This chapter aims to provide an intuitive review of articular cartilage mechanical properties and its response to loading in the context of its biochemical composition and structural organization. The implications of how changes to articular cartilage biomechanics with joint degeneration upset the normal feedback system of the chondrocyte and its ability to regulate the structure-function relationship of articular cartilage will be discussed.

Articular cartilage is a connective tissue that lines the bony surfaces of diarthrodial joints. Its primary function is to support the loads acting across the joint while producing minimal friction and wear. More specifically, articular cartilage provides compliance to otherwise hard bony surfaces, distributing the joint contact forces over a sufficiently large area to minimize contact pressures at the articular surfaces, and stresses transmitted to the bone. In some joints, this function is further enhanced by additional soft-tissue structures that enhance joint congruence, such as menisci and labra. Since bone remodels significantly in response to stresses, whereas cartilage does not, the compliance of healthy cartilage produces suitable homeostasis in the bone remodeling process, helping to maintain normal joint anatomy. The mechanical breakdown of cartilage, however initiated, compromises this primary function, leading to a cascade of events that compromise joint health, function and anatomy.

Forces acting across diarthrodial joints are combinations of (internal) muscle forces and external loads, including gravitational, inertial, and lifting forces. These same forces also produce moments about the joint axis of rotation, which are calculated as the product of the force times the distance from the force line of action to the axis of rotation (the moment arm). It would be a gross underestimation to assume that forces transmitted across diarthrodial joints are roughly equal to body weight (gravitational force) or loads acting on our extremities in activities of daily living (lifting forces). Due to the compactness of the musculoskeletal system, namely the proximity of muscles to the skeleton, muscles must apply much higher forces across a joint than the external forces acting on the body, to also balance the moments exerted by external forces about the joint axis of rotation.

Newton’s second law of motion tells us that the sum of all forces acting on a body (including inertial forces) must be balanced. Importantly, the same law of physics tells us
that the sum of all moments acting on a body must also be balanced. Let us illustrate this basic concept by examining the force required in the biceps muscle to balance the weight of an object held in the hand (Figure 1). For this example, we consider that a 10 N weight (about 2 pounds) is held in the hand with the upper arm held vertically and the forearm held horizontally. The distance from the hand to the elbow joint is 30 cm (approximately 1 foot), and the distance from the biceps muscle insertion on the forearm to the elbow axis of rotation is 6 cm (approximately 2 inches). The moment exerted by the handheld weight about the elbow axis of rotation is 10 N × 30 cm = 300 N•cm. Consider that the force exerted by the biceps muscle is F; its moment about the elbow axis of rotation is F × 6 cm. Accordingly, to maintain moment equilibrium about the elbow, these two moments must balance each other, F × 6 cm = 300 N•cm, from which it follows that F = 50 N (about 10 pounds). Using force equilibrium, we conclude that the contact force exerted at the elbow joint is the difference between the muscle force and the handheld weight, thus 40 N. In other words, in this example, the force in the muscle is five times higher, and the joint contact force is four times higher, than the external force acting on the musculoskeletal system. These relations scale with the magnitude of the handheld weight; thus, for a weightlifter performing a bicep curl using a 1,000 N weight (500 N in each hand), the joint contact force in each elbow would be 2,000 N (approximately 400 pounds, or nearly three times body weight).

These multiplication factors apply across all diarthrodial joints. Lower extremity joints experience greater magnitudes of joint loads than upper extremity joints; they also typically have larger articular surfaces. Higher extremity joints are typically smaller in size, especially in the hand and wrist, and support smaller external forces; however, some joints such as the thumb and shoulder may exhibit up to 10-fold multiplication factors relating external forces to joint contact forces.^1,2 Thus, regardless of location, all diarthrodial joints transmit contact forces several times greater than the external forces acting on the musculoskeletal structures spanning those joints.

Articular cartilage distributes this contact force over a relatively large fraction of the articular surfaces. A joint contact force F distributed over a contact area A produces an average contact pressure p=F/A. For example, for a closed kinematic chain exercise for the knee joint (eg, squatting), the quadriceps muscle force is approximately equal to 1,600 N at 60° of flexion, producing a comparable contact force at the patellofemoral joint.³ The resulting articular contact area is approximately 650 mm² (which is roughly half the surface area of the patellar articular layer⁴), producing an average contact pressure . One megapascal (MPa) is equal to one hundred forty-five pounds per square inch; if a person could hang his/her weight from a single fingertip, this would be roughly equivalent to the pressure exerted on that tip. In general, activities of daily living produce average articular contact pressures in the range 1 to 6 MPa⁵; strenuous sports activities may conceivably produce contact pressures up to 12 MPa for intermittent loading durations, though the evidence for such elevated values is limited. It has been estimated from in vitro cadaver studies that cartilage and its underlying subchondral bone plate may crack when articular contact stresses exceed 15 MPa.⁶ Thus, under normal loading conditions articular cartilage is well suited to support the wide range of loads acting across diarthrodial joints.

Articular cartilage is a hydrated porous permeable tissue whose interstitial fluid (water and electrolytes) contributes 60% to 85% to the tissue’s weight.⁷ The extracellular matrix (ECM) consists primarily of collagen (15% to 22% of the wet weight, 50% to 80% of the dry weight) and proteoglycans (4% to 7% of the wet weight, 15% to 30% of the dry weight).⁸ Chondrocytes occupy less than 10% of the tissue volume. Collagen is predominantly of type II, which forms fibrils with a diameter varying between 20 and 200 nm, but not fibers. Other ECM collagens include types VI, IX, and XI. Cartilage proteoglycans have a bottle-brush appearance, with a core protein and glycosaminoglycan side chains consisting of chondroitin sulfate (CS) and keratan sulfate (KS). A link protein ties these aggrecans along a hyaluronic acid backbone, forming macromolecular complexes with molar masses on the order of millions. Both CS and KS are negatively charged in solution, thus conferring a fixed-charge density (FCD) to cartilage.⁹

The fibrillar organization and composition of the ECM varies significantly from the articular surface to the subchondral bone. The superficial zone starts at the articular surface and extends by hundreds of nanometers; it is characterized by elevated collagen and water content and very low proteoglycan content. The collagen fibrils are oriented parallel to the articular surface, with a preferential direction¹⁰ believed to coincide with the “split-line” direction, named after the method of visualizing it by pricking the surface with a needle. The functional significance of the split-line directions remains unclear, though it appears that they coincide with directions of greatest curvature of the articular surfaces.^11,12 With increasing distance from the articular surface, collagen fibrils progressively rotate to form the middle (or transitional) zone and then become perpendicular to the cartilage-subchondral bone interface in the deep (or radial) zone. In the middle zone, the collagen fibrils are often split between two families that emanate from the superficial zone in opposite directions, eventually merging into a single family in the deep zone.^10,13 Proteoglycan content is greatest in the middle zone, followed by the deep zone, whereas collagen and water content progressively diminish from the articular surface to the subchondral bone. A tidemark delineates the interface between the deep zone and the zone of calcified cartilage where this tissue meets bone.

Other functionally significant cartilage constituents include superficial zone protein (SZP), which is believed to confer beneficial lubrication and wear properties at the articular surface.^14,15 Cartilage thickness varies approximately from less than 1 mm thick on average in smaller upper extremity joints¹⁶ up to 3 mm thick on average in larger extremity joints.¹⁷ Some locations in the tibial plateaus and the patella may be up to 7 mm thick.⁴

Unlike other connective tissues, such as tendons and ligaments which sustain tensile forces, cartilage is subjected primarily to compressive loads. It is therefore an interesting characteristic of articular cartilage that its ECM consists substantially of fibrillar collagen, a microscopically rope-like material which is best suited to resist tensile forces. As it turns out, collagen fibrils interact mechanically with the other main ECM constituents, interstitial fluid and proteoglycans, to provide the functional response that confers cartilage its remarkable load-bearing and frictional properties.

The porous ECM of articular cartilage is permeable to the interstitial fluid.¹⁸ Upon mechanical loading of cartilage, this interstitial fluid pressurizes and flows from high pressure (loaded) to low pressure (unloaded) regions. However, the frictional resistance to this flow is very significant as fluid molecules flow past the ECM matrix constituents. Experimentally, this frictional resistance is quantitatively assessed by measuring the material property called the hydraulic permeability, represented by the symbol k. From measurements of k, it is estimated that the characteristic velocity of interstitial fluid flow in articular cartilage is on the order of 0.1 µm/s. For comparison purposes, the diameter of a chondrocyte is approximately 16 µm. In effect, interstitial fluid flows so slowly within cartilage that fluid volume loss from articular layers may be considered negligible during activities of daily living. Measurements from MRI suggest that the fluid volume loss is less than 6% of the cartilage volume in a low extremity joint subjected to strenuous exercise.¹⁹

The primary functional effect of interstitial fluid pressurization is to stiffen articular cartilage under dynamic loading conditions.²⁰ In vitro measurements performed in human patellofemoral joints show that a physiologic level of cyclical contact pressure (p = 3.3 MPa) prescribed at one cycle per second produces no more than ε = 9% cyclical change in cartilage thickness.²¹ The stiffness of cartilage under cyclical compressive loading is called the dynamic compressive Young modulus E_dyn. Its value may be estimated from the ratio of the prescribed pressure p to the compressive strain ε; thus, for human patellofemoral joint cartilage, E_dyn = 37 MPa. In contrast, if the contact pressure is maintained for sufficiently long durations, the fluid pressure subsides leading to much
larger compressive strains under physiologic pressures. This type of response is often characterized under laboratory conditions, using much smaller compressive pressures p, to yield a stiffness measure called the equilibrium compressive Young modulus, E_eq. Typical measurements of this equilibrium stiffness yield values on the order of E_eq = 0.4 MPa, nearly 100 times smaller than the dynamic modulus.²² This comparison between dynamic and equilibrium moduli helps us better appreciate the functional importance of interstitial fluid pressurization for resisting compressive pressures and maintaining cartilage deformations to within levels not harmful to chondrocyte viability.

Proteoglycans are negatively charged macromolecules enmeshed within the collagen matrix. Due to electrostatic interactions, more cations (eg, Na⁺) transport into cartilage than anions (eg, Cl⁻) to neutralize the proteoglycan charge. This mechanism produces a higher concentration of ions inside the tissue than in its external bathing solution, leading to an influx of water which causes the tissue to pressurize and swell. This is called Donnan osmotic swelling, and the resulting interstitial fluid pressure is the Donnan pressure. Donnan swelling effectively stiffens articular cartilage since it pressurizes the collagen matrix, similar to an inflated balloon.²³ Measurements performed in various bathing solution concentrations suggest that Donnan swelling contributes approximately 60% to the measured compressive stiffness E_eq.^24,25 In contrast, complete enzymatic digestion of the proteoglycans of articular cartilage has been shown to decrease its compressive equilibrium Young modulus E_eq by a factor of 100 (down to approximately 0.003 MPa).²⁵ Therefore, macromolecular proteoglycans also contribute significantly to the structural stiffness of the fiber-composite-like cartilage ECM.

Collagen fibrils are able to sustain large tensile loads but otherwise buckle under compression. Proteoglycans enmeshed within the collagen matrix serve as a “ground matrix” that stabilizes the collagen network by helping it to resist compression.²⁶ The primary functional role of collagen fibrils in cartilage is to resist transverse tissue expansion upon axial compressive loading when the interstitial fluid is pressurized.^27,28 To better appreciate this functional role, assume that collagen is inextensible (infinitely stiff in tension) and consider a cylindrical plug of cartilage subjected to a compressive pressure p (Figure 2). Upon rapid application of this pressure, there is insufficient time for the interstitial fluid to flow out of the tissue; therefore, the fluid pressurizes and the volume of the cylindrical plug must be substantially preserved as it is being loaded (since mass must be conserved and the densities of ECM and interstitial fluid are nearly constant). If the collagen is inextensible, the cylindrical plug cannot expand in the direction transverse to loading; since its volume is to be
preserved, the height of the plug may not change either, that is, the plug acts as an infinitely stiff spring.²⁹ Of course, in reality, the collagen is not perfectly inextensible so that the cartilage plug will get compressed a little (Figure 2, C). Nevertheless, this hypothetical example clearly shows that the tensile stiffness of the collagen matrix, when coupled with interstitial fluid pressurization, contributes considerable stiffness to cartilage under compressive loading. This mechanism explains why E_dyn is nearly 100 times greater than E_eq.