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Publicado: 29 de noviembre de 2011
A qualitative engineering analysis of mandibular fracture repair mechanics
JDB/752741.v1
Page 1 of 27
Paper title: A qualitative engineering analysis of mandibular fracture repair mechanics
Full author names: Thomas R. Katona
Full institutional mailing addresses: Indiana University School of Dentistry Indiana University - Purdue University, Indianapolis (IUPUI) 1121 W. Michigan St.Indianapolis, IN 46202
Email addresses: tkatona@iupui.edu
A qualitative engineering analysis of mandibular fracture repair mechanics
Page 2 of 27
ABSTRACT Objectives. The purpose of this analytical study was to examine and critique the engineering foundations of commonly accepted biomechanical principles of mandible fracture repair. Materials and Methods. Basic principles of staticequilibrium were applied to intact and plated mandibles, but instead of the traditional lever forces, the mandibles were subjected to more realistic occlusal forces. Results. These loading conditions produced stress distributions within the intact mandible that were very different and more complex than the customary lever-based gradient. The analyses also demonstrated the entirely differentmechanical environments within intact and plated mandibles. Conclusions. Because the loading and geometry of the leveridealized mandible is incomplete, the associated widely accepted bone stress distribution (tension on top, compression on the bottom) should not be assumed. Furthermore, the stress gradients within the bone of an intact mandible should not be extrapolated to the mechanical environmentwithin the plated regions of a fractured mandible.
A qualitative engineering analysis of mandibular fracture repair mechanics
Page 3 of 27
1. Introduction The mandible has long been regarded as a lever [1-13]. There have been questions about its class I vs. II vs. III classification, or it being a lever in the first place [14-16] and the loading assumptions [17]. But, it is the lever model,coupled with the bending beam analogy of the mandible, that form the foundation of the generally accepted (longitudinal) stress distribution pattern depicted in Figure 1(a) [18-21] and its variant, Figure 1(b) [18, 20, 22, 23]. The lever is an oversimplified structural representation of the jaw, so biomechanical concepts derived from it should be suspect. In the present context, the lever’sintrinsic verticalonly occlusal force is its primary drawback. Thus, the principal purposes of this article are to demonstrate, with basic analytical engineering mechanics, but barebones mathematics, the shortcomings of the lever/beam model-based concepts that relate to the surgery of the mandible. More specifically, the central issues involve (1) the relationship between occlusal force direction and theassociated stress distributions within an intact mandible and (2), the extrapolation of those stress fields to a plated fractured mandible.
2. Materials and Methods Figure 2(a) is a partial (because dimensions irrelevant to this discussion are omitted) freebody-diagram (FBD) of the frame- (vs. lever-, Figure 1) idealized mandible. An FBD, used in equilibrium analysis, shows all external loads(forces and moments) that act on an isolated object (i.e., the mandible or a portion of it) of interest. For the purposes of this project, the crucial difference between the lever (Figure 1) and the frame model is that in the latter, the direction of force vector T is not necessarily vertical, Figures 2 and 3. (The governing equations for Figure 2(a) are derived and solved elsewhere [24].)
Aqualitative engineering analysis of mandibular fracture repair mechanics
Page 4 of 27
The FBD in Figure 2(b) is of an imaginary or real (i.e., fractured) segment of the mandible that is anterior to the arbitrarily defined (at distance h from the occlusal contact) circle, ○, on the approximated centroidal axis (dashed line) of the mandible. V and H represent the internal shear and normal...
JDB/752741.v1
Page 1 of 27
Paper title: A qualitative engineering analysis of mandibular fracture repair mechanics
Full author names: Thomas R. Katona
Full institutional mailing addresses: Indiana University School of Dentistry Indiana University - Purdue University, Indianapolis (IUPUI) 1121 W. Michigan St.Indianapolis, IN 46202
Email addresses: tkatona@iupui.edu
A qualitative engineering analysis of mandibular fracture repair mechanics
Page 2 of 27
ABSTRACT Objectives. The purpose of this analytical study was to examine and critique the engineering foundations of commonly accepted biomechanical principles of mandible fracture repair. Materials and Methods. Basic principles of staticequilibrium were applied to intact and plated mandibles, but instead of the traditional lever forces, the mandibles were subjected to more realistic occlusal forces. Results. These loading conditions produced stress distributions within the intact mandible that were very different and more complex than the customary lever-based gradient. The analyses also demonstrated the entirely differentmechanical environments within intact and plated mandibles. Conclusions. Because the loading and geometry of the leveridealized mandible is incomplete, the associated widely accepted bone stress distribution (tension on top, compression on the bottom) should not be assumed. Furthermore, the stress gradients within the bone of an intact mandible should not be extrapolated to the mechanical environmentwithin the plated regions of a fractured mandible.
A qualitative engineering analysis of mandibular fracture repair mechanics
Page 3 of 27
1. Introduction The mandible has long been regarded as a lever [1-13]. There have been questions about its class I vs. II vs. III classification, or it being a lever in the first place [14-16] and the loading assumptions [17]. But, it is the lever model,coupled with the bending beam analogy of the mandible, that form the foundation of the generally accepted (longitudinal) stress distribution pattern depicted in Figure 1(a) [18-21] and its variant, Figure 1(b) [18, 20, 22, 23]. The lever is an oversimplified structural representation of the jaw, so biomechanical concepts derived from it should be suspect. In the present context, the lever’sintrinsic verticalonly occlusal force is its primary drawback. Thus, the principal purposes of this article are to demonstrate, with basic analytical engineering mechanics, but barebones mathematics, the shortcomings of the lever/beam model-based concepts that relate to the surgery of the mandible. More specifically, the central issues involve (1) the relationship between occlusal force direction and theassociated stress distributions within an intact mandible and (2), the extrapolation of those stress fields to a plated fractured mandible.
2. Materials and Methods Figure 2(a) is a partial (because dimensions irrelevant to this discussion are omitted) freebody-diagram (FBD) of the frame- (vs. lever-, Figure 1) idealized mandible. An FBD, used in equilibrium analysis, shows all external loads(forces and moments) that act on an isolated object (i.e., the mandible or a portion of it) of interest. For the purposes of this project, the crucial difference between the lever (Figure 1) and the frame model is that in the latter, the direction of force vector T is not necessarily vertical, Figures 2 and 3. (The governing equations for Figure 2(a) are derived and solved elsewhere [24].)
Aqualitative engineering analysis of mandibular fracture repair mechanics
Page 4 of 27
The FBD in Figure 2(b) is of an imaginary or real (i.e., fractured) segment of the mandible that is anterior to the arbitrarily defined (at distance h from the occlusal contact) circle, ○, on the approximated centroidal axis (dashed line) of the mandible. V and H represent the internal shear and normal...
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