Using specialised software and appropriate workflows, medical images can be used to build geometrically accurate CAD and finite element models of tissue structures such as bones. The spatial variation of the properties of the bone can also be extracted and applied to the individual finite elements that correspond to bone so that geometry and mechanical properties can be accurately specified. Subsequently, loads can be applied in the usual fashion, and quantities of interest such as implant and bone deflections, strains and stresses can be extracted. A typical workflow for this process is illustrated in Figure 2.
Often, a "typical" bone is used for implant design studies. Implant designers can also develop and maintain databases of many bones that can be made representative of the wider population, so that design decisions are not based on the results of one-implant/one-bone studies.
Figure 2: Workflow for generating and solving realistic finite element models of prostheses implanted in bones
Finite element models can also be extended to include the effects of processes such as the reaction of biological tissues to the presence of a prosthesis. For most man-made structures, the physical and mechanical properties of the structure are essentially static. Stiffness, for example, does not change much with time and most changes that do occur such as wear and corrosion are not by design (although of course they may be allowed for in design) and are generally undesirable.
In contrast, the properties of many biological structures are dynamic. This allows tissues to respond to changes in demand, which is known generically as "tissue adaption." Examples are the increases in muscle mass, strength or endurance that accompany certain forms of athletic training. Sometimes the effects of tissue adaption are undesirable, for example, the cardiac hypertrophy that accompanies arterial hypertension as a result of the heart having to work harder to pump blood through clogged arteries. By analogy to thermostats used to control temperature, the cellular processes that control tissue adaption have been described as a "mechanostat." In other words load-bearing tissues adapt to keep some measure of the loading within a "normal" range. Average loading above normal leads to new tissue formation and/or change in tissue properties, and loading below normal leads to tissue loss.
With regard to load-bearing orthopaedic implants, local changes in bone stress caused by the presence of the implant cause a change in the mechanical environment of the bone close to the prosthesis and consequent local changes in bone mechanical properties (bone adaption). With most joint replacement prostheses, the much greater stiffness of the implant with respect to the bone means that local bone stresses around the implant are reduced, a phenomenon known as "stress shielding." This ultimately leads to bone adaption manifested as a loss of bone density around the implant. Changes in stress distribution in the bone as a result of implantation of a hip femoral prosthesis together with bone density changes (visible as local darkening of the X-ray image) subsequent to implantation are shown in Figure 3.
Figure 3: Strain differences and bone density reductions as a result of bone remodelling due to the presence of a hip femoral prosthesis
The detailed mechanism of bone adaption is the subject of intensive research and is not yet fully understood. In broad terms it involves the regulation of cellular processes in response to changes in the mechanical environment sensed by the cell population of the bone. The exact stimulus to which cells respond is not fully understood. Changes in fluid flow, cell deformation induced by deformation of the bone substrate and chemical signals induced by local cell death caused by local micro-damage have all been proposed. Fortunately, experience has shown that a detailed understanding of the mechanism of bone remodelling is not necessary to produce phenomenological mathematical models that can be incorporated into finite element models to estimate changes in bone density as a result of the mechanical changes induced by the presence of implants. Figure 4 shows the results of a simulation of the effects of the presence of a prosthesis on the density of the bone around the prosthesis as a result of bone remodelling.
Figure 4: Simulation of bone density changes around a hip resurfacing prosthesis as a result of bone remodelling. Dark blue, low bone-density regions within the femoral head expand with time, but elsewhere bone density hardly changes
Joint replacement components may be fixed to the skeleton with or without acrylic bone cement. Cemented implants have the advantage of immediate fixation to the skeleton, but cement fatigue failure has been implicated in long-term implant loosening and many surgeons choose uncemented implants for younger or more active patients.
Uncemented joint replacement components achieve fixation to the surrounding bone by inducing an appropriate bone-healing response, which results in bone healing and bone growth up to and into the surface of the implant. Uncemented implants are furnished with textured or porous surfaces and coatings, which may include bioactive coatings such as hydroxyapatite to encourage bone in-growth and long-term implant stability. Research has shown that initial stability, which is dependent on the shape and surface characteristics of the implant, is critical to achieving long-term stability. Relative motion between implant and bone at this stage must be kept below 100-150 µm for bone in-growth to occur. Relatively straightforward finite element models can be used to assess implant-bone relative motion, but it is also possible to incorporate more sophisticated approaches based on mathematical models of the fracture healing process to predict the evolution of the tissues at the implant-bone interface.
When an uncemented prosthesis is implanted by a surgeon, the initial conditions at the implant-bone interface are a mixture of regions of direct bone contact and regions where the implant and bone are separated by fibrous granulation tissue. Similar to a healing fracture, the evolution of the tissues at the interface, which is partly controlled by the mechanical environment, is critical to long-term implant stability. As with bone remodelling, several phenomenological mathematical models of the fracture healing process have been proposed 3,4
and these can be used by implant designers to assess the relative performance of candidate designs. Figure 5 shows the results of a simulation for a short-stem hip replacement femoral component. This illustrates the distribution of tissues in contact with the implant as a function of time from implantation; the image on the left shows the initial condition of total fibrous encapsulation and the image on the right shows the equilibrium tissue distribution at the end of the healing process.
Figure 5: Evolution of tissues surrounding part of a total hip replacement prosthesis
Images 3,4,5 courtesy of DePuy
Kinematics and virtual wear testing
The kinematics of the replaced joint is an important consideration for implant designers. This is particularly so in the knee. This is a complex joint whose kinematic behaviour is determined by the actuation forces generated by muscles and motion constraints generated by the interactions of multiple joint-contact surfaces and ligaments. Unlike hip replacement patients, those with knee replacements often describe their replaced knee as not "feeling" like their own knee, an observation possibly related to the altered kinematics imposed by the prosthesis. Explicit time-integration finite element software, similar to that used in vehicle crash-worthiness simulation and for simulating other events involving large motions between components, is particularly appropriate for simulating the kinematics of knee replacements.
A further problem with knee replacements is the wear of the polyethylene insert that forms the tibial side of the knee joint bearing. The insert articulates with the metal femoral component and in many cases, intentionally or unintentionally, also with the metal tibial component that is fixed into the tibia. Because wear of the tibial insert results in material loss and a sometimes substantial change in shape of the bearing surface, wear and knee kinematics are coupled. Again, phenomenological models that relate the local rate of material loss from the surface of the insert to the local mechanical conditions (relative sliding distances, contact pressures) have been developed. Coupling these models with the finite element model for prediction of sliding distances and contact pressures and algorithms for adjusting the finite element mesh as wear progresses provides an important benefit. It allows the volume of wear debris that is generated (important as the biological response to wear debris has been implicated in component loosening) and the kinematic behaviour of the worn component (important for knee joint function) to be predicted. Figure 6 shows a comparison of wear prediction by a finite element model and wear observed on a tibial insert retrieved at revision surgery.
Figure 6: Comparison of finite element prediction of wear (left) and wear measured on a retrieved tibial insert using surface profilometry
Images courtesy of Lucy Knight, University of Southampton
This article has presented just some of the applications of finite element modelling relevant to orthopaedic implant design. Numerous other interesting and useful techniques are continually being developed. Coupling finite element models to stochastic/probabilistic methods5
allows for the effects of uncertainty, in terms of traditional engineering factors such as materials variability and manufacturing tolerances and biological factors to be included such as the individual response of a patient's physiology to the presence of an implant. In this way failure probabilities rather than simple deterministic pass/fail criteria can be calculated.
Related techniques such as parametric optimisation can be used to identify component designs that best match particular design requirements (for example, maximising the amount of bone that forms at the interface between the implant and bone). Further reading on these and other techniques and an interesting historical perspective on their development as design tools can be found in the recommended reading.
1. N.W.M. Bishop and D. Sherratt, "Finite Element Based Fatigue Calculations," NAFEMS, www.nafems.org
2. WARP3D, http://cern49.cee.uiuc.edu/cfm/warp3d.html
D.R. Carter et al., "Correlations Between Mechanical Stress History and Tissue Differentiation in Initial Fracture Healing," J. Ortho. Res., 6, 736-748 (1988).
4. D. Lacroix et al., "Biomechanical Model to Simulate Tissue Differentiation and Bone Regeneration: Application to Fracture Healing," Medical & Biological Engineering and Computing, 40, 14-21 (2002).
5. P.J. Laz and M. Browne, "A Review of Probabilistic Analysis in Orthopaedic Biomechanics," Proceedings of the Institution of Mechanical Engineers Part H Engineering in Medicine, 224, 8,
927- 43 (2010).
1. R. Huiskes and E.Y. Chao, "A Survey of Finite Element Analysis in Orthopaedic Biomechanics: The First Decade," J. Biomechanics, 16, 6, 385-409 (1983).
2. R. Huiskes and S.J. Hollister, "From Structure to Process, From Organ to Cell: Recent Developments of FE analysis in Orthopaedic Biomechanics," J. Biomechanical Engineering, 115, 4B, 520-527 (1993).
3. P.J. Prendergast, "Finite Element Models in Tissue Mechanics and Orthopaedic Implant Design," Clinical Biomechanics, 12, 6, 343-366 (1997).
4. J. Vander Sloten et al., "Applications of Computer Modelling for the Design of Orthopaedic, Dental and Cardiovascular Biomaterials," Proceedings of the Institution of Mechanical Engineers Part H Engineering in Medicine, 212, 6, 489-500 (1998).
5. Special Issue on "Finite Element Modelling of Medical Devices," Eds. P.J. Prendergast, C. Lally and A.B. Lennon, Medical Engineering and Physics, 31,4, 419-494 (2009).
Dr Andrew New
is Director of Apogee Engineering Analysis Solutions Ltd,
Hill House, Chapel Street, New Buckenham, NR16 2BB, UK,
tel. +44 (0)1953 861 233