BME/ME 456 Biomechanics
Biomechanics of Artificial Joints
I. Overview
Total joint replacement has become a widely accepted treatment for many destructive joint diseases including osteoarthritis, rhematoid arthritis, osteonecrosis and very severe pathologic fractures. Of total joint replacments, the two most commonly replaced joints and most successfully replaced joints are the knee and the hip. Sir John Charnely, a British Orthopaedic surgeon who was knighted for his development of joint replacements, developed the fundamental principles of the artificial hip and designed a a hip in the mid and late 1960's that still sees widespread use today. Frank Gunston developed one of the first artificial knee joints in 1969. Since then, joint replacement surgery has become one of the most successful orthopaedic treatements. The number of hip replacements done in the world per year numbers between 500,000 and 1 million. The total number of knee replacements done in the world per year is less, but probably still numbers between 250,000 and 500,000. Of all the factors leading to total hip replacement, osteoarthritis or OA, is the most common, accounting for 65% of all total hips.
When a patient complains of pain, it is often also evident on x-rays that arthritis is destroying the joint. Shown below are a normal hip (on the left) and a hip with arthritis (on the right):
On the left, you can see a space between the head of the femur and the acetabulum. The space is due to the cartilage in the joint which doesn't show up on x-ray. On the right, little space exists, indicating that most of the cartilage in the space is gone. The picture below, (from http://www.wokc2.com/topic5.htm), shows a degenerative knee joint:
Again, you can see no joint space between the tibia and distal femur, indicative of severe arthritis.
Both hip and knee joints have been very successful in achieving the goal of pain free mobility for patients. Most patients will be able to ambulate and move painlessly about 3 weeks after their operation. For patients in their late 50's and older with moderate activity (like brisk walking for excercise), a good hip replacement will last 15 and sometimes 20 years or more. Looking at clinical statistics, 90% of all patients with hip prostheses will be pain free and ambulating normally 10 years after their operation. There are still a number of deficiences and mechanics issues that limit the application of joint replacements in younger and more active populations, however. Among these problems are wear of the joint and loosening of the artificial joint from the surrounding bone. In this section we will describe artificial hip and knee joint replacements and discuss mechanical factors that affect their performance.
II. Hip and Knee Replacement Fundamentals
The basic idea of joint replacement surgery is to replace the diseased articular surface with one made from a synthetic material. This new joint surface must then be part of the artificial joint which itself is fixed to the bone near the joint. The major design issues in artificial joint replacement are 1) the geometric and material design of the articulating surfaces and 2) design of the interface between the artificial joint and the surrounding bone. Most joint replacements use a polyethylene for the bearing surface and either a titanium alloy or a chrome-cobalt alloy for the rest of the joint. It is the metal part of the joint in most cases that interfaces with the bone. The are two widely used methods for interfacing the joint with the bone: 1) using a Polymethylmethacrylate (PMMA) cement to adhere the metal to the bone or 2) using a porous metal surface to create a bone ingrowth interface. These two types of interfaces are illustrated below (from the website: (http://www.healthpages.org/AHP/LIBRARY/HLTHTOP/TKR/):
A schematic of a hip replacement from your text (p. 396) is shown below
In the above picture, you can see that both the acetabulum (the "socket") and the proximal femur (the "ball" of the hip joint) have been replaced. The femoral side is completely metal. The acetabular side is composed of the polyethylene bearing surface that may or may not have a metal backing. Both the components in this schematic are shown to be fixed to bone with PMMA cement. A schematic of a knee replacement is shown below (from the website http://www.healthpages.org/AHP/LIBRARY/HLTHTOP/TKR/):
You can see that there are three major components to a total knee: 1) the femoral component that replaces the distal femur, 2) the tibial component that is inserted into the proximal tibia, and 3) the patellar component that replaces the back of the patella. As with the hip joint, the articulating surface is metal on polyethylene, and the metal parts of the implant interface with bone.
III. Clinical Performance of Joint Replacements
As discussed in the text, the three major determinants of total joint performance are:
1. Surgical
Factors
a.
surgical experience and skills
b.
patient selection
2.
Prosthetic Factors
a.
prosthetic materials
b.
shape
c.
prosthetic fixation
d.
surgical instrumentation
3.
Patient Factors
a.
patient compliance to surgical instructions
b.
patient activity
c.
patient weight
d.
general health
e. patient bone quality
The most common cause of total joint failure is asceptic or mechanical loosening. A critical determinant of joint longevity is the fixation between the prosthesis and the bone. A good bone material fixation is necessary to have a pain free joint. When the bone implant interface starts to fail, a soft fibrous tissue develops at the interface that allows more relative motion between the implant and the bone under loading. This leads to migration of the implant and causes pain to the patient. After a certain period the pain becomes intolerable and the implant must be replaced, a procedure known as a revision. There are a number of factors that may contribute to asceptic or mechanical loosening. Among these factors are bone necrosis (death) due to head from cement polymerization, mechanical damage done during surgery, wear debris, and mechanical loosening from fatigue at the interface. The last two factors are mechanical in nature and can be accounted for in implant design. We will discuss these factors in more detail in the next sections.
As described in the text, the best indicator of clinical performance of a given prosthesis is the percent of revisions that are performed for a given prosthesis. Of course, this indicator itself is not perfect since orthopaedic surgeons tend to choose specific prostheses based on individual preference, so there is some influence of surgical skill on revision indicators. One of the most extensive studies as cited in the text was carried out in Sweden. The number of revisions at multiple total joint centers was tabulated from a total of 92,675 cases, due to the unique ability to track patients in a national database. The results (taken from the text, p. 398) are shown in the graph below:
The results showed for instance that Charnley hips had about a 92% survival rate after 10 years while Muller curved hips had a 82% survival rate after 10 years. Again, a particular surgeon may have better results with a Muller than a Charnely, but these results show on average in Sweden that the Charnley had a better survival rate. This chart reflects the current results worldwide figures that suggest 10 year survivorship of cemented hips is at about 90%.
IV. Wear in Total Joint Replacements
Although not covered in detail in the text, wear is now considered one of the most signficiant factors limiting the longevity of total joints. Improvements in implant metallurgy, surgical techniques, patient selection, and cementing techniques have boosted total joint lifetimes so that most moderately active patients in their 60's can expect 10 to 15 years of pain free activity with a joint replacement. Beyond this however, or in a younger patient population, wear is a significant factor leading to joint revision.
The two factors leading to wear debris that most affect joint replacements are foreign body wear and subsurface fatigue. Foreign body wear occurs when a piece of material comes between the articulating joint surfaces. The presence of the piece of material generates additional stress concentrations of the articulating surfaces. The second type of wear is sub-surface fatigue. High contact stresses in the polyethylene can cause cracks to form and propagate beneath the surface of the polyethylene. These cracks can cause material particles to break from the surface creating wear debris. An example of this type of cracking in the tibial component of a total knee is shown below:
The wear particles can track down the interface between the bone and implant.
Macrophage cells will respond to the wear particles by engulfing the particles
and resorbing bone at the interface. The bone is replaced by soft tissue, creating
a more compliant interface. Over time, this will lead to implant loosening.
Reduced
wear from surface fatigue failure and delamination of polyethylene can be achieved
by reducing the cyclic contact stresses on the polyethylene, improving the toughness
and wear characteristics of polyethylene, or a combination of the two.
V. Interface Mechanics of Total Joints
In addition to wear, the most frequent source of total joint failure is debonding of the implant bone interface due to fatigue failure of the bone implant interface or adverse bone adaptation around the total joint. In this section, we discuss the principles of interface mechanics and how they relate to total joint replacement design.
a. Load transfer in composite materials
Just as all biological tissues are composite materials and structures, so are bone implant combinations composite structures. Because of the difference in material properties of the bone and the implant, an interface is created when the two materials are put together. One of the most important issues in bone implant interfaces is how load is transferred from the implant to the surrounding bone. If the two materials are bonded and equal force is applied to both as illustrated in the figure from your text (p. 417) below:
then the strain in each bar must be equal:
If we use Hooke's law and also the fact that stress is force/area, we obtain:
which leads to the result in the text on page 416:
Next, we also know that the total force is the sum of the forces in each bar:
If we use the Hooke's law relationship given above, we can find a relationship between the forces defined in terms of area and Young's modulus:
We also know that deformation on parallel materials gives us Voight's model or the rule of mixtures:
which when substituted in for E and A in the immediately proceeding equation gives us:
which is the equation on p. 417 of the text.
As described in the text, load transfer between the proximal femoral compoent and the surrounding bone is analagous to the case where there are two bars bonded together, but the first bar only is the site of load application, and it carries the total load as:
. The first bar, in our case the implant, will take all of the intial force, in our case the contact force with the acetabulum. However, at the point where the prosthesis is imbedded in the bone, there must be load transfer between the implant and the bone. Based on our original analysis of load sharing in composite structures, we know that at some distance past the point where the implant meets the bone the force distribtution between the implant and the bone will be:
where the subscript i denotes implant and b denotes bone. Thus, the force in the implant drops from the total force F to a lesser force that depends on the stiffness ratio of the implant to the bone. Conversely, the force in the bone must rise from 0 to a greater force that depends on the stiffness ratio of the bone to the implant. The transfer of load must take place through shear stress at the bone implant interface. It is this shear stress repeated many cycles per day that determines the longevity of the bone implant interface. As discussed in the text, this shear stress distribution may be represented by a shear lag distribution function.
The above results indicate two major points. First, the stiffness ratio of the implant to the bone will determine how much load is borne by each. Since the ratio EA/(E1A1 + E2A2) is generally weighted much more towards the implant, this explains why the implant carries most of the load and leads to stress shielding of the bone. Second, the need of the interface to carry high stress stresses to create the transition between the implant and the bone load carrying explains the reason why the bone implant interface is the critical design feature of most implants.
Another important determinant of interface stresses are the characteristics of the bond between the implant and bone. Bonding characteristics can range from completely bonded to non-bonded interfaces with no friction. On the latter, no interface shear stresses can be generated due to the lack of friction at the interface. In this case, significant compressive stresses must be generated to withstand the applied force. In an implant situation, these compressive stresses can only be generated when the implant subsides into the bone. If the interface is bonded, then significant shear stresses can be generated at the interface to support the implant. A bonded interface is characteristic of a cemented prosthesis, while a non-bonded interface is characteristic of a non-cemented press fit prosthesis. These principles are illustrated in the text on p. 421 and repeated in the figure below:
b. Load Transfer in Intramedullary Fixation
The examples in section V.a illustrated load transfer between two composite materials of simple shape. The above ideas are especially relevant to fixation and load transfer in the proximal tibia due to a single stem tibial component. In this section we look more closely at characteristics of load transfer in an intramedullary stem, which is more relevant to total hip replacements. Consider a stiff intramedullary stem in more compliant surrounding bone. In this case we consider both axial and bending loads on the stem bone composite. In this case, the load sharing regions can be divided into proximal, middle and distal regions of load sharing. As with the composite bar, the load is totally borne by the stem in the proximal region and then transferred to load sharing in the middle region and finally load is completely borne by the bone in the distal loading. The principles for axial loading and bending are shown in figure 19 from the text (p. 422) repeated below:
What we see is that initially a very large load is borne by the stem both axially and in bending. See very soon the load must be shared by the bone and the implant, there is a high shear stress in the interface when the load is transferred. This is shown in the second figure from the top, where very high interface stresses are seen at the point of load transfer. Next, similar to our previous results from analyzing composite bars, we see that load is shared between bone and implant in the ratios of implant stiffness to bone stiffness. The higher the implant stiffness the more load is borne by the implant as shown in the equations below:
where ein is the normal load share under axial load and eit is the tranverse load share under bending loads. This again demonstrates that stress shielding is due to high implant stiffness relative to bone stiffness.
In the figure above showing load sharing, parameters ln and lt appear. These parameters are the fixation components for the normal and transverse directions. The are determined by the axial and flexural rigidity of the bone and stem, and the elastic modulus and thickness of the interface layer, whether it is PMMA or porous coating. It can be seen from these results that the mismatch between bone and implant stiffness is a significant factor in determining both stress shielding and interface stresses. A higher mismatch between implant and bone stiffness means a greater degree of stress shielding because more load is borne by the implant. However, at the same time, since the implant carries more of the stress, less load must be transferred to the bone which translates into lower interfaces stresses.
c. Influence of Interface Conditions and Design on Stem/Cement/Bone Stresses
Besides relative implant bone stiffness, another important parameter affecting cemented implant interfaces is the bonding between the implant and the cement. If we loose bonding between the implant and the cement, then this interface cannot carry shear stresses, only compressive stresses. If this happens, then we have the situation illustrated in the bonded vs press fit scenario pictured above, where the implant will subside in the bone to generate compressive stresses capable of bearing the applied load. In addition to implant subsidence, debonding of the implant from the cement will lead to higher cement mantle stresses.
When looking at interface conditions for cemented implants, there are two types of debonding that can occur. The first type of debonding is separation of the metal stem from the cement. Debonding of the metal from the cement occurs in many cemented implants. If debonding occurs, the amount of shear stress that can be borne at the metal-cement interface is reduced, an the interface must withstand the applied load through compressive forces, as illustrated in the stem example above. The figure below from the text p. 423, shows how shear stresses at the interface change when the stem becomes unbonded from the cement:
As expected, debonding drastically reduces shear stress at the cement metal
interface. This shows that shear stresses are a significant mode of load transfer
for bonded implants. Likewise, progressive debonding states from completely
bonded, to unbonded with friction (transfers compressive loads and shear stress
under compression via Coulomb's friction law where 
to frictionless unbonded that can only carry compressive stress and the effects of these bonding states on tensile stresses in the cement mantle is shown below (p. 424 in text):
These figures also represent the general trend the debonding of the metal from the stem increases stress in the cement mantle.
The second type of debonding that can occur is between the cement and the bone. Again, using continuum finite element models, this debonding is represented as a change in contact conditions. If the contact conditions at the the bone-cement interface are changed from completely bonded to unbonded, there is an increase in stresses at the implant cement interface, as shown below (p. 424 from the text):
Left part of figure shows cement stem stresses with bonded bone cement interface while the middle part of the figure shows increased stresses at the cement stem interface.
Avoiding debonding depends both on prosthesis design and surgical experience with cement pressurization. Removing voids in cement during mixing is critical to avoid fatigue failure of cement, as is designing stems that avoid stress concentrations in the cement.
In addition to bonding affects, the stem material stiffness can have a significant affect on both interface motion and stress shielding, in contradictory ways. Comparing a titanium stem with an isoelastic stem (has the same stiffness as bone), it is shown in the text (p. 443) that the titanium stem produces less interface motion.
This is important since reduce interface motion will reduce cement stresses and cement metal debonding. In addition, as expected, higher friction (indicative of better bonding) also reduces interface motion.
A disadvantage of a stiff stem, however, is stress shielding. As seen in the simple stem analysis above, a stiffer implant to bone stiffness ration means that the stem will carry more load. This means that the bone stresses will likely be much lower than stresses in the intact bone and will lead to bone resorption through excessive bone remodeling. These resorption affects can be predicted using numerical bone adaptation simulations. A comparison between numerically predicted change in cortical area and experimental results from a canine total hip replacement.
In sum, these analyses suggest that successful total hip stem design is a tradeoff among many factors. Stiff stems will reduce interface motion, but will lead to more bone resorption. Increasing surface roughness of the metal will increase the friction coefficient of the metal cement interface, but this will also increase the localized stress concentrations within the cement, possibly creating wear debris.
The design of tibial components of knee protheses may also affect stress shielding. The next figure from the text (p. 473), shows the effect of stem length and stem material (polyethylene vs. metal backed) on stresses in the tibia. Longer stems and metal stems produce more stress shielding than all polyethylene components. However, polyethylene components may be more at risk for fatigue failure and wear.
d. Acetabular Cup Design Influences on Interface Stresses
As with femoral stems, the acetabular cup designs significantly influence stresses in the cement mantle and surrounding bone. The acetabular cup design features, however, are more restricted than the femoral stem. With acetabular cup, itself made of polyethylene, the design choices are basically whether or not to use a metal backing, and whether screws are used. Screws through the acetabular cup provide additional fixation, but also carry surgical risks. The advantage of metal backing is that is reduces the average stress in the cement mantle. However, it does produce stress concentrations at the rim of the cup, which may lead to a higher risk of failure. In addition, metal backing may lead to more stress shielding. A comparison of non-metal backed to metal backed components to cement mantle stresses (p. 427 in text) is shown below:
This figure shows the rim stress concentrations associated with the metal backing, although overall the cement stresses are lower.
e. Brief Notes on Porous Coated Implant Design
As noted above, an alternative to cemented implant interface is a porous coated implant interface. The theory behind porous coating is that bone will grow into 300 to 500 micron pores on the implant surface. This will eliminate the poor mechanical properties of the cement. However, porous coated implants have not overtaken cemented implants in terms of clinical usage. That may be for two reasons 1) porous coated implants rely on a biological (osteogenesis) process that is not as predictable as an immediate cemented interface. The interface bond develops over time and 2) porous coated implant interface is much more dependent on precise surgical fit to obtain an implant bone. In hip stems, porous coating is most often limited to the proximal portion of the implant. This is because an implant completely covered with porous coating will most likely have ingrowth at the tip. This leads to extreme stress shielding. Finally, as noted in the text, the stability of porous coated implants is more dependent on the location of ingrowth than on the depth of ingrowth. This means that the ability to control ingrowth location is perhaps the most critical aspect of porous coated implants, but the one aspect most difficult to control.
