The influence of yield surface shape and damage in the depth-dependent response of bone tissue to nanoindentation using spherical and Berkovich indenters

Prevention and treatment of osteoporosis rely on understanding of the micromechanical behaviour of bone and its influence on fracture toughness and cell-mediated adaptation processes. Postyield properties may be assessed by nonlinear finite element simulations of nanoindentation using elastoplastic and damage models. This computational study aims at determining the influence of yield surface shape and damage on the depth-dependent response of bone to nanoindentation using spherical and conical tips. Yield surface shape and damage 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 is well described by multilinear regressions for both tip shapes. For conical tips, indentation depth was not statistically significant (p<0.0001). For spherical tips, damage was not a significant parameter (p<0.0001). The gained knowledge can be used for developing an inverse method for identification of postelastic properties of bone from nanoindentation.

Three-dimensional surface reconstruction within noncontact diffuse optical tomography using structured light

A main field in biomedical optics research is diffuse optical tomography, where intensity variations of the transmitted light traversing through tissue are detected. Mathematical models and reconstruction algorithms based on finite element methods and Monte Carlo simulations describe the light transport inside the tissue and determine differences in absorption and scattering coefficients. Precise knowledge of the sample's surface shape and orientation is required to provide boundary conditions for these techniques. We propose an integrated method based on structured light three-dimensional (3-D) scanning that provides detailed surface information of the object, which is usable for volume mesh creation and allows the normalization of the intensity dispersion between surface and camera. The experimental setup is complemented by polarization difference imaging to avoid overlaying byproducts caused by inter-reflections and multiple scattering in semitransparent tissue.

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.

Size and shape of the lunate surface in different types of pincer impingement: theoretical implications for surgical therapy.

OBJECTIVE Acetabular rim trimming is indicated in pincer hips with an oversized lunate surface but could result in a critically decreased size of the lunate surface in pincer hips with acetabular malorientation. There is a lack of detailed three-dimensional anatomy of lunate surface in pincer hips. Therefore, we questioned how does (1) size and (2) shape of the lunate surface differ among hips with different types of pincer impingement? METHOD We retrospectively compared size and shape of the lunate surface between acetabular retroversion (48 hips), deep acetabulum (34 hips), protrusio acetabuli (seven hips), normal acetabuli (30 hips), and hip dysplasia (45 hips). Using magnetic resonance imaging (MRI) arthrography with radial slices we measured size in percentage of the femoral head coverage and shape using the outer (inner) center-edge angles and width of lunate surface. RESULTS Hips with retroversion had a decreased size and deep hips had normal size of the lunate surface. Both had a normal shape of the outer acetabular rim. Protrusio hips had an increased size and a prominent outer acetabular rim. In all three types of pincer hips the acetabular fossa was increased. CONCLUSION Size and shape of the lunate surface differs substantially among different types of pincer impingement. In contrast to hips with protrusio acetabuli, retroverted and deep hips do not have an increased size of the lunate surface. Acetabular rim trimming in retroverted and deep hips should be performed with caution. Based on our results, acetabular reorientation would theoretically be the treatment of choice in retroverted hips.

Validation of statistical shape model based reconstruction of the proximal femur - A morphology study

Seventeen bones (sixteen cadaveric bones and one plastic bone) were used to validate a method for reconstructing a surface model of the proximal femur from 2D X-ray radiographs and a statistical shape model that was constructed from thirty training surface models. Unlike previously introduced validation studies, where surface-based distance errors were used to evaluate the reconstruction accuracy, here we propose to use errors measured based on clinically relevant morphometric parameters. For this purpose, a program was developed to robustly extract those morphometric parameters from the thirty training surface models (training population), from the seventeen surface models reconstructed from X-ray radiographs, and from the seventeen ground truth surface models obtained either by a CT-scan reconstruction method or by a laser-scan reconstruction method. A statistical analysis was then performed to classify the seventeen test bones into two categories: normal cases and outliers. This classification step depends on the measured parameters of the particular test bone. In case all parameters of a test bone were covered by the training population's parameter ranges, this bone is classified as normal bone, otherwise as outlier bone. Our experimental results showed that statistically there was no significant difference between the morphometric parameters extracted from the reconstructed surface models of the normal cases and those extracted from the reconstructed surface models of the outliers. Therefore, our statistical shape model based reconstruction technique can be used to reconstruct not only the surface model of a normal bone but also that of an outlier bone.

Wetting and spreading of a surfactant film on solid particles: influence of sharp edges and surface irregularities

In addition to particle size and surface chemistry, the shape of particles plays an important role in their wetting and displacement by the surfactant film in the lung. The role of particle shape was the subject of our investigations using a model system consisting of a modified Langmuir-Wilhelmy surface balance. We measured the influence of sharp edges (lines) and other highly curved surfaces, including sharp corners or spikes, of different particles on the spreading of a dipalmitoylphosphatidyl (DPPC) film. The edges of cylindrical sapphire plates (circular curved edges, 1.65 mm radius) were wetted at a surface tension of 10.7 mJ/m2 (standard error (SE) = 0.45, n = 20) compared with that of 13.8 mJ/m2 (SE = 0.20, n = 20) for cubic sapphire plates (straight linear edges, edge length 3 mm) (p < 0.05). The top surfaces of the sapphire plates (cubic and cylindrical) were wetted at 8.4 mJ/m2 (SE = 0.54, n = 20) and 9.1 mJ/m2 (SE = 0.50, n = 20), respectively, but the difference was not significant (p > 0.05). The surfaces of the plates showed significantly higher resistance to spreading compared to that of the edges, as substantially lower surface tensions were required to initiate wetting (p < 0.05). Similar results were found for talc particles, were the edges of macro- and microcrystalline particles were wetted at 7.2 mJ/m2 (SE = 0.52, n = 20) and 8.2 mJ/m2 (SE = 0.30, n = 20) (p > 0.05), respectively, whereas the surfaces were wetted at 3.8 mJ/m2 (SE = 0.89, n = 20) and 5.8 mJ/m2 (SE = 0.52, n = 20) (p < 0.05), respectively. Further experiments with pollen of malvaceae and maize (spiky and fine knobbly surfaces) were wetted at 10.0 mJ/m2 (SE = 0.52, n = 10) and 22.75 mJ/m2 (SE = 0.81, n = 10), respectively (p < 0.05). These results show that resistance to spreading of a DPPC film on various surfaces is dependent on the extent these surfaces are curved. This is seen with cubic sapphire plates which have at their corners a radius of curvature of about 0.75 microm, spiky malvaceae pollen with an even smaller radius on top of their spikes, or talc with various highly curved surfaces. These highly curved surfaces resisted wetting by the DPPC film to a higher degree than more moderately curved surfaces such as those of cylindrical sapphire plates, maize pollens, or polystyrene spheres, which have a surface free energy similar to that of talc but a smooth surface. The macroscopic plane surfaces of the particles demonstrated the greatest resistance to spreading. This was explained by the extremely fine grooves in the nanometer range, as revealed by electron microscopy. In summary, to understand the effects of airborne particles retained on the surfaces of the respiratory tract, and ultimately their pathological potential, not only the particle size and surface chemistry but also the particle shape should be taken in consideration.

Biomechanical evaluation of the interfacial strength of a chemically modified sandblasted and acid-etched titanium surface

The functional capacity of osseointegrated dental implants to bear load is largely dependent on the quality of the interface between the bone and implant. Sandblasted and acid-etched (SLA) surfaces have been previously shown to enhance bone apposition. In this study, the SLA has been compared with a chemically modified SLA (modSLA) surface. The increased wettability of the modSLA surface in a protein solution was verified by dynamic contact angle analysis. Using a well-established animal model with a split-mouth experimental design, implant removal torque testing was performed to determine the biomechanical properties of the bone-implant interface. All implants had an identical cylindrical shape with a standard thread configuration. Removal torque testing was performed after 2, 4, and 8 weeks of bone healing (n = 9 animals per healing period, three implants per surface type per animal) to evaluate the interfacial shear strength of each surface type. Results showed that the modSLA surface was more effective in enhancing the interfacial shear strength of implants in comparison with the conventional SLA surface during early stages of bone healing. Removal torque values of the modSLA-surfaced implants were 8-21% higher than those of the SLA implants (p = 0.003). The mean removal torque values for the modSLA implants were 1.485 N m at 2 weeks, 1.709 N m at 4 weeks, and 1.345 N m at 8 weeks; and correspondingly, 1.231 N m, 1.585 N m, and 1.143 N m for the SLA implants. The bone-implant interfacial stiffness calculated from the torque-rotation curve was on average 9-14% higher for the modSLA implants when compared with the SLA implants (p = 0.038). It can be concluded that the modSLA surface achieves a better bone anchorage during early stages of bone healing than the SLA surface; chemical modification of the standard SLA surface likely enhances bone apposition and this has a beneficial effect on the interfacial shear strength.

Reconstruction of patient-specific 3D bone surface from 2D calibrated fluoroscopic images and point distribution model

Reconstruction of patient-specific 3D bone surface from 2D calibrated fluoroscopic images and a point distribution model is discussed. We present a 2D/3D reconstruction scheme combining statistical extrapolation and regularized shape deformation with an iterative image-to-model correspondence establishing algorithm, and show its application to reconstruct the surface of proximal femur. The image-to-model correspondence is established using a non-rigid 2D point matching process, which iteratively uses a symmetric injective nearest-neighbor mapping operator and 2D thin-plate splines based deformation to find a fraction of best matched 2D point pairs between features detected from the fluoroscopic images and those extracted from the 3D model. The obtained 2D point pairs are then used to set up a set of 3D point pairs such that we turn a 2D/3D reconstruction problem to a 3D/3D one. We designed and conducted experiments on 11 cadaveric femurs to validate the present reconstruction scheme. An average mean reconstruction error of 1.2 mm was found when two fluoroscopic images were used for each bone. It decreased to 1.0 mm when three fluoroscopic images were used.

Cell shape-dependent early responses of fibroblasts to cyclic strain

Randomly spread fibroblasts on fibronectin-coated elastomeric membranes respond to cyclic strain by a varying degree of focal adhesion assembly and actin reorganization. We speculated that the individual shape of the cells, which is linked to cytoskeletal structure and pre-stress, might tune these integrin-dependent mechanotransduction events. To this aim, fibronectin circles, squares and rectangles of identical surface area (2000μm(2)) were micro-contact printed onto elastomeric substrates. Fibroblasts plated on these patterns occupied the corresponding shapes. Cyclic 10% equibiaxial strain was applied to patterned cells for 30min, and changes in cytoskeleton and cell-matrix adhesions were quantified after fluorescence staining. After strain, megakaryocytic leukemia-1 protein translocated to the nucleus in most cells, indicating efficient RhoA activation independently of cell shape. However, circular and square cells (with radial symmetry) showed a significantly greater increase in the number of actin stress fibers and vinculin-positive focal adhesions after cyclic strain than rectangular (bipolar) cells of identical size. Conversely, cyclic strain induced larger changes in pY397-FAK positive focal complexes and zyxin relocation from focal adhesions to stress fibers in bipolar compared to symmetric cells. Thus, radially symmetric cells responded to cyclic strain with a larger increase in assembly, whereas bipolar cells reacted with more pronounced reorganization of actin stress fibers and matrix contacts. We conclude that integrin-mediated responses to external mechanical strain are differentially modulated in cells that have the same spreading area but different geometries, and do not only depend on mere cell size.

Reflection of solar wind hydrogen from the lunar surface

The solar wind continuously flows out from the Sun and directly interacts with the surfaces of dust and airless planetary bodies throughout the solar system. A significant fraction of solar wind ions reflect from an object's surface as energetic neutral atoms (ENAs). ENA emission from the Moon was first observed during commissioning of the Interstellar Boundary Explorer (IBEX) mission on 3 December 2008. We present the analysis of 10 additional IBEX observations of the Moon while it was illuminated by the solar wind. For the viewing geometry and energy range (> 250 eV) of the IBEX-Hi ENA imager, we find that the spectral shape of the ENA emission from the Moon is well-represented by a linearly decreasing flux with increasing energy. The fraction of the incident solar wind ions reflected as ENAs, which is the ENA albedo and defined quantitatively as the ENA reflection coefficient RN, depends on the incident solar wind speed, ranging from ~0.2 for slow solar wind to ~0.08 for fast solar wind. The average energy per incident solar wind ion that is reflected to space is 30 eV for slow solar wind and 45 eV for fast solar wind. Once ionized, these ENAs can become pickup ions in the solar wind with a unique spectral signature that reaches 3vSW. These results apply beyond the solar system; the reflection process heats plasmas that have significant bulk flow relative to interstellar dust and cools plasmas having no net bulk flow relative to the dust.

Comparison of partial least squares regression and principal component regression for pelvic shape prediction.

This paper studied two different regression techniques for pelvic shape prediction, i.e., the partial least square regression (PLSR) and the principal component regression (PCR). Three different predictors such as surface landmarks, morphological parameters, or surface models of neighboring structures were used in a cross-validation study to predict the pelvic shape. Results obtained from applying these two different regression techniques were compared to the population mean model. In almost all the prediction experiments, both regression techniques unanimously generated better results than the population mean model, while the difference on prediction accuracy between these two regression methods is not statistically significant (α=0.01).

Quantitative analysis of imprint shape and its relation to mechanical properties measured by microindentation in bone

Microindentation in bone is a micromechanical testing technique routinely used to extract material properties related to bone quality. As the analysis of microindentation data is based on assumptions about the contact between sample and surface, the aim of this study was 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 topology was measured by atomic force microscopy. Statistical shape modeling of the residual imprint allowed to define a mean shape and to describe the variability in terms of 21 principal components related to imprint depth, surface curvature and roughness. The indentation profile of bone was found to be highly consistent and free of any pile up while differing mostly by depth between species and direction. A few of the topological parameters, in particular depth, showed significant but rather weak and inconsistent correlations to variations in mechanical properties. The mechanical response of bone as well as the residual imprint shape was highly consistent within each category. We could thus verify that bone is rather homogeneous in its micromechanical properties and that indentation results are not strongly influenced by small deviations from an ideally flat surface.

How to be in a good shape? The influence of clone morphology on cell competition

Cell competition is a conserved mechanism where slow proliferating cells (so called losers) are eliminated by faster proliferating neighbors (so called winners) through apoptosis.(1) It is an important process which prevents developmental malformations and maintains tissue fitness in aging adults.(2) Recently, we have shown that the probability of elimination of loser cells correlates with the surface of contact between losers and winners in Myc-induced competition.(3) Moreover, we have characterized an active mechanism that increases the surface of contact between losers and winners, hence accelerating the elimination of loser cells. This is the first indication that cell shape and mechanics can influence cell competition. Here, we will discuss the consequence of the relationship between shape and competition, as well as the relevance of this model for other modes of competition.