Abstract
Finite element method (FEM) is among the methods of approximation, which is abundantly used to solve the real-life problems that cannot be solved with the analytical methods. The biological systems are complex in nature in terms of geometry, material properties, functioning, and case-to-case deviation. Thus, the standard analytical methods suffer catastrophic limitations in this area. Mainly for this reason, biomechanics is highly enriched with the integration of FEM, which opens a new window with extended capabilities against a logically acceptable margin of approximation. This chapter focuses on designing customized medical devices (orthopaedic and dental implants) and correlating their design with the presented clinical condition and, thus, leading to a criteria of design prescription based on clinical conditions.
TopBackground
Designing of medical devices has been greatly benefited by the integration of FEM in the product development process over the last decade (Driscoll, 2019). FEM is a numerical tool, which is used to solve boundary value problems. In this method, a complex entity is considered to be a combination of finite number of small entities of regular configuration, known as Elements. As for example, in case of solid structural analysis, a complex geometry is considered to be composed of an aggregation of small geometrical elements of regular shape (Fig. 1a). We can take the example of a complex brick structure (Fig. 1b). It’s quite difficult to identify the status of stress or deformation of any particular point within the irregular structure. But we may calculate these entities for each brick, which is a regular structure. Each brick passes its force output to the next brick in the sequence, and there this force acts as the input force. Once the mechanical parameters of all the bricks are calculated, we can aggregate the individual outcomes and obtain the overall results for the whole structure or for any particular zone of interest. Unlike the bricks which are cemented to each other through the interfacing surface, the elements in the FE system are connected to each other at certain defined points, known as Nodes, which can pass information from one element to another. A system of field equations is considered, expressed as PDEs, that represent the particular aspect of physics we are concerned with. This is calculated for each element and the individual contribution of each element is assembled to obtain the system output. With this consideration, mechanical analyses of complex and irregular structures are possible which is otherwise impossible through analytical methods. This clearly indicates that the analytical outcome will be approximated to an extent dependent on the structural complexity and the number of elements we break it to. The process of breaking down the complex structure into finite number of elements is known as Meshing. The more the number of elements we will mesh the structure into (resulting in smaller elements), more closer we will be able to reach to the real outcome (Fig. 1c). But solution with higher mesh size is achieved against higher computational demand. Generally, this method generates stiffness matrices and solves them. The size of these matrices increases with increase in number of elements, imposing higher computational load. This is further elaborated under the section ‘FE Analysis’.
Key Terms in this Chapter
Total Hip Replacement: Surgical process of replacing the articular surfaces of the hip joint by the acetabular and femoral implant components.
Stress-Shielding: Reduction of physiological stress from the bone at a particular location, often due to implantation, resulting in depletion of bone tissue in that location, as governed by Wolff’s law.
Bone Remodelling: It is a continuous process over time by which the old bone tissue is replaced by new ones. Additionally, through this process, the bone re-adjusts its structure and density in a location wise manner if there is any alteration in the biomechanical environment which may be a pathology, altered activities, etc.
Implant: A medical device surgically inserted within the body. Their uses include replacement of a joint or support to a fractured bone (orthopaedic), replacement of lost tooth/teeth (dental), maintenance of arterial lumen (stent), reconstruction of breast or buttocks (cosmetic), etc.
Element (in FEM): It is a building block of the volume of an object and is of a regular geometry which is any one of the list of geometries that a FE software package contains.
Mesh (in FEM): The process of virtual splitting of a volume into multiple blocks of regular shape (elements) in a FE model.
Node (in FEM): The points through which the various elements connect to each other and transfers force, displacement, etc. in a meshed FE model.