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.

Precision of fit of implant-supported screw-retained 10-unit computer-aided-designed and computer-aided-manufactured frameworks made from zirconium dioxide and titanium: an in vitro study

OBJECTIVE To analyze the precision of fit of implant-supported screw-retained computer-aided-designed and computer-aided-manufactured (CAD/CAM) zirconium dioxide (ZrO) frameworks. MATERIALS AND METHODS Computer-aided-designed and computer-aided-manufactured ZrO frameworks (NobelProcera) for a screw-retained 10-unit implant-supported reconstruction on six implants (FDI positions 15, 13, 11, 21, 23, 25) were fabricated using a laser (ZrO-L, N = 6) and a mechanical scanner (ZrO-M, N = 5) for digitizing the implant platform and the cuspid-supporting framework resin pattern. Laser-scanned CAD/CAM titanium (TIT-L, N = 6) and cast CoCrW-alloy frameworks (Cast, N = 5) fabricated on the same model and designed similar to the ZrO frameworks were the control. The one-screw test (implant 25 screw-retained) was applied to assess the vertical microgap between implant and framework platform with a scanning electron microscope. The mean microgap was calculated from approximal and buccal values. Statistical comparison was performed with non-parametric tests. RESULTS No statistically significant pairwise difference was observed between the relative effects of vertical microgap between ZrO-L (median 14 μm; 95% CI 10-26 μm), ZrO-M (18 μm; 12-27 μm) and TIT-L (15 μm; 6-18 μm), whereas the values of Cast (236 μm; 181-301 μm) were significantly higher (P < 0.001) than the three CAD/CAM groups. A monotonous trend of increasing values from implant 23 to 15 was observed in all groups (ZrO-L, ZrO-M and Cast P < 0.001, TIT-L P = 0.044). CONCLUSIONS Optical and tactile scanners with CAD/CAM technology allow for the fabrication of highly accurate long-span screw-retained ZrO implant-reconstructions. Titanium frameworks showed the most consistent precision. Fit of the cast alloy frameworks was clinically inacceptable.

Chemical compositions of solid particles present in the Greenland NEEM ice core over the last 110,000 years

This study reports the chemical composition of particles present along Greenland’s North Greenland Eemian Ice Drilling (NEEM) ice core, back to 110,000 years before present. Insoluble and soluble particles larger than 0.45 μm were extracted from the ice core by ice sublimation, and their chemical composition was analyzed using scanning electron microscope and energy dispersive X-ray spectroscopy and micro-Raman spectroscopy. We show that the dominant insoluble components are silicates, whereas NaCl, Na₂SO₄, CaSO ₄, and CaCO₃ represent major soluble salts. For the first time, particles of CaMg(CO₃)₂ and Ca(NO₃)₂ 4H₂O are identified in a Greenland ice core. The chemical speciation of salts varies with past climatic conditions. Whereas the fraction of Na salts (NaCl + Na₂SO₄) exceeds that of Ca salts (CaSO₄+ CaCO₃) during the Holocene (0.6–11.7 kyr B.P.), the two fractions are similar during the Bølling-Allerød period (12.9–14.6 kyr B.P.). During cold climate such as over the Younger Dryas (12.0–12.6 kyr B.P.) and the Last Glacial Maximum (15.0–26.9 kyr B.P.), the fraction of Ca salts exceeds that of Na salts, showing that the most abundant ion generally controls the salt budget in each period. High-resolution analyses reveal changing particle compositions: those in Holocene ice show seasonal changes, and those in LGM ice show a difference between cloudy bands and clear layers, which again can be largely explained by the availability of ionic components in the atmospheric aerosol body of air masses reaching Greenland.

Evaluation of the Morphological Characteristics of Laser-Irradiated Dentin

OBJECTIVE The aim of this study was to investigate the effect of different energy settings of Er:YAG laser irradiation on dentin surface morphology with respect to the number of opened dentinal tubules. BACKGROUND DATA An ideally prepared dentin surface with opened dentinal tubules is a prerequisite for adhesive fixation. No study, however, has yet compared the numbers of opened dentinal tubules with regard to statistical differences. METHODS Conventional preparations using a bur with or without additional acid etching acted as control groups. Dentin specimens were prepared from human third molars and randomly divided into eight groups according to the energy settings of the laser (1, 1.5, 4, 6, 7.5, and 8 W) and two controls (bur and bur plus acid etching). After surface preparation, dentin surfaces were analyzed with a scanning electron microscope, and the number of opened dentinal tubules in a defined area was counted. RESULTS The control groups showed smooth surfaces with (bur plus acid etching) and without opened dentinal tubules (bur), whereas all laser-irradiated surfaces showed rough surfaces. Using the energy setting of 4 W resulted in significantly more opened dentinal tubules than the conventional preparation technique using the bur with additional acid etching. In contrast, the energy setting of 8 W showed significantly fewer opened dentinal tubules, and also exhibited signs of thermal damage. CONCLUSIONS The Er:YAG laser with an energy setting of 4 W generates a dentin surface with opened dentinal tubules, a prerequisite for adhesive fixation.

CAD/CAM fabrication accuracy of long- vs. short-span implant-supported FDPs

OBJECTIVE To compare the precision of fit of long-span vs. short-span implant-supported screw-retained fixed dental prostheses (FDPs) made from computer-aided-design/computer-aided-manufactured (CAD/CAM) titanium and veneered with ceramic. The null hypothesis was that there is no difference in the vertical microgap between long-span and short-span FDPs. MATERIALS AND METHODS CAD/CAM titanium frameworks for an implant-supported maxillary FDP on implants with a flat platform were fabricated on one single master cast. Group A consisted of six 10-unit FDPs connected to six implants (FDI positions 15, 13, 11, 21, 23, 25) and group B of six 5-unit FDPs (three implants, FDI positions 21, 23, 25). The CAD/CAM system from Biodenta Swiss AG (Berneck, Switzerland) was used for digitizing (laser scanner) the master cast and anatomical CAD of each framework separately. The frameworks were milled (CAM) from a titanium grade V monobloc and veneered with porcelain. Median vertical distance between implant and FDP platforms from the non-tightened implants (one-screw test on implant 25) was calculated from mesial, buccal, and distal scanning electron microscope measurements. RESULTS All measurements showed values <40 μm. Total median vertical microgaps were 23 μm (range 2-38 μm) for group A and 7 μm (4-24 μm) for group B. The difference between the groups was statistically significant at implant 21 (P = 0.002; 97.5% CI -27.3 to -4.9) and insignificant at implant 23 (P = 0.093; -3.9 to 1.0). CONCLUSIONS CAD/CAM fabrication including laboratory scanning and porcelain firing was highly precise and reproducible for all long- and short-span FDPs. While all FDPs showed clinically acceptable values, the short-span FDPs were statistically more precise at the 5-unit span distance.