Finite element modelling versus classic beam theory: comparing methods for stress estimation in a morphologically diverse sample of vertebrate long bones

Tibial strains are sensitive to speed perturbations, but not grade perturbations, during running

A fatigue-failure process is hypothesized to govern the development of tibial stress fractures, where bone damage is highly dependent on the peak strain magnitude. To date, much of the work examining tibial strain during running has ignored uphill and downhill running despite the prevalence of this terrain. This study examined the sensitivity of tibial strain to changes in running grade and speed using a combined musculoskeletal-finite element modelling routine. Seventeen participants ran on a treadmill at ±10, ±5 and 0 deg; at each grade, participants ran at 3.33 m s-1 and at a grade-adjusted speed of 2.50 and 4.17 m s-1 for uphill and downhill grades, respectively. Force and motion data were recorded in each grade and speed combination. Muscle and joint contact forces were estimated using inverse-dynamics-based static optimization. These forces were applied to a participant-adjusted finite element model of the tibia. None of the strain variables (50th and 95th percentile strain and strained volume ≥4000 με) differed as a function of running grade; however, all strain variables were sensitive to running speed (F1≥9.59, P≤0.03). In particular, a 1 m s-1 increase in speed resulted in a 9% (∼260 με) and 155% (∼600 mm3) increase in peak strain and strained volume, respectively. Overall, these findings suggest that faster running speeds, but not changes in running grade, may be more deleterious to the tibia.

Biomechanics illuminates form-function relationships in bird bills

The field of comparative biomechanics examines how form, mechanical properties and environmental interactions shape the function of biological structures. Biomechanics has advanced by leaps and bounds as rapid technological progress opens up new research horizons. In this Review, I describe how our understanding of the avian bill, a morphologically diverse multifunctional appendage, has been transformed by employing a biomechanical perspective. Across functions from feeding to excavating hollows in trees and as a vocal apparatus, the study of the bill spans both solid and fluid biomechanics, rendering it useful to understand general principles across disciplines. The different shapes of the bill across bird species result in functional and mechanical trade-offs, thus representing a microcosm of many broader form-function questions. Using examples from diverse studies, I discuss how research into bird bills has been shaped over recent decades, and its influence on our understanding of avian ecology and evolution. Next, I examine how bill material properties and geometry influence performance in dietary and non-dietary contexts, simultaneously imposing trade-offs on other functions. Following an examination of the interactions of bills with fluids and their role as part of the vocal apparatus, I end with a discussion of the sensory biomechanics of the bill, focusing specifically on the bill-tip mechanosensory organ. With these case studies, I highlight how this burgeoning and consequential field represents a roadmap for our understanding of the function and evolution of biological structures.

Baculum shape complexity correlates to metrics of post-copulatory sexual selection in Musteloidea

The penis bone, or baculum, is present in many orders of mammals, although its function is still relatively unknown, mainly due to the challenges with studying the baculum in vivo. Suggested functions include increasing vaginal friction, prolonging intromission and inducing ovulation. Since it is difficult to study baculum function directly, functional morphology can give important insights. Shape complexity techniques, in particular, are likely to offer a useful metric of baculum morphology, especially since finding homologous landmarks on such a structure is challenging. This study focuses on measuring baculum shape complexity in the Musteloidea-a large superfamily spanning a range of body sizes with well-developed, qualitatively diverse bacula. We compared two shape complexity metrics-alpha shapes and ariaDNE and conducted analyses over a range of six different coefficients, or bandwidths, in 32 species of Musteloidea. Overall, we found that shape complexity, especially at the baculum distal tip, is associated with intromission duration using both metrics. These complexities can include hooks, bifurcations and other additional projections. In addition, alpha shapes complexity was also associated with relative testes mass. These results suggest that post-copulatory mechanisms of sexual selection are probably driving the evolution of more complex-shaped bacula tips in Musteloidea and are likely to be especially involved in increasing intromission duration during copulation.

Metatarsal fusion resisted bending as jerboas (Dipodidae) transitioned from quadrupedal to bipedal

Hind limbs undergo dramatic changes in loading conditions during the transition from quadrupedal to bipedal locomotion. For example, the most early diverging bipedal jerboas (Rodentia: Dipodidae) are some of the smallest mammals in the world, with body masses that range between 2–4 g. The larger jerboa species exhibit developmental and evolutionary fusion of the central three metatarsals into a single cannon bone. We hypothesize that small body size and metatarsal fusion are mechanisms to maintain the safety factor of the hind limb bones despite the higher ground reaction forces associated with bipedal locomotion. Using finite-element analysis to model collisions between the substrate and the metatarsals, we found that body size reduction was insufficient to reduce bone stress on unfused metatarsals, based on the scaled dynamics of larger jerboas, and that fused bones developed lower stresses than unfused bones when all metatarsals are scaled to the same size and loading conditions. Based on these results, we conclude that fusion reinforces larger jerboa metatarsals against high ground reaction forces. Because smaller jerboas with unfused metatarsals develop higher peak stresses in response to loading conditions scaled from larger jerboas, we hypothesize that smaller jerboas use alternative dynamics of bipedal locomotion to reduce the impact of collisions between the foot and substrate.

Softening the steps to gigantism in sauropod dinosaurs through the evolution of a pedal pad

How sauropod dinosaurs were able to withstand the forces associated with their immense size represents one of the most challenging biomechanical scenarios in the evolution of terrestrial tetrapods, but also one lacking robust biomechanical testing. Here, we use finite element analyses to quantify the biomechanical effects of foot skeletal postures with and without the presence of a soft tissue pad in sauropodomorphs. We find that none of the models can maintain bone stresses that fall within optimal bone safety factors in the absence of a soft tissue pad. Our findings suggest that a soft tissue pad in sauropods would have reduced bone stresses by combining the mechanical advantages of a functionally plantigrade foot with the plesiomorphic skeletally digitigrade saurischian condition. The acquisition of a developed soft tissue pad by the Late Triassic-Early Jurassic may represent one of the key adaptations for the evolution of gigantism that has become emblematic of these dinosaurs.

Diversity and function of the fused anuran radioulna

In tetrapods, fusion between elements of the appendicular skeleton is thought to facilitate rapid movements during running, flying, and jumping. Although such fusion is widespread, frogs stand out because adults of all living species exhibit fusion of the zeugopod elements (radius and ulna, tibia and fibula), regardless of jumping ability or locomotor mode. To better understand what drives the maintenance of limb bone fusion in frogs, we use finite element modeling methods to assess the functional consequences of fusion in the anuran radioulna, the forearm bone of frogs that is important to both locomotion and mating behavior (amplexus). Using CT scans of museum specimens, measurement tools, and mesh‐editing software, we evaluated how different degrees of fusion between the radius and ulna affect the von Mises stress and bending resistance of the radioulna in three loading scenarios: landing, amplexus, and long‐axis loading conditions. We find that the semi‐fused state observed in the radioulna exhibits less von Mises stress and more resistance to bending than unfused or completely fused models in all three scenarios. Our results suggest that radioulna morphology is optimized to minimize von Mises stress across different loading regimes while also minimizing volume. We contextualize our findings in an evaluation of the diversity of anuran radioulnae, which reveals unique, permanent pronation of the radioulna in frogs and substantial variation in wall thickness. This work provides new insight into the functional consequences of limb bone fusion in anuran evolution.

One step further in biomechanical models in palaeontology: a nonlinear finite element analysis review

Finite element analysis (FEA) is no longer a new technique in the fields of palaeontology, anthropology, and evolutionary biology. It is nowadays a well-established technique within the virtual functional-morphology toolkit. However, almost all the works published in these fields have only applied the most basic FEA tools i.e., linear materials in static structural problems. Linear and static approximations are commonly used because they are computationally less expensive, and the error associated with these assumptions can be accepted. Nonetheless, nonlinearities are natural to be used in biomechanical models especially when modelling soft tissues, establish contacts between separated bones or the inclusion of buckling results. The aim of this review is to, firstly, highlight the usefulness of non-linearities and secondly, showcase these FEA tool to researchers that work in functional morphology and biomechanics, as non-linearities can improve their FEA models by widening the possible applications and topics that currently are not used in palaeontology and anthropology.

Bionic Design of the Vertical Bracket of Wide Angle Auroral Imager by Additive Manufacturing

In the aerospace field, lightweight design is a never-ending pursuit. By integrating structural bionics and structural optimization, the vertical bracket of a wide angle auroral imager is designed and manufactured by additive manufacturing technology in this work. Initially, the classical topology optimization is utilized for the vertical bracket to find the optimal material layout and primary load carrying paths. Drawing on the width-to-diameter ratio and the bone mineral density distribution of human femur, the vertical support is designed as a bionic structure with a solid middle section and thin wall in other parts. Afterwards, size optimization is maintained for the bionic design model to obtain the optimal model. The simulation results show that the three-way eigenfrequencies of bionic optimized structure are 320 Hz, 303 Hz, and 765 Hz, respectively, which are closely approximate to the original structure. However, the mass of bionic optimized structure is reduced by 23%. Benefiting from Selective laser melting, the complex optimized design can be rapidly manufactured. The three-way eigenfrequencies of the optimized structure measured by the 0.2 g sweep tests are 307 Hz, 292 Hz, and 736 Hz, respectively. The vibration test of bionic optimized structure verifies the accuracy of the simulation results. This study indicates that the combination of structural bionics and structural optimization provides a powerful tool kit to the design of similar support structure for space applications.

SegmentGeometry: a tool for measuring second moment of area in 3D slicer

Second moment of area is a measure of how well the cross-section of a beam will resist bending because of its shape. Many have used second moment of area to investigate the mechanical adaptations of biological structures from stingray jaws to animal limb bones. In this context it is important to acknowledge the assumptions of beam theory, in which second moment of area plays a key role, if reasonable results are desired. For example, to minimize shear the structure should be at least ten times longer than it is wide and deflection should be minimal. Analyzing the internal geometry of biological structures has never been easier or more accessible given the wide, and growing availability of micro-CT scans. Here, we offer a guide on the care that needs to be taken when interpreting second moment of area, and present open-access, open-source software that can process hundreds if not thousands of structures in a short time frame. SegmentGeometry, an extension for the open-source imaging platform 3D Slicer, iterates slice-by-slice through 3D structures calculating second moment of area and other cross-sectional properties. We analyzed two case studies to demonstrate the power of this tool and to highlight interpretations that can be gleaned from second moment of area. Second moment of area is just one part of the Euler-Bernoulli beam theory and considering the full equation would greatly increase the number and diversity of questions that can be answered.

Musculoskeletal modeling of sprawling and parasagittal forelimbs provides insight into synapsid postural transition

The sprawling-parasagittal postural shift was a major transition during synapsid evolution, underpinned by reorganization of the forelimb, and considered key to mammalian ecological diversity. Determining when and how this transition occurred in the fossil record is challenging owing to limited comparative data on extant species. Here, we built forelimb musculoskeletal models of three extant taxa that bracket sprawling-parasagittal postures-tegu lizard, echidna, and opossum-and tested the relationship between three-dimensional joint mobility, muscle action, and posture. Results demonstrate clear functional variation between postural grades, with the parasagittal opossum occupying a distinct region of pose space characterized by a highly retracted and depressed shoulder joint that emphasizes versatility and humeral elevation. Applying our data to the fossil record support trends of an increasingly retracted humerus and greater elevation muscle moment arms indicative of more parasagittal postures throughout synapsid evolution.

Beam theory for rapid strain estimation in the mouse tibia compression model

The mouse tibia compression model is a leading model for studying bone's mechanoadaptive response to load. In studying this mechanoadaptive response, (FE) modelling is often used to determine the stress/strain within the tibia. The development of such models can be challenging and computationally expensive. An alternate approach is to use continuum mechanics based analytical theories, such as beam theory (BT). However, applying BT to the mouse tibia requires the fibula be neglected, introducing error in the stress/strain distribution. While several studies have applied BT to the mouse tibia, no study has explored the accuracy of this approach. To address these questions, this work investigates the use of BT in determining stress/strain within the mouse tibia. By comparing BT against FE modelling, it was found that BT can accurately predict tibial stress/strain if correction factors are applied to account for the effect of the fibula. The 25, 37, 50 and 75% cross sections are studied. Focusing on the 37% cross section, without correction, BT can have errors of approximately 21.6%. With correction, this is reduced to 6.6%. Such correction factors are presented. The developed BT model is applicable in the diaphysis and distal metaphysis, where the assumptions of BT are valid. This work verifies BT for determining localised strains in a mouse tibia compression model. This is anticipated to provide efficiency dividends, allowing for high throughput modelling of the mouse tibia, advancing study of bone's mechanoadaptive response.

Efficacy of shear strain gradients as an osteogenic stimulus

The question of which mechanical variables are responsible for inducing osteogenic activity is unresolved despite extensive experimental and theoretical investigation. Candidate variables include strain magnitude, loading frequency, the interaction of magnitude and frequency (strain rate), and strain gradients. An additional challenge is discerning the coordination of periosteal and endosteal expansion during growth, and whether this coordination (or lack thereof) is fully dependent or partially independent of the local mechanical environment. In this study, under the assumption that calculated stresses correspond to relative strain magnitudes, we specify alternative growth algorithms of bone cross-sectional size and geometry to explore skeletal growth under alternative scenarios of osteogenic activity that are tracking 1) an attractor stress, 2) local stress magnitude or 3) steepness of stress gradients. These developmental simulations are initiated from two initial geometries (symmetrical and asymmetrical ellipses) under a time-varying torsional load whose magnitude is proportional to body size growth in a model primate. In addition, we model endosteal expansion under three conditions hypothesized in the literature, in which endosteal expansion is 1) independent of the mechanical milieu, 2) completely dependent on the mechanical milieu, and 3) a "hybrid" model in which intrinsic biological (independent) growth is operative early but gives way to mechanically-sensitive (dependent) growth at later ages. Three variables were recorded over each growth simulation: the safety factor (ratio of yield stress to actual stress), an efficiency ratio (invested bone area per unit of stress), and proximity to an isostress condition (an optimal design criterion in which stress is invariant throughout the structure). The attractor stress algorithm produces the most "adapted" bones in terms of mechanical competence and economy of material. Localized osteogenic activity that is guided in direct proportion to stress magnitude produces competent bones but with variable adult geometries depending on conditions of endosteal expansion. Stress gradients also produce functional but relatively inefficient bones, with widely variable safety factors during growth and heterogeneous stress fields. If, in fact, the osteocyte network monitors strain gradients to generate osteogenic signals, the resulting morphology is competent but falls well short of an optimal mechanical solution.

A 3D journey on virtual surfaces and inner structure of ossa genitalia in Primates by means of a non-invasive imaging tool

Novel bio-imaging techniques such as micro-Computed Tomography provide an opportunity to investigate animal anatomy and morphology by overcoming limitations imposed by traditional anatomical drawings. The primate genital bones are complex anatomical structures whose occurrence in both male penis (baculum) and female clitoris (baubellum) may be difficult to assess in individual cadavers. We tested a 3-step methodological protocol, including different techniques ranging from inexpensive/simple to more expensive/sophisticated ones, by applying it to a sample of primate species, and resulting in different levels of data complexity: (1) presence/absence manual palpation method; (2) 2D X-ray plates; 3) 3D micro-CT scans. Manual palpation failed on 2 out of 23 specimens by detecting 1 false negative and 1 false positive; radiography failed once confirming the false positive, however firmly disproved by micro-CT; micro-CT analysis reported the presence of 9 bacula out of 11 male specimens and 1 baubellum out of 12 female specimens. A different baculum position was identified between strepsirrhine and haplorrhine species. We also aim to assess micro-CT as a non-invasive technique providing updated anatomical descriptions of primate ossa genitalia. Micro-CT 3D volumes showed the surface of some bones as rough, with a jagged appearance, whereas in others the surface appeared very smooth and coherent. In addition, four main types of bone internal structure were identified: 1) totally hollow; 2) hollow epiphyses and solid diaphysis with few or several channels inside; 3) totally solid with intricate Haversian channels; 4) totally solid with some channels (structure of single baubellum scanned). Ossa genitalia appeared as a living tissue having its own Haversian-like channels. The high resolution of micro-CT 3D-images of primate genital bones disclosed additional form variability to that available from genital bone 2D images of previous studies, and showed for the first time new internal and external morphological characters. Moreover, micro-CT non-invasive approach proved appropriate to recover much of scientific knowledge still hidden and often neglected in both museum specimens and primate cadavers only destined to necropsy.

Inferring locomotor behaviours in Miocene New World monkeys using finite element analysis, geometric morphometrics and machine-learning classification techniques applied to talar morphology

The talus is one of the most commonly preserved post-cranial elements in the platyrrhine fossil record. Talar morphology can provide information about postural adaptations because it is the anatomical structure responsible for transmitting body mass forces from the leg to the foot. The aim of this study is to test whether the locomotor behaviour of fossil Miocene platyrrhines could be inferred from their talus morphology. The extant sample was classified into three different locomotor categories and then talar strength was compared using finite-element analysis. Geometric morphometrics were used to quantify talar shape and to assess its association with biomechanical strength. Finally, several machine-learning (ML) algorithms were trained using both the biomechanical and morphometric data from the extant taxa to infer the possible locomotor behaviour of the Miocene fossil sample. The obtained results show that the different locomotor categories are distinguishable using either biomechanical or morphometric data. The ML algorithms categorized most of the fossil sample as arboreal quadrupeds. This study has shown that a combined approach can contribute to the understanding of platyrrhine talar morphology and its relationship with locomotion. This approach is likely to be beneficial for determining the locomotor habits in other fossil taxa.

Testing hypotheses for the function of the carnivoran baculum using finite-element analysis

The baculum (os penis) is a mineralized bone within the glans of the mammalian penis and is one of the most morphologically diverse structures in the mammal skeleton. Recent experimental work provides compelling evidence for sexual selection shaping the baculum, yet the functional mechanism by which this occurs remains unknown. Previous studies have tested biomechanical hypotheses for the role of the baculum based on simple metrics such as length and diameter, ignoring the wealth of additional shape complexity present. For the first time, to our knowledge, we apply a computational simulation approach (finite-element analysis; FEA) to quantify the three-dimensional biomechanical performance of carnivoran bacula (n = 74) based upon high-resolution micro-computed tomography scans. We find a marginally significant positive correlation between sexual size dimorphism and baculum stress under compressive loading, counter to the 'vaginal friction' hypothesis of bacula becoming more robust to overcome resistance during initial intromission. However, a highly significant negative relationship exists between intromission duration and baculum stress under dorsoventral bending. Furthermore, additional FEA simulations confirm that the presence of a ventral groove would reduce deformation of the urethra. We take this as evidence in support of the 'prolonged intromission' hypothesis, suggesting the carnivoran baculum has evolved in response to pressures on the duration of copulation and protection of the urethra.

New Guinea bone daggers were engineered to preserve social prestige

Bone daggers were once widespread in New Guinea. Their purpose was both symbolic and utilitarian; they functioned as objects of artistic expression with the primary function of stabbing and killing people at close quarters. Most daggers were shaped from the tibiotarsus of cassowaries, but daggers shaped from the femora of respected men carried greater social prestige. The greater cross-sectional curvature of human bone daggers indicates superior strength, but the material properties of cassowary bone are unknown. It is, therefore, uncertain whether the macrostructure of human bone daggers exists to compensate for inferior material properties of human femora or to preserve the symbolic value of a prestigious object. To explore this question, we used computed tomography to examine the structural mechanics of 11 bone daggers, 10 of which are museum-accessioned objects of art. We found that human and cassowary bones have similar material properties and that the geometry of human bone daggers results in higher moments of inertia and a greater resistance to bending. Data from finite-element models corroborated the superior mechanical performance of human bone daggers, revealing greater resistance to larger loads with fewer failed elements. Taken together, our findings suggest that human bone daggers were engineered to preserve symbolic capital, an outcome that agrees well with the predictions of signalling theory.

Investigating the running abilities of Tyrannosaurus rex using stress-constrained multibody dynamic analysis

The running ability of Tyrannosaurus rex has been intensively studied due to its relevance to interpretations of feeding behaviour and the biomechanics of scaling in giant predatory dinosaurs. Different studies using differing methodologies have produced a very wide range of top speed estimates and there is therefore a need to develop techniques that can improve these predictions. Here we present a new approach that combines two separate biomechanical techniques (multibody dynamic analysis and skeletal stress analysis) to demonstrate that true running gaits would probably lead to unacceptably high skeletal loads in T. rex. Combining these two approaches reduces the high-level of uncertainty in previous predictions associated with unknown soft tissue parameters in dinosaurs, and demonstrates that the relatively long limb segments of T. rex—long argued to indicate competent running ability—would actually have mechanically limited this species to walking gaits. Being limited to walking speeds contradicts arguments of high-speed pursuit predation for the largest bipedal dinosaurs like T. rex, and demonstrates the power of multiphysics approaches for locomotor reconstructions of extinct animals.

A study of the progression of damage in an axially loaded Branta leucopsis femur using X-ray computed tomography and digital image correlation

This paper uses X-ray computed tomography to track the mechanical response of a vertebrate (Barnacle goose) long bone subjected to an axial compressive load, which is increased gradually until failure. A loading rig was mounted in an X-ray computed tomography system so that a time-lapse sequence of three-dimensional (3D) images of the bone’s internal (cancellous or trabecular) structure could be recorded during loading. Five distinct types of deformation mechanism were observed in the cancellous part of the bone. These were (i) cracking, (ii) thinning (iii) tearing of cell walls and struts, (iv) notch formation, (v) necking and (vi) buckling. The results highlight that bone experiences brittle (notch formation and cracking), ductile (thinning, tearing and necking) and elastic (buckling) modes of deformation. Progressive deformation, leading to cracking was studied in detail using digital image correlation. The resulting strain maps were consistent with mechanisms occurring at a finer-length scale. This paper is the first to capture time-lapse 3D images of a whole long bone subject to loading until failure. The results serve as a unique reference for researchers interested in how bone responds to loading. For those using computer modelling, the study not only provides qualitative information for verification and validation of their simulations but also highlights that constitutive models for bone need to take into account a number of different deformation mechanisms.

A review of trabecular bone functional adaptation: what have we learned from trabecular analyses in extant hominoids and what can we apply to fossils?

Many of the unresolved debates in palaeoanthropology regarding evolution of particular locomotor or manipulative behaviours are founded in differing opinions about the functional significance of the preserved external fossil morphology. However, the plasticity of internal bone morphology, and particularly trabecular bone, allowing it to respond to mechanical loading during life means that it can reveal greater insight into how a bone or joint was used during an individual's lifetime. Analyses of trabecular bone have been commonplace for several decades in a human clinical context. In contrast, the study of trabecular bone as a method for reconstructing joint position, joint loading and ultimately behaviour in extant and fossil non-human primates is comparatively new. Since the initial 2D studies in the late 1970s and 3D analyses in the 1990 s, the utility of trabecular bone to reconstruct behaviour in primates has grown to incorporate experimental studies, expanded taxonomic samples and skeletal elements, and improved methodologies. However, this work, in conjunction with research on humans and non-primate mammals, has also revealed the substantial complexity inherent in making functional inferences from variation in trabecular architecture. This review addresses the current understanding of trabecular bone functional adaptation, how it has been applied to hominoids, as well as other primates and, ultimately, how this can be used to better interpret fossil hominoid and hominin morphology. Because the fossil record constrains us to interpreting function largely from bony morphology alone, and typically from isolated bones, analyses of trabecular structure, ideally in conjunction with that of cortical structure and external morphology, can offer the best resource for reconstructing behaviour in the past.

More than one way of being a moa: differences in leg bone robustness map divergent evolutionary trajectories in Dinornithidae and Emeidae (Dinornithiformes)

The extinct moa of New Zealand included three families (Megalapterygidae; Dinornithidae; Emeidae) of flightless palaeognath bird, ranging in mass from <15 kg to >200 kg. They are perceived to have evolved extremely robust leg bones, yet current estimates of body mass have very wide confidence intervals. Without reliable estimators of mass, the extent to which dinornithid and emeid hindlimbs were more robust than modern species remains unclear. Using the convex hull volumetric-based method on CT-scanned skeletons, we estimate the mass of a female Dinornis robustus (Dinornithidae) at 196 kg (range 155–245 kg) and of a female Pachyornis australis (Emeidae) as 50 kg (range 33–68 kg). Finite element analysis of CT-scanned femora and tibiotarsi of two moa and six species of modern palaeognath showed that P. australis experienced the lowest values for stress under all loading conditions, confirming it to be highly robust. In contrast, stress values in the femur of D. robustus were similar to those of modern flightless birds, whereas the tibiotarsus experienced the highest level of stress of any palaeognath. We consider that these two families of Dinornithiformes diverged in their biomechanical responses to selection for robustness and mobility, and exaggerated hindlimb strength was not the only successful evolutionary pathway.

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.