Role of Biomechanics in Periodontal Therapy

Dr. Angelo A. Caputo and Dr. Robert S. Wylie

For most dental applications, the main information required is the location and intensity of stress concentrations. This information can indicate areas of structural weakness and potential failure due to either fracture or exceeding the yield strength of the material. Further, stress concentrations in biologic structures are regions with the greatest proclivity for cellular change (e.g. resorption or apposition). These data are obtainable from the isochromatic fringe patterns. To facilitate examination of the isochromatics, one should eliminate the isoclinics. Eliminating the isoclinics is accomplished in a circular polariscope, which has filters called quarter-wave plates. These filters cause partially canceling rotations of the light, which negate the isoclinic fringes, revealing only the isochromatic fringes (Fig. 1-9).

Figure 1-9

It should be noted that as force is applied to a structure, the number of isochromatic fringes increases. If the structure is responding within the straight line portion of the stress-strain curve, the number of fringes will be proportional to the applied loads. For example, the shape and distribution of the isochromatic fringes of the two loaded beams in Fig. 1-10 are identical. The only difference between the two beams is the proportionally increased number of fringes due to the increase in load.

Figure 1-10

Interpretation of Photoelastic Patterns

• More lines - higher stress
• Closer lines - more concentrated stress

Stress Concentrations

• Bearing - contact
• Geometric discontinuity
• Modulus mismatch

Significance of Stress Concentrations

• Potential structural failure
• Stimulus for biologic change

When the overall isochromatic fringe pattern is considered, interpretation is quite straightforward with the use of the following two principles: (1) the larger the number of fringes, the higher the stress intensity; and (2) the closer the isochromatic fringes are to each other, the higher the stress concentration. Stress concentrations will develop under three general conditions. The first is the bearing of one body on another. This condition is seen with the loaded beams in Figs. 1-10 and 1-11. Bearing stress concentrations can be observed at the central load point and at the two beam supports. A second stress concentrating mechanism is a geometric discontinuity, such as a constriction, a sharp angle, or other nonuniform shape factors. Examples of geometric discontinuities are shown by the notch in the tension side of the beam in Fig. 1-11 and the sharp angle and reduced cross section of the beam in Fig. 1-12. A modulus mismatch between two portions of a structure will also cause a stress concentrating effect, as in Fig. 1-13, where steel balls are imbedded in a low modulus matrix. Stresses are concentrated near the balls even though the external force is not applied directly to the balls.

Figure 1-11

Figure 1-12

Figure 1-13

Application of Photoelastic Principles

• Two-dimensional
• Three-dimensional
• Quasi-three-dimensional

The previous discussion has been relative to the basic principles of photoelasticity. Application of these principles to obtain information relevant to clinical dentistry may take one of four approaches: (1) two-dimensional technique, (2) three-dimensional technique, (3) quasi-three-dimensional technique, or (4) a technique using a combination of these three approaches.

Two-dimensional technique

• Planar model
• Loads in plane of model
• No stress variation through thickness

• Ease of fabrication
• Multiple load situations
• Various appliances

• Imperfect geometric fidelity

The two-dimensional technique uses a model that maintains geometric fidelity in one plane, such as a sagittal section of a tooth (Fig. 1-14). A requirement for true two-dimensional photoelastic analysis is that there be no variation of stress through the thickness of the model. Consequently, forces applied to the model must be in the plane of the model. An example of this approach is shown in Fig. 1-15 illustrating the reduction of stress concentrations for a tipped molar splinted to an anterior teeth.

Figure 1-14

Figure 1-15

The two-dimensional technique has three advantages: (1) the models are relatively easy to fabricate; (2) a wide variety of loading conditions can be applied to the model, and (3) different appliances may be tested on the same model. However, the technique suffers the major disadvantage of imperfectly reproducing the three-dimensional geometry of the oral situation. Consequently, the full three-dimensional stress distribution cannot be determined.

Three-dimensional Technique

• No restrictions on geometry, load, or stress variations
• Based on stress freezing, or locking in of stresses

• Apply loads at specific elevated temperature
• Lower to room temperature, loads in place
• Stresses remain in model
• Section model
• Two-dimensional analysis of each section
• Build three-dimensional stress picture

• Good geometric fidelity
• Three-dimensional stress picture

• Destruction of model to obtain data
• Need separate model for each load, appliance

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References

1. Craig, R.G. Restorative Dental Materials, 7th ed. St.Louis: The C.V. Mosby Co. 1985.
2. Cochran, G.V.B. A primer of Orthopaedic Biomechanics. New York: Churchill Livingtone, 1982.
3. Fung, Y.C. Biomechanics. New York: Springer-Verlag New York, Inc., 1981.
4. Durelli, A.J., and Riley, W.F., Introduction to Photomechanics. Englewood cliffs, N.J.; Prentice-Hall, Inc., 1965.
5. Brodsky, J.F., Caputo, A.A., and Furstman, L.L. Root tipping: A photoelastic-histopathologic correlation. Am. J. Orthod. 67:1, 1975.
6. de Alba, J.A., Caputo, A.A., and Chaconas, S.J. Effects of orthodontic intermaxillary Class III mechanics on craniofacial structures: I. Photoelastic analysis. Angle Orthod. 49:21, 1979.
7. de Alba, J.A., Caputo, A.A., and Chaconas, S.J. Effects of orthodontic intermaxillary Class III mechanics on craniofacial structures: II. Computerized cephalometrics. Angle Orthod. 49:29, 1979.