Modal analysis of nanoindentation data, confirming that reduced bone turnover may cause increased tissue mineralization/elasticity
Introduction
As bones are the predominant load carriers in the vertebrate animal kingdom, their mechanical properties (in particular elasticity and strength) have always been of great interest for biomedicine and the scientific community at large. However, bone exhibits a hierarchical organization (Lakes, 1993, Katz et al., 1984, Weiner and Wagner, 1998), and mechanical properties involving quantities of the dimension "force per area" need to be assigned to a specific observation scale, on which these forces and areas are recorded. As regards elasticity and strength, two such observation scales are of particular interest for the biomedical field:
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the macroscopic scale with a material volume measuring some hundreds of micrometers to milimeters cubed, where cortical and trabecular bone are distinguished. At this length scale bone exhibits pore spaces with characteristic sizes of tens to hundreds of micrometers, populated by biological cells (Buckwalter et al., 1995); and
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the extracellular bone tissue, with material volumes at the tens of micrometers-scale, consisting of a nanocomposite made of hydroxyapatite, collagen, and water with non-collageneous organics (Lees, 1987).
It is widely believed that the activities of bone cells at the higher one of these two levels not only govern the size of these pore spaces (and hence, the amount of bone tissue available for actually carrying the loads), but also the characteristics of the extracellular bone matrix itself. In this context, several mechanisms have been proposed, and the present paper focusses on the following research question: Does excessive bone resorption cause extracellular tissue elasticity increase?
The relevance of this question is inferred from the following deliberations reported in literature:
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Within a certain physiological load window (Frost, 1964, Frost, 1992, Rubin and Lanyon, 1985, Turner, 1998, Hsieh et al., 2001, Rubin et al., 2001), mechanical stimulation is known to increase the rate of bone remodeling or turnover, i.e. the cellular processes leading to resorption of old extracellular bone tissue and subsequent formation of new tissue. On the other hand, bone turnover is associated to the mineralization degree at the tissue scale (Boivin and Meunier, 2002, Meunier and Boivin, 1997, Boivin et al., 2000), with higher turnover resulting in lower mineralization. The "complete" (or secondary) mineralization of the tissue would last up to years (Marotti et al., 1972, Bala et al., 2010), and would be hindered simply by tissue resorption before its full "maturation". Conversely, the fingerprint of low turnover would be highly mineralized tissue.
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Increased bone tissue mineralization causes an increase in the tissue elastic modulus, according to the micromechanical theory applied to, and experimentally validated for, extracellular bone tissue, as reported, among others, by Crolet et al., 1993, Hellmich et al., 2004, Fritsch and Hellmich, 2007, Grimal et al., 2011.
The present paper aims at giving an answer to the aforementioned research question, by presenting a correspondingly designed nanoindentation study and its evaluation. In this context, it is important that the tested samples all consist of very similar tissue, so that any differences between tissue properties from one tested sample to another result only from the resorption activities as described above, with any other causes remaining highly improbable. A short literature review, see e.g. the Appendix of Hellmich et al. (2008), evidences that bone tissue within adult bony organs is, when spatially averaged over long bone cross sections, constant over space and time. This was independently shown by both microscopic and radiographic analyses revealing mineral density distributions (Boivin and Meunier, 2002, Akkus et al., 2003, Roschger et al., 2003, Bossy et al., 2004), and by nanoindentation studies (Hoffler et al., 2000a, Rho et al., 2002, Feng and Jasiuk, 2011, Wolfram et al., 2010).
Accordingly, the current study was performed on mid-shafts from adult female human femurs provided by the Melbourne Femur Research Collection (MFRC), discriminating regions of potentially higher and lower mineralization, and hence, higher and lower tissue elastic modulus:
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anteroposterior regions, being closely aligned with the neutral axis of the bending beam structure "human femur" (Feik et al., 2000, Thomas et al., 2005, Thomas et al., 2006), therefore undergoing lower mechanical stimulation, lower turnover, and exhibiting higher mineralization and tissue elasticity) versus mediolateral regions (with higher mechanical stimulation, higher turnover, lower mineralization and lower tissue elasticity); and
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endosteal regions with significantly reduced formation activities indicated by trabecularization of cortical bone (Simmons et al., 1991, Cooper et al., 2007), and with expectedly higher mineralization and higher tissue modulus, versus periosteal regions (with expectedly lower mineralization and lower tissue modulus).
The correspondingly obtained nanoindentation data underwent a modal analysis as introduced by Furin et al., 2016, Kariem et al., 2015, in order to identify those indented half-spaces the stiffnesses of which were not affected by microcracks.
Section snippets
Selection and preparation of femoral mid shaft samples
Two femoral mid-shaft sections were obtained from bone samples collected in 1990–1993 and 1998 by the Victorian Institute of Forensic Medicine as part of the Melbourne Femur Research Collection (MFRC). Ethical approval was given by the Office for Research Ethics and Integrity as part of a larger study, conducted by the researchers at Melbourne Dental School, where the collection is housed. The femurs, coded 269 and 275, originated from female donors without diseases directly affecting bone, and
Results
We applied the deconvolution algorithm to all experimental data. The following results are expressed as the expected value and standard deviation of the right-most Gaussian distribution depicted in Fig. 2, Fig. 3.
The average modulus of the undamaged bone material on the endosteal surface of all four tested samples was = 29.34 ± 0.74 GPa (Fig. 2A); while the intracortical modulus amounted to 26.23 ± 1.93 GPa (Fig. 2B); and the periosteal modulus amounted to
Discussion
The present study confirmed that lower bone turnover leads to higher extracellular tissue elasticity, most likely through increased levels of bone mineralization. Thereby, the elasticity values were determined from a modal analysis of data obtained from a nanoindentation grid technique. This allowed for identification of the bone tissue elasticity at the observation scale of a few micrometers; as it is well known that the maximum indentation size (here 250 nm) needs to be less than one tenth of
Acknowledgements
The authors would like to acknowledge the kind, expert assistance of Dr. Tim Spelman in the statistical analysis of this project, as well as the assistance of David Thomas in the handling of the samples. We are grateful to the mortuary staff and the staff of the Donor Tissue Bank of the Victorian Institute of Forensic Medicine Australia for their assistance in the collection of the bone specimens used for this study, and we are particularly grateful to the next-of-kin of the donors for
Authors’ roles
Conceptual study design: all. Sample cutting and identification: RB. Nanoindentation sample preparation and tests: MIP. Data analysis: MIP. Manuscript drafting: MIP and CH. Revising manuscript content: all. Approving final version of manuscript: RB, JGC, PP, CH.
References (88)
- et al.
A continuous wave technique for the measurement of the elastic properties of cortical bone
J. Biomech.
(1984) - et al.
Time sequence of secondary mineralization and microhardness in cortical and cancellous bone from ewes
Bone
(2010) - et al.
Alendronate increases bone strength by increasing the mean degree of mineralization of bone tissue in osteoporotic women
Bone
(2000) - et al.
Collagen orientation in compact bone: I. A new method for the determination of the proportion of collagen parallel to the plane of compact bone sections
Metab. Bone Dis. Relat. Res.
(1984) - et al.
The nanogranular nature of C-S-H
J. Mech. Phys. Solids
(2007) - et al.
Age-dependent change in the 3D structure of cortical porosity at the human femoral midshaft
Bone
(2007) - et al.
Compact bone: numerical simulation of mechanical characteristics
J. Biomech.
(1993) - et al.
Bone strain and microcracks at stress fracture sites in human metatarsals
Bone
(2000) - et al.
A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites
J. Mech. Phys. Solids
(1996) - et al.
Nanoindentation of biological materials
Nano Today
(2006)
Shape and size of isolated bone mineralites measured using atomic force microscopy
J. Orthop. Res.
Anisotropic properties of human tibial cortical bone as measured by nanoindentation
J. Orthop. Res.
Multi-scale characterization of swine femoral cortical bone
J. Biomech.
Universal' microstructural patterns in cortical and trabecular, extracellular and extravascular bone materials: micromechanics-based prediction of anisotropic elasticity
J. Theor. Biol.
Ductile sliding between mineral crystals followed by rupture of collagen crosslinks: Experimentally supported micromechanical explanation of bone strength
Journal of Theoretical Biology
Perspectives: bone's mechanical usage windows
Bone Miner.
A two-parameter model of the effective elastic tensor for cortical bone
J. Biomech.
High-resolution AFM imaging of intact and fractured trabecular bone
Bone
Mineral-collagen interactions in elasticity of bone ultrastructure – a continuum micromechanics approach
Eur. J. Mech. A
Nanoindentation discriminates the elastic properties of individual human bone lamellae under dry and physiological conditions
Bone
Heterogeneity of bone lamellar-level elastic moduli
Bone
Development of a fluorescent light technique for evaluating microdamage in bone subjected to fatigue loading
J. Biomech.
Micro-poro-elasticity of baghdadite-based bone tissue engineering scaffolds: a unifying approach based on ultrasonics, nanoindentation, and homogenization theory
Mater. Sci. Eng. C
Bone nodules on chitosan-polygalacturonic acid-hydroxyapatite nanocomposite films mimic hierarchy of natural bone
Acta Biomater.
Ultrasonic contact pulse transmission for elastic wave velocity and stiffness determination: influence of specimen geometry and porosity
Eng. Struct.
Extracellular bone matrix exhibits hardening elastoplasticity and more than double cortical strength: evidence from homogeneous compression of non-tapered single micron-sized pillars welded to a rigid substrate
J. Mech. Behav. Biomed. Mater.
Anisotropic tissue elasticity in human lumbar vertebra, by means of a coupled ultrasound-micromechanics approach
Mater. Lett.
Bone mineral density reflects bone mass but also the degree of mineralization of bone: therapeutic implications
Bone
Surface roughness criteria for cement paste nanoindentation
Cem. Concr. Res.
Micromechanics of elastoplastic porous polycrystals: Theory, algorithm, and application to osteonal bone
International Journal of Plasticity
The effect of bone microstructure on the initiation and growth of microcracks
J. Orthop. Res.
Principal stiffness orientation and degree of anisotropy of human osteons based on nanoindentation in three distinct planes
J. Mech. Behav. Biomed. Mater.
Microstructural elasticity and regional heterogeneity in human femoral bone of various ages examined by nano-indentation
J. Biomech.
Elastic properties of human cortical and trabecular lamellar bone measured by nanoindentation
Biomaterials
Constant mineralization density distribution in cancellous human bone
Bone
Examination of compact bone microdamage using back-scattered electron microscopy
Bone
Aging and matrix microdamage accumulation in human compact bone
Bone
A model for two types of calcium silicate hydrate in the microstructure of Portland cement pastes
Cem. Concr. Res.
Three rules for bone adaptation to mechanical stimuli
Bone
A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models
J. Biomech.
In vivo trabecular microcracks in human vertebral bone
Bone
Rehydration of vertebral trabecular bone: influences on its anisotropy, its stiffness and the indentation work with a view to age, gender and vertebral level
Bone
Ultrasonic wave propagation in human cortical bone – II. Measurements of elastic properties and microhardness
J. Biomech.
Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur
J. Biomech.
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