Elastic Anisotropy of Human Cortical Bone Secondary Osteons Measured by Nanoindentation
Abstract
The identification of anisotropic elastic properties of lamellar bone based on nanoindentation data is an open problem. Therefore, the purpose of this study was to develop a method to estimate the orthotropic elastic constants of human cortical bone secondary osteons using nanoindentation in two orthogonal directions. Since the indentation modulus depends on all elastic constants and, for anisotropic materials, also on the indentation direction, a theoretical model quantifying the indentation modulus from the stiffness tensor of a given material was implemented numerically (Swadener and Pharr, 2001, “Indentation of Elastically Anisotropic Half-Spaces by Cones and Parabolae of Revolution,” Philos. Mag. A, 81(2), pp. 447–466). Nanoindentation was performed on 22 osteons of the distal femoral shaft: A new holding system was designed in order to indent the same osteon in two orthogonal directions. To interpret the experimental results and identify orthotropic elastic constants, an inverse procedure was developed by using a fabric-based elastic model for lamellar bone. The experimental indentation moduli were found to vary with the indentation direction and showed a marked anisotropy. The estimated elastic constants showed different degrees of anisotropy among secondary osteons of the same bone and these degrees of anisotropy were also found to be different than the one of cortical bone at the macroscopic level. Using the log-Euclidean norm, the relative distance between the compliance tensors of the estimated mean osteon and of cortical bone at the macroscopic level was 9.69%: Secondary osteons appeared stiffer in their axial and circumferential material directions, and with a greater bulk modulus than cortical bone, which is attributed to the absence of vascular porosity in osteonal properties. The proposed method is suitable for identification of elastic constants from nanoindentation experiments and could be adapted to other (bio)materials, for which it is possible to describe elastic properties using a fabric-based model.
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Elastic moduli measured by nanoindentation are on the order of 23 GPa and 26 GPa for osteonal and interstitial lamellae, respectively, in the longitudinal direction.
“Elastic moduli measured by nanoindentation are on the order of 23 GPa and 26 GPa for osteonal and interstitial lamellae, respectively, in the longitudinal direction (36, 37)”
From Bone Mechanical Properties in Healthy and Diseased States (2018) · cites this paper as [37]
Nanoindentation elastic moduli are approximately 45% lower in the transverse direction.
“and are approximately 45% lower in the transverse direction (37).”
From Bone Mechanical Properties in Healthy and Diseased States (2018) · cites this paper as [37]
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- Authors
- Franzoso, G., & Zysset, P. K.
- Affiliations
- Politecnico di Milano (IT)
- TU Wien (AT)
- ORCID
- Zysset, Philippe K.
- Venue
- Journal of Biomechanical Engineering
- Publisher
- ASME International
- Published
- 2008-12-09
- Volume
- 131
- Issue
- 2
- Pages
- 021001-021001
- ISSN
- 0148-0731 (ISSN-L)
- 1528-8951
- OpenAlex
- W1986620590
- Cited by
- 89
- References
- 43
- Citations by year
- 2026: 2 · 2025: 5 · 2024: 1 · 2023: 2 · 2022: 3 · 2021: 2 · 2020: 9 · 2019: 8 · 2018: 4 · 2017: 1 · 2016: 6 · 2015: 5 · 2014: 6 · 2013: 7 · 2012: 11
- FWCI
- 5.39
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Biomechanical Engineering (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Health Sciences › Medicine › Orthopedics and Sports Medicine › Bone health and osteoporosis research
- Physical Sciences › Engineering › Mechanics of Materials › Metal and Thin Film Mechanics
- Physical Sciences › Engineering › Biomedical Engineering › Elasticity and Material Modeling
- Keywords
- elastic anisotropy, cortical bone, secondary osteons, orthotropic elastic constants, indentation modulus, stiffness tensor, compliance tensor, distal femur, bone porosity
- MeSH terms
- Biomechanical Phenomena, Elasticity, Femur, Haversian System, Humans, Models, Theoretical, Anisotropy
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