Insight into differences in nanoindentation properties of bone

Abstract

Nanoindentation provides the ideal framework to determine mechanical properties of bone at the tissue scale without being affected by the size, shape, and porosity of the bone. However, the values of tissue level mechanical properties vary significantly between studies. Since the differences in the bone sample, hydration state, and test parameters complicate direct comparisons across the various studies, these discrepancies in values cannot be compared directly. The objective of the current study is to evaluate and compare mechanical properties of the same bones using a broad range of testing parameters. Wild type C56BL6 mice tibiae were embedded following different processes and tested in dry and rehydrated conditions. Spherical and Berkovich indenter probes were used, and data analysis was considered within the elasto-plastic (Oliver-Pharr), viscoelastic and visco-elastic-plastic frameworks. The mean values of plane strain modulus varied significantly depending on the hydration state, probe geometry and analysis method. Indentations in dry bone analyzed using a visco-elastic-plastic approach gave values of 34 GPa. After rehydrating the same bones and indenting them with a spherical tip and utilizing a viscoelastic analysis, the mean modulus value was 4 GPa, nearly an order of magnitude smaller. Results suggest that the hydration state, probe geometry and the limitations and assumptions of each analysis method influence significantly the measured mechanical properties. This is the first time that such a systematic study has been carried out and it has been concluded that the discrepancies in the mechanical properties of bone measured by nanoindentation found in the literature should not be attributed only to the differences between the bones themselves, but also to the testing and analysis protocols.

Potential for estimation of Young's modulus based on computed tomography numbers in bone: A validation study using a nano-indentation test on murine maxilla

“…Young's modulus, as measured by NI test in this study, was in the range of 13.32 GPa to 38.15 GPa, which was similar to or slightly higher than the moduli determined in previous NI studies that measured the tibia and femurs of mice [33][34][35][36][37] (Table 2). It has been indicated that the bone elastic modulus obtained from NI was generally lower under wet conditions than in the dry state [36,[38][39][40].…”

“…It has been indicated that the bone elastic modulus obtained from NI was generally lower under wet conditions than in the dry state [36,[38][39][40]. However, in the previous studies, the samples were first dried, followed by rehydration, after at least 24 hours of immersion in various solutions, such as 3.7% formaldehyde, 4% paraformaldehyde, Ringer's solution, and ethanol.…”

“…The method is suitable for determining the relative difference in elastic modulus between samples [36]. To enhance a model solution without errors and incomplete convergence, most of the mathematical models require a single number modulus for each model element without using a non-linear equation representing such as viscoelastic properties.…”

“…To enhance a model solution without errors and incomplete convergence, most of the mathematical models require a single number modulus for each model element without using a non-linear equation representing such as viscoelastic properties. Therefore, the use of the Oliver and Pharr to method was reasonable for the purpose of this study, as compared with other methods including viscoelasticity-plasticity analysis for estimating the elastic, plastic, and viscous properties, and that can be used to analyze the creep behavior of bone [36].…”

A study of human and bovine trabecular bones using nanoindentation and quantitative backscattered electron imaging

“…h f can be represented as the plastic deformation (he) (Bhushan & Li, 2003;Ferguson, 2009). The elastic deformation (he) can be defined as the difference between the maximum displacement and the final displacement -Floreza et al, 2013).…”