Computational and experimental methodology for site-matched investigations of the influence of mineral mass fraction and collagen orientation on the axial indentation modulus of lamellar bone

Relationships between mineralization, collagen orientation and indentation modulus were investigated in bone structural units from the mid-shaft of human femora using a site-matched design. Mineral mass fraction, collagen fibril angle and indentation moduli were measured in registered anatomical sites using backscattered electron imaging, polarized light microscopy and nano-indentation, respectively. Theoretical indentation moduli were calculated with a homogenization model from the quantified mineral densities and mean collagen fibril orientations. The average indentation moduli predicted based on local mineralization and collagen fibers arrangement were not significantly different from the average measured experimentally with nanoindentation (p=0.9). Surprisingly, no substantial correlation of the measured indentation moduli with tissue mineralization and/or collagen fiber arrangement was found. Nano-porosity, micro-damage, collagen cross-links, non-collagenous proteins or other parameters affect the indentation measurements. Additional testing/simulation methods need to be considered to properly understand the variability of indentation moduli, beyond the mineralization and collagen arrangement in bone structural units.

Measuring the mechanical properties of plant cells by combining micro-indentation with osmotic treatments

Growth in plants results from the interaction between genetic and signalling networks and the mechanical properties of cells and tissues. There has been a recent resurgence in research directed at understanding the mechanical aspects of growth, and their feedback on genetic regulation. This has been driven in part by the development of new micro-indentation techniques to measure the mechanical properties of plant cells in vivo. However, the interpretation of indentation experiments remains a challenge, since the force measures results from a combination of turgor pressure, cell wall stiffness, and cell and indenter geometry. In order to interpret the measurements, an accurate mechanical model of the experiment is required. Here, we used a plant cell system with a simple geometry, Nicotiana tabacum Bright Yellow-2 (BY-2) cells, to examine the sensitivity of micro-indentation to a variety of mechanical and experimental parameters. Using a finite-element mechanical model, we found that, for indentations of a few microns on turgid cells, the measurements were mostly sensitive to turgor pressure and the radius of the cell, and not to the exact indenter shape or elastic properties of the cell wall. By complementing indentation experiments with osmotic experiments to measure the elastic strain in turgid cells, we could fit the model to both turgor pressure and cell wall elasticity. This allowed us to interpret apparent stiffness values in terms of meaningful physical parameters that are relevant for morphogenesis.

Thickness of softened human enamel removed by toothbrush abrasion: an in vitro study

The aim of the study was to assess the thickness of softened enamel removed by toothbrushing. Human enamel specimens were indented with a Knoop diamond. Softening was performed with citric acid or orange juice. The specimens were brushed in a brushing machine with a manual soft toothbrush in toothpaste slurry or in artificial saliva. Enamel loss was calculated from the change in indentation depth of the same indent before and after abrasion. Mean surface losses (95% confidence interval) were recorded in treatment groups (in nanometers): (1) citric acid, abrasion with slurry = 339 (280-398); (2) citric acid, abrasion with artificial saliva = 16 (5-27); (3) orange juice, abrasion with slurry = 268 (233-303); (4) orange juice, abrasion with artificial saliva = 14 (5-23); (5) no softening, abrasion with slurry = 28 (10-46). The calculated thickness of the softened enamel varied between 254 and 323 nm, depending on the acid used.

DensiProbe Spine: a novel instrument for intraoperative measurement of bone density in transpedicular screw fixation

STUDY DESIGN.: Cadaver study. OBJECTIVE.: To determine bone strength in vertebrae by measuring peak breakaway torque or indentation force using custom-made pedicle probes. SUMMARY OF BACKGROUND DATA.: Screw performance in dorsal spinal instrumentation is dependent on bone quality of the vertebral body. To date no intraoperative measuring device to validate bone strength is available. Destructive testing may predict bone strength in transpedicular instrumentations in osteoporotic vertebrae. Insertional torque measurements showed varying results. METHODS.: Ten human cadaveric vertebrae were evaluated for bone mineral density (BMD) measurements by quantitative computed tomography. Peak torque and indentation force of custom-made probes as a measure for mechanical bone strength were assessed via a transpedicular approach. The results were correlated to regional BMD and to biomechanical load testing after pedicle screw implementation. RESULTS.: Both methods generated a positive correlation to failure load of the respective vertebrae. The correlation of peak breakaway torque to failure load was r = 0.959 (P = 0.003), therewith distinctly higher than the correlation of indentation force to failure load, which was r = 0.690 (P = 0.040). In predicting regional BMD, measurement of peak torque also performed better than that of indentation force (r = 0.897 [P = 0.002] vs. r = 0.777 [P = 0.017]). CONCLUSION.: Transpedicular measurement of peak breakaway torque is technically feasible and predicts reliable local bone strength and implant failure for dorsal spinal instrumentations in this experimental setting.

Influence of Surface Roughness on Mechanical Properties of Two Computer-aided Design/Computer-aided Manufacturing (CAD/CAM) Ceramic Materials

SUMMARY The aim of this study was to evaluate the influence of surface roughness on surface hardness (Vickers; VHN), elastic modulus (EM), and flexural strength (FLS) of two computer-aided design/computer-aided manufacturing (CAD/CAM) ceramic materials. One hundred sixty-two samples of VITABLOCS Mark II (VMII) and 162 samples of IPS Empress CAD (IPS) were ground according to six standardized protocols producing decreasing surface roughnesses (n=27/group): grinding with 1) silicon carbide (SiC) paper #80, 2) SiC paper #120, 3) SiC paper #220, 4) SiC paper #320, 5) SiC paper #500, and 6) SiC paper #1000. Surface roughness (Ra/Rz) was measured with a surface roughness meter, VHN and EM with a hardness indentation device, and FLS with a three-point bending test. To test for a correlation between surface roughness (Ra/Rz) and VHN, EM, or FLS, Spearman rank correlation coefficients were calculated. The decrease in surface roughness led to an increase in VHN from (VMII/IPS; medians) 263.7/256.5 VHN to 646.8/601.5 VHN, an increase in EM from 45.4/41.0 GPa to 66.8/58.4 GPa, and an increase in FLS from 49.5/44.3 MPa to 73.0/97.2 MPa. For both ceramic materials, Spearman rank correlation coefficients showed a strong negative correlation between surface roughness (Ra/Rz) and VHN or EM and a moderate negative correlation between Ra/Rz and FLS. In conclusion, a decrease in surface roughness generally improved the mechanical properties of the CAD/CAM ceramic materials tested. However, FLS was less influenced by surface roughness than expected.

Controlled toothbrush abrasion of softened human enamel

The aim of this in vitro study was to compare toothbrush abrasion of softened enamel after brushing with two (soft and hard) toothbrushes. One hundred and fifty-six human enamel specimens were indented with a Knoop diamond. Salivary pellicle was formed in vitro over a period of 3 h. Erosive lesions were produced by means of 1% citric acid. A force-measuring device allowed a controlled toothbrushing force of 1.5 N. The specimens were brushed either in toothpaste slurry or with toothpaste in artificial saliva for 15 s. Enamel loss was calculated from the change in indentation depth of the same indent before and after abrasion. Mean surface losses (95% CI) were recorded in ten treatment groups: (1) soft toothbrush only [28 (17-39) nm]; (2) hard toothbrush only [25 (16-34) nm]; (3) soft toothbrush in Sensodyne MultiCare slurry [46 (27-65) nm]; (4) hard toothbrush in Sensodyne MultiCare slurry [45 (24-66) nm]; (5) soft toothbrush in Colgate sensation white slurry [71 (55-87) nm]; (6) hard toothbrush in Colgate sensation white slurry [85 (60-110) nm]; (7) soft toothbrush with Sensodyne MultiCare [48 (39-57) nm]; (8) hard toothbrush with Sensodyne MultiCare [40 (29-51) nm]; (9) soft toothbrush with Colgate sensation white [51 (37-65) nm]; (10) hard toothbrush with Colgate sensation white [52 (36-68) nm]. Neither soft nor hard toothbrushes produced significantly different toothbrush abrasion of softened human enamel in this model (p > 0.05).

Light curing through glass ceramics: effect of curing mode on micromechanical properties of dual-curing resin cements

OBJECTIVES The aim of this study was to investigate micromechanical properties of five dual-curing resin cements after different curing modes including light curing through glass ceramic materials. MATERIALS AND METHODS Vickers hardness (VH) and indentation modulus (Y HU) of Panavia F2.0, RelyX Unicem 2 Automix, SpeedCEM, BisCem, and BeautiCem SA were measured after 1 week of storage (37 °C, 100 % humidity). The resin cements were tested following self-curing or light curing with the second-generation light-emitting diode (LED) curing unit Elipar FreeLight 2 in Standard Mode (1,545 mW/cm(2)) or with the third-generation LED curing unit VALO in High Power Mode (1,869 mW/cm(2)) or in XtraPower Mode (3,505 mW/cm(2)). Light curing was performed directly or through glass ceramic discs of 1.5 or 3 mm thickness of IPS Empress CAD or IPS e.max CAD. VH and Y HU were analysed with Kruskal-Wallis tests followed by pairwise Wilcoxon rank sum tests (α = 0.05). RESULTS RelyX Unicem 2 Automix resulted in the highest VH and Y HU followed by BeautiCem SA, BisCem, SpeedCEM, and finally Panavia F2.0. Self-curing of RelyX Unicem 2 Automix and SpeedCEM lowered VH and Y HU compared to light curing whereas self-curing of Panavia F2.0, BisCem, and BeautiCem SA led to similar or significantly higher VH and Y HU compared to light curing. Generally, direct light curing resulted in similar or lower VH and Y HU compared to light curing through 1.5-mm-thick ceramic discs. Light curing through 3-mm-thick discs of IPS e.max CAD generally reduced VH and Y HU for all resin cements except SpeedCEM, which was the least affected by light curing through ceramic discs. CONCLUSIONS The resin cements responded heterogeneously to changes in curing mode. The applied irradiances and light curing times adequately cured the resin cements even through 1.5-mm-thick ceramic discs. CLINICAL RELEVANCE When light curing resin cements through thick glass ceramic restorations, clinicians should consider to prolong the light curing times even with LED curing units providing high irradiances.

An anisotropic elastic-viscoplastic damage model for bone tissue

A new anisotropic elastic-viscoplastic damage constitutive model for bone is proposed using an eccentric elliptical yield criterion and nonlinear isotropic hardening. A micromechanics-based multiscale homogenization scheme proposed by Reisinger et al. is used to obtain the effective elastic properties of lamellar bone. The dissipative process in bone is modeled as viscoplastic deformation coupled to damage. The model is based on an orthotropic ecuntric elliptical criterion in stress space. In order to simplify material identification, an eccentric elliptical isotropic yield surface was defined in strain space, which is transformed to a stress-based criterion by means of the damaged compliance tensor. Viscoplasticity is implemented by means of the continuous Perzyna formulation. Damage is modeled by a scalar function of the accumulated plastic strain D(κ) , reducing all element s of the stiffness matrix. A polynomial flow rule is proposed in order to capture the rate-dependent post-yield behavior of lamellar bone. A numerical algorithm to perform the back projection on the rate-dependent yield surface has been developed and implemented in the commercial finite element solver Abaqus/Standard as a user subroutine UMAT. A consistent tangent operator has been derived and implemented in order to ensure quadratic convergence. Correct implementation of the algorithm, convergence, and accuracy of the tangent operator was tested by means of strain- and stress-based single element tests. A finite element simulation of nano- indentation in lamellar bone was finally performed in order to show the abilities of the newly developed constitutive model.

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.

Tissue properties of the human vertebral body sub-structures evaluated by means of microindentation

Purpose The better understanding of vertebral mechanical properties can help to improve the diagnosis of vertebral fractures. As the bone mechanical competence depends not only from bone mineral density (BMD) but also from bone quality, the goal of the present study was to investigate the anisotropic indentation moduli of the different sub-structures of the healthy human vertebral body and spondylophytes by means of microindentation. Methods Six human vertebral bodies and five osteophytes (spondylophytes) were collected and prepared for microindentation test. In particular, indentations were performed on bone structural units of the cortical shell (along axial, circumferential and radial directions), of the endplates (along the anterio-posterior and lateral directions), of the trabecular bone (along the axial and transverse directions) and of the spondylophytes (along the axial direction). A total of 3164 indentations down to a maximum depth of 2.5 µm were performed and the indentation modulus was computed for each measurement. Results The cortical shell showed an orthotropic behavior (indentation modulus, Ei, higher if measured along the axial direction, 14.6±2.8 GPa, compared to the circumferential one, 12.3±3.5 GPa, and radial one, 8.3±3.1 GPa). Moreover, the cortical endplates (similar Ei along the antero-posterior, 13.0±2.9 GPa, and along the lateral, 12.0±3.0 GPa, directions) and the trabecular bone (Ei= 13.7±3.4 GPa along the axial direction versus Ei=10.9±3.7 GPa along the transverse one) showed transversal isotropy behavior. Furthermore, the spondylophytes showed the lower mechanical properties measured along the axial direction (Ei=10.5±3.3 GPa). Conclusions The original results presented in this study improve our understanding of vertebral biomechanics and can be helpful to define the material properties of the vertebral substructures in computational models such as FE analysis.

Experimental validation of a mean field model of mineralized collagen fiber arrays at two levels of hierarchy

In the course of this study, stiffness of a fibril array of mineralized collagen fibrils modeled with a mean field method was validated experimentally at site-matched two levels of tissue hierarchy using mineralized turkey leg tendons (MTLT). The applied modeling approaches allowed to model the properties of this unidirectional tissue from nanoscale (mineralized collagen fibrils) to macroscale (mineralized tendon). At the microlevel, the indentation moduli obtained with a mean field homogenization scheme were compared to the experimental ones obtained with microindentation. At the macrolevel, the macroscopic stiffness predicted with micro finite element (μFE) models was compared to the experimental stiffness measured with uniaxial tensile tests. Elastic properties of the elements in μFE models were injected from the mean field model or two-directional microindentations. Quantitatively, the indentation moduli can be properly predicted with the mean-field models. Local stiffness trends within specific tissue morphologies are very weak, suggesting additional factors responsible for the stiffness variations. At macrolevel, the μFE models underestimate the macroscopic stiffness, as compared to tensile tests, but the correlations are strong.

Surface Roughness and Microhardness of Two Recent CAD/CAM-Materials After Storage

Objectives: To investigate surface roughness and microhardness of two recent resin-ceramic materials for computer-aided design/computer-aided manufacturing (CAD/CAM) after polishing with three polishing systems. Surface roughness and microhardness were measured immediately after polishing and after six months storage including monthly artificial toothbrushing. Methods: Sixty specimens of Lava Ultimate (3M ESPE) and 60 specimens of VITA ENAMIC (VITA Zahnfabrik) were roughened in a standardized manner and polished with one of three polishing systems (n=20/group): Sof-Lex XT discs (SOFLEX; three-step (medium-superfine); 3M ESPE), VITA Polishing Set Clinical (VITA; two-step; VITA Zahnfabrik), or KENDA Unicus (KENDA; one-step; KENDA Dental). Surface roughness (Ra; μm) was measured with a profilometer and microhardness (Vickers; VHN) with a surface hardness indentation device. Ra and VHN were measured immediately after polishing and after six months storage (tap water, 37°C) including monthly artificial toothbrushing (500 cycles/month, toothpaste RDA ~70). Ra- and VHN-values were analysed with nonparametric ANOVA followed by Wilcoxon rank sum tests (α=0.05). Results: For Lava Ultimate, Ra (mean [standard deviation] before/after storage) remained the same when polished with SOFLEX (0.18 [0.09]/0.19 [0.10]; p=0.18), increased significantly with VITA (1.10 [0.44]/1.27 [0.39]; p=0.0001), and decreased significantly with KENDA (0.35 [0.07]/0.33 [0.08]; p=0.03). VHN (mean [standard deviation] before/after storage) decreased significantly regardless of polishing system (SOFLEX: 134.1 [5.6]/116.4 [3.6], VITA: 138.2 [10.5]/115.4 [5.9], KENDA: 135.1 [6.2]/116.7 [6.3]; all p<0.0001). For VITA ENAMIC, Ra (mean [standard deviation] before/after storage) increased significantly when polished with SOFLEX (0.37 [0.18]/0.41 [0.14]; p=0.01) and remained the same with VITA (1.32 [0.37]/1.31 [0.40]; p=0.58) and with KENDA (0.81 [0.35]/0.78 [0.32]; p=0.21). VHN (mean [standard deviation] before/after storage) remained the same regardless of polishing system (SOFLEX: 284.9 [24.6]/282.4 [31.8], VITA: 284.6 [28.5]/276.4 [25.8], KENDA: 292.6 [26.9]/282.9 [24.3]; p=0.42-1.00). Conclusion: Surface roughness and microhardness of Lava Ultimate was more affected by storage and artificial toothbrushing than was VITA ENAMIC.

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.

Microstructural and mechanical characterization of contemporary lingual orthodontic brackets.

OBJECTIVES To investigate the composition and the microstructural and mechanical characterization of three different types of lingual brackets. MATERIALS AND METHODS Incognito™ (3M Unitek), In-Ovation L (DENTSPLY GAC) and STb™ (Light Lingual System, ORMCO) lingual brackets were studied under the scanning electron microscope employing backscattered electron imaging and their elemental composition was analysed by energy-dispersive X-ray microanalysis. Additionally, Vickers hardness was assessed using a universal hardness-testing machine, and the indentation modulus was measured according to instrumented indentation test. Two-way analysis of variance was conducted employing bracket type and location (base and wing) as discriminating variable. Significant differences among groups were allocated by post hoc Student-Newman-Keuls multiple comparison analysis at 95% level of significance. RESULTS Three different phases were identified for Incognito and In-Ovation L bracket based on mean atomic number contrast. On the contrary, STb did not show mean atomic contrast areas and thus it is recognized as a single phase. Incognito is a one-piece bracket with the same structure in wing and base regions. Incognito consists mainly of noble metals while In-Ovation L and STb show similar formulations of ferrous alloys in wing and base regions. No significant differences were found between ferrous brackets in hardness and modulus values, but there were significant differences between wing and base regions. Incognito illustrated intermediate values with significant differences from base and wing values of ferrous brackets. CONCLUSIONS/IMPLICATIONS Significant differences exist in microstructure, elemental composition, and mechanical properties among the brackets tested; these might have a series of clinical implications during mechanotherapy.