Ian R. Grosse

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.

Using occlusal wear information and finite element analysis to investigate stress distributions in human molars

Simulations based on finite element analysis (FEA) have attracted increasing interest in dentistry and dental anthropology for evaluating the stress and strain distribution in teeth under occlusal loading conditions. Nonetheless, FEA is usually applied without considering changes in contacts between antagonistic teeth during the occlusal power stroke. In this contribution we show how occlusal information can be used to investigate the stress distribution with 3D FEA in lower first molars (M1). The antagonistic crowns M1 and P2–M1 of two dried modern human skulls were scanned by μCT in maximum intercuspation (centric occlusion) contact. A virtual analysis of the occlusal power stroke between M1 and P2–M1 was carried out in the Occlusal Fingerprint Analyser (OFA) software, and the occlusal trajectory path was recorded, while contact areas per time‐step were visualized and quantified. Stress distribution of the M1 in selected occlusal stages were analyzed in strand7, considering occlusal information taken from OFA results for individual loading direction and loading area. Our FEA results show that the stress pattern changes considerably during the power stroke, suggesting that wear facets have a crucial influence on the distribution of stress on the whole tooth. Grooves and fissures on the occlusal surface are seen as critical locations, as tensile stresses are concentrated at these features. Properly accounting for the power stroke kinematics of occluding teeth results in quite different results (less tensile stresses in the crown) than usual loading scenarios based on parallel forces to the long axis of the tooth. This leads to the conclusion that functional studies considering kinematics of teeth are important to understand biomechanics and interpret morphological adaptation of teeth.

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.

Ontologies for supporting engineering analysis models

In this paper we lay the foundations for exchanging, adapting, and interoperating engineering analysis models (EAMs). Our primary foundation is based upon the concept that engineering analysis models are knowledge-based abstractions of physical systems, and therefore knowledge sharing is the key to exchanging, adapting, and interoperating EAMs within or across organizations. To enable robust knowledge sharing, we propose a formal set of ontologies for classifying analysis modeling knowledge. To this end, the fundamental concepts that form the basis of all engineering analysis models are identified, described, and typed for implementation into a computational environment. This generic engineering analysis modeling ontology is extended to include distinct analysis subclasses. We discuss extension of the generic engineering analysis modeling class for two common analysis subclasses: continuum-based finite element models and lumped parameter or discrete analysis models. To illustrate how formal ontologies of engineering analysis modeling knowledge might facilitate knowledge exchange and improve reuse, adaptability, and interoperability of analysis models, we have developed a prototype engineering analysis modeling knowledge base, called ON-TEAM, based on our proposed ontologies. An industrial application is used to instantiate the ON-TEAM knowledge base and illustrate how such a system might improve the ability of organizations to efficiently exchange, adapt, and interoperate analysis models within a computer-based engineering environment. We have chosen Java as our implementation language for ON-TEAM so that we can fully exploit object-oriented technology, such as object inspection and the use of metaclasses and metaobjects, to operate on the knowledge base to perform a variety of tasks, such as knowledge inspection, editing, maintenance, model diagnosis, customized report generation of analysis models, model selection, automated customization of the knowledge interface based on the user expertise level, and interoperability assessment of distinct analysis models.

The Structural Rigidity of the Cranium of Australopithecus africanus: Implications for Diet, Dietary Adaptations, and the Allometry of Feeding Biomechanics

Australopithecus africanus is an early hominin (i.e., human relative) believed to exhibit stress‐reducing adaptations in its craniofacial skeleton that may be related to the consumption of resistant food items using its premolar teeth. Finite element analyses simulating molar and premolar biting were used to test the hypothesis that the cranium of A. africanus is structurally more rigid than that of Macaca fascicularis, an Old World monkey that lacks derived australopith facial features. Previously generated finite element models of crania of these species were subjected to isometrically scaled loads, permitting a direct comparison of strain magnitudes. Moreover, strain energy (SE) in the models was compared after results were scaled to account for differences in bone volume and muscle forces. Results indicate that strains in certain skeletal regions below the orbits are higher in M. fascicularis than in A. africanus. Moreover, although premolar bites produce von Mises strains in the rostrum that are elevated relative to those produced by molar biting in both species, rostral strains are much higher in the macaque than in the australopith. These data suggest that at least the midface of A. africanus is more rigid than that of M. fascicularis. Comparisons of SE reveal that the A. africanus cranium is, overall, more rigid than that of M. fascicularis during premolar biting. This is consistent with the hypothesis that this hominin may have periodically consumed large, hard food items. However, the SE data suggest that the A. africanus cranium is marginally less rigid than that of the macaque during molar biting. It is hypothesized that the SE results are being influenced by the allometric scaling of cranial cortical bone thickness. Anat Rec, 293:583–593, 2010.

Ontologies for supporting engineering design optimization

This paper presents an optimization ontology and its implementation into a prototype computational knowledge base tool dubbed ONTOP (ONT ology for OP timization). Salient features of ONTOP include a knowledge base which incorporates both standardized optimization terminology, formal method definitions, and often unrecorded optimization details, such as any idealizations and assumptions that may be made when creating an optimization model, as well as the model developer’s rationale and justification behind these idealizations and assumptions. ONTOP was developed using Protege, a Java-based, free open-source ontology development environment created by Stanford University. Two engineering design optimization case studies are presented. The first case study consists of the optimization of a structural beam element and demonstrates ONTOP ’s ability to address the variations in an optimal solution that may arise when different techniques and approaches are used. A second case study, a more complex design problem which deals with the optimization of an impeller of a pediatric left ventricular heart assist device, demonstrates the wealth of knowledge ONTOP is able to capture. Together, these test beds help illustrate the potential value of an ontology in representing application-specific knowledge while facilitating both the sharing and exchanging of this knowledge in engineering design optimization.© 2006 ASME

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.

Viewpoints: Diet and Dietary Adaptations in Early Hominins: The Hard Food Perspective

Recent biomechanical analyses examining the feeding adaptations of early hominins have yielded results consistent with the hypothesis that hard foods exerted a selection pressure that influenced the evolution of australopith morphology. However, this hypothesis appears inconsistent with recent reconstructions of early hominin diet based on dental microwear and stable isotopes. Thus, it is likely that either the diets of some australopiths included a high proportion of foods these taxa were poorly adapted to consume (i.e., foods that they would not have processed efficiently), or that aspects of what we thought we knew about the functional morphology of teeth must be wrong. Evaluation of these possibilities requires a recognition that analyses based on microwear, isotopes, finite element modeling, and enamel chips and cracks each test different types of hypotheses and allow different types of inferences. Microwear and isotopic analyses are best suited to reconstructing broad dietary patterns, but are limited in their ability to falsify specific hypotheses about morphological adaptation. Conversely, finite element analysis is a tool for evaluating the mechanical basis of form-function relationships, but says little about the frequency with which specific behaviors were performed or the particular types of food that were consumed. Enamel chip and crack analyses are means of both reconstructing diet and examining biomechanics. We suggest that current evidence is consistent with the hypothesis that certain derived australopith traits are adaptations for consuming hard foods, but that australopiths had generalized diets that could include high proportions of foods that were both compliant and tough.

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.

The Feeding Biomechanics and Dietary Ecology of Paranthropus boisei

The African Plio‐Pleistocene hominins known as australopiths evolved derived craniodental features frequently interpreted as adaptations for feeding on either hard, or compliant/tough foods. Among australopiths, Paranthropus boisei is the most robust form, exhibiting traits traditionally hypothesized to produce high bite forces efficiently and strengthen the face against feeding stresses. However, recent mechanical analyses imply that P. boisei may not have been an efficient producer of bite force and that robust morphology in primates is not necessarily strong. Here we use an engineering method, finite element analysis, to show that the facial skeleton of P. boisei is structurally strong, exhibits a strain pattern different from that in chimpanzees (Pan troglodytes) and Australopithecus africanus, and efficiently produces high bite force. It has been suggested that P. boisei consumed a diet of compliant/tough foods like grass blades and sedge pith. However, the blunt occlusal topography of this and other species suggests that australopiths are adapted to consume hard foods, perhaps including grass and sedge seeds. A consideration of evolutionary trends in morphology relating to feeding mechanics suggests that food processing behaviors in gracile australopiths evidently were disrupted by environmental change, perhaps contributing to the eventual evolution of Homo and Paranthropus. Anat Rec, 298:145–167, 2015.