Julian L. Davis

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.

Finite element analysis of performance in the skulls of marmosets and tamarins

Reliance on plant exudates is a relatively rare dietary specialization among mammals. One well‐studied example of closely related exudate feeders is the New World marmosets and tamarins. Whereas marmosets actively gouge tree bark with their incisors to stimulate the flow of sap, tamarins are opportunistic exudate feeders that do not gouge bark. Several studies of the dentaries and jaw adductors indicate that marmosets exhibit specializations for increased gape at the expense of bite force. Few studies, however, have looked to the cranium of marmosets for evidence of functional specializations. Using 3D finite element models of the marmoset Callithrix jacchus and the tamarin Saguinus fuscicollis, we investigated the performance of the cranium under loading regimes that mimicked unilateral molar biting and bark‐gouging. We investigated three measures of performance: the efficiency with which muscle force is transferred to bite force, the extent to which the models are stressed (a predictor of failure), and the work expended by muscles as they deform the skull (total strain energy). We found that during molar biting the two models exhibited similar levels of performance, though the Saguinus model had slightly higher mechanical efficiency, a slightly lower state of stress, and expended more energy on deformation. In contrast, under the bark‐gouging load, Callithrix exhibited much higher mechanical efficiency than Saguinas, but did so at the expense of more work and higher levels of von Mises stress. This analysis illustrates that differences in the shapes of the skulls of Callithrix and Saguinus confer differences in performance. Whether these aspects of performance are targets of selection awaits broader comparative analyses.

An Efficient Method of Modeling Material Properties Using a Thermal Diffusion Analogy: An Example Based on Craniofacial Bone

The ability to incorporate detailed geometry into finite element models has allowed researchers to investigate the influence of morphology on performance aspects of skeletal components. This advance has also allowed researchers to explore the effect of different material models, ranging from simple (e.g., isotropic) to complex (e.g., orthotropic), on the response of bone. However, bones complicated geometry makes it difficult to incorporate complex material models into finite element models of bone. This difficulty is due to variation in the spatial orientation of material properties throughout bone. Our analysis addresses this problem by taking full advantage of a finite element programs ability to solve thermal-structural problems. Using a linear relationship between temperature and modulus, we seeded specific nodes of the finite element model with temperatures. We then used thermal diffusion to propagate the modulus throughout the finite element model. Finally, we solved for the mechanical response of the finite element model to the applied loads and constraints. We found that using the thermal diffusion analogy to control the modulus of bone throughout its structure provides a simple and effective method of spatially varying modulus. Results compare favorably against both experimental data and results from an FE model that incorporated a complex (orthotropic) material model. This method presented will allow researchers the ability to easily incorporate more material property data into their finite element models in an effort to improve the models accuracy.

Quantifying utricular stimulation during natural behavior.

The use of natural stimuli in neurophysiological studies has led to significant insights into the encoding strategies used by sensory neurons. To investigate these encoding strategies in vestibular receptors and neurons, we have developed a method for calculating the stimuli delivered to a vestibular organ, the utricle, during natural (unrestrained) behaviors, using the turtle as our experimental preparation. High-speed digital video sequences are used to calculate the dynamic gravito-inertial (GI) vector acting on the head during behavior. X-ray computed tomography (CT) scans are used to determine the orientation of the otoconial layer (OL) of the utricle within the head, and the calculated GI vectors are then rotated into the plane of the OL. Thus, the method allows us to quantify the spatio-temporal structure of stimuli to the OL during natural behaviors. In the future, these waveforms can be used as stimuli in neurophysiological experiments to understand how natural signals are encoded by vestibular receptors and neurons. We provide one example of the method, which shows that turtle feeding behaviors can stimulate the utricle at frequencies higher than those typically used in vestibular studies. This method can be adapted to other species, to other vestibular end organs, and to other methods of quantifying head movements.

Ontogeny of bite force in a validated biomechanical model of the American alligator

ABSTRACT Three-dimensional computational modeling offers tools with which to investigate forces experienced by the skull during feeding and other behaviors. American alligators (Alligator mississippiensis) generate some of the highest measured bite forces among extant tetrapods. A concomitant increase in bite force accompanies ontogenetic increases in body mass, which has been linked with dietary changes as animals increase in size. Because the flattened skull of crocodylians has substantial mediolaterally oriented muscles, crocodylians are an excellent model taxon in which to explore the role of mediolateral force components experienced by the feeding apparatus. Many previous modeling studies of archosaur cranial function focused on planar analysis, ignoring the mediolateral aspects of cranial forces. Here, we used three-dimensionally accurate anatomical data to resolve 3D muscle forces. Using dissection, imaging and computational techniques, we developed lever and finite element models of an ontogenetic series of alligators to test the effects of size and shape on cranial loading and compared estimated bite forces with those previously measured in vivo in A. mississippiensis. We found that modeled forces matched in vivo data well for intermediately sized individuals, and somewhat overestimated force in smaller specimens and underestimated force in larger specimens, suggesting that ontogenetically static muscular parameters and bony attachment sites alone cannot account for all the variation in bite force. Adding aponeurotic muscle attachments would likely improve force predictions, but such data are challenging to model and integrate into analyses of extant taxa and are generally unpreserved in fossils. We conclude that anatomically accurate modeling of muscles can be coupled with finite element and lever analyses to produce reliable, reasonably accurate estimate bite forces and thus both skeletal and joint loading, with known sources of error, which can be applied to extinct taxa. Summary: A high-fidelity 3D computational model of alligator bite force that can be used for inferring feeding behavior in fossils.

A Multilevel Hierarchical Finite Element Model for Capillary Failure in Soft Tissue

Bruising, the result of capillary failure due to trauma, is a common indication of abuse. However, the etiology of capillary failure has yet to be determined as the scale change from tissue to capillary represents several orders of magnitude. As a first step toward determining bruise etiology, we have developed a multilevel hierarchical finite element model (FEM) of a portion of the upper human arm using a commercial finite element tool and a series of three interconnected hierarchical submodels. The third and final submodel contains a portion of the muscle tissue in which a single capillary is embedded. Nonlinear, hyperelastic material properties were applied to skin, adipose, muscle, and capillary wall materials. A pseudostrain energy method was implemented to subtract rigid-body-like motion of the submodel volume experienced in the global model, and was critical for convergence and successful analyses in the submodels. The deformation and hoop stresses in the capillary wall were determined and compared with published capillary failure stress. For the dynamic load applied to the skin of the arm (physiologically simulating a punch), the model predicted that approximately 8% volume fraction of the capillary wall was above the reference capillary failure stress, indicating bruising would likely occur.

Connecting Finite Element Modeling With Strengths of Materials and Vibrations Using Beam Experiments

Students tend to compartmentalize individual classes throughout their time in school; associating that which is taught in one class with only that class. A finite element class offers a unique opportunity to illustrate the connection between several engineering topics through modeling and experiments since it is used to solve many different types of problems (e.g. force-deflection, stress-strain, heat transfer, fluid transport, and vibrations). In addition, providing hands-on experiments is an excellent way to illustrate concepts. Particularly, experiments can help students visualize the additional abstractions present in a finite element model while demonstrating the connections between several prerequisite engineering courses. Here we present experiments that connect finite element modeling with two classes: Strength of Materials and Vibrations. These experiments highlight the effects of finite element modeling choices and illustrate errors in the approximations.Copyright