A generalized anisotropic quadric yield criterion and its application to bone tissue at multiple length scales

Nonlinear computational analysis of materials showing elasto-plasticity or damage relies on knowledge of their yield behavior and strengths under complex stress states. In this work, a generalized anisotropic quadric yield criterion is proposed that is homogeneous of degree one and takes a convex quadric shape with a smooth transition from ellipsoidal to cylindrical or conical surfaces. If in the case of material identification, the shape of the yield function is not known a priori, a minimization using the quadric criterion will result in the optimal shape among the convex quadrics. The convexity limits of the criterion and the transition points between the different shapes are identified. Several special cases of the criterion for distinct material symmetries such as isotropy, cubic symmetry, fabric-based orthotropy and general orthotropy are presented and discussed. The generality of the formulation is demonstrated by showing its degeneration to several classical yield surfaces like the von Mises, Drucker–Prager, Tsai–Wu, Liu, generalized Hill and classical Hill criteria under appropriate conditions. Applicability of the formulation for micromechanical analyses was shown by transformation of a criterion for porous cohesive-frictional materials by Maghous et al. In order to demonstrate the advantages of the generalized formulation, bone is chosen as an example material, since it features yield envelopes with different shapes depending on the considered length scale. A fabric- and density-based quadric criterion for the description of homogenized material behavior of trabecular bone is identified from uniaxial, multiaxial and torsional experimental data. Also, a fabric- and density-based Tsai–Wu yield criterion for homogenized trabecular bone from in silico data is converted to an equivalent quadric criterion by introduction of a transformation of the interaction parameters. Finally, a quadric yield criterion for lamellar bone at the microscale is identified from a nanoindentation study reported in the literature, thus demonstrating the applicability of the generalized formulation to the description of the yield envelope of bone at multiple length scales.

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.

Natural tracer profiles across argillaceous formations

Argillaceous formations generally act as aquitards because of their low hydraulic conductivities. This property, together with the large retention capacity of clays for cationic contaminants, has brought argillaceous formations into focus as potential host rocks for the geological disposal of radioactive and other waste. In several countries, programmes are under way to characterise the detailed transport properties of such formations at depth. In this context, the interpretation of profiles of natural tracers in pore waters across the formations can give valuable information about the large-scale and long-term transport behaviour of these formations. Here, tracer-profile data, obtained by various methods of pore-water extraction for nine sites in central Europe, are compiled. Data at each site comprise some or all of the conservative tracers: anions (Cl(-), Br(-)), water isotopes (delta(18)O, delta(2)H) and noble gases (mainly He). Based on a careful evaluation of the palaeo-hydrogeological evolution at each site, model scenarios are derived for initial and boundary pore-water compositions and an attempt is made to numerically reproduce the observed tracer distributions in a consistent way for all tracers and sites, using transport parameters derived from laboratory or in situ tests. The comprehensive results from this project have been reported in Mazurek et al. (2009). Here the results for three sites are presented in detail, but the conclusions are based on model interpretations of the entire data set. In essentially all cases, the shapes of the profiles can be explained by diffusion acting as the dominant transport process over periods of several thousands to several millions of years and at the length scales of the profiles. Transport by advection has a negligible influence on the observed profiles at most sites, as can be shown by estimating the maximum advection velocities that still give acceptable fits of the model with the data. The advantages and disadvantages of different conservative tracers are also assessed. The anion Cl(-) is well suited as a natural tracer in aquitards, because its concentration varies considerably in environmental waters. It can easily be measured, although the uncertainty regarding the fraction of the pore space that is accessible to anions in clays remains an issue. The stable water isotopes are also well suited, but they are more difficult to measure and their values generally exhibit a smaller relative range of variation. Chlorine isotopes (delta(37)Cl) and He are more difficult to interpret because initial and boundary conditions cannot easily be constrained by independent evidence. It is also shown that the existence of perturbing events such as the activation of aquifers due to uplift and erosion, leading to relatively sharp changes of boundary conditions, can be considered as a pre-requisite to obtain well-interpretable tracer signatures. On the other hand, gradual changes of boundary conditions are more difficult to parameterise and so may preclude a clear interpretation.

Surface-patterned micromechanical elements by polymer injection molding with hybrid molds

Hybrid molds enable the fabrication of polymeric parts with features of different length scales by injection molding. The resulting polymer microelements combine optical or biological functionalities with designed mechanical properties. Two applications are chosen for illustration of this concept: As a first example, microelements for optical communication via fiber-to-fiber coupling are manufactured by combining two molds to a small mold insert. Both molds are fabricated using lithography and electroplating. As a second example, microcantilevers (μCs) for chemical sensing are surface patterned using a modular mold composed of a laser-machined cavity defining the geometry of the μCs, and an opposite flat tool side which is covered by a patterned polymer foil. Injection molding results in an array of 35 μm-thick μCs with microscale surface topographies. In both cases, when the mold is assembled and closed, reliefs are transferred onto one surface of the molded element whose outlines are defined by the micromold cavity. The main advantage of these hybrid methods lies in the simple integration of optical surface structures and gratings onto the surface of microcomponents with different sizes and orientations. This allows for independent development of functional properties and combinations thereof.

Numerical study of Anderson localization of terahertz waves in disordered waveguides

We present a numerical study of electromagnetic wave transport in disordered quasi-one-dimensional waveguides at terahertz frequencies. Finite element method calculations of terahertz wave propagation within LiNbO3 waveguides with randomly arranged air-filled circular scatterers exhibit an onset of Anderson localization at experimentally accessible length scales. Results for the average transmission as a function of waveguide length and scatterer density demonstrate a clear crossover from diffusive to localized transport regime. In addition, we find that transmission fluctuations grow dramatically when crossing into the localized regime. Our numerical results are in good quantitative agreement with theory over a wide range of experimentally accessible parameters both in the diffusive and localized regime opening the path towards experimental observation of terahertz wave localization.

Relating orogen width to shortening, erosion, and exhumation during Alpine collision

We investigate along-strike width changes of the thickened, accreted lower plate (TALP) in the Central and in the Eastern Alps. We set the width of the TALP in relation to the inferred amount of collisional shortening and exhumation along six orogen-scale cross sections. Taking the present-day, along-strike gradients in the amount of collisional shortening to represent the temporal evolution of the collisional wedge, it may be concluded that the cross-sectional area of the TALP diminishes during ongoing shortening, indicating that the erosional flux outpaced the accretionary flux. Higher amounts of collisional shortening systematically coincide with smaller widths of the TALP and dramatic increases of the reconstructed eroded rock column. Higher amounts of shortening also coincide with larger amplitudes of orogen-scale, upright folds, with higher exhumation and with higher exhumation rates. Hence, erosion did play a major role in reducing by >30 km the vertical crustal thickness in order to accommodate and allow shortening by folding. Long-term climate differences cannot explain alternating changes of width by a factor of almost 2 along straight segments of the orogen on length scales less than 200 km, as observed from the western Central Alps to the easternmost Eastern Alps. Sedimentary or paleontological evidences supporting such paleo-climatic differences are lacking, suggesting that erosional processes did not directly control the width of the orogen.

Spatio-temporal co-ordination of RhoA, Rac1 and Cdc42 activation during prototypical edge protrusion and retraction dynamics

The three canonical Rho GTPases RhoA, Rac1 and Cdc42 co-ordinate cytoskeletal dynamics. Recent studies indicate that all three Rho GTPases are activated at the leading edge of motile fibroblasts, where their activity fluctuates at subminute time and micrometer length scales. Here, we use a microfluidic chip to acutely manipulate fibroblast edge dynamics by applying pulses of platelet-derived growth factor (PDGF) or the Rho kinase inhibitor Y-27632 (which lowers contractility). This induces acute and robust membrane protrusion and retraction events, that exhibit stereotyped cytoskeletal dynamics, allowing us to fairly compare specific morphodynamic states across experiments. Using a novel Cdc42, as well as previously described, second generation RhoA and Rac1 biosensors, we observe distinct spatio-temporal signaling programs that involve all three Rho GTPases, during protrusion/retraction edge dynamics. Our results suggest that Rac1, Cdc42 and RhoA regulate different cytoskeletal and adhesion processes to fine tune the highly plastic edge protrusion/retraction dynamics that power cell motility.

Spatio-temporal Rho GTPase signaling - where are we now?

Rho-family GTPases are molecular switches that transmit extracellular cues to intracellular signaling pathways. Their regulation is likely to be highly regulated in space and in time, but most of what is known about Rho-family GTPase signaling has been derived from techniques that do not resolve these dimensions. New imaging technologies now allow the visualization of Rho GTPase signaling with high spatio-temporal resolution. This has led to insights that significantly extend classic models and call for a novel conceptual framework. These approaches clearly show three things. First, Rho GTPase signaling dynamics occur on micrometer length scales and subminute timescales. Second, multiple subcellular pools of one given Rho GTPase can operate simultaneously in time and space to regulate a wide variety of morphogenetic events (e.g. leading-edge membrane protrusion, tail retraction, membrane ruffling). These different Rho GTPase subcellular pools might be described as 'spatio-temporal signaling modules' and might involve the specific interaction of one GTPase with different guanine nucleotide exchange factors (GEFs), GTPase-activating proteins (GAPs) and effectors. Third, complex spatio-temporal signaling programs that involve precise crosstalk between multiple Rho GTPase signaling modules regulate specific morphogenetic events. The next challenge is to decipher the molecular circuitry underlying this complex spatio-temporal modularity to produce integrated models of Rho GTPase signaling.

Sixty-four-detector CT angiography of infrarenal aortic neck length and angulation: prospective analysis of interobserver variability

PURPOSE: To quantify the interobserver variability of abdominal aortic aneurysm (AAA) neck length and angulation measurements. MATERIALS AND METHODS: A total of 25 consecutive patients scheduled for endovascular AAA repair underwent follow-up 64-row computed tomographic (CT) angiography in 0.625-mm collimation. AAA neck length and angulation were determined by four blinded, independent readers. AAA neck length was defined as the longitudinal distance between the first transverse CT slice directly distal to the lowermost renal artery and the first transverse CT slice that showed at least a 15% larger outer aortic wall diameter versus the diameter measured directly below the lowermost renal artery. Infrarenal AAA neck angulation was defined as the true angle between the longitudinal axis of the proximal AAA neck and the longitudinal axis of the AAA lumen as analyzed on three-dimensional CT reconstructions. RESULTS: Mean deviation in aortic neck length determination was 32.3% and that in aortic neck angulation was 32.1%. Interobserver variability of aortic neck length and angulation measurements was considerable: in any reader combination, at least one measurement difference was outside the predefined limits of agreement. CONCLUSIONS: Assessment of the longitudinal extension and angulation of the infrarenal aortic neck is associated with substantial observer variability, even if measurement is carried out according to a standardized protocol. Further studies are mandatory to assess dedicated technical approaches to minimize variance in the determination of the longitudinal extension and angulation of the infrarenal aortic neck.

Electroweak Sudakov effects in W, Z and γ production at large transverse momentum

We study electroweak Sudakov effects in single W, Z and γ production at large transverse momentum using soft collinear effective theory. We present a factorized form of the cross section near the partonic threshold with both QCD and electroweak effects included and compute the electroweak corrections arising at different scales. We analyze their size relative to the QCD corrections as well as the impact of strong-electroweak mixing terms. Numerical results for the vector-boson cross sections at the Large Hadron Collider are presented.

Incision length for kidney transplantation does not influence short- or long-term outcome: a prospective randomized controlled trial

BACKGROUND: While previous studies suggest advantages of minimally invasive surgery in living donor nephrectomy, similar data are lacking for kidney transplant recipients. Our aim was to prospectively evaluate short- and long-term outcome for kidney transplant recipients, comparing a short transverse (ST) to a classical hockey-stick (HS) incision. METHODS: Sixty-six patients were randomized into two groups: ST vs. HS from January 2008 to May 2010. ST was defined as incision length ≤9 cm and HS as >14 cm. Perioperative data were collected, with evaluation of intra- and postoperative complications and quality of recovery (QoR) score. RESULTS: There were no significant differences in patient demographics, early or long-term postoperative pain. There were no significant differences in QoR scores between the ST and HS group. Predictive for a worse QoR was persisting incisional pain at the 30-month follow-up. Thirty-days mortality, morbidity, and long-term kidney function did not differ between the two groups (p = 1.00, p = 0.62 and p = 0.66, respectively). CONCLUSIONS: Patient satisfaction as well as graft function and patient mortality was not influenced by incision length. With patient and graft safety being paramount, especially in times of organ shortage, incision length should reflect the requirement for a successful transplantation and not be a measure of feasibility.

Assessment of Transverse Isotropy in Clinical-Level CT Images of Trabecular Bone Using the Gradient Structure Tensor

The aim of this study was to develop a GST-based methodology for accurately measuring the degree of transverse isotropy in trabecular bone. Using femoral sub-regions scanned in high-resolution peripheral QCT (HR-pQCT) and clinical-level-resolution QCT, trabecular orientation was evaluated using the mean intercept length (MIL) and the gradient structure tensor (GST) on the HR-pQCT and QCT data, respectively. The influence of local degree of transverse isotropy (DTI) and bone mineral density (BMD) was incorporated into the investigation. In addition, a power based model was derived, rendering a 1:1 relationship between GST and MIL eigenvalues. A specific DTI threshold (DTI thres) was found for each investigated size of region of interest (ROI), above which the estimate of major trabecular direction of the GST deviated no more than 30° from the gold standard MIL in 95% of the remaining ROIs (mean error: 16°). An inverse relationship between ROI size and DTI thres was found for discrete ranges of BMD. A novel methodology has been developed, where transversal isotropic measures of trabecular bone can be obtained from clinical QCT images for a given ROI size, DTI thres and power coefficient. Including DTI may improve future clinical QCT finite-element predictions of bone strength and diagnoses of bone disease.