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.

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.

Augmentation of mechanical properties in osteoporotic vertebral bones--a biomechanical investigation of vertebroplasty efficacy with different bone cements

Recent clinical trials have reported favorable early results for transpedicular vertebral cement reinforcement of osteoporotic vertebral insufficiencies. There is, however, a lack of basic data on the application, safety and biomechanical efficacy of materials such as polymethyl-methacrylate (PMMA) and calciumphospate (CaP) cements. The present study analyzed 33 vertebral pairs from five human cadaver spines. Thirty-nine vertebrae were osteoporotic (bone mineral density < 0.75 g/cm2), 27 showed nearly normal values. The cranial vertebra of each pair was augmented with either PMMA (Palacos E-Flow) or experimental brushite cement (EBC), with the caudal vertebra as a control. PMMA and EBC were easy to inject, and vertebral fillings of 20-50% were achieved. The maximal possible filling was inversely correlated to the bone mineral density (BMD) values. Cement extrusion into the spinal canal was observed in 12% of cases. All specimens were subjected to axial compression tests in a displacement-controlled mode. From load-displacement curves, the stiffness, S, and the maximal force before failure, Fmax, were determined. Compared with the native control vertebrae, a statistically significant increase in vertebral stiffness and Fmax was observed by the augmentation. With PMMA the stiffness increased by 174% (P = 0.018) and Fmax by 195% (P = 0.001); the corresponding augmentation with EBC was 120% (P = 0.03) and 113% (P = 0.002). The lower the initial BMD, the more pronounced was the augmentation effect. Both PMMA and EBC augmentation reliably and significantly raised the stiffness and maximal tolerable force until failure in osteoporotic vertebral bodies. In non-porotic specimens, no significant increase was achieved.

Numerical model of the human cornea based on stromal microstructure: identification of mechanical properties for two age groups

The optical quality of the human eye mainly depends on the refractive performance of the cornea. The shape of the cornea is a mechanical balance between intraocular pressure and tissue intrinsic stiffness. Several surgical procedures in ophthalmology alter the biomechanics of the cornea to provoke local or global curvature changes for vision correction. Legitimated by the large number of surgical interventions performed every day, the demand for a deeper understanding of corneal biomechanics is rising to improve the safety of procedures and medical devices. The aim of our work is to propose a numerical model of corneal biomechanics, based on the stromal microstructure. Our novel anisotropic constitutive material law features a probabilistic weighting approach to model collagen fiber distribution as observed on human cornea by Xray scattering analysis (Aghamohammadzadeh et. al., Structure, February 2004). Furthermore, collagen cross-linking was explicitly included in the strain energy function. Results showed that the proposed model is able to successfully reproduce both inflation and extensiometry experimental data (Elsheikh et. al., Curr Eye Res, 2007; Elsheikh et. al., Exp Eye Res, May 2008). In addition, the mechanical properties calculated for patients of different age groups (Group A: 65-79 years; Group B: 80-95 years) demonstrate an increased collagen cross-linking, and a decrease in collagen fiber elasticity from younger to older specimen. These findings correspond to what is known about maturing fibrous biological tissue. Since the presented model can handle different loading situations and includes the anisotropic distribution of collagen fibers, it has the potential to simulate clinical procedures involving nonsymmetrical tissue interventions. In the future, such mechanical model can be used to improve surgical planning and the design of next generation ophthalmic devices.

Variation of the mechanical properties of PMMA to suit osteoporotic cancellous bone

Poly(methyl methacrylate) (PMMA) is by far the most frequently used bone substitute material for vertebroplasty. However, there are serious complications, such as cement leakage and an increased fracture rate of the adjacent vertebral bodies. The latter may be related to the mechanical properties of the augmented segment within the osteoporotic spine. A possible counter-measure is prophylactic augmentation at additional levels, but this aggravates the risk for the patient. Introduction of pores is a possible method to reduce the inherent high stiffness of PMMA. This study investigates the effect of porosity on the mechanical properties of PMMA bone cement. Different fractions of a highly viscous liquid were mixed into the PMMA during preparation. An open-porous material with adjustable mechanical properties resulted after removal of the aqueous phase. Different radiopacifiers were admixed to investigate their suitability for vertebroplasty. The final material was characterized mechanically by compressive testing, microscopically and radiologically. In addition, the monomer release subsequent to hardening was measured by means of gas chromatography. The Young's modulus in compression could be varied between 2800 +/- 70 MPa and 120 +/- 150 MPa, and the compression ultimate strength between 170 +/- 5 MPa and 8 +/- 9 MPa for aqueous fractions ranging between 0 and 50% of volume. Only a slight decrease of the Young's modulus and small changes of ultimate strength were found when the mixing time was increased. An organic hydrophilic and lipophilic radiopacifier led to a higher Young's modulus of the porous material; however, the ultimate strength was not significantly affected by adding different radiopacifiers to the porous cement. The radiopacity was lost after washing the aqueous phase out of the pores. No separation occurred between the aqueous and the PMMA phase during injection into an open porous ceramic material. The monomer released was found to increase for increasing aqueous fractions, but remained comparable in magnitude to standard PMMA. This study demonstrates that a conventional PMMA can be modified to obtain a range of mechanical properties, including those of osteoporotic bone.

Mechanical control of morphogenesis at the shoot apex

Morphogenesis does not just require the correct expression of patterning genes; these genes must induce the precise mechanical changes necessary to produce a new form. Mechanical characterization of plant growth is not new; however, in recent years, new technologies and interdisciplinary collaborations have made it feasible in young tissues such as the shoot apex. Analysis of tissues where active growth and developmental patterning are taking place has revealed biologically significant variability in mechanical properties and has even suggested that mechanical changes in the tissue can feed back to direct morphogenesis. Here, an overview is given of the current understanding of the mechanical dynamics and its influence on cellular and developmental processes in the shoot apex. We are only starting to uncover the mechanical basis of morphogenesis, and many exciting questions remain to be answered.

DXA predictions of human femoral mechanical properties depend on the load configuration

The aim of this study was to evaluate the ability of dual energy X-rays absorptiometry (DXA) areal bone mineral density (aBMD) measured in different regions of the proximal part of the human femur for predicting the mechanical properties of matched proximal femora tested in two different loading configurations. 36 pairs of fresh frozen femora were DXA scanned and tested until failure in two loading configurations: a fall on the side or a one-legged standing. The ability of the DXA output from four different regions of the proximal femur in predicting the femoral mechanical properties was measured and compared for the two loading scenarios. The femoral neck DXA BMD was best correlated to the femoral ultimate force for both configurations and predicted significantly better femoral failure load (R2=0.80 vs. R2=0.66, P<0.05) when simulating a side than when simulating a standing configuration. Conversely, the work to failure was predicted similarly for both loading configurations (R2=0.54 vs. R2=0.53, P>0.05). Therefore, neck BMD should be considered as one of the key factors for discriminating femoral fracture risk in vivo. Moreover, the better predictive ability of neck BMD for femoral strength if tested in a fall compared to a one-legged stance configuration suggests that DXA's clinical relevance may not be as high for spontaneous femoral fractures than for fractures associated to a fall.

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.

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.