The use of finite element analysis to estimate the changing strength of bone following treatment for osteoporosis

Excerpt

Finite element analysis (FEA) is a computational technique widely used to estimate the behavior of structures under loading. It is particularly valuable to investigate those conditions which cannot be studied directly by experimentation, and therefore, provides valuable information that cannot be obtained in more direct ways. It has been beneficial in helping to create and optimize non-biological structures for instance, how to engineer an airplane wing to prevent failure from excessive fatigue loading but can also help us to understand how a structure might behave mechanically under various conditions that cannot be reproduced experimentally. Briefly, the technique uses a series of small elements that can be a variety of shapes, and that are connected at nodal points, to computer-generate a morphological structure, such as a hip joint. The elements can be assigned properties that are indicative of the tissue properties that small areas of the biological structure have, either relying on measurements that have been made of the properties of the material, or in those cases in which the properties have not been measured, estimating them based on what we do know. For most models, properties for elastic modulus (tissue stiffness) are assigned to the entire structure, which can be a poor representation of bone tissue properties given one’s heterogeneity, rather than to individual elements, A virtual load can be applied to this structure, and the displacement (or deformation) of the structure under that loading condition can be estimated. A second method, known as the flexibility method, is based on known displacements. Knowing the load and the displacement, it is possible to calculate the stresses and strains within the structure, which can provide valuable information to estimate how the structure will “perform” mechanically. Stresses and strains are “derived” parameters that require calculation from the estimated displacements, so are less accurate (or more variable) than the estimated displacements [1]. Nevertheless, the FEA can provide an estimate of the stresses and strains within a structure that cannot be determined in other ways because they cannot be directly measured. If it were possible to do an experiment in which the effect could be directly measured, then FEA is not particularly helpful (just do the experiment). But it is a valuable tool for making predictions about how a structure will behave mechanically and when it might fail in situations in which it is impossible to make such measurements. …