Elastic properties and masticatory bone stress in the Macaque mandible

Abstract

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. ...

Finite‐element modeling of the anthropoid mandible: The effects of altered boundary conditions

“…A multitude of variables act simultaneously during a strain gauge experiment (e.g., orientation and magnitude of the applied load, nature of constraints, material property variation, and geometric subtleties of the real specimen), whereas in a finite-element analysis these variables are necessarily subject to a number of simplifying assumptions. This discrepancy might lead to different results and interpretations of the stress-strain behavior of the mandibular bone Dechow and Hylander, 2000). Our objective was to portray the difficulties encountered when attempting to validate finite-element models from an in vitro context where some parameters are ostensibly under investigator control.…”

“…The elastic properties vary directionally between different regions in the mandible (Dechow and Hylander, 2000). Developing a model without directional dependence of elastic properties, although very convenient and significantly less time-consuming, will provide only a first approximation of the strain field in a loaded mandible.…”

Bone strain gradients and optimization in vertebrate skulls

“…The primate data are analyzed at the generic level to increase the number of sites sampled within each taxonomic unit and to increase the number of experiments on any one site. Data on genus Macaca are pooled from M. fascicularis and M. mulatta (Hylander a, 1985Hylander et al 1991;Dechow and Hylander 2000;Hylander and Johnson 1997;Ross 2001, unpublished data). The data from Aotus come from three individuals of unknown species (Ross and Hylander 1996;Ross 2001).…”

“…When mean c-max values were not given, they were estimated from mean values of e 1 and e 2 . When peak c-max values were not reported (Dechow and Hylander 2000), the maximum values of e 1 and e 2 re- corded during a single experiment were used to estimate peak c-max. In the case of the data from the pigs, neither c-max nor maximum e 1 and e 2 data were available, so peak c-max data are not presented (Herring and Teng 2000;Herring et al 1996Herring et al , 2001Rafferty et al 2000).…”

Finite element analysis in functional morphology

“…However, this approach provides at best only an approximation of how structures respond under the applied loads, and there are limits to where strain gauges can be placed and they measure strain only in the plane of the gauge (Hylander, 1984;Dechow and Hylander, 2000;Ross, 2001).…”