An efficient method of modeling material properties using a thermal diffusion analogy: an example based on craniofacial bone

Bite force production and the origin of Homo

The divergence of Homo from gracile australopiths has been described as a trend of decreasing dentognathic size and robusticity, precipitated by stone tool use and/or a shift to softer foods, including meat. Yet, mechanical evidence supporting this narrative is sparse, and isotopic and archaeological data have led to the suggestion that a shift away from a gracile australopith-like diet would not have occurred in the most basal members of Homo but rather only with the appearance of Homo erectus, implying that the origin of our genus is not rooted in dietary change. Here, we provide mechanical evidence that Homo habilis exhibits an australopith-like pattern of facial strain during biting but, unlike most australopiths, was not suited for a diet that required forceful processing by the molar teeth. Homo habilis was at elevated risk of distractive jaw joint forces during those bites, constraining muscle recruitment so as to avoid generating uncomfortable/dangerous levels of tension in the joint. Modern humans have similar limitations. This suggests that selection on skeletal traits favouring forceful postcanine processing was relaxed by the earliest stages in the evolution of our genus, implying that dietary or food processing changes played an important role in the emergence of Homo.

Finite element modeling of meniscal tears using continuum damage mechanics and digital image correlation

Meniscal tears are a common, painful, and debilitating knee injury with limited treatment options. Computational models that predict meniscal tears may help advance injury prevention and repair, but first these models must be validated using experimental data. Here we simulated meniscal tears with finite element analysis using continuum damage mechanics (CDM) in a transversely isotropic hyperelastic material. Finite element models were built to recreate the coupon geometry and loading conditions of forty uniaxial tensile experiments of human meniscus that were pulled to failure either parallel or perpendicular to the preferred fiber orientation. Two damage criteria were evaluated for all experiments: von Mises stress and maximum normal Lagrange strain. After we successfully fit all models to experimental force-displacement curves (grip-to-grip), we compared model predicted strains in the tear region at ultimate tensile strength to the strains measured experimentally with digital image correlation (DIC). In general, the damage models underpredicted the strains measured in the tear region, but models using von Mises stress damage criterion had better overall predictions and more accurately simulated experimental tear patterns. For the first time, this study has used DIC to expose strengths and weaknesses of using CDM to model failure behavior in soft fibrous tissue.

Finite element analysis relating shape, material properties, and dimensions of taenioglossan radular teeth with trophic specialisations in Paludomidae (Gastropoda)

The radula, a chitinous membrane with embedded tooth rows, is the molluscan autapomorphy for feeding. The morphologies, arrangements and mechanical properties of teeth can vary between taxa, which is usually interpreted as adaptation to food. In previous studies, we proposed about trophic and other functional specialisations in taenioglossan radulae from species of African paludomid gastropods. These were based on the analysis of shape, material properties, force-resistance, and the mechanical behaviour of teeth, when interacting with an obstacle. The latter was previously simulated for one species (Spekia zonata) by the finite-element-analysis (FEA) and, for more species, observed in experiments. In the here presented work we test the previous hypotheses by applying the FEA on 3D modelled radulae, with incorporated material properties, from three additional paludomid species. These species forage either on algae attached to rocks (Lavigeria grandis), covering sand (Cleopatra johnstoni), or attached to plant surface and covering sand (Bridouxia grandidieriana). Since the analysed radulae vary greatly in their general size (e.g. width) and size of teeth between species, we additionally aimed at relating the simulated stress and strain distributions with the tooth sizes by altering the force/volume. For this purpose, we also included S. zonata again in the present study. Our FEA results show that smaller radulae are more affected by stress and strain than larger ones, when each tooth is loaded with the same force. However, the results are not fully in congruence with results from the previous breaking stress experiments, indicating that besides the parameter size, more mechanisms leading to reduced stress/strain must be present in radulae.

The cranial biomechanics and feeding performance of Homo floresiensis

Homo floresiensis is a small-bodied hominin from Flores, Indonesia, that exhibits plesiomorphic dentognathic features, including large premolars and a robust mandible, aspects of which have been considered australopith-like. However, relative to australopith species, H. floresiensis exhibits reduced molar size and a cranium with diminutive midfacial dimensions similar to those of later Homo, suggesting a reduction in the frequency of forceful biting behaviours. Our study uses finite-element analysis to examine the feeding biomechanics of the H. floresiensis cranium. We simulate premolar (P³) and molar (M²) biting in a finite-element model (FEM) of the H. floresiensis holotype cranium (LB1) and compare the mechanical results with FEMs of chimpanzees, modern humans and a sample of australopiths (MH1, Sts 5, OH5). With few exceptions, strain magnitudes in LB1 resemble elevated levels observed in modern Homo. Our analysis of LB1 suggests that H. floresiensis could produce bite forces with high mechanical efficiency, but was subject to tensile jaw joint reaction forces during molar biting, which perhaps constrained maximum postcanine bite force production. The inferred feeding biomechanics of H. floresiensis closely resemble modern humans, suggesting that this pattern may have been present in the last common ancestor of Homo sapiens and H. floresiensis.

Feeding Biomechanics in Billfishes: Investigating the Role of the Rostrum through Finite Element Analysis

Billfishes are large pelagic fishes that have an extreme elongation of the upper jaw bones forming the rostrum. Recent kinematic and biomechanical studies show the rostrum to be associated to feeding, however, it is less clear how the wide range of morphologies present among billfish may affect their striking behavior. In this study, we aim to assess the mechanical performance of different rostrum morphologies under loads that simulate feeding and to test existing hypotheses of species-specific feeding behaviors. We use finite element analysis (FEA)-a physics-based method that predicts patterns of stress and strain in morphologically complex structures under specified boundary conditions-to test hypotheses on the form and mechanical performance of billfish rostra. Patterns of von Mises stress and total strain energy suggest that distinct rostral morphologies may be functionally segregated. The rounder blue marlin rostrum may be better suited for a wide range of slashing motions to disable prey, whereas the more flattened swordfish rostrum appears to be more specialized for lateral swiping during prey capture. The almost homogenous stress distribution along each rostrum implies their possible use as a predatory weapon regardless of morphological differences between species. The mechanical implications of other less commonly reported behaviors such as spearing are discussed, as well as the potential impact of hydrodynamics in shaping the evolution of the rostrum in this lineage. Anat Rec, 2019. © 2019 American Association for Anatomy.

The biomechanical role of the chondrocranium and sutures in a lizard cranium

The role of soft tissues in skull biomechanics remains poorly understood. Not least, the chondrocranium, the portion of the braincase which persists as cartilage with varying degrees of mineralization. It also remains commonplace to overlook the biomechanical role of sutures despite evidence that they alter strain distribution. Here, we examine the role of both the sutures and the chondrocranium in the South American tegu lizard Salvator merianae We use multi-body dynamics analysis (MDA) to provide realistic loading conditions for anterior and posterior unilateral biting and a detailed finite element model to examine strain magnitude and distribution. We find that strains within the chondrocranium are greatest during anterior biting and are primarily tensile; also that strain within the cranium is not greatly reduced by the presence of the chondrocranium unless it is given the same material properties as bone. This result contradicts previous suggestions that the anterior portion (the nasal septum) acts as a supporting structure. Inclusion of sutures to the cranium model not only increases overall strain magnitudes but also leads to a more complex distribution of tension and compression rather than that of a beam under sagittal bending.

The Biomechanics of Bony Facial "Buttresses" in South African Australopiths: An Experimental Study Using Finite Element Analysis

Australopiths exhibit a number of derived facial features that are thought to strengthen the face against high and/or repetitive loads associated with a diet that included mechanically challenging foods. Here, we use finite element analysis (FEA) to test hypotheses related to the purported strengthening role of the zygomatic root and "anterior pillar" in australopiths. We modified our previously constructed models of Sts 5 (Australopithecus africanus) and MH1 (A. sediba) to differ in the morphology of the zygomatic root, including changes to both the shape and positioning of the zygomatic root complex, in addition to creating variants of Sts 5 lacking anterior pillars. We found that both an expanded zygomatic root and the presence of "anterior pillars" reinforce the face against feeding loads. We also found that strain orientations are most compatible with the hypothesis that the pillar evolved to resist loads associated with premolar loading, and that this morphology has an ancillary effect of strengthening the face during all loading regimes. These results provide support for the functional hypotheses. However, we found that an anteriorly positioned zygomatic root increases strain magnitudes even in models with an inflated/reinforced root complex. These results suggest that an anteriorly placed zygomatic root complex evolved to enhance the efficiency of bite force production while facial reinforcement features, such as the anterior pillar and the expanded zygomatic root, may have been selected for in part to compensate for the weakening effect of this facial configuration. Anat Rec, 300:171-195, 2017. © 2016 Wiley Periodicals, Inc.

The Biomechanics of Zygomatic Arch Shape

Mammalian zygomatic arch shape is remarkably variable, ranging from nearly cylindrical to blade-like in cross section. Based on geometry, the arch can be hypothesized to be a sub-structural beam whose ability to resist deformation is related to cross sectional shape. We expect zygomatic arches with different cross sectional shapes to vary in the degree to which they resist local bending and torsion due to the contraction of the masseter muscle. A stiffer arch may lead to an increase in the relative proportion of applied muscle load being transmitted through the arch to other cranial regions, resulting in elevated cranial stress (and thus, strain). Here, we examine the mechanics of the zygomatic arch using a series of finite element modeling experiments in which the cross section of the arch of Pan troglodytes has been modified to conform to idealized shapes (cylindrical, elliptical, blade-like). We find that the shape of the zygomatic arch has local effects on stain that do not conform to beam theory. One exception is that possessing a blade-like arch leads to elevated strains at the postorbital zygomatic junction and just below the orbits. Furthermore, although modeling the arch as solid cortical bone did not have the effect of elevating strains in other parts of the face, as had been expected, it does have a small effect on stress associated with masseter contraction. These results are counterintuitive. Even though the arch has simple beam-like geometry, we fail to find a simple mechanical explanation for the diversity of arch shape. Anat Rec, 299:1734-1752, 2016. © 2016 Wiley Periodicals, Inc.

Human feeding biomechanics: performance, variation, and functional constraints

The evolution of the modern human (Homo sapiens) cranium is characterized by a reduction in the size of the feeding system, including reductions in the size of the facial skeleton, postcanine teeth, and the muscles involved in biting and chewing. The conventional view hypothesizes that gracilization of the human feeding system is related to a shift toward eating foods that were less mechanically challenging to consume and/or foods that were processed using tools before being ingested. This hypothesis predicts that human feeding systems should not be well-configured to produce forceful bites and that the cranium should be structurally weak. An alternate hypothesis, based on the observation that humans have mechanically efficient jaw adductors, states that the modern human face is adapted to generate and withstand high biting forces. We used finite element analysis (FEA) to test two opposing mechanical hypotheses: that compared to our closest living relative, chimpanzees (Pan troglodytes), the modern human craniofacial skeleton is (1) less well configured, or (2) better configured to generate and withstand high magnitude bite forces. We considered intraspecific variation in our examination of human feeding biomechanics by examining a sample of geographically diverse crania that differed notably in shape. We found that our biomechanical models of human crania had broadly similar mechanical behavior despite their shape variation and were, on average, less structurally stiff than the crania of chimpanzees during unilateral biting when loaded with physiologically-scaled muscle loads. Our results also show that modern humans are efficient producers of bite force, consistent with previous analyses. However, highly tensile reaction forces were generated at the working (biting) side jaw joint during unilateral molar bites in which the chewing muscles were recruited with bilateral symmetry. In life, such a configuration would have increased the risk of joint dislocation and constrained the maximum recruitment levels of the masticatory muscles on the balancing (non-biting) side of the head. Our results do not necessarily conflict with the hypothesis that anterior tooth (incisors, canines, premolars) biting could have been selectively important in humans, although the reduced size of the premolars in humans has been shown to increase the risk of tooth crown fracture. We interpret our results to suggest that human craniofacial evolution was probably not driven by selection for high magnitude unilateral biting, and that increased masticatory muscle efficiency in humans is likely to be a secondary byproduct of selection for some function unrelated to forceful biting behaviors. These results are consistent with the hypothesis that a shift to softer foods and/or the innovation of pre-oral food processing techniques relaxed selective pressures maintaining craniofacial features that favor forceful biting and chewing behaviors, leading to the characteristically small and gracile faces of modern humans.

An efficient method to capture the impact of total knee replacement on a variety of simulated patient types: A finite element study

Osteoporosis resulting in a reduction in bone stiffness and thinning of the cortex is almost universal in older patients. In this study a novel method to generate computational models of the distal femur which incorporate the effects of ageing and endosteal trabecularisation are presented. Application of this method to pre- and post-knee arthroplasty scenarios is then considered. These computational methods are found to provide a simple yet effective tool for assessing the post-arthroplasty mechanical environment in the knee for different patient types and can help evaluate vulnerability to supracondylar periprosthetic fracture following implantation. Our results show that the stresses in the periprosthetic region increase dramatically with ageing; this is particularly true for higher flexion angles. Stresses in the anterior region of the femoral cortex were also found to increase significantly post-implantation. The most dramatic increases in stresses and strains at these locations were observed in old osteoporotic patients, explaining why this patient group in particular is at greater risk of periprosthetic fractures.

Mechanical evidence that Australopithecus sediba was limited in its ability to eat hard foods

Australopithecus sediba has been hypothesized to be a close relative of the genus Homo. Here we show that MH1, the type specimen of A. sediba, was not optimized to produce high molar bite force and appears to have been limited in its ability to consume foods that were mechanically challenging to eat. Dental microwear data have previously been interpreted as indicating that A. sediba consumed hard foods, so our findings illustrate that mechanical data are essential if one aims to reconstruct a relatively complete picture of feeding adaptations in extinct hominins. An implication of our study is that the key to understanding the origin of Homo lies in understanding how environmental changes disrupted gracile australopith niches. Resulting selection pressures led to changes in diet and dietary adaption that set the stage for the emergence of our genus.

Dietary adaptations of extinct early humans are often inferred from dental microwear data. Here, the authors employ mechanical analyses to show that Australopithecus sediba had limited ability to consume hard foods.

Validation experiments on finite element models of an ostrich (Struthio camelus) cranium

The first finite element (FE) validation of a complete avian cranium was performed on an extant palaeognath, the ostrich (Struthio camelus). Ex-vivo strains were collected from the cranial bone and rhamphotheca. These experimental strains were then compared to convergence tested, specimen-specific finite element (FE) models. The FE models contained segmented cortical and trabecular bone, sutures and the keratinous rhamphotheca as identified from micro-CT scan data. Each of these individual materials was assigned isotropic material properties either from the literature or from nanoindentation, and the FE models compared to the ex-vivo results. The FE models generally replicate the location of peak strains and reflect the correct mode of deformation in the rostral region. The models are too stiff in regions of experimentally recorded high strain and too elastic in regions of low experimentally recorded low strain. The mode of deformation in the low strain neurocranial region is not replicated by the FE models, and although the models replicate strain orientations to within 10° in some regions, in most regions the correlation is not strong. Cranial sutures, as has previously been found in other taxa, are important for modifying both strain magnitude and strain patterns across the entire skull, but especially between opposing the sutural junctions. Experimentally, we find that the strains on the surface of the rhamphotheca are much lower than those found on nearby bone. The FE models produce much higher principal strains despite similar strain ratios across the entirety of the rhamphotheca. This study emphasises the importance of attempting to validate FE models, modelling sutures and rhamphothecae in birds, and shows that whilst location of peak strain and patterns of deformation can be modelled, replicating experimental data in digital models of avian crania remains problematic.

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.

Biomechanical implications of intraspecific shape variation in chimpanzee crania: moving toward an integration of geometric morphometrics and finite element analysis

In a broad range of evolutionary studies, an understanding of intraspecific variation is needed in order to contextualize and interpret the meaning of variation between species. However, mechanical analyses of primate crania using experimental or modeling methods typically encounter logistical constraints that force them to rely on data gathered from only one or a few individuals. This results in a lack of knowledge concerning the mechanical significance of intraspecific shape variation that limits our ability to infer the significance of interspecific differences. This study uses geometric morphometric methods (GM) and finite element analysis (FEA) to examine the biomechanical implications of shape variation in chimpanzee crania, thereby providing a comparative context in which to interpret shape-related mechanical variation between hominin species. Six finite element models (FEMs) of chimpanzee crania were constructed from CT scans following shape-space Principal Component Analysis (PCA) of a matrix of 709 Procrustes coordinates (digitized onto 21 specimens) to identify the individuals at the extremes of the first three principal components. The FEMs were assigned the material properties of bone and were loaded and constrained to simulate maximal bites on the P(3) and M(2) . Resulting strains indicate that intraspecific cranial variation in morphology is associated with quantitatively high levels of variation in strain magnitudes, but qualitatively little variation in the distribution of strain concentrations. Thus, interspecific comparisons should include considerations of the spatial patterning of strains rather than focus only on their magnitudes.

Finite element analysis of a femur to deconstruct the paradox of bone curvature

Most long limb bones in terrestrial mammals exhibit a longitudinal curvature and have been found to be loaded in bending. Bone curvature poses a paradox in terms of the mechanical function of limb bones, for many believe the curvature in these bones increases bending stress, potentially reducing the bone's load carrying capacity (i.e., its mechanical strength). The aim of this study is to investigate the role of longitudinal bone curvature in the design of limb bones. In particular, it has been hypothesized that bone curvature results in a trade-off between the bone's mechanical strength and its bending predictability. We employed finite element analysis (FEA) of abstract and realistic human femora to address this issue. Geometrically simplified human femur models with different curvatures were developed and analyzed with a commercial FEA tool to examine how curvature affects the bone's bending predictability and load carrying capacity. Results were post-processed to yield probability density functions (PDFs) describing the circumferential location of maximum equivalent stress for various curvatures in order to assess bending predictability. To validate our findings, a finite element model was built from a CT scan of a real human femur and compared to the simplified femur model. We found general agreement in trends but some quantitative differences most likely due to the geometric differences between the digitally reconstructed and the simplified finite element models. As hypothesized by others, our results support the hypothesis that bone curvature can increase bending predictability, but at the expense of bone strength.

Probabilistic finite element analysis of a craniofacial finite element model

We employed a probabilistic finite element analysis (FEA) method to determine how variability in material property values affects stress and strain values in a finite model of a Macaca fascicularis cranium. The material behavior of cortical bone varied in three ways: isotropic homogeneous, isotropic non-homogeneous, and orthotropic non-homogeneous. The material behavior of the trabecular bone and teeth was always treated as isotropic and homogeneous. All material property values for the cranium were randomized with a Gaussian distribution with either coefficients of variation (CVs) of 0.2 or with CVs calculated from empirical data. Latin hypercube sampling was used to determine the values of the material properties used in the finite element models. In total, four hundred and twenty six separate deterministic FE simulations were executed. We tested four hypotheses in this study: (1) uncertainty in material property values will have an insignificant effect on high stresses and a significant effect on high strains for homogeneous isotropic models; (2) the effect of variability in material property values on the stress state will increase as non-homogeneity and anisotropy increase; (3) variation in the in vivo shear strain values reported by Strait et al. (2005) and Ross et al. (2011) is not only due to variations in muscle forces and cranial morphology, but also due to variation in material property values; (4) the assumption of a uniform coefficient of variation for the material property values will result in the same trend in how moderate-to-high stresses and moderate-to-high strains vary with respect to the degree of non-homogeneity and anisotropy as the trend found when the coefficients of variation for material property values are calculated from empirical data. Our results supported the first three hypotheses and falsified the fourth. When material properties were varied with a constant CV, as non-homogeneity and anisotropy increased the level of variability in the moderate-to-high strains decreased while the level of variability in the moderate-to-high stresses increased. However, this is not the pattern observed when CVs calculated from empirical data were applied to the material properties where the lowest level of variability in both stresses and strains occurred when the cranium was modeled with a low level of non-homogeneity and anisotropy. Therefore, when constant material property variability is assumed, inaccurate trends in the level of variability present in modest-to-high magnitude stresses and strains are produced. When the cranium is modeled with the highest level of accuracy (high non-homogeneity and anisotropy) and when randomness in the material properties is calculated from empirical data, there is a large level of variability in the significant strains (CV=0.369) and a low level of variability in the modest-to-high magnitude stresses (CV=0.150). This result may have important implications with regard to the mechanical signals driving bone remodeling and adaptation through natural selection.

Sensitivity and ex vivo validation of finite element models of the domestic pig cranium

A finite element (FE) validation and sensitivity study was undertaken on a modern domestic pig cranium. Bone strain data were collected ex vivo from strain gauges, and compared with results from specimen-specific FE models. An isotropic, homogeneous model was created, then input parameters were altered to investigate model sensitivity. Heterogeneous, isotropic models investigated the effects of a constant-thickness, stiffer outer layer (representing cortical bone) atop a more compliant interior (representing cancellous bone). Loading direction and placement of strain gauges were also varied, and the use of 2D membrane elements at strain gauge locations as a method of projecting 3D model strains into the plane of the gauge was investigated. The models correctly estimate the loading conditions of the experiment, yet at some locations fail to reproduce correct principal strain magnitudes, and hence strain ratios. Principal strain orientations are predicted well. The initial model was too stiff by approximately an order of magnitude. Introducing a compliant interior reported strain magnitudes more similar to the ex vivo results without notably affecting strain orientations, ratios or contour patterns, suggesting that this simple heterogeneity was the equivalent of reducing the overall stiffness of the model. Models were generally insensitive to moderate changes in loading direction or strain gauge placement, except in the squamosal portion of the zygomatic arch. The use of membrane elements made negligible differences to the reported strains. The models therefore seem most sensitive to changes in material properties, and suggest that failure to model local heterogeneity in material properties and structure of the bone may be responsible for discrepancies between the experimental and model results. This is partially attributable to a lack of resolution in the CT scans from which the model was built, and partially due to an absence of detailed material properties data for pig cranial bone. Thus, caution is advised when using FE models to estimate absolute numerical values of breaking stress and bite force unless detailed input parameters are available. However, if the objective is to compare relative differences between models, the fact that the strain environment is replicated well means that such investigations can be robust.