Experimental, theoretical and numerical investigation of the nonlinear micromechanical properties of bone

Aging societies suffer from an increasing incidence of bone fractures. Bone strength depends on the amount of mineral measured by clinical densitometry, but also on the micromechanical properties of the bone hierarchical organization. A good understanding has been reached for elastic properties on several length scales, but up to now there is a lack of reliable postyield data on the lower length scales. In order to be able to describe the behavior of bone at the microscale, an anisotropic elastic-viscoplastic damage model was developed using an eccentric generalized Hill criterion and nonlinear isotropic hardening. The model was implemented as a user subroutine in Abaqus and verified using single element tests. A FE simulation of microindentation in lamellar bone was finally performed show-ing that the new constitutive model can capture the main characteristics of the indentation response of bone. As the generalized Hill criterion is limited to elliptical and cylindrical yield surfaces and the correct shape for bone is not known, a new yield surface was developed that takes any convex quadratic shape. The main advantage is that in the case of material identification the shape of the yield surface does not have to be anticipated but a minimization results in the optimal shape among all convex quadrics. The generality of the formulation was demonstrated by showing its degeneration to classical yield surfaces. Also, existing yield criteria for bone at multiple length scales were converted to the quadric formulation. Then, a computational study to determine the influence of yield surface shape and damage on the in-dentation response of bone using spherical and conical tips was performed. The constitutive model was adapted to the quadric criterion and yield surface shape and critical damage were varied. They were shown to have a major impact on the indentation curves. Their influence on indentation modulus, hardness, their ratio as well as the elastic to total work ratio were found to be very well described by multilinear regressions for both tip shapes. For conical tips, indentation depth was not a significant fac-tor, while for spherical tips damage was insignificant. All inverse methods based on microindentation suffer from a lack of uniqueness of the found material properties in the case of nonlinear material behavior. Therefore, monotonic and cyclic micropillar com-pression tests in a scanning electron microscope allowing a straightforward interpretation comple-mented by microindentation and macroscopic uniaxial compression tests were performed on dry ovine bone to identify modulus, yield stress, plastic deformation, damage accumulation and failure mecha-nisms. While the elastic properties were highly consistent, the postyield deformation and failure mech-anisms differed between the two length scales. A majority of the micropillars showed a ductile behavior with strain hardening until failure by localization in a slip plane, while the macroscopic samples failed in a quasi-brittle fashion with microcracks coalescing into macroscopic failure surfaces. In agreement with a proposed rheological model, these experiments illustrate a transition from a ductile mechanical behavior of bone at the microscale to a quasi-brittle response driven by the growth of preexisting cracks along interfaces or in the vicinity of pores at the macroscale. Subsequently, a study was undertaken to quantify the topological variability of indentations in bone and examine its relationship with mechanical properties. Indentations were performed in dry human and ovine bone in axial and transverse directions and their topography measured by AFM. Statistical shape modeling of the residual imprint allowed to define a mean shape and describe the variability with 21 principal components related to imprint depth, surface curvature and roughness. The indentation profile of bone was highly consistent and free of any pile up. A few of the topological parameters, in particular depth, showed significant correlations to variations in mechanical properties, but the cor-relations were not very strong or consistent. We could thus verify that bone is rather homogeneous in its micromechanical properties and that indentation results are not strongly influenced by small de-viations from the ideal case. As the uniaxial properties measured by micropillar compression are in conflict with the current literature on bone indentation, another dissipative mechanism has to be present. The elastic-viscoplastic damage model was therefore extended to viscoelasticity. The viscoelastic properties were identified from macroscopic experiments, while the quasistatic postelastic properties were extracted from micropillar data. It was found that viscoelasticity governed by macroscale properties has very little influence on the indentation curve and results in a clear underestimation of the creep deformation. Adding viscoplasticity leads to increased creep, but hardness is still highly overestimated. It was possible to obtain a reasonable fit with experimental indentation curves for both Berkovich and spherical indenta-tion when abandoning the assumption of shear strength being governed by an isotropy condition. These results remain to be verified by independent tests probing the micromechanical strength prop-erties in tension and shear. In conclusion, in this thesis several tools were developed to describe the complex behavior of bone on the microscale and experiments were performed to identify its material properties. Micropillar com-pression highlighted a size effect in bone due to the presence of preexisting cracks and pores or inter-faces like cement lines. It was possible to get a reasonable fit between experimental indentation curves using different tips and simulations using the constitutive model and uniaxial properties measured by micropillar compression. Additional experimental work is necessary to identify the exact nature of the size effect and the mechanical role of interfaces in bone. Deciphering the micromechanical behavior of lamellar bone and its evolution with age, disease and treatment and its failure mechanisms on several length scales will help preventing fractures in the elderly in the future.

Interactive Diffraction from Biological Nanostructures

We describe a technique for interactive rendering of diffraction effects produced by biological nanostructures, such as snake skin surface gratings. Our approach uses imagery from atomic force microscopy that accurately captures the geometry of the nanostructures responsible for structural colouration, that is, colouration due to wave interference, in a variety of animals. We develop a rendering technique that constructs bidirectional reflection distribution functions (BRDFs) directly from the measured data and leverages pre-computation to achieve interactive performance. We demonstrate results of our approach using various shapes of the surface grating nanostructures. Finally, we evaluate the accuracy of our pre-computation-based technique and compare to a reference BRDF construction technique.

A moiré deflectometer for antimatter

The precise measurement of forces is one way to obtain deep insight into the fundamental interactions present in nature. In the context of neutral antimatter, the gravitational interaction is of high interest, potentially revealing new forces that violate the weak equivalence principle. Here we report on a successful extension of a tool from atom optics—the moiré deflectometer—for a measurement of the acceleration of slow antiprotons. The setup consists of two identical transmission gratings and a spatially resolving emulsion detector for antiproton annihilations. Absolute referencing of the observed antimatter pattern with a photon pattern experiencing no deflection allows the direct inference of forces present. The concept is also straightforwardly applicable to antihydrogen measurements as pursued by the AEgIS collaboration. The combination of these very different techniques from high energy and atomic physics opens a very promising route to the direct detection of the gravitational acceleration of neutral antimatter.

AEgIS experiment: Towards antihydrogen beam production for antimatter gravity measurements

AEgIS (Antimatter Experiment: Gravity, Interferometry, Spectroscopy) is an experiment that aims to perform the first direct measurement of the gravitational acceleration g of antihydrogen in the Earth’s field. A cold antihydrogen beam will be produced by charge exchange reaction between cold antiprotons and positronium excited in Rydberg states. Rydberg positronium (with quantum number n between 20 and 30) will be produced by a two steps laser excitation. The antihydrogen beam, after being accelerated by Stark effect, will fly through the gratings of a moir´e deflectometer. The deflection of the horizontal beam due to its free fall will be measured by a position sensitive detector. It is estimated that the detection of about 103 antihydrogen atoms is required to determine the gravitational acceleration with a precision of 1%. In this report an overview of the AEgIS experiment is presented and its current status is described. Details on the production of slow positronium and its excitation with lasers are discussed.

Structure–mechanics relationships in mineralized tendons

In this paper, we review the hierarchical structure and the resulting elastic properties of mineralized tendons as obtained by various multiscale experimental and computational methods spanning from nano- to macroscale. The mechanical properties of mineralized collagen fibres are important to understand the mechanics of hard tissues constituted by complex arrangements of these fibres, like in human lamellar bone. The uniaxial mineralized collagen fibre array naturally occurring in avian tendons is a well studied model tissue for investigating various stages of tissue mineralization and the corresponding elastic properties. Some avian tendons mineralize with maturation, which results in a graded structure containing two zones of distinct morphology, circumferential and interstitial. These zones exhibit different amounts of mineral, collagen, pores and a different mineral distribution between collagen fibrillar and extrafibrillar space that lead to distinct elastic properties. Mineralized tendon cells have two phenotypes: elongated tenocytes placed between fibres in the circumferential zone and cuboidal cells with lower aspect ratios in the interstitial zone. Interestingly some regions of avian tendons seem to be predestined to mineralization, which is exhibited as specific collagen cross-linking patterns as well as distribution of minor tendon constituents (like proteoglycans) and loss of collagen crimp. Results of investigations in naturally mineralizing avian tendons may be useful in understanding the pathological mineralization occurring in some human tendons.

Is "milk crust" a transient form of golden retriever ichthyosis?

BACKGROUND A recessive inherited form of lamellar ichthyosis is well recognized in golden retrievers. In this breed, young puppies demonstrate a self-limiting scaling disorder which is commonly recognized by breeders, who use the term "milk crust" to describe this syndrome. HYPOTHESIS/OBJECTIVES To determine whether "milk crust" is a new keratinization disorder or a self-limiting form of golden retriever ichthyosis. ANIMALS A total of 179 golden retriever dogs (21 dams and 158 puppies) were examined. METHODS Dermatological examination and assessment of the patatin-like phospholipase-1 (PNPLA1) genotype by PCR testing of buccal mucosal swabs. Skin biopsies from one affected puppy were evaluated for histopathological abnormalities. RESULTS Forty-five of 158 (28%) puppies exhibited scaling at 8 weeks of age; 113 of 158 (72%) were dermatologically normal. Of 144 analysed samples, 40 of 144 (28%) puppies demonstrated a homozygous mutation of the PNPLA1 genotype [of which, 36 of 40 (90%) had signs of scaling], 77 of 144 (53%) demonstrated a heterozygous mutation and 27 of 144 (19%) were a normal wild-type. In six of 17 (35%) dams, a homozygous mutation of the PNPLA1 genotype was found, eight of 17 (47%) demonstrated a heterozygous mutation and three of 17 (18%) were normal wild-type. Dams with a homozygous mutation were clinically unaffected. A 1 year follow-up revealed that 23 of 28 (82%) puppies affected with this syndrome failed to develop typical signs of ichthyosis. In five of 28 (18%) dogs there was persistence of mild scaling. CONCLUSIONS AND CLINICAL IMPORTANCE We hypothesize that the clinical syndrome termed "milk crust" could represent a transient form of golden retriever ichthyosis. Remission is not fully linked to PNPLA1 genotype, suggesting that unknown factors may contribute to the clinical disease.

THE ULTRASTRUCTURAL ORGANIZATION OF THE HYPOGLOSSAL NUCLEUS IN THE RAT (SYNAPTOLOGY, CRANIAL NERVES)

An ultrastructural study of the hypoglossal nucleus (XII) in the rat has revealed two distinct neuronal populations. Hypoglossal motoneurons comprised the largest population of neurons in XII and were identified following injection of horseradish peroxidase (HRP) into the tongue. Motoneurons were large (25-50(mu)m), multipolar in shape and distributed throughout XII. The nucleus was large, round and centrally located, and the cytoplasm was characterized by dense lamellar arrays of rough endoplasmic reticulum. In contrast, a second population of small (10-18(mu)m), round to oval shaped neurons was found restricted to the ventral and dorsolateral regions of XII. The nucleus was markedly invaginated and eccentric, the cytoplasm scant and filled with free ribosomes, and the absence of lamellar arrays of rough endoplasmic reticulum was conspicuous. Neurons of this type were never found to contain HRP reaction product. These results demonstrate that the hypoglossal nucleus does not consist solely of motoneurons, but includes a distinctly separate, presumably non-motoneuronal pool. Arguments are presented in favor of this second neuron population being interneurons. The functional significance of these findings in relation to tongue control is discussed. ^

Dynamic population coding in primary visual cortex

More than a century ago Ramon y Cajal pioneered the description of neural circuits. Currently, new techniques are being developed to streamline the characterization of entire neural circuits. Even if this 'connectome' approach is successful, it will represent only a static description of neural circuits. Thus, a fundamental question in neuroscience is to understand how information is dynamically represented by neural populations. In this thesis, I studied two main aspects of dynamical population codes. ^ First, I studied how the exposure or adaptation, for a fraction of a second to oriented gratings dynamically changes the population response of primary visual cortex neurons. The effects of adaptation to oriented gratings have been extensively explored in psychophysical and electrophysiological experiments. However, whether rapid adaptation might induce a change in the primary visual cortex's functional connectivity to dynamically impact the population coding accuracy is currently unknown. To address this issue, we performed multi-electrode recordings in primary visual cortex, where adaptation has been previously shown to induce changes in the selectivity and response amplitude of individual neurons. We found that adaptation improves the population coding accuracy. The improvement was more prominent for iso- and orthogonal orientation adaptation, consistent with previously reported psychophysical experiments. We propose that selective decorrelation is a metabolically inexpensive mechanism that the visual system employs to dynamically adapt the neural responses to the statistics of the input stimuli to improve coding efficiency. ^ Second, I investigated how ongoing activity modulates orientation coding in single neurons, neural populations and behavior. Cortical networks are never silent even in the absence of external stimulation. The ongoing activity can account for up to 80% of the metabolic energy consumed by the brain. Thus, a fundamental question is to understand the functional role of ongoing activity and its impact on neural computations. I studied how the orientation coding by individual neurons and cell populations in primary visual cortex depend on the spontaneous activity before stimulus presentation. We hypothesized that since the ongoing activity of nearby neurons is strongly correlated, it would influence the ability of the entire population of orientation-selective cells to process orientation depending on the prestimulus spontaneous state. Our findings demonstrate that ongoing activity dynamically filters incoming stimuli to shape the accuracy of orientation coding by individual neurons and cell populations and this interaction affects behavioral performance. In summary, this thesis is a contribution to the study of how dynamic internal states such as rapid adaptation and ongoing activity modulate the population code accuracy. ^