and the total ion concentration in the tissue needs to be greater than that in the bath. The ion imbalance leads to an internal swelling pressure greater than the pressure in the bath. This swelling pressure is restrained by the stress from the solid matrix that resists expansion. It is thought that collagen provides most of the resistance to swelling pressure.

How much the swelling pressure contributes to load support depends on the load that is applied. In light loads, the swelling pressure has significant contribution. For highly loaded structures in physiological range and in dynamically loaded structures, it is uncertain how much the swelling pressure contributes.

In early osteoarthritis, the loss of swelling pressure is less severe than the compromise of mechanical properties of the solid matrix.

Joint Lubrication

Lubrication is the process of reduction friction, and/or wear, between moving surfaces through applying a lubricant.

The lubricating system of synovial joints is highly effective, allowing various intensities and durations of loads with relatively little wear over the lifetime of the joint. The coefficient of friction of a healthy joint is 0.005. This refers to the resistance to movement between two surfaces in contact. This is even lower than the friction of highly polished machine bearings and steel on ice such as in ice skating which have coefficients of 0.01.

Lubrication can occur through different mechanisms, and mainly occurs through boundary lubrication which provides protection in areas of contact, and fluid film lubrication which provides protection in areas of noncontact, or a combination of both which is called mixed lubrication.

Fluid film lubrication is where there is a film of fluid/lubricant (synovial fluid) completely separates the articulating surfaces. It supports contact loads through the fluid pressure in the film. Fluid film lubrication can operate in may forms

Hydrodynamic lubrication: occurs through continuous motion of the surfaces where a thin fluid film is created that supports the load. It occurs in high speeds and low loads.
Squeeze-film lubrication: the two surfaces approach each other without sliding, pressure builds up because the fluid can't be instantaneously squeezed out, which provides a cushioning effect. Localised depressions are also created where lubricant is trapped. The non-newtonian properties also prolongs the squeeze-film time.
Elastohydronamic lubrication: large pressures causes deformation of an articulating surface and therefore enlargement of the load bearing surface area. This is important as speed increases.

The non-newtonian properties of synovial fluid, with its shear thinning effect, increases the load carrying capacity, the area over which a load is spread, and the duration of the squeeze-film time.

Boundary lubrication is where surfaces are protected from surface-to-surface contact via single layer of lubricant (lubricin) that is adsorbed on each load bearing surface. This single layer is a monolayer of macromolecules attached to each surface. This form of lubrication dominates in the presence of low shear velocity, low fluid viscosity, and high contact pressure, where the articulating surfaces get progressively closer together until contact occurs.

Mixed lubrication The transition point between these two mechanisms of lubrication is termed mixed lubrication. Articular cartilage is extremely but not perfectly smooth, at the nanoscale level it has an undulating surface with tiny "asperites". Fluid film lubrication occurs in regions of cartilage non-contact, and boundary lubrication occurs in areas of contact.

There is also shift of fluid film to boundary lubrication with time over the same location. Boosted lubrication occurs, which is where the solvent component of synovial fluid passes into the articular cartilage during squeeze-film action which yields a concentrated gel of protein complexes that coats and lubricates the surfaces.