Joris Soons

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.

Quantification of tympanic membrane elasticity parameters from in situ point indentation measurements: Validation and preliminary study

Correct quantitative parameters to describe tympanic membrane elasticity are an important input for realistic modeling of middle ear mechanics. In the past, several attempts have been made to determine tympanic membrane elasticity from tensile experiments on cut-out strips. The strains and stresses in such experiments may be far out of the physiologically relevant range and the elasticity parameters are only partially determined. We developed a setup to determine tympanic membrane elasticity in situ, using a combination of point micro-indentation and Moiré profilometry. The measuring method was tested on latex phantom models of the tympanic membrane, and our results show that the correct parameters can be determined. These parameters were calculated by finite element simulation of the indentation experiment and parameter optimization routines. When the apparatus was used for rabbit tympanic membranes, Moiré profilometry showed that there is no measurable displacement of the manubrium during the small indentations. This result greatly simplifies boundary conditions, as we may regard both the annulus and the manubrium as fixed without having to rely on fixation interventions. The technique allows us to determine linear elastic material parameters of a tympanic membrane in situ. In this way our method takes into account the complex geometry of the membrane, and parameters are obtained in a physiologically relevant range of strain.

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 finchs 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.

Adaptation and function of the bills of Darwin's finches: divergence by feeding type and sex

Abstract Darwins finches are a model system for studying adaptive diversification. However, despite the large body of work devoted to this system, rather little is known about the functional consequences of variation in the size and shape of bills. We test, using two methods, if natural or sexual selection, or both, has resulted in functional divergence in bill and head morphology. Firstly, we compare data on head-shape and bite-forces across nine species of Darwins finches. Secondly, we use micro-CT scans and finite-element models to test the prediction that the shape of the bill in representatives of the different feeding types is adaptively related to use of the bill. Sexual dimorphism in head-shape and bite-force was detected, with females having longer bills than males for a given body size. Moreover, our results show strong differences in bill- and head-morphology between feeding types, with base-crushers having higher bite-forces and also relatively high bite-forces at the tip compared to probers and tip-biters. Finally, our finite-element models suggest that the shape of the bill in the tip-biters and base-crushers confers mechanical advantages by minimising stress in tip-loading and base-loading conditions, respectively, thus reducing probabilities of fracture. Our data support the contention that bill-shape is adaptive and evolves under selection for mechanical optimisation through natural selection on feeding mode.

Cytoarchitecture of the Mouse Organ of Corti from Base to Apex, Determined Using In Situ Two-Photon Imaging

ABSTRACTThe cells in the organ of Corti are highly organized, with a precise 3D microstructure hypothesized to be important for cochlear function. Here we provide quantitative data on the mouse organ of Corti cytoarchitecture, as determined using a new technique that combines the imaging capabilities of two-photon microscopy with the autofluorescent cell membranes of the genetically modified mTmG mouse. This combination allowed us to perform in situ imaging on freshly excised tissue, thus minimizing any physical distortions to the tissue that extraction from the cochlea and chemical fixation and staining might have caused. 3D image stacks of the organ of Corti were obtained from base to apex in the cochlear duct, from which 3D lengths and relative angles for inner and outer hair cells, Deiters’ cells, phalangeal processes, and inner and outer pillars were measured. In addition, intercellular distances, diameters, and stereocilia shapes were obtained. An important feature of this study is the quantitative reporting of the longitudinal tilts of the outer hair cells towards the base of the cochlea, the tilt of phalangeal processes towards the apex, and Deiters’ cells that collectively form a Y-shaped building block that is thought to give rise to the lattice-like organization of the organ of Corti. The variations of this Y-shaped element along the cochlear duct and between the rows of outer hair cells are shown with the third row morphologically different from the other rows, and their potential importance for the cochlear amplifier is discussed.

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. Youngs 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.

Elasticity modulus of rabbit middle ear ossicles determined by a novel micro-indentation technique

For the purpose of creating a finite element model of the middle ear, the ossicles can be modelled as rigid bodies or as linear elastic materials. The general elasticity parameters used are usually measured on larger bones like the femur. In order to obtain a highly realistic model, the actual elastic modulus (Youngs modulus) of the ossicles themselves is needed. We developed a novel 2-needle indentation method of determining the Youngs modulus of small samples based on Sneddons solution. We introduce the second needle in such a way that small specimens can be clamped between the two needles and a symmetry plane is obtained, so that geometry-dependent sample deformations are avoided. A finite element calculated correction factor is used to compensate for the small thickness of the samples. The system was tested on several materials with known parameters in order to validate the technique, and was then used to determine the elasticity parameters of incus and malleus in rabbit. No significant differences between measurement locations were found, and we found an average Youngs modulus of 16+/-3 GPa.

Digital Stroboscopic Holography Setup for Deformation Measurement at Both Quasi-Static and Acoustic Frequencies

A setup for digital stroboscopic holography that combines the advantages of full-field digital holographic interferometry with a high temporal resolution is presented. The setup can be used to identify and visualize complicated vibrational patterns with nanometer amplitudes, ranging from quasi-static to high frequency vibrations. By using a high-energy pulsed laser, single-shot holograms can be recorded and stability issues are avoided. Results are presented for an acoustically stimulated rubber membrane and the technique is evaluated by means of an accuracy and a repeatability test. The presented technique offers wide application possibilities in areas such as biomechanics and industrial testing.

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

One of natures 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 Darwins 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.

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

In recent years, there has been a surge in the development of finite-element (FE) models aimed at testing biological hypotheses. For example, recent modelling efforts suggested that the beak in Darwins finches probably evolved in response to fracture avoidance. However, knowledge of the material properties of the structures involved is crucial for any model. For many biological structures, these data are not available and may be difficult to obtain experimentally given the complex nature of biological structures. Beaks are interesting as they appear to be highly optimized in some cases. In order to understand the biomechanics of this small and complex structure, we have been developing FE models that take into account the bilayered structure of the beak consisting of bone and keratin. Here, we present the results of efforts related to the determination and validation of the elastic modulus of bone and keratin in bird beaks. The elastic moduli of fresh and dried samples were obtained using a novel double-indentation technique and through an inverse analysis. A bending experiment is used for the inverse analysis and the validation of the measurements. The out-of-plane displacements during loading are measured using digital speckle pattern interferometry.