Issue 10

D. Taylor et alii, Frattura ed Integrità Strutturale, 10 (2009) 12-20; DOI: 10.3221/IGF-ESIS.10.02 18 P RACTICAL APPLICATIONS : THE MANAGEMENT OF BONE DEFECTS great advantage of the TCD is that it can be applied very easily to practical problems; in this respect the stress- based methods are particularly attractive because they can be used in any situation where a stress analysis can be conducted using FEA or similar numerical techniques. Stress concentrations frequently arise in bone as a result of disease or clinical intervention. Surgeons use the terminology “bone defect” to refer to any hole which occurs in a bone, i.e. any part of the bone cortex or internal cancellous structure which is missing. Defects occur for various reasons, for example they may also arise following a complex fracture: when the broken parts of a bone are reassembled there may be some pieces missing. Also, holes may be deliberately drilled to take samples for biopsy or for the fixation of fracture plates which may be later removed. One method for the replacement of the anterior cruciate ligament in the knee involves taking a piece of bone from the patella of the other knee, often leaving a square hole with sharp corners. In a previous study we showed that the impact energy of this patella was significantly reduced by the presence of the hole, and that the situation could be considerably improved by cutting a hole with round corners [24]. This is a good example of how a concept which is very obvious to the mechanical engineer can have immediate benefits in the field of medicine. If the hole is considered to confer significant risk of failure, the surgeon may fill it using a bone graft material. Various types of materials are used, including the patient’s own bone (taken from some other site and ground into a powder) and various artificial materials. Over a period of time, the patient’s own natural healing processes will cause the hole to be filled with new, living bone, so the bone graft material is intended only as a temporary substitute, required to last for a few months at the most. Artificial bone graft materials are designed to provide a scaffold for the rapid ingrowth of bone, and recently there has been much interest in the use of tissue engineering techniques for the development of these materials. Scaffolds have been made from a wide variety of materials, including porous metals, ceramics and hydrogels. There is great interest in the use of resorbable materials which can gradually dissolve, aiding the development of new bone, but current versions of these materials are relatively weak, increasing the risk of fracture in the critical period just after surgery. A major problem is the lack of a predictive model to aid surgeons in deciding what to do about a given defect, whether to use a bone graft material and, if so, what the properties of that material should be. Such a predictive model, presented in the form of a computer simulation of the defective bone, could greatly aid in the planning of surgical operations. As an initial step towards developing such a tool, we carried out some simple simulations of the behaviour of bone defects. Fig 7 shows the geometry used for the finite element model: the bone is envisaged as a simple tube, containing a defect: we modelled square and circular holes of various sizes. A complete description of the methodology and results can be found in a recent publicatio n [25]. In brief, we used a damage mechanics approach to predict the increase of fatigue damage due to cyclic loading in normal daily activities. The TCD was incorporated by performing all the damage calculations at the critical point, i.e. a distance L/2 from the hole, rather than at the hot spot. The capacity of bone to repair itself was included in the model as a constant, negative damage rate, following earlier work [26]. The use of different bone graft materials was modelled by filling the hole with a material of given Young’s modulus, E o . Bone ingrowth was included in the simulation by allowing the Young’s modulus of the graft material to gradually increase over time, from E o to a value typical for normal cortical bone (17GPa). Fig. 7 s hows an example of the results of the simulation. If repair and ingrowth are not modelled, damage increases rapidly. Incorporating ingrowth causes damage to level out to a plateau value, and the additional incorporation of repair allows the damage to return to normal levels after peaking. The value of the peak is of course the critical one: provided this is less than unity we predict that no failure will occur.As Fig.8 shows, there is a very strong effect arising from the value of E o , the stiffness of the bone graft material. This occurs because the stress concentrating effect of the hole is greatly reduced, even when the material in the hole has much less stiffness than the surrounding bone. This analysis enabled us to make a specification for a safe value of E o ,as a function of hole size as shown in Fig.8 . Obviously the result also depends on the shape of the hole, and on the assumed daily loading, i.e. the activity level of the person. These predictions show that small holes (in this case less than 5mm diameter) do not need to be filled in with graft material: this finding is in agreement with the current practice of surgeons who regard such small holes as innocuous. Larger holes do require filling, but here we predict that the material needed can have an E o value which is considerably smaller than that of normal bone: this finding is original and potentially of great value to researchers and manufacturers who are developing new types of bone graft materials. This work is very preliminary in nature, but has the potential to be developed to a greater level of sophistication, for example incorporating the changing behaviour of resorbable materials and the effect of different postoperative activity levels, such as walking with the support of a crutch or cane or carrying out more strenuous exercise. A