Elizabeth R. Dumont

Requirements for comparing the performance of finite element models of biological structures

The widespread availability of three-dimensional imaging and computational power has fostered a rapid increase in the number of biologists using finite element analysis (FEA) to investigate the mechanical function of living and extinct organisms. The inevitable rise of studies that compare finite element models brings to the fore two critical questions about how such comparative analyses can and should be conducted: (1) what metrics are appropriate for assessing the performance of biological structures using finite element modeling? and, (2) how can performance be compared such that the effects of size and shape are disentangled? With respect to performance, we argue that energy efficiency is a reasonable optimality criterion for biological structures and we show that the total strain energy (a measure of work expended deforming a structure) is a robust metric for comparing the mechanical efficiency of structures modeled with finite elements. Results of finite element analyses can be interpreted with confidence when model input parameters (muscle forces, detailed material properties) and/or output parameters (reaction forces, strains) are well-documented by studies of living animals. However, many researchers wish to compare species for which these input and validation data are difficult or impossible to acquire. In these cases, researchers can still compare the performance of structures that differ in shape if variation in size is controlled. We offer a theoretical framework and empirical data demonstrating that scaling finite element models to equal force: surface area ratios removes the effects of model size and provides a comparison of stress-strength performance based solely on shape. Further, models scaled to have equal applied force:volume ratios provide the basis for strain energy comparison. Thus, although finite element analyses of biological structures should be validated experimentally whenever possible, this study demonstrates that the relative performance of un-validated models can be compared so long as they are scaled properly.

The effects of gape angle and bite point on bite force in bats.

SUMMARY Models of mammalian mastication predict that bite force is affected by both the degree of mouth opening (gape angle) and the point along the tooth row at which force is transferred to a food item (bite point). Despite the widespread use of these models in comparative analyses, experimental data documenting bite force in non-human mammals are extremely limited. The goal of this study is to document variation in non-stimulated bite force associated with change in gape angle and bite point in a broad range of species. We focus on plant-visiting bats because they exhibit a relatively primitive cranial morphology and are good models for generalized mammals. Assessments of the relationship between gape angle and bite force within and among species demonstrate that bite force decreases significantly as gape angle increases. The relationship between bite force and bite point within each of seven species demonstrates that unilateral molar biting universally generates the highest forces while the unilateral canine biting produces the lowest forces. Bilateral canine biting is intermediate. Beyond these general patterns, differences among species suggest that bite force reflects variation in craniofacial architecture. Finally, these data suggest that behavioral variation in gape angle and bite point may be important variables in comparative, functional analyses of feeding.

Morphological innovation, diversification and invasion of a new adaptive zone

How ecological opportunity relates to diversification is a central question in evolutionary biology. However, there are few empirical examples of how ecological opportunity and morphological innovation open new adaptive zones, and promote diversification. We analyse data on diet, skull morphology and bite performance, and relate these traits to diversification rates throughout the evolutionary history of an ecologically diverse family of mammals (Chiroptera: Phyllostomidae). We found a significant increase in diversification rate driven by increased speciation at the most recent common ancestor of the predominantly frugivorous subfamily Stenodermatinae. The evolution of diet was associated with skull morphology, and morphology was tightly coupled with biting performance, linking phenotype to new niches through performance. Following the increase in speciation rate, the rate of morphological evolution slowed, while the rate of evolution in diet increased. This pattern suggests that morphology stabilized, and niches within the new adaptive zone of frugivory were filled rapidly, after the evolution of a new cranial phenotype that resulted in a certain level of mechanical efficiency. The tree-wide speciation rate increased non linearly with a more frugivorous diet, and was highest at measures of skull morphology associated with morphological extremes, including the most derived Stenodermatines. These results show that a novel stenodermatine skull phenotype played a central role in the evolution of frugivory and increasing speciation within phyllostomids.

Enamel Thickness and Dietary Adaptation among Extant Primates and Chiropterans

Among fossil primates, thick enamel has been interpreted as an adaptation to hard-object feeding. However, correlations between thickness of enamel and diet have not been investigated rigorously among extant taxa. Thickness of enamel was compared within and between congeneric pairs that feed on hard and soft objects from two primate and three chiropteran families. Within each pair, the hard-object feeder exhibits relatively thicker enamel than its congener that feeds on softer items. However, there is overlap in both types of feeders, and the hypothesis that a specific value of enamel thickness be used to separate hard- and soft-object feeders is rejected. Dietary inferences based on thickness of enamel should be made only within an appropriate taxonomic context.

Cranial shape in fruit, nectar, and exudate feeders: Implications for interpreting the fossil record

At least 29 species of fossil primates have been referred to fruit, nectar, and/or exudate feeding dietary niches. Many studies have detailed the morphological correlates of fruit feeding in comparison to insectivory and folivory. In contrast, few studies have sought to differentiate the morphological correlates of fruit feeding from those of nectar and exudate feeding. This study investigates the differences between fruit, nectar, and exudate feeders using 22 cranial and dentary shape variables representing 28 species of living marsupials, bats, and primates. Discriminant function analysis is used to investigate the differences between these dietary categories using both the complete data set and a reduced data set composed of variables that might reasonably be available from fragmentary fossil material. The success rates of post-hoc classifications are 94 and 88%, respectively. These results demonstrate that it is possible to discriminate among fruit, nectar, and exudate feeders among fossil taxa with a reasonable degree of certainty using the data and techniques outlined here. Nectar feeders exhibit a unique combination of features that are associated with reduced masticatory strength and their role as pollination agents. Exudate feeder skulls and dentaries exhibit a combination of features that reflect the high stresses encountered by the anterior dentition through bark gouging behavior. Fruit feeders are morphologically diverse, exhibiting cranial and mandibular shape values that overlap with both nectar and exudate feeders. It is suggested that this diversity reflects the variety of physical properties represented among fruits, and the tendency for individual frugivore species to specialize on particular fruits.

Bone density and the lightweight skeletons of birds

The skeletons of birds are universally described as lightweight as a result of selection for minimizing the energy required for flight. From a functional perspective, the weight (mass) of an animal relative to its lift-generating surfaces is a key determinant of the metabolic cost of flight. The evolution of birds has been characterized by many weight-saving adaptations that are reflected in bone shape, many of which strengthen and stiffen the skeleton. Although largely unstudied in birds, the material properties of bone tissue can also contribute to bone strength and stiffness. In this study, I calculated the density of the cranium, humerus and femur in passerine birds, rodents and bats by measuring bone mass and volume using helium displacement. I found that, on average, these bones are densest in birds, followed closely by bats. As bone density increases, so do bone stiffness and strength. Both of these optimization criteria are used in the design of strong and stiff, but lightweight, manmade airframes. By analogy, increased bone density in birds and bats may reflect adaptations for maximizing bone strength and stiffness while minimizing bone mass and volume. These data suggest that both bone shape and the material properties of bone tissue have played important roles in the evolution of flight. They also reconcile the conundrum of how bird skeletons can appear to be thin and delicate, yet contribute just as much to total body mass as do the skeletons of terrestrial mammals.

Techniques for Modeling Muscle‐induced Forces in Finite Element Models of Skeletal Structures

This work introduces two mechanics‐based approaches to modeling muscle forces exerted on curvilinear bone structures and compares the results with two traditional ad hoc methods of muscle loading. These new models use a combination of tensile, tangential, and normal traction loads to account for muscle fibers wrapped around curved bone surfaces. A computer program was written to interface with a commercial finite element analysis tool to automatically apply traction loads to surface faces of elements in muscle attachment regions according to the various muscle modeling methods. We modeled a highly complex skeletal structure, the skull of a Jamaican fruit bat (Artibeus jamaicensis), to compare the four muscle‐loading methods. While reasonable qualitative agreement was found in the states of stress of the skull between the four muscle load modeling methods, there were substantial quantitative differences predicted in the stress states in some high stressed regions of the skull. Furthermore, our mechanics‐based models required significantly less total applied muscle force to generate a bite‐point reaction force identical to those produced by the ad hoc muscle loading models. Although the methods are not validated by in vivo data, we submit that muscle‐load modeling methods that account for the underlying physics of muscle wrapping on curved bone surfaces are likely to provide more realistic results than ad hoc approaches that do not. We also note that, due to the geometric complexity of many bone structures—such as the skull analyzed here—load transmission paths are difficult to conceptualize a priori. Consequently, it is difficult to predict spatially where the results of finite element analyses are likely to be compromised by using ad hoc muscle modeling methods. For these reasons, it is recommended that a mechanics‐based method be adopted for determination of the proper traction loads to be applied to skeletal structures due to muscular activity. Anat Rec, 290:1069–1088, 2007.

Mid-facial tissue depths of white children: an aid in facial feature reconstruction.

Available facial tissue thickness standards for facial feature reconstruction are based on adult measurements. Mid-facial tissue thicknesses for male and female white adolescents are presented here. Measurements were taken from lateral radiographs produced in an orthodontic practice. Statistical analysis indicates that age, sex, and to some extent, dental occlusion pattern are factors that should be taken into account when attempting facial feature reconstructions.

The effects of modeling simplifications on craniofacial finite element models: The alveoli (tooth sockets) and periodontal ligaments

Several finite element models of a primate cranium were used to investigate the biomechanical effects of the tooth sockets and the material behavior of the periodontal ligament (PDL) on stress and strain patterns associated with feeding. For examining the effect of tooth sockets, the unloaded sockets were modeled as devoid of teeth and PDL, filled with teeth and PDLs, or simply filled with cortical bone. The third premolar on the left side of the cranium was loaded and the PDL was treated as an isotropic, linear elastic material using published values for Youngs modulus and Poissons ratio. The remaining models, along with one of the socket models, were used to determine the effect of the PDLs material behavior on stress and strain distributions under static premolar biting and dynamic tooth loading conditions. Two models (one static and the other dynamic) treated the PDL as cortical bone. The other two models treated it as a ligament with isotropic, linear elastic material properties. Two models treated the PDL as a ligament with hyperelastic properties, and the other two as a ligament with viscoelastic properties. Both behaviors were defined using published stress-strain data obtained from in vitro experiments on porcine ligament specimens. Von Mises stress and strain contour plots indicate that the effects of the sockets and PDL material behavior are local. Results from this study suggest that modeling the sockets and the PDL in finite element analyses of skulls is project dependent and can be ignored if values of stress and strain within the alveolar region are not required.

Predicting bite force in mammals: two-dimensional versus three-dimensional lever models.

SUMMARY Bite force is a measure of whole-organism performance that is often used to investigate the relationships between performance, morphology and fitness. When in vivo measurements of bite force are unavailable, researchers often turn to lever models to predict bite forces. This study demonstrates that bite force predictions based on two-dimensional (2-D) lever models can be improved by including three-dimensional (3-D) geometry and realistic physiological cross-sectional areas derived from dissections. Widely used, the 2-D method does a reasonable job of predicting bite force. However, it does so by over predicting physiological cross-sectional areas for the masseter and pterygoid muscles and under predicting physiological cross-sectional areas for the temporalis muscle. We found that lever models that include the three dimensional structure of the skull and mandible and physiological cross-sectional areas calculated from dissected muscles provide the best predictions of bite force. Models that accurately represent the biting mechanics strengthen our understanding of which variables are functionally relevant and how they are relevant to feeding performance.