Determination and validation of the elastic moduli of small and complex biological samples: bone and keratin in bird beaks

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.

Finite-element modelling reveals force modulation of jaw adductors in stag beetles

Male stag beetles carry large and heavy mandibles that arose through sexual selection over mating rights. Although the mandibles of Cyclommatus metallifer males are used in pugnacious fights, they are surprisingly slender. Our bite force measurements show a muscle force reduction of 18% for tip biting when compared with bites with the teeth located halfway along the mandibles. This suggests a behavioural adaptation to prevent failure. We confirmed this by constructing finite-element (FE) models that mimic both natural bite situations as well as the hypothetical situation of tip biting without muscle force modulation. These models, based on micro-CT images, investigate the material stresses in the mandibles for different combinations of bite location and muscle force. Young's modulus of the cuticle was experimentally determined to be 5.1 GPa with the double indentation method, and the model was validated by digital image correlation on living beetles. FE analysis proves to be a valuable tool in the investigation of the trade-offs of (animal) weapon morphology and usage. Furthermore, the demonstrated bite force modulation in male stag beetles suggests the presence of mechanosensors inside the armature.

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.

Is Beak Morphology in Darwin's Finches Tuned to Loading Demands?

One of nature's premier illustrations of adaptive evolution concerns the tight correspondence in birds between beak morphology and feeding behavior. In seed-crushing birds, beaks have been suggested to evolve at least in part to avoid fracture. Yet, we know little about mechanical relationships between beak shape, stress dissipation, and fracture avoidance. This study tests these relationships for Darwin's finches, a clade of birds renowned for their diversity in beak form and function. We obtained anatomical data from micro-CT scans and dissections, which in turn informed the construction of finite element models of the bony beak and rhamphotheca. Our models offer two new insights. First, engineering safety factors are found to range between 1 and 2.5 under natural loading conditions, with the lowest safety factors being observed in species with the highest bite forces. Second, size-scaled finite element (FE) models reveal a correspondence between inferred beak loading profiles and observed feeding strategies (e.g. edge-crushing versus tip-biting), with safety factors decreasing for base-crushers biting at the beak tip. Additionally, we identify significant correlations between safety factors, keratin thickness at bite locations, and beak aspect ratio (depth versus length). These lines of evidence together suggest that beak shape indeed evolves to resist feeding forces.

Hierarchical multiscale structure-property relationships of the red-bellied woodpecker (Melanerpes carolinus) beak

We experimentally studied beaks of the red-bellied woodpecker to elucidate the hierarchical multiscale structure-property relationships. At the macroscale, the beak comprises three structural layers: an outer rhamphotheca layer (keratin sheath), a middle foam layer and an inner bony layer. The area fraction of each layer changes along the length of the beak giving rise to a varying constitutive behaviour similar to functionally graded materials. At the microscale, the rhamphotheca comprises keratin scales that are placed in an overlapping pattern; the middle foam layer has a porous structure; and the bony layer has a big centre cavity. At the nanoscale, a wavy gap between the keratin scales similar to a suture line was evidenced in the rhamphotheca; the middle foam layer joins two dissimilar materials; and mineralized collagen fibres were revealed in the inner bony layer. The nano- and micro-indentation tests revealed that the hardness (associated with the strength, modulus and stiffness) of the rhamphotheca layer (approx. 470 MPa for nano and approx. 320 MPa for micro) was two to three times less than that of the bony layer (approx. 1200 MPa for nano and approx. 630 MPa for micro). When compared to other birds (chicken, finch and toucan), the woodpecker's beak has more elongated keratin scales that can slide over each other thus admitting dissipation via shearing; has much less porosity in the bony layer thus strengthening the beak and focusing the stress wave; and has a wavy suture that admits local shearing at the nanoscale. The analysis of the woodpeckers' beaks provides some understanding of biological structural materials' mechanisms for energy absorption.

Structural tissue organization in the beak of Java and Darwin's finches

Birds are well known for occupying diverse feeding niches, and for having evolved diverse beak morphologies associated with dietary specialization. Birds that feed on hard seeds typically possess beaks that are both deep and wide, presumably because of selection for fracture avoidance, as suggested by prior studies. It follows then that birds that eat seeds of different size and hardness should vary in one or more aspects of beak morphology, including the histological organization of the rhamphotheca, the cellular interface that binds the rhamphotheca to the bone, and the organization of trabeculae in the beak. To explore this expectation we here investigate tissue organization in the rhamphotheca of the Java finch, a large granivorous bird, and describe interspecific differences in the trabecular organization of the beak across 11 species of Darwin's finches. We identify specializations in multiple layers of the horny beak, with the dermis anchored to the bone by Sharpey's fibers in those regions that are subjected to high stresses during biting. Moreover, the rhamphotheca is characterized by a tight dermo-epidermal junction through interdigitations of these two tissues. Herbst corpuscles are observed in high density in the dermis of the lateral aspect of the beak as observed in other birds. Finally, the trabecular organization of the beak in Darwin's finches appears most variable in regions involved most in food manipulation, with the density of trabeculae in the beak generally mirroring loading regimes imposed by different feeding habits and beak use in this clade.

Multi-layered bird beaks: a finite-element approach towards the role of keratin in stress dissipation

Bird beaks are layered structures, which contain a bony core and an outer keratin layer. The elastic moduli of this bone and keratin were obtained in a previous study. However, the mechanical role and interaction of both materials in stress dissipation during seed crushing remain unknown. In this paper, a multi-layered finite-element (FE) model of the Java finch's upper beak (Padda oryzivora) is established. Validation measurements are conducted using in vivo bite forces and by comparing the displacements with those obtained by digital speckle pattern interferometry. Next, the Young modulus of bone and keratin in this FE model was optimized in order to obtain the smallest peak von Mises stress in the upper beak. To do so, we created a surrogate model, which also allows us to study the impact of changing material properties of both tissues on the peak stresses. The theoretically best values for both moduli in the Java finch are retrieved and correspond well with previous experimentally obtained values, suggesting that material properties are tuned to the mechanical demands imposed during seed crushing.

Full-field optical deformation measurement in biomechanics: digital speckle pattern interferometry and 3D digital image correlation applied to bird beaks

In this paper two easy-to-use optical setups for the validation of biomechanical finite element (FE) models are presented. First, we show an easy-to-build Michelson digital speckle pattern interferometer (DSPI) setup, yielding the out-of-plane displacement. We also introduce three-dimensional digital image correlation (3D-DIC), a stereo photogrammetric technique. Both techniques are non-contact and full field, but they differ in nature and have different magnitudes of sensitivity. In this paper we successfully apply both techniques to validate a multi-layered FE model of a small bird beak, a strong but very light biological composite. DSPI can measure very small deformations, with potentially high signal-to-noise ratios. Its high sensitivity, however, results in high stability requirements and makes it hard to use it outside an optical laboratory and on living samples. In addition, large loads have to be divided into small incremental load steps to avoid phase unwrapping errors and speckle de-correlation. 3D-DIC needs much larger displacements, but automatically yields the strains. It is more flexible, does not have stability requirements, and can easily be used as an optical strain gage.