Elastic properties and masticatory bone stress in the macaque mandible.
One important limitation of mechanical analyses with strain gages is the difficulty in directly estimating patterns of stress or loading in skeletal elements from strain measurements. Because of the inherent anisotropy in cortical bone, orientation of principal strains and stresses do not necessarily coincide, and it has been demonstrated theoretically that such differences may be as great as 45 degrees (Cowin and Hart, 1990). Likewise, relative proportions of stress and strain magnitudes may differ. This investigation measured the elastic properties of a region of cortical bone on both the buccal and lingual surfaces of the lower border of the macaque mandible. The elastic property data was then combined with macaque mandibular strain data from published and a new in vivo strain gage experiment to determine directions and magnitudes of maximum and minimum principal stresses. The goal was to compare the stresses and strains and assess the differences in orientation and relative magnitude between them. The main question was whether these differences might lead to different interpretations of mandibular function. Elastic and shear moduli, and Poisson's ratios were measured using an ultrasonic technique from buccal and lingual cortical surfaces in 12 macaque mandibles. Mandibular strain gage data were taken from a published set of experiments (Hylander, 1979), and from a new experiment in which rosette strain gauges were fixed to the buccal and lingual cortices of the mandibular corpus of an adult female Macaca fascicularis, after which bone strain was recorded during mastication. Averaged elastic properties were combined with strain data to calculate an estimate of stresses in the mandibular corpus. The elastic properties were similar to those of the human mandibular cortex. Near its lower border, the macaque mandible was most stiff in a longitudinal direction, less stiff in an inferosuperior direction, and least stiff in a direction normal to the bone's surface. The lingual aspect of the mandible was slightly stiffer than the buccal aspect. Magnitudes of stresses calculated from average strains ranged from a compressive stress of -16.00 GPa to a tensile stress of 8.84 GPa. The orientation of the principal stresses depended on whether the strain gage site was on the working or balancing side. On the balancing side of the mandibles, maximum principal stresses were oriented nearly perpendicular to the lower border of the mandible. On the working side of the mandibles, the orientation of the maximum principal stresses was more variable than on the balancing side, indicating a larger range of possible mechanisms of loading. Near the lower border of the mandible, differences between the orientation of stresses and strains were 12 degrees or less. Compared to ratios between maximum and minimum strains, ratios between maximum and minimum stresses were more divergent from a ratio of 1.0. Results did not provide any major reinterpretations of mandibular function in macaques, but rather confirmed and extended existing work. The differences between stresses and strains on the balancing side of the mandible generally supported the view that during the power stroke the mandible was bent and slightly twisted both during mastication and transducer biting. The calculated stresses served to de-emphasize the relative importance of torsion. On the working side, the greater range of variability in the stress analysis compared to the strain analysis suggested that a more detailed examination of loadings and stress patterns in each individual experiment would be useful to interpret the results. Torsion was evident on the working side; but in a number of experiments, further information was needed to interpret other superimposed regional loading patterns, which may have included parasagittal bending and reverse parasagittal bending.
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