Figure 1.1
Biomechanics - application of mechanics (motion of bodies) to biologic systems.
Biomechanics includes:
Biomechanics is the application of mechanics (motion of bodies) to biologic systems. This is a multifactorial discipline which includes: external effects of applied forces; stress analysis - internal effects of applied forces; mechanical properties; fluid mechanics; and heat transfer. It would seem that this subject would have little pertinence to the field of periodontology. Nothing could be further from the truth! Even though the primary cause of periodontitis is bacterial, and primary treatment is bacteriocidal, biomechanical considerations become very important once the disease process is under control. Indeed, a successful result from periodontic therapy is only the beginning for the restorative dentist. Not only must restorations that will permit the altered oral tissues to be maintained plaque free be designed, these same restorations must distribute the forces of mastication to supporting structures that are less able to receive them. The ravages of periodontitis result in decreased alveolar bone, loss of teeth, and loss of the periodontal ligament (PDL) attachment area. The necessary surgery can further reduce the area of periodontal support by elimination of osseous defects and root amputation. The clinician must restore function to a mouth less able to accomodate it. Unless occlusal stresses are reduced and evenly distributed, normal occlusion can become traumatic.
In order to determine, control, and redistribute stresses within the craniofacial complex, a knowledge of the forces that will be applied and the mechanical properties of the materials that must withstand these forces is necessary. Oral rehabilitation is inherently difficult because the functional and parafunctional forces that occur within the mouth result in extremely complex structural responses by the oral tissues. Determination of the resulting stresses can be accomplished only with appropriate stress analysis techniques and sufficient information of the characteristics of the oral tissues and restorative materials. The objective of seeking this knowledge is, of course, to predict the clinical performance of treatment modalities and to provide guidelines for their use.
The external effects of forces on structures (bodies) are determined using the three Laws of Newton. Internal responses to applied loads are determined by means of stress analysis. In other words, stress analysis is some means by which the stresses within a structure subjected to prescribed loads may be predicted. The techniques of stress analysis can be separated into theoretical and experimental subgroups. The theoretical approaches use mathematical formulation and solution of the resulting equations. The experimental techniques usually involve measurements of various types made directly on the structures of interest or through the use of modeling of the structure.
Mathematical Analysis
Theoretical stress analysis involves using the basic laws of physics (e.g., conservation of energy, conservation of momentum, and conservation of mass) and the constitutive equations (which specify the stress-strain relations) of the materials of which the structure is made to formulate the governing differential or integral equations for the structure.
These equations are then solved imposing the appropriate boundary conditions (applied loads and support conditions) using either analytic or numeric methods. Although the inclusion of any type of material behavior (elastic, elastoplastic, viscoelastic, etc.) is conceptually possible, there has been no general application of the theoretical approach to dental structures. Utilization of the analytic techniques has been hampered by the extreme complexity of the geometries involved, incomplete knowledge of the mechanical properties of the oral tissues, and difficulty in specifying the boundary conditions for correct solution of the equations.
Finite Element Analysis
The finite element stress analysis technique models actual continuous structures with discrete-element mathematical representations. This approach transforms the problem into one of matrix algebra, which may be solved with the aid of a digital computer.
| The basic concept of this technique is the visualization of the actual structure, which is a continuum, as an assemblage of a finite number of discrete structural elements connected at a finite number of points. The finite elements are formed by figuratively cutting the original structure into segments. For two-dimensional applications, triangles of various sizes and shapes are usually the finite elements of choice, as in Fig. 1-1, where the finite element configuration for a molar with an amalgam restoration over a base is illustrated. Each element retains the mechanical characteristics of the original structure by specifying the appropriate mechanical properties. Additionally, a numbering system is required to identify the elements and their connecting points, called nodes, and a coordinate system must be established to identify uniquely the location of the nodal points. A large number of simultaneous linear equations are computer generated, which establishes compatibility within each element. | Figure 1.1 |
This technique has some very distinct advantages, among which is the ability to obtain accurately the stresses throughout the structure under consideration. Further, the inclusion of any type of anisotropy (directional characteristics) and inhomogeneity is conceptually possible by inserting the appropriate distribution of materials properties at the nodes of the elements. This latter point is attractive, but from a practical standpoint, the mechanical properties of tooth structure and periodontal tissue are not well known. The output of the analysis will be only as good as the input information. The finite element analysis is not inherently restricted to simple geometric configurations. However, axisymmetric and two-dimensional configurations are most readily analyzed. Analysis of structural shapes of greater geometric complexity may not be feasible. Another factor that may limit the scope of application of the finite element technique is the inability to specify accurately the boundary conditions of the problem. For example, specification of the forces acting on a removable partial denture as it functions and moves relative to the abutment teeth and supporting mucosa is virtually impossible.
As the geometry and loadings become more complex, application of the theoretical techniques becomes very difficult, if it is possible at all. Under these circumstances, various experimental techniques can be used to predict stresses or strains and to measure the mechanical response of a structure to simulated or actual loads. The experimental approach may use either models of the structure of interest or the actual structure, depending on the technique employed. Since it is virtually impossible to model all aspects of material behavior at one time, considerable ingenuity is often required to prepare a model that will produce meaningful results. However, excellent model systems that provide very useful predictive stress and strain results have been developed for various dental structures.
Strain gages
Characteristics of Strain GagesElectrical strain gages use the principle that certain electrical resistance elements undergo a change of resistance when they are subjected to strain. Tension produces an increase in resistance; compression causes a decrease in resistance. Therefore, if such a strain gage were bonded to the surface of a structure under load, monitoring the resistance change would yield a knowledge of the strain at that point.
| This description presents a very simplified concept of the operation of a strain gage. In actuality a highly sophisticated technology has evolved for the use of these devices. Strain measurement with strain gages began with the use of simple wire coils with limited accuracy and sensitivity. From this primitive stage developed the use of foils and semiconductors, which are highly sensitive, precision strain-measuring tools (Fig 1-2).Strain rosettes of various configurations that measure the strain at several different directions at a given point have been developed. |  Figure 1-2 |
Strain gages have the advantages of very accurate strain measurement capacity on an actual structure in either simulated or real function. The main drawbacks of strain gages lie in the elaborate electrical equipment required to collect and record the strain data and, more important, the fact that they are devices that measure strains at discrete points on the surface to which they are bonded. No direct internal strain information is obtained.
Holography
Characteristics of Holography Figure 1-3 |  Figure 1-4 |
Photoelasticity
Advantages| Photoelastic stress analysis is based on the property of some transparent materials to exhibit colorful patterns when viewed with polarized light (Fig. 1-5). These patterns occur as the result of alteration of the polarized light by the internal stresses into two waves that travel at different velocities.4 This phenomenon of double refraction is known also as birefringence. The patterns that develop are consequently related to the distribution of the internal stresses and are called the photoelastic effect. To use this special characteristic, one must fabricate a model of the structure of interest (e.g., a tooth). This model, made from a transparent material capable of exhibiting a photoelastic response, is subjected to loads representative of functionally applied forces. The stresses that develop in the model as the result of the applied loads can then be visualized by examining the model with polarizing filters. There are several advantages to this experimental stress analysis technique: |  Figure 1-5 |
Photoelastic stress analysis has developed into a powerful, accurate, and widely used technique in engineering and industry. It has facilitated the design of complicated structures and machinery and has had wide application in the aerospace industry. In recent years, photoelasticity has experienced steadily increasing application in dentistry.
Modeling concepts
There are two main considerations in modeling a particular prosthesis-oral structure situation. The first is related to geometric reproduction of the situation. The model may reflect either full or partial three-dimensional fidelity. Also, the model may be fabricated life size, smaller than life size, or larger than life size.
The second modeling consideration is related to the simulation of mechanical properties of the system to be studied. It is not possible to model all the mechanical properties of a structural element. Consequently, a decision must be made as to which properties are most pertinent to the clinical problem at hand. Since the operating range for all dental structures and restorations should end before the onset of permanent deformation (i.e., before the yield strength of the material is reached), the modulus of elasticity is the appropriate parameter for modeling. In general, selection of photoelastic materials for prostheses and tissue modeling is based on relative modulus values.
Photoelastic observations
| As already mentioned, the photoelastic technique provides a visual display of the stresses in a model. These stresses are revealed in a device called a polariscope. The main elements of a polariscope are the polarizing filters and a light source. This type of polariscope is called a plane polariscope. When the polarizers are oriented so that their axes are at right angles, the polarizers are said to be crossed (Fig. 1-6).The field of view through crossed polarizers is dark. When the polarizers are oriented so that their axes are parallel, the field of view is light (Fig. 1-7). |  Figure 1-6  Figure1-7 |
| Two types of fringes are revealed by a plane polariscope. The array of colored patterns is called isochromatic fringes. These fringes are related to stress intensity. The other set of fringes in a dark field polariscope appears as dark lines and is called isoclinics. These fringes superimpose on the isochromatics and are related to stress direction, as shown in Fig. 1-8 for a centrally loaded beam. Use of the arrays of isoclinics and isochromatics in conjunction with elasticity equations leads to calculation of every stress component throughout the model. The usefulness of precise stress values is open to serious question because of the reported variations in the mechanical properties of biologic structures. It is foolish to believe that the results of any stress analysis technique could predict the precise stress values in any particular patient. |  Figure 1-8 |
(con't)