Finite element modeling of shell shape in the freshwater turtle Pseudemys concinna reveals a trade‐off between mechanical strength and hydrodynamic efficiency

Aquatic species can experience different selective pressures on morphology in different flow regimes. Species inhabiting lotic regimes often adapt to these conditions by evolving low‐drag (i.e., streamlined) morphologies that reduce the likelihood of dislodgment or displacement. However, hydrodynamic factors are not the only selective pressures influencing organismal morphology and shapes well suited to flow conditions may compromise performance in other roles. We investigated the possibility of morphological trade‐offs in the turtle Pseudemys concinna. Individuals living in lotic environments have flatter, more streamlined shells than those living in lentic environments; however, this flatter shape may also make the shells less capable of resisting predator‐induced loads. We tested the idea that “lotic” shell shapes are weaker than “lentic” shell shapes, concomitantly examining effects of sex. Geometric morphometric data were used to transform an existing finite element shell model into a series of models corresponding to the shapes of individual turtles. Models were assigned identical material properties and loaded under identical conditions, and the stresses produced by a series of eight loads were extracted to describe the strength of the shells. “Lotic” shell shapes produced significantly higher stresses than “lentic” shell shapes, indicating that the former is weaker than the latter. Females had significantly stronger shell shapes than males, although these differences were less consistent than differences between flow regimes. We conclude that, despite the potential for many‐to‐one mapping of shell shape onto strength, P. concinna experiences a trade‐off in shell shape between hydrodynamic and mechanical performance. This trade‐off may be evident in many other turtle species or any other aquatic species that also depend on a shell for defense. However, evolution of body size may provide an avenue of escape from this trade‐off in some cases, as changes in size can drastically affect mechanical performance while having little effect on hydrodynamic performance. J. Morphol. 2011. © 2011 Wiley‐Liss, Inc.     

Internal selection against the evolution of left-right reversal

Among metazoan species, left-right reversals in primary asymmetry have rarely gone to fixation. This suggests that a general mechanism suppresses the evolution of polarity reversal. Most metazoans appear externally symmetric and reproduce by external fertilization or copulation with genitalia located in the midline. Thus, reversal should generate little exogenous disadvantage when interacting with the external environment or in mating with the common wild-type. Accordingly, an endogenously caused fitness reduction may be responsible for the general absence of reversed species. However, how this selection operates is little understood. Phenotypic changes associated with reversal are usually inseparable from zygotic pleiotropy. By exploiting hermaphroditism and the maternal inheritance of left-right polarity, we generated dextral and sinistral snails that share the same zygotic genotype. Before hatching, these sinistrals developed lethal morphological anomalies more frequently than dextrals. Their shell shape at maturity differed from the mirror image of the dextral shell. These interchiral differences demonstrate pleiotropy in maternal effects of the polarity or linked genes. Variation in interchiral differences between parental crosses suggests the presence of epistatic variation in relative performance of sinistrals. Our results show that internal selection operates against polarity reversal, and we suggest that this is due to changes in blastomere configuration.     

Wing shape versus asymmetry as an indicator of changing environmental conditions in insects

Abstract In insects, the fluctuating asymmetry of bilaterally symmetrical traits has been suggested as an indicator of environmental stress because asymmetry is expected to increase when stressful conditions disturb the normal development of organisms. However, the extensive literature on asymmetry–stress associations is indeterminate. Here we contrast changes in asymmetry with changes in an alternate stress indicator, the shape of insect wings. The development of wing shape involves numerous genes that act throughout egg-to-adult development, so stresses that act at a specific time could alter shape in specific ways. Shape changes, as measured by the Procrustes technique, were considered in five data sets: exposure of Drosophila melanogaster (Meigen) to multiple stresses involving ethanol, low nutrition and cold shocks; exposure of a chironomid ( Chironomus tepperi (Skuse)), a blowfly ( Lucilia cuprina (Wiedemann)), and lightbrown apple moth ( Epiphyas postvittana (Walker)) to pesticides; and development of C. tepperi under saline conditions. All these conditions influenced viability and development time. In none of these cases was a change in symmetry of wing size or wing shape detected. In contrast, in four of the five data sets there was a change in wing shape. These results suggest that wing shape may be altered more commonly by stress than trait asymmetry. Wing-shape monitoring may be useful in detecting stressful environmental conditions during development, at least under controlled conditions.     

Analysis of arch‐like bones: The rodent mandible as a case study

Bone strength is determined by the mechanical properties of bone material, and the size and shape of the whole bone, i.e., its architecture. The mandible of vertebrates has been traditionally regarded as a beam oriented in relation to main masticatory loads, i.e., the longer dimension of its cross‐section being parallel to the load. Rodents follow this pattern but, in addition, their mandible possesses an intriguing arch‐like shape that is apparent when seen in the lateral view. Little attention was given to the structural capacity of this trait. The advantage of an arch is that it can withstand a greater load than a horizontal beam. The objective of this study was to model the rodent mandible like an arch to evaluate its structural strength. The bending moment in an arch‐like mandible was 15–25% lower with respect to a beam‐like mandible. Further, bending varies with mandible “slenderness” and incisor procumbency, a functionally relevant rodent trait. In the rodent Ctenomys talarum (Caviomorpha; Ctenomyidae), bone stress was substantially reduced when the mandible was modeled as an arch‐like structure as compared with a beam‐like structure, and safety factors were 15–34% higher. The shape of rodents' mandible might confer a functional advantage to high and repeatedly applied loads resulting from a unique feeding mode: gnawing. J. Morphol. 277:879–887, 2016. © 2016 Wiley Periodicals, Inc.     

Straightening of curved pattern of collagen fibers under load controls aortic valve shape

The network of collagen fibers in the aortic valve leaflet is believed to play an important role in the strength and durability of the valve. However, in addition to its stress-bearing role, such a fiber network has the potential to produce functionally important shape changes in the closed valve under pressure load. We measured the average pattern of the collagen network in porcine aortic valve leaflets after staining for collagen. We then used finite element simulation to explore how this collagen pattern influences the shape of the closed valve. We observed a curved or bent pattern, with collagen fibers angled downward from the commissures toward the center of the leaflet to form a pattern that is concave toward the leaflet free edge. Simulations showed that these curved fiber trajectories straighten under pressure load, leading to functionally important changes in closed valve shape. Relative to a pattern of straight collagen fibers running parallel to the leaflet free edge, the concave pattern of curved fibers produces a closed valve with a 40% increase in central leaflet coaptation height and with decreased leaflet billow, resulting in a more physiological closed valve shape. Furthermore, simulations show that these changes in loaded leaflet shape reflect changes in leaflet curvature due to modulation of in-plane membrane stress resulting from straightening of the curved fibers. This effect appears to play an important role in normal valve function and may have important implications for the design of prosthetic and tissue engineered replacement valves.     

Role of load history in intervertebral disc mechanics and intradiscal pressure generation

Solid–fluid interactions play an important role in mediating viscoelastic behaviour of biological tissues. In the intervertebral disc, water content is governed by a number of factors, including age, disease and mechanical loads, leading to changes in stiffness characteristics. We hypothesized that zonal stress distributions depend on load history, or the prior stresses experienced by the disc. To investigate these effects, rat caudal motion segments were subjected to compressive creep biomechanical testing in vitro using a protocol that consisted of two phases: a Prestress Phase (varied to represent different histories of load) followed immediately by an Exertion Phase, identical across all Prestress groups. Three analytical models were used to fit the experimental data in order to evaluate load history effects on gross and zonal disc mechanics. Model results indicated that while gross transient response was insensitive to load history, there may be changes in the internal mechanics of the disc. In particular, a fluid transport model suggested that the role of the nucleus pulposus in resisting creep during Exertion depended on Prestress conditions. Separate experiments using similarly defined load history regimens were performed to verify these predictions by measuring intradiscal pressure with a fibre optic sensor. We found that the ability for intradiscal pressure generation was load history-dependent and exhibited even greater sensitivity than predicted by analytical models. A 0.5?MPa Exertion load resulted in 537.2?kPa IDP for low magnitude Prestress compared with 373.7?kPa for high magnitude Prestress. Based on these measurements, we developed a simple model that may describe the pressure-shear environment in the nucleus pulposus. These findings may have important implications on our understanding of how mechanical stress contributes to disc health and disease etiology.     

Effect of loading rate on endplate and vertebral body strength in human lumbar vertebrae

Previous studies have implied that increases in loading rate resulted in changes in vertebral mechanical properties and these changes were causative factors in the different fracture types seen with high-speed events. Thus many researchers have explored the vertebral body response under various loading rate conditions. No other study has investigated the role of the endplate in high-speed vertebral injuries. The current study determined changes in the endplate and vertebral body strength with increases in displacement rate. The endplate and vertebral body failure loads in individual lumbar vertebrae were documented for two displacement rates: 10 and 2500 mm/s. Using cross-sectional areas from the endplate and vertebral body, failure stresses for both components were calculated and compared. Both the endplate and vertebral body failure loads increased significantly with increased loading rate (p<0.005). Although the vertebral body failure stress increased significantly with loading rate as well (p<0.01), the endplate stresses did not (p>0.35). In addition, the endplate and vertebral strengths were not significantly different under high-speed loading (p>0.60), which inhibits possible predictions as to which bony component would fail initially during a high-speed injury event. It is possible that load distribution may contribute more to the fracture patterns seen at high speeds over vertebral component strength.     

Urbanization disrupts latitude‐size rule in 17‐year cicadas

Many ectotherms show a decrease in body size with increasing latitude due to changes in climate, a pattern termed converse Bergmann's rule. Urban conditions—particularly warmer temperatures and fragmented landscapes—may impose stresses on development that could disrupt these body size patterns. To test the impact of urbanization on development and latitudinal trends in body size, we launched a citizen science project to collect periodical cicadas (Magicicada septendecim) from across their latitudinal range during the 2013 emergence of Brood II. Periodical cicadas are long‐lived insects whose distribution spans a broad latitudinal range covering both urban and rural habitats. We used a geometric morphometric approach to assess body size and developmental stress based on fluctuating asymmetry in wing shape. Body size of rural cicadas followed converse Bergmann's rule, but this pattern was disrupted in urban habitats. In the north, urban cicadas were larger than their rural counterparts, while southern populations showed little variation in body size between habitats. We detected no evidence of differences in developmental stress due to urbanization. To our knowledge, this is the first evidence that urbanization disrupts biogeographical trends in body size, and this pattern highlights how the effects of urbanization may differ over a species’ range.     

Macromolecular biophysics of the plant cell wall: Concepts and methodology

Plant cell walls provide form and mechanical strength to the living plant, but the relationship between their complex architecture and their remarkable ability to withstand external stress is not well understood. Primary cell walls are adapted to withstand tensile stresses while secondary cell walls also need to withstand compressive stresses. Therefore, while primary cell walls can with advantage be flexible and elastic, secondary cell walls must be rigid to avoid buckling under compressive loads. In addition, primary cell walls must be capable of growth and are subjected to cell separation forces at the cell corners. To understand how these stresses are resisted by cell walls, it will be necessary to find out how the walls deform internally under load, and how rigid are specific constituents of each type of cell wall. The most promising spectroscopic techniques for this purpose are solid-state nuclear magnetic resonance (NMR), and Fourier-transform infrared (FTIR) and Raman microscopy. By NMR relaxation experiments, it is possible to probe thermal motion in each cell-wall component. Novel adaptations of FTIR and Raman spectroscopy promise to allow mechanical stress and strain upon specific polymers to be examined in situ within the cell wall.     

Simulating distal radius fracture strength using biomechanical tests: a modeling study examining the influence of boundary conditions

Distal radius fracture strength has been quantified using in vitro biomechanical testing. These tests are frequently performed using one of two methods: (1) load is applied directly to the embedded isolated radius or (2) load is applied through the hand with the wrist joint intact. Fracture loads established using the isolated radius method are consistently 1.5 to 3 times greater than those for the intact wrist method. To address this discrepancy, a validated finite element modeling procedure was used to predict distal radius fracture strength for 22 female forearms under boundary conditions simulating the isolated radius and intact wrist method. Predicted fracture strength was highly correlated between methods (r = 0.94; p < 0.001); however, intact wrist simulations were characterized by significantly reduced cortical shell load carriage and increased stress and strain concentrations. These changes resulted in fracture strength values less than half those predicted for the isolated radius simulations (2274 ± 824 N for isolated radius, 1124 ± 375 N for intact wrist; p < 0.001). The isolated radius method underestimated the mechanical importance of the trabecular compartment compared to the more physiologically relevant intact wrist scenario. These differences should be borne in mind when interpreting the physiologic importance of mechanical testing and simulation results.     

Method for the design and analysis of a non-linear anisotropic lower limb prosthetic socket

A simplified computer-based structural analysis procedure has been developed for evaluating the stresses in a lower limb prosthetic socket when subjected to external loads. This technique has been tested by studying a simple linear axisymmetric shell subjected to uniform loads. It was found that the stress and strain distributions obtained are close to those determined by a finite element technique. The method that has been proposed involves an incremental procedure, which can be used to analyse the behaviour of a prosthetic socket of irregular shape made from non-linear anisotropic materials. By employing the proposed procedure to study an example, in which a simplified lower limb prosthetic socket is subject to internal pressure and frictional forces, the effects of the material non-linearity have been found to be significant.     

Facilitation among plants can accelerate density‐dependent mortality and steepen self‐thinning lines in stressful environments

The speed and slope of plant self‐thinning are all affected by plant–plant interactions across environmental gradients. Possible mechanisms driving the self‐thinning dynamics include the relative strength of root versus shoot competition, and the interplay between competition and facilitation. Although these mechanisms often act in concert, their relative importance has not yet been fully explored. We used both a one‐layer and a two‐layer zone‐of‐influence (ZOI) model to examine how competition and facilitation drive self‐thinning across stress gradients. As a development of the traditional ZOI model, the two‐layer version explicitly models shoot and root growth and neighbor interactions, and thus the overall size‐symmetry of competition is regulated by the relative strength of root versus shoot competition. One‐layer model simulations revealed that increasingly asymmetric competition accelerated thinning, and steepened (slope ranged from about –1 to –4/3) and lowered self‐thinning lines. Stress slowed down density‐dependent mortality considerably when competition was not completely symmetric. Stress significantly decreased the self‐thinning intercept, while facilitation simply counteracted stress effects. Both stress and facilitation showed little effect on the slope. In the two‐layer model, both stress and facilitation affected mortality in the same way as in the one‐layer version when competition was not completely symmetric. Different from the one‐layer model, the two‐layer version showed that the effects of stress and facilitation on the self‐thinning slope were mediated by the asymmetry of competition. As stress increased, the overall asymmetry of competition shifted from asymmetric to symmetric due to increased relative strength of root competition. High stress thus dramatically flattened self‐thinning lines, whereas the inclusion of facilitation counteracted stress and led to steeper self‐thinning lines. Our two‐layer model is based on the current knowledge of plant–plant interactions, and better represents ecological realities. It can help elaborate experiments for testing the role of competition and facilitation in driving plant population dynamics.     

A contact-coupled finite element analysis of the natural adult hip

A non-linear two-dimensional finite element model was used to study phenomena of stress redistribution in the natural adult hip resulting from parametric material property variations in the juxtarticular regions of the femoral head. Despite the geometrical simplifications employed, the intra-articular contact stresses (computed using the FEAP program) were found to be in reasonable qualitative agreement with previous in vitro data for the case of a normal hip. Generalized sclerotic changes in the subchondral plate, as reflected either in apparent modulus increases or in plate thickening, were found to have only minor effects on the computed contact stress distribution, although stress levels within the plate itself were markedly influenced. Localized subchondral plate sclerosis, by contrast, led to marked stress elevations in the cartilage immediately overlying the stiffened bone. Cartilage modulus increases caused increased load uptake for a given imposed deformation, but involved stress distribution increases which were very nearly linearly proportional to the increases in resultant load magnitude. Friction coefficient elevations had no noticeable effects on normal contact stress or upon overall load transmission, but involved complex, possibly slip-related, changes in intra-articular and cartilaginous shear stresses.     

Osmotic stress at the barley root affects expression of circadian clock genes in the shoot

The circadian clock is an important timing system that controls physiological responses to abiotic stresses in plants. However, there is little information on the effects of the clock on stress adaptation in important crops, like barley. In addition, we do not know how osmotic stress perceived at the roots affect the shoot circadian clock. Barley genotypes, carrying natural variation at the photoperiod response and clock genes Ppd‐H1 and HvELF3, were grown under control and osmotic stress conditions to record changes in the diurnal expression of clock and stress‐response genes and in physiological traits. Variation at HvELF3 affected the expression phase and shape of clock and stress‐response genes, while variation at Ppd‐H1 only affected the expression levels of stress genes. Osmotic stress up‐regulated expression of clock and stress‐response genes and advanced their expression peaks. Clock genes controlled the expression of stress‐response genes, but had minor effects on gas exchange and leaf transpiration. This study demonstrated that osmotic stress at the barley root altered clock gene expression in the shoot and acted as a spatial input signal into the clock. Unlike in Arabidopsis, barley primary assimilation was less controlled by the clock and more responsive to environmental perturbations, such as osmotic stress.     

Stress amplification during development of the tendon-to-bone attachment

Mechanical stress is necessary to sustain the mineral content of bone in adults. However, in a developing neonatal mouse, the mineralization of soft tissues progresses despite greatly reduced average mechanical stresses. In adults, these reduced loads would likely lead to bone loss. Although biochemical factors may partly explain these different responses, it is unclear how mineralization is initiated in low load environments. We present here the effect of morphometric data and initial modeling supporting a hypothesis that mechanical factors across several length scales amplify stresses, and we suggest that these stresses are of a level adequate to contribute to mechanical signaling for initiation of mineralization at the developing tendon-to-bone enthesis. A mineral gradient is evident across the insertion from the onset of mineralization. This grading maintains a constant size from early postnatal time points to adulthood. At the tissue level, this grading contributes to reduced stresses in an adult animal and to a minor elevation of stresses in a neonatal animal. At the cellular level, stress concentrations around mineralizing chondrocytes are enhanced in neonatal animals compared with adult animals. The enhancement of stresses around cells at early time points may serve to amplify and transduce low loads in order to initiate mineralization.     

Bite Force Performance,Fluctuating Asymmetry and Antisymmetry in the Mandible of Inbred and Outbred Wild-Derived Strains of Mice (<Emphasis Type="Italic">Mus musculus domesticus</Emphasis>)

Developmental instability, as measured by fluctuating asymmetry is generally considered to increase with genetic and environmental stresses. Few studies have, however, addressed the role of asymmetry in altering organism performance. Here, we measured bite force performance in three strains of inbred and outbred mice derived from wild ancestors. We quantified size and shape directional, and fluctuating asymmetry, as well as inter-individual variation of their mandibles using geometric morphometrics. We also developed a way to estimate shape antisymmetry, to filter it out of the fluctuating asymmetry component. Contrary to our expectations, we found no significant link between bite force and asymmetry levels. Inbreeding did not produce any clear and significant increase or decrease in neither inter-individual variance, nor fluctuating asymmetry. Furthermore, fluctuating asymmetry levels were unrelated to inter-individual variance levels, although these two types of variation affected the same areas of the mandible. We did not highlight any impact of inbreeding depression on bite force. Fluctuating asymmetry was reduced in the mandible, which we argue may be linked to its functional relevance. We found some significant but very reduced antisymmetry possibly linked to lateralization. This lateralization did not relate to any bite force difference. Our results show that neither inbreeding, nor asymmetry (combining fluctuating, directional asymmetry and antisymmetry) significantly affect bite force performance in mice, and that despite affecting the same morphological regions, developmental stability and canalization are independent.     

Characterizing drought stress and trait influence on maize yield under current and future conditions

Global climate change is predicted to increase temperatures, alter geographical patterns of rainfall and increase the frequency of extreme climatic events. Such changes are likely to alter the timing and magnitude of drought stresses experienced by crops. This study used new developments in the classification of crop water stress to first characterize the typology and frequency of drought‐stress patterns experienced by European maize crops and their associated distributions of grain yield, and second determine the influence of the breeding traits anthesis‐silking synchrony, maturity and kernel number on yield in different drought‐stress scenarios, under current and future climates. Under historical conditions, a low‐stress scenario occurred most frequently (ca. 40%), and three other stress types exposing crops to late‐season stresses each occurred in ca. 20% of cases. A key revelation shown was that the four patterns will also be the most dominant stress patterns under 2050 conditions. Future frequencies of low drought stress were reduced by ca. 15%, and those of severe water deficit during grain filling increased from 18% to 25%. Despite this, effects of elevated CO₂ on crop growth moderated detrimental effects of climate change on yield. Increasing anthesis‐silking synchrony had the greatest effect on yield in low drought‐stress seasonal patterns, whereas earlier maturity had the greatest effect in crops exposed to severe early‐terminal drought stress. Segregating drought‐stress patterns into key groups allowed greater insight into the effects of trait perturbation on crop yield under different weather conditions. We demonstrate that for crops exposed to the same drought‐stress pattern, trait perturbation under current climates will have a similar impact on yield as that expected in future, even though the frequencies of severe drought stress will increase in future. These results have important ramifications for breeding of maize and have implications for studies examining genetic and physiological crop responses to environmental stresses.     

Effect of composition on shape of bird eggs

Numerous studies over the past 90 years have described the various bird egg shapes in mathematical terms but few studies have considered the underlying reasons for such interspecific egg shape variability. This study investigated how the size and composition, i.e. proportions of shell, yolk and albumen, were associated with egg shape. Geometric morphometrics were used to generate principal components, which were analysed in relation to taxonomy (i.e. avian order) and degree of neonatal developmental maturity, which correlates with egg composition. The analysis confirmed previous results that most of the variation in shape is associated with degree of elongation (i.e. length divided by breadth) and asymmetry (i.e. position of the broadest part of the egg away from the mid‐point of the egg's length). Egg shape reflected avian order but not developmental maturity. The degree of elongation of an egg is related to absolute egg mass and the proportion of yolk. By contrast, the degree of asymmetry is related to the proportion of shell and the mass of the egg relative to female body mass. Although significant, the models explained little of the variation in egg shape and so it was concluded that other factors, such as pelvis size and shape, could be more important in determining egg shape in birds.     

Evaluation of a subject-specific finite-element model of the equine metacarpophalangeal joint under physiological load

The equine metacarpophalangeal (MCP) joint is frequently injured, especially by racehorses in training. Most injuries result from repetitive loading of the subchondral bone and articular cartilage rather than from acute events. The likelihood of injury is multi-factorial but the magnitude of mechanical loading and the number of loading cycles are believed to play an important role. Therefore, an important step in understanding injury is to determine the distribution of load across the articular surface during normal locomotion. A subject-specific finite-element model of the MCP joint was developed (including deformable cartilage, elastic ligaments, muscle forces and rigid representations of bone), evaluated against measurements obtained from cadaver experiments, and then loaded using data from gait experiments. The sensitivity of the model to force inputs, cartilage stiffness, and cartilage geometry was studied. The FE model predicted MCP joint torque and sesamoid bone flexion angles within 5% of experimental measurements. Muscle–tendon forces, joint loads and cartilage stresses all increased as locomotion speed increased from walking to trotting and finally cantering. Perturbations to muscle–tendon forces resulted in small changes in articular cartilage stresses, whereas variations in joint torque, cartilage geometry and stiffness produced much larger effects. Non-subject-specific cartilage geometry changed the magnitude and distribution of pressure and the von Mises stress markedly. The mean and peak cartilage stresses generally increased with an increase in cartilage stiffness. Areas of peak stress correlated qualitatively with sites of common injury, suggesting that further modelling work may elucidate the types of loading that precede joint injury and may assist in the development of techniques for injury mitigation.