Study of the interaction of two bodies in relative motion (via the concepts of friction, wear and lubrication).¹

• Definition: Resistance to movement between two surfaces in contact.
• Laws of dry friction² – frictional force is:

1. Proportional to the force (N) acting to press the surfaces together.
2. Independent of the contact area between the two surfaces.
3. Independent of the sliding speed between the surfaces.

• Friction also depends on the surface roughness (Ra) of the two surfaces in question. Ra is a measure of the irregularities on the surface of an object, these irregularities are also known as “asperities”. Surfaces with asperities of smaller amplitude and frequency are therefore smoother and produce less friction.

Figure 1. The frictional force (F) resists force A, slowing the forward motion of the box. N represents the force acting to push the two objects together and always acts perpendicular to F. In this case N = the weight of the white box.

Coefficient of friction

• The coefficient of friction (µ) is a ratio of the frictional force (F) and the load acting between the two surfaces (N):³
• ^{μ = f/N.}

• As it is the ratio between two forces it has no units and is always between 0 and 1. A greater µ means more force is required for the objects to slide, i.e. the bearing will be less efficient.
• Friction is a key principle in orthopaedics as it results in wear.

·         Definition: The removal of material from two surfaces under load, due to the sliding motion between them.¹

·         Like friction, wear is independent of the contact area between the two surfaces, and proportional to the force pressing the surfaces together.

·         However, importantly, the amount of wear is also proportional the sliding distance travelled by the surfaces.

·         NB. Corrosive wear is an exception to these rules being both independent of the loading between surfaces and sliding distance.

·         Reducing wear is key to the survivorship of natural and prosthetic joints.

Mechanisms of wear

• Wear can be broadly categorised into:
•  MECHANICAL – dependent on loading and sliding distance:
• Adhesive
• Abrasive
• Fatigue
• Erosive
• CHEMICAL – independent of loading and sliding distance:
• Corrosive

Adhesive wear

• Asperities from the two surfaces under load adhere to each other forming bonds (cold welding). As the surfaces slide over each other, some of the adhered asperities from one surface will shear off, remaining stuck to the other surface.
• This usually occurs between two surfaces that have similar molecular structures, as bonds form easily between them.
• Example: in metal-on-metal hip bearings.

Fig 2a. two asperities bond to each other.

Fig 2b. as the materials pass over each other the bonded asperity shears off its original surface and now becomes part of the other surface. 

Abrasive wear

• Asperities from the harder surface literally knock off the asperities from the softer surface, as they slide.
• This usually occurs between two materials of different hardness.
• Example: between a metal femoral head and polyethylene liner.

Figure 2c. and 2d. These show how the asperities of the harder bearing surface break off the softer asperities of the surface below.

Fatigue wear

• Repeated cyclical loading of one surface, at loads greater than the fatigue strength, leads to small cracks forming under the surface. Through repeated loading these cracks propagate, eventually joining together, and the loose material comes away from the surface.
• Example: delamination of the polyethylene in total knee replacements (TKRs)

Figure 2e. Here loads much lower than that needed for abrasive wear, after repeated cycles, gradually cause cracks to form under the surface. These cracks eventually coalesce and fragments of the surface break off.

Erosive wear

• Hard particles travelling in fluid interposed between the two surfaces remove some of the surface as they collide into it.

Figure 2f. The presence of third body particles carried in the lubricant fluid can lead to erosion of the bearing surfaces. 

Corrosive wear

• Material is removed via a chemical reaction.
• In crevice corrosion small crevices between surfaces (e.g. between trunion and femoral head) trap fluid which becomes stagnant. Fluid at the apex of the crevice quickly uses up its O₂, where fluid at the entrance to the crevice remains well oxygenated. This oxygen gradient leads to the formation of an anode (area of metal giving up electrons and forming positive metal ions) in the area of low O₂ and a cathode (area of metal receiving electrons) in the high O₂ environment. The positive metal ions in the fluid lower pH leading to acidic fluid formation and thus dissolution of the material.
• Example: the crevice formed between the trunion and femoral head can lead to corrosive trunion wear.

Figure 2g. The difference in O2 tension between the apex of the cravice and the entrance to the crevice leads to the formation of an anode and cathode. As the anode gives off electrons (e-) to the cathode, pH at the apex decreases, leading to acidic erosion of the surfaces.

• Definition: A substance placed between two bearing surfaces in order to reduce friction.⁴
• Viscosity = the ability of a material to resist shear force.
• Mechanical wear only occurs when the shear forces acting over the surface of a body are great enough to break off asperities (as discussed above). With the addition of a viscous lubricant, much of the shear force produced by the sliding object is taken by the fluid, reducing shear at the body surface, leading to reduced wear.

How different lubricants respond to shear force

• As two objects slide over each other, the interposed lubricant changes shape due to the shear forces across it. The amount it changes shape is known as the shear strain and the rate at which it changes shape is known as the shear strain rate. (This can also be described as the “velocity gradient”.)
• All fluids can be broadly divided into three groups, regarding how they react to shear strain rate:

1. Newtonian fluid – aka. Isoviscous – viscosity remains the same regardless of the rate of shear strain acting in the fluid, e.g. water.
2. Thixotropic fluid – aka. Shear-thinning – the fluid becomes less viscous as the rate of shear strain is increased – e.g. tomato ketchup, as the bottle is shaken more vigorously the fluid is poured out more easily.
3. Dilatant fluid – aka. Shear-thickening – the fluid becomes more viscous as shear strain rate rises – e.g. liquid body armour, when hit by a bullet (i.e. high shear strain rate) it becomes very viscous and stiff.

• Synovial fluid = thixotropic – i.e. In a joint at rest the fluid is more viscous. As the sliding speed in the joint increases, the fluid becomes thinner, and less resistant to shear strain.

Figure 3. This graph shows how the shear strain rate effects the viscosity of Newtonian, dilatant and thixotropic fluids.

Modes of lubrication

• Lubricants can act to reduce friction in three ways:

1. Boundary lubrication
2. Fluid film lubrication
3. Mixed lubrication

Boundary lubrication

• Here the depth of the lubricant between the surfaces is less than the surface roughness (i.e. height of the asperities) of each surface.¹
• The asperities on the surfaces still make contact, allowing wear to take place. However, the lubricant does form a protective barrier on each surface which absorbs some of the shear force acting on the surface, reducing the amount of wear.
• This is the least effective mode of lubrication.

Figure 4a. In boundary lubrication the fluid forms a protective barrier, but does not prevent asperity contact.

Fluid film lubrication

• Here the depth of the fluid between the surfaces is greater than the surface roughness.¹
• The fluid film between the objects is sufficient to hold the surfaces apart so that the asperities do not touch.
• It can be subdivided into:
• Hydrodynamic lubrication
• Elastohydrodynamic lubrication

This is a very effective form of lubrication, resulting in negligible wear, but requires specific conditions to occur

Figure 4b. In fluid film lubrication, the surfaces are held apart, preventing asperity contact, which leads to a very low wear rate.

Mixed lubrication

• Here the fluid between the objects is deep enough to prevent many of the asperities meeting, but the larger asperities will still touch, resulting in some wear.¹
• The effectiveness of this mode of lubrication lies somewhere between boundary and fluid film.

Figure 4(c). Mixed lubrication provides enough fluid to prevent smaller asperity contact, but larger surface asperities will still cause wear.

Hydrodynamic/elastohydrodynamic lubrication¹

• Hydrodynamic and elastohydrodynamic describe the two types of fluid film lubrication.
• In elastohydrodynamic lubrication, the fluid film on its own is not quite thick enough to prevent asperity contact. However, the compressive forces acting through the fluid act to elastically deform the asperities, making them more flat, reducing surface roughness temporarily. The reduced surface roughness and the presence of the fluid combine to give fluid film lubrication.
• In hydrodynamic lubrication, the fluid film is thick enough to prevent asperity contact without any change in the surface roughness.
• As suggested by its subgroup names (hydro-/elastohydro-dynamic), one of the keys to achieving fluid film lubrication is motion.

The Stribeck curve

• Three variables determine what mode of lubrication a joint can achieve:¹

1. Lubricant viscosity
2. Sliding speed between surfaces
3. Load acting to push the two surfaces together

• The Stribeck curve describes how changes in these variables affects what mode of lubrication is seen, and ultimately how this affects friction.
• In boundary lubrication µ is constant as the lubricant just acts as a protective barrier over the asperities (which remain in contact).
• As viscosity or sliding speed increases (or load decreases), µ decreases.
• By how much these variables change will determine if the joint achieves mixed or fluid film lubrication.
• A transition point occurs when increasing viscosity or sliding speed starts to increase µ paradoxically. This occurs due to the effects of drag from the lubricant fluid, acting on the bearing surfaces.¹
• By attempting to alter these three variables we could potential improve the efficiency of both natural and prosthetic joints.
• Examples include:
• Advising on weight loss will decrease the load on the joint.
• One of the guiding principles of large head metal-on-metal hip arthroplasties was that increasing head diameter led to a greater sliding speed at the bearing surface, increasing the possibility of fluid film lubrication.
• Although clinical data would now suggest fluid film lubrication is seldom achieved in these or any prosthetic joints.

Figure 5. A stribeck curve showing how the coefficient of friction between two surfaces is affected by lubricant viscosity, sliding speed and load

• The lambda ratio is an important predictor of wear.
• λ = Fluid-film thickness : surface roughness (Ra)
• λ<1 = boundary lubrication
• 1<λ<3 = mixed lubrication
• λ>3 = fluid-film lubrication

• The bearing surfaces in synovial joints consist of articular cartilage, separated with a synovial fluid lubricant.

Articular cartilage

• Composite of chondrocytes, extracellular matrix and water:⁶
• Chondrocytes:
  • Specialised cells that produce matrix contents.
• Matrix:
  • Collagen (mostly type II).
  • Proteoglycans – protein core surrounded by glycosaminoglycan molecules (keratin sulfate and chondroitin sulphate).
• Mechanical properties:
• Viscoelastic – able to tolerate significant deformation before plastic deformation/wear.
• Acts like a sponge, with its fluid contents moving through it in response to the compression and tension forces acting across it. This is key in maintaining a decent fluid film between surfaces.
• Low surface roughness – in healthy joints…

Synovial fluid (SF)

• Ultrafiltrate of blood plasma, with additional components (hyaluronic acid, proteoglycans, prostaglandins) secreted by the synovium and articular chondrocytes.^7,8
• Key molecules to SF lubrication are:⁸
• Hyaluronic acid
• Proteoglycan 4 (aka. lubricin)
• Surface-active phospholipids
• Thixotropic fluid – meaning at lower sliding speeds viscosity is greater.

• As discussed earlier (see Tribology – basics: Lubrication) the key to effective lubrication is to maintain a fluid film between the articulating surfaces, sufficient to prevent asperity contact. The movement of fluid into/out of articular cartilage’s permeable structure aims to maintain this fluid film under loading via three methods:

1. Weeping lubrication
2. Boosted lubrication
3. Squeeze-film lubrication

• The unique interaction between synovial fluid and articular cartilage allows synovial joints to achieve a coefficient of friction as low as 0.002.⁷

Weeping lubrication

• Direct compression forces fluid out of articular cartilage (similar to squeezing a saturated sponge).
• Osmotic pressure, from the presence of proteoglycans in cartilage structure, acts to draw the fluid back in once the load is released.

Figure 6(a). In weeping lubrication, loading cartilage causes fluid to leak out like water from a sponge.

Squeeze-film lubrication

• As pressure is applied to press the two articulating surfaces together, the fluid starts to squeeze away from the areas of high contact stress to the lower pressure areas.
• However, as the fluid is viscous, this fluid movement is not instantaneous, allowing time for hydrostatic pressure to build in the fluid film. This pressure is enough to keep the surfaces separated.³
• This is a very temporary phenomenon, lasting only a few seconds. After this time the fluid movement has occurred and the film thickness starts to reduce.
• The viscoelasticity of cartilage aids squeeze-film lubrication, as loading deforms cartilage, increasing its surface area. This not only reduces stress at the surface, but also slows the movement of fluid prolonging the squeeze-film affect.
• Increasing cartilage surface area also acts to decrease shear strain rate, which increases synovial fluid viscosity.³

Figure 6(b). In squeeze film lubrication, hydrostatic forces from the compressed fluid film act to hold the surfaces apart.

Figure 6(c) In boosted lubrication, prolonged loading pushes fluid into the cartilage. As large proteins (e.g.hyaluronate) cannot pass into the cartilage matrix, fluid viscosity increases.

Boosted lubrication

• On more prolonged loading, synovial fluid is pushed back into the articular cartilage. However, the larger molecules (e.g. hyaluronic acid, lubricin) in the fluid are unable to permeate the matrix and therefore remain in the joint.
• The higher protein concentration in the fluid remaining in the joint space increases viscosity.
• Increasing viscosity increases the likelihood of fluid film lubrication (see Tribology – basics: The Stribeck curve).

Synovial fluid lubrication in gait

• It is likely synovial joints use all these methods of lubrication at some point in the gait cycle. For example:³
• Squeeze-film lubrication in heel strike.
• Boosted lubrication in prolonged joint loading (e.g. during stance).
• Weeping lubrication during toe-off.
• With these unique methods of increasing/maintaining fluid film thickness, synovial joints can achieve elastohydrodynamic/hydrodynamic lubrication. In particular during the swing phase of gait, when the sliding speed is at its maximum.

Boundary lubrication in synovial joints

• During prolonged stance periods it is likely boundary lubrication is used. A hydrophobic monolayer, made up of lubricin and phospholipids, covers the articulating surfaces, reducing the coefficient of friction between them.³

• An understanding of tribology is key in arthroplasty due to the effect of wear on joint life-span.

Wear and aseptic loosening

• In 1977 Wilert and Semlitsch identified the inflammatory response to wear debris as the route cause for aseptic peri-prosthetic osteolysis, eventually leading to aseptic loosening.⁸
• Aseptic loosening is now the most frequent reason for revision surgery in total hip replacements.
• Mechanism of aseptic osteolysis:⁷
• Friction at the bearing (and non-bearing) surfaces leads to production of wear particles.
• Local macrophages attempt to phagcytose wear particles, while releasing cytokines.
• Some cytokines (including platelet-derived growth factor (PDGF)) stimulate local osteoblasts to produce RANKL, which stimulates osteoclasts to resorb local bone.
• Wear particles are dispersed throughout the joint via the movement of joint fluid.
• The number and size of wear particles produced is proportional to the inflammatory response and hence the amount of osteolysis, thus limiting wear particle formation is critical to joint survivorship.

Effective joint space

• Schmalzried et al. first coined the term “effective joint space” after their study found macrophages laden with polyethylene particles as distal as the femoral canal cement plug, with associated signs of osteolysis.⁹
• Effective joint space = any area where the prosthesis/cement touches bone.⁷
• Wear particles can travel in joint fluid down potential channels around the prosthesis, due to changes in the fluid pressure gradient around the implant. The fluid (+ particles) follows the path of least resistance.
• Well integrated implants can “seal off” areas around prostheses, limiting the access of fluid to these areas.
• Common areas that are susceptible to form channels for wear particles to travel include:⁷
• Screw holes in acetabular component.
• Cement mantle defects.
• Area around screws.
• Junctions of smooth and porous material.

Figure 7. This diagram demonstrates the effective joint space in an THA.

Modes of wear⁹

• Wear can occur between any two surfaces in motion, which means it is not limited to the bearing surfaces. There are four different modes of wear (these should be differentiated from “mechanisms of wear” listed earlier):

• Note: several modes of wear can be occurring in a joint at the same time.

Figure 8. These diagrams show the 4 modes of wear in a THA.

Volumetric and linear wear

• Charnley et al.¹⁰ described how femoral head migration through the polyethylene cup formed a cylindrical shaped path (see Figure 9(a)). Livermore et al.¹¹ used this finding to calculate an estimate of volumetric wear, from radiographically measured linear wear:
• Cylinder volume = πr²h
• r = radius of cross-section of cylinder
• h = height of cylinder
• Therefore to estimate volumetric wear:

Figure 9(a) This demonstrates how the spherical femoral head carves out a cylindrical wear path, during linear wear, with a cylinder height of W.

Figure 9(b)This demonstrates how Livermore et al suggested linear wear could be estimated from plain radiographs of the hip.

• Livermore et al.¹¹ calculated the linear wear from plain radiographs using the following method – see Figure 9(b):
• The precise centre of the femoral head was located (O).
• Magnification factor was then calculated using the following equation:

Magnification factor = true femoral head radius (i.e. known implant radius)/apparent head radius (measured from radiograph).

• The shortest distance from the centre of the femoral head (O) to the cup-cement interface (A) was located using a compass. This showed the point in the polyethylene which had the most linear wear.
• A line was then drawn between O and A, and the distance along this line from the head-cup interface (A’) and A was measured, and then multiplied by the magnification factor to give an estimate for linear wear (w).

• Livermore found increasing femoral head diameter increased volumetric wear, but reduced linear wear. He determined, for metal-on-UHMWPE, a 28 mm head had the best balance of wear characteristics.

Important factors influencing wear

• These can broadly be divided into:

1. Patient factors
2. Implant factors
3. Surgical factors

Patient factors

• Increasing patient weight leads to greater joint reaction forces (JRF) at the hip, leading to more friction, and subsequently wear.
• Younger patients are often more active, with more high impact activities. This increases JRF, increasing wear.

Implant factors

• Bearing materials are probably the most important factor influencing wear. The use of highly polished implants (polishing reduces surface asperities), ceramic implants and highly cross-linked ultra-high molecular weight polyethylene (UHMWPE) has led to bearings with lower coefficients of friction, reducing wear (see section on “Materials” for more detail).
• In THA, reducing femoral head size reduces volumetric wear, but increases linear wear.¹¹
• In THA, radial clearance affects wear. Polar bearings allow lubricant fluid in the joint to be drawn between bearing surfaces, reducing friction. However, this must be balanced with the increased contact stresses encountered with a less congruent design. However, completely congruent bearings allow little fluid in, and equatorial bearings lock fluid out, leading to higher wear rates. A small amount of positive radial clearance is therefore ideal.¹¹
• In TKA, increasing conformity results in lower contact stresses, and therefore reduced wear.
• In TKA, better locking mechanisms reduce backside wear in modular implants.¹²

Surgical factors

• Adequate wash out of the joint before closure reduces the amount of third body wear particles (e.g. from cement/bone reamings).
• In THA, increasing femoral offset reduces JRF, reducing friction (see section on “THA biomechanics” for more details.¹³
• In THA, medialising the acetabular component (i.e. reducing acetabular offset) increases the abductor moment arm, and reduces the moment arm of the centre of body weight acting about the hip.¹⁴ Together these will reduce JRF.