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Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur
Journal of Biomechanics 32 (1999) 1005}1012
Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur Philippe K. Zysset*, X. Edward Guo, C. Edward Ho%er, Kristin E. Moore, Steven A. Goldstein Orthopaedic Research Laboratories, University of Michigan, USA Received 29 July 1998; accepted 31 May 1999
Abstract The mechanical properties of bone tissue are determined by composition as well as structural, microstructural and nanostructural organization. The aim of this study was to quantify the elastic properties of bone at the lamellar level and compare these properties among osteonal, interstitial and trabecular microstructures from the diaphysis and the neck of the human femur. A nanoindentation technique with a custom irrigation system was used for simultaneously measuring force and displacement of a diamond tip pressed 500 nm into the moist bone tissue. An isotropic elastic modulus was calculated from the unloading curve with an assumed Poisson ratio of 0.3, while hardness was de"ned as the maximal force divided by the corresponding contact area. The elastic moduli ranged from 6.9$4.3 GPa in trabecular tissue from the femoral neck of a 74 yr old female up to 25.0$4.3 GPa in interstitial tissue from the diaphyseal cortex of a 69 yr old female. The mean elastic modulus was found to be signi"cantly in#uenced by the type of lamella (p(10\) and by donor (p(10\). The interaction between the type of lamella and the donor was also highly signi"cant (p(10\). Hardness followed a similar distribution as elastic modulus among types of lamellae and donor, but with lower statistical contrast. It is concluded that the nanostructure of bone tissue must di!er substantially among lamellar types, anatomical sites and individuals and suggests that tissue heterogeneity is of potential importance in bone fragility and adaptation. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Bone lamella; Elastic modulus; Femur; Hardness; Nanoindentation
1. Introduction Improved preventive and therapeutic strategies for skeletal diseases such as osteoporosis rely on a better understanding of the lamellar mechanical properties of bone and their in#uence on cell-mediated adaptation processes. The macroscopic mechanical properties of bones are determined by composition as well as nanostructural (lamella), microstructural (osteon/trabecular packet) and structural (compacta/trabecula) organization (Ascenzi, 1988; Currey, 1988; Martin and Ishida, 1989).
* Corresponding author. Laboratoire de MeH canique AppliqueH e et d'Analyse de FiabiliteH (LMAF), Ecole Polytechnique FeH deH rale de Lausanne, ME-Ecublens, CH-1015 Lausanne, Switzerland. Tel.: #4121-693-59-73; fax: #41-21-693-35-09. E-mail address: Philippe.Zysset@ep#.ch (P.K. Zysset)
While water content, mineral content, microstructure and porosity have all been found to in#uence the elastic behavior of bone or bone microstructural elements, little is known about the intrinsic elastic properties of the bone lamella, namely the anisotropic type I collagen "ber and hydroxyapatite crystal composite. Most of the previous work devoted to the local mechanical quality of bone tissue quanti"ed microhardness or acoustic impedance, which correlate to some extent, but remain physically distinct properties from elasticity constants such as Young's modulus (Amprino, 1958; Evans et al., 1990; Gardner et al., 1992; Hodgskinson et al., 1989; Katz and Meunier, 1993; Meunier et al., 1988; Weaver, 1966). In addition, available experimental results on elastic properties of bone tissue di!er highly according to the adopted technique because the representative volume elements and the deformation mechanisms do not coincide (Guo and Goldstein, 1997). For instance, the reported elastic moduli of trabecular tissue range from
0021-9290/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 1 - 9 2 9 0 ( 9 9 ) 0 0 1 1 1 - 6
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1.3 to 14.8 GPa, which extends beyond the standard deviation of a speci"c experimental technique. A number of micromechanical models with increasing sophistication have been proposed to quantify the relationship between composition, hierarchical organization and selected macroscopic mechanical properties such as anisotropic elasticity (Crolet et al., 1993; Katz, 1980; Sasaki et al., 1991; Wagner and Weiner, 1992). Unfortunately, the elastic properties of bone tissue lamellae used by these models often remain speculative and lack experimental support (Bundy, 1989). Consequently, the objective of this work was to quantify elastic modulus and hardness of human bone at the lamellar level and test the hypothesis that these properties are identical in osteonal, interstitial and trabecular microstructures.
2. Materials and methods Eight fresh frozen, unembalmed human femurs were obtained through the University of Michigan Anatomical Donations Program with no prior history of fracture or osteosarcoma. Donors included four females and four males ranging from 53 to 93 yr old. Mean age and standard deviation were 75.3$11.7 yr, and the partial means of females and males were not statistically di!erent as calculated by an independent t-test (p'0.05). Bone specimens were sectioned into 3 mm slices along a transverse plane from the posterior mid-diaphysis and the neck of the femurs with an Exakt precision diamond band saw (Exakt Medical Instruments Inc., Oklahoma City, OK) under constant water irrigation. An Isomet diamond blade saw (Buehler Ltd, Lake Blu!, IL) was used to cut a small sector, approximately one-eighth of the circumference, from the posterior and lateral aspects of the mid-diaphysis and the neck, respectively. The specimens from the neck including trabecular tissue had their marrow removed using a soft water jet followed by an ultrasonic bath. All specimens were then embedded in a weakly exothermal liquid plastic (Measurements Group Inc., Raleigh, NC) and allowed to cure overnight at room temperature (&233C). After rehydration, the samples were polished with progressive grades of silicon carbide paper and "nished manually on a soft cloth with a 0.25 lm diamond slurry. Finally, the samples were cleaned in a distilled water ultrasonic bath for 5 min. Prior to mechanical testing, preparation of the samples was controlled under the optical microscope where the lamellar microstructure of the bone had to appear as clear as in Fig. 1. Nanoindentation is an evolution of the conventional hardness test for assessment of the mechanical properties of thin "lms and surface layers. In particular, this recent technique reduces the depth of indentation to submicron range, extends the spatial resolution to about 1 lm and
allows for estimation of the elastic modulus under speci"c assumptions and careful calibration. The theoretical basis of the method relies on the Boussinesq solution of indentation of an elastic half-space by a rigid, axisymmetric indenter derived by Sneddon (1965). The relationship between contact sti!ness and the elastic properties of the sample is the following: dP 2 E , " (A (1) dh (p (1!l) where P is the load, h is the depth, A is the projected contact area of the indenter as a function of depth h, E is Q the elastic modulus and l is the Poisson ratio of the sample. Application of this solution to the unloading procedure of nanoindentation with a deformable pyramidal Berkovich tip was then proposed by Oliver and Pharr (1992). The relationship between contact sti!ness and the elastic properties of the sample becomes dP 2 "b (AE , dh (p
(2)
where b is an empirical indenter shape factor and the reduced modulus E is given by 1 (1!l) (1!l) # " (3) E E E with the indices i and s corresponding to the indenter and the sample, respectively. In addition, critical assumptions of this derivation are 1. The constitutive behavior of the sample is elastic with time-independent plasticity. 2. The solution for the elastic deformation of an irreversibly indented surface geometry is similar to the one of a #at semi-in"nite half space. 3. The Poisson ratio l of the sample is known. These assumptions have been examined in experimental and numerical studies and found to be acceptable for a range of materials such as aluminum, quartz, sapphire, fused silica, soda lime glass and tungsten (Oliver and Pharr, 1992). Recently, this technique has also been applied to bone tissue (Ho%er et al., 1997; Rho et al., 1997). In this study, a Nanoindenter II (Nano Instruments Inc., Oak Ridge, TN) was used to assess elastic properties of the bone samples at room temperature (&233C). The system has force and displacement resolutions of 0.3 lN and 0.16 nm, respectively. The calibration procedure provided an average elastic modulus of 75.1 GPa for fused silica to be compared with the 72 MPa value provided by the manufacturer of the calibration sample (#4.3%). An irrigation system was developed to maintain moisture of
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Fig. 1. Bone specimens were retrieved from the diaphysis and the neck of eight human femurs and embedded in plastic. Indentation locations were de"ned in 30 lm squares in osteonal, interstitial or trabecular lamellae.
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the wet specimens with a physiological saline solution during the few hours of testing (Fig. 2). In addition, bacterial degradation of bone collagen was inhibited by adding 0.5 mg/ml of gentamicin (Life Technologies, Grand Island, NY). For the mid-diaphysis specimens, nine osteonal and nine interstitial regions were selected randomly under the microscope. For the neck specimens, nine osteonal, nine interstitial and nine trabecular regions were selected. Each region covered a square of 30 lm and an indentation was programmed at each corner contributing to a total of 180 indents per donor (Fig. 1). Following the "ndings of our former validation study, the indentation depth and rate were 500 nm and 10 nm/s, respectively (Ho%er et al., 1997). After removing 85% of the maximal load, constant load was held for 1 min to measure drifting of the displacement transducer due to both the thermal e!ect on the transducers capacitor and the viscous e!ect of the bone tissue behavior. In subsequent analysis, the measured drift was then subtracted from the original displacement}time data. Hardness and elastic moduli were computed from the unloading force-displacement curves with the Nanoindenter II soft-
ware, according to Eqs. (2) and (3). The de"nition of hardness was the mean pressure under the indenter at maximal depth. Following the method of Oliver and Pharr (1992), a window (for instance 20}95%) of the unloading curve is "tted to a power function and the slope used in Eq. (2) is then calculated analytically for the maximal depth (Fig. 3). Calculation of the elastic moduli with Eq. (3) assumed a Berkovich diamond tip with an elastic modulus of 1141 GPa, a Poisson ratio of 0.07 and an isotropic, elasto-plastic bone sample property with a Poisson ratio of 0.3. Statistical analysis was started by calculating a table of means and standard deviations of both elastic moduli and hardness for all combinations of microstructures (MICRO) and donors (BODY). Then, a linear regression between hardness and elastic modulus was done. Finally, a mixed model with microstructure (MICRO) as "xed e!ect, donor (BODY) and interaction (MICRO*BODY) as random e!ects was analyzed with the robust Winsor method (Miller, 1986). Tukey post-hoc tests were run for multiple comparisons of means (S-Plus, Mathsoft, Seattle, WA).
Fig. 2. Scheme of the experimental setup including the Nanoindenter II system mounted on an air pressurized table and the custom saline irrigation system. The indentation tip is suspended by elastic springs. Displacements of the tip are measured by a capacitor, while forces are recorded by an induction transducer. An xyz table allows for selection of the indentation locations under a light microscope and for positioning the sample under the indentation tip with a micron accuracy. The 3 mm thick bone specimens is mounted on an aluminum cylinder and irrigated from a central hole with a connection to the periphery for out#ow.
P.K. Zysset et al. / Journal of Biomechanics 32 (1999) 1005}1012
Fig. 3. Force}displacement curves obtained by indentation of osteonal and trabecular lamellae. Hardness is the average pressure under the tip at maximal depth, while the elastic modulus is calculated from the bold portion of the unloading curve. The constant load period towards the end of the unloading phase allows to estimate the e!ect of drifting of the displacement transducer. However, this e!ect was found to be negligible in the calculation of the mechanical properties.
3. Results Typical force-displacement curves from which the elastic moduli and hardness of wet bone tissue were calculated are shown in Fig. 3, indicating a di!erent response of cortical and trabecular tissue. The correction procedure to account for drifting of the displacement transducer was found to have a negligible e!ect on our results since both hardness and elastic modulus di!ered by less than 1% from those calculated from the uncorrected data. A total of 39 indentations failed probably due to invasion of water on the surface of the tissue and were attributed zero values for both elastic modulus and hardness. The remaining 1401 indentations were used for preliminary statistical analysis. As expected, elastic modulus correlated with hardness (n"1401, r"0.75, p(10\). In diaphyseal femoral bone, the average elastic moduli were 19.1$5.4 GPa in osteonal and 21.2$5.3 GPa in interstitial lamellae. In the neck, the average moduli were 15.8$5.3 GPa in osteonal, 17.5$5.3 GPa in interstitial and 11.4$5.6 GPa in trabecular lamellae. As shown in Fig. 4, the error on these elastic moduli by varying Poisson s ratio between 0.2 and 0.4 remains within $10%. Average hardness ranged from 0.234 to 0.760 GPa and followed a similar distribution among the di!erent microstructures. The distributions of elastic modulus and hardness for the eight individuals are detailed in Figs. 5a and b. The mixed model analysis required the use of the full set of 1440 observations, but robustness of the Winsor method prevents the estimations and related tests from being in#uenced by the zero values. The model provided a very
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Fig. 4. The e!ect of Poisson ratio on the calculation of elastic modulus for an isotropic material as compared to the selected value of 0.3. It is likely that the actual Poisson s ratio of bone tissue is positive and that the error associated with its estimation in the nanoindentation technique ranges between #9.9%. and !8.2%.
high signi"cance for both the MICRO and BODY factors (p(10\), con"rming that both microstructure and donor a!ect the mechanical properties of bone tissue. The null hypothesis that the interaction factors MICRO*BODY are all zero was also rejected (p(10\), suggesting that the microstructural di!erences vary from one individual to another. The multiple comparisons with Tukey post hoc tests for the e!ect of MICRO revealed that the mechanical properties of trabecular bone were signi"cantly lower than those of compact bone from the neck and the diaphysis (p(0.05), except for hardness of the osteonal bone from the neck (p'0.05). The mechanical properties of the neck were also signi"cantly lower than those from the diaphysis (p(0.05), except for the elastic modulus of osteonal tissue (p'0.05). Due to the random e!ects, the null hypotheses that the mechanical properties in osteonal and interstitial bone are identical could not be rejected in both diaphysis and neck (p'0.05).
4. Discussion The "rst attempts to quantify the mechanical properties of bone microstructure were microhardness tests with indentation sizes on the order of 50 lm and weights on the order of 100 g (Amprino, 1958; Weaver, 1966). In particular, the extensive study by Weaver provided hardness values between 0.049 and 0.579 GPa for fresh human bone as well as a number of interesting conclusions: 1. Microhardness of dry bone is increased by 30}40% as compared to fresh bone, while microhardness of bone subjected to natural protein degradation over 24 h at 43C is decreased by 20%.
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Fig. 5. (a) Means and standard deviations of elastic moduli measured in "ve microstructures and eight individuals. There is evidence of the in#uence of both MICRO and BODY factors but also of the MICRO*BODY interaction term, since the e!ect of MICRO is di!erent in each individual. (b) Means and standard deviations of hardness for the same factors.
2. Microhardness was found to be an accurate and reliable measure of the degree of mineralization. In particular, the progression of mineralization that accompanies skeletal maturation was re#ected by an increase in the microscopic hardness. 3. Microhardness of cortical bone taken from selected sites within an individual varied widely, but there was little variability in the hardness of the same bone taken from standard sites in di!erent individuals. 4. On the one hand, microhardness of cortical bone is quite uniform after skeletal maturity and is not signi"cantly a!ected by osteoporosis. On the other hand,
bone from patients with Paget's disease, renal rickets and osteogenesis imperfecta showed highly reduced hardness. The average hardness range obtained with nanoindentation compares favorably with the results obtained by Weaver, especially when the 6 orders of magnitude di!erence in indentation force is recalled. Weaver's "rst conclusion motivated the need for an irrigation system and an antibacterial treatment for our specimens when the measurement period exceeds a few hours. In addition, we demonstrated in a preliminary study that the embedded
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and rewet specimens provided statistically equivalent indentation results to the wet specimens (Ho%er et al., 1997). The di!erence we noticed between diaphyseal and neck bone hardness corroborates Weaver's measurements in the "bula, but the importance of the BODY factor and the MICRO*BODY interaction revealed by our analysis diverges with his third conclusion that seemingly lacks of statistical support. In contrast with Weaver's fourth conclusion, we observed signi"cant di!erences between individuals of similar age, but did not investigate yet the e!ect of disease. A recent nanoindentation study examined the mechanical properties of dry human vertebral and tibial bone (Rho et al., 1997). As expected from Weaver's work, the elastic moduli and hardness values of dry bone were higher than in the present study, but a signi"cant di!erence between osteonal and interstitial bone properties was found. Another technique allowing for investigation of bone elasticity at the lamellar level is scanning acoustic microscopy (Meunier et al., 1988; Gardner et al., 1992; Katz and Meunier, 1993). While the GHz frequency range of this technique provides resolution on the order of a micron, calculation of elastic moduli from the acoustic impedance which contains information on both density and wave velocity seems to remain a major di$culty that does not appear with nanoindentation. In agreement with previous studies (Hodgskinson et al., 1989; Evans et al., 1990), elastic modulus correlates with hardness. Evans et al. (1990) found higher correlations (r"0.96) between elastic modulus and hardness that we attribute to the wider range of species, anatomical locations and therefore mineral content of their data. The average elastic modulus of diaphyseal cortical bone measured by nanoindentation was 20.1$5.4 GPa as compared to 17.0$1.7 GPa and 20.0$1.3 GPa measured in the longitudinal direction by mechanical and ultrasonic testing, respectively (Reilly and Burstein, 1975; Ashman et al., 1984). This coincidence has to be moderated by the fact that the isotropic nanoindentation modulus represents some weighted average of anisotropic moduli and the longitudinal elastic modulus of bone lamellae is therefore likely to be larger (Vlassak and Nix, 1994). Given this perspective, haversian porosity and cement line interface e!ects could then reconcile the macroscopic and lamellar elastic properties. The average elastic modulus of trabecular bone measured by nanoindentation was 11.4$5.6 GPa as compared to the 1.3 to 14.8 GPa range reported in a review paper by Guo and Goldstein (1997). The nanoindentation results are consistent with the upper part of this range, because they do not account for local strain heterogeneities due to lacunae or cement lines that become of signi"cant importance when testing microspecimens.
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The elastic modulus of human bone tissue was found to depend strongly on tissue type, anatomical location and individual. The di!erence in elastic modulus obtained between compact and trabecular tissue contradicts the original assumption by Wol! (1892) and the suggestion by Carter and Hayes (1977) that compact and trabecular bone are made of the same tissue. These di!erences may be attributed to variations in canalicular porosity or mineralization of the extracellular matrix (Currey, 1969; Scha%er and Burr, 1988). Collagen orientation distribution, however, may have in#uenced the interpretation of the average elastic properties of trabecular bone, since trabecular packets were tested randomly along multiple orientations, while Haversian bone was tested exclusively along its longitudinal axis. The di!erence in elastic properties found between anatomical locations may involve turnover rate and osteon type. A higher turnover rate reduces the mean age of the osteons and therefore reduces mineralization and the associated elastic properties. According to the work by Ascenzi et al., a di!erent distribution of osteon types, distinguished by predominant collagen "ber orientation, may be present in the neck as compared to the diaphysis which may also lead to distinct average mechanical properties (Ascenzi and Bonucci, 1967,1968,1972; Ascenzi et al., 1990,1994). Interestingly, the cortical shell of the neck exhibits intermediate elastic properties when compared to diaphyseal and trabecular femoral bone, which may prevent deleterious local deformation mismatches with the trabecular microstructure that could reduce the strength of the femoral neck. The distinct distributions of lamellar properties found among individuals provide a new perspective in the understanding of bone fragility. Failure may be strongly a!ected by heterogeneity of the tissue, allowing for strain concentration, damage accumulation and crack propagation. Undoubtedly, extensive studies and careful statistical analysis will be required to gain more insight in the distribution of these lamellar properties in human populations and in their potential relationship with aging and disease. In conclusion, a nanoindentation technique has been utilized to quantify hardness and elastic moduli of wet human femoral bone at the lamellar level of organization. Extending the "ndings of previous studies on hardness, signi"cant di!erences in elastic properties have been found among tissue types, anatomical sites and individuals. In the future, multiple experimental techniques will be needed to clarify the origin of these variations, to provide input for micromechanical models of bone tissue and to improve our understanding of the consequences of aging and disease on the mechanical integrity of human bone. We believe nanoindentation will continue to be an important experimental method supporting these studies.
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Acknowledgements This work was funded by NIH grant no. AR34399. The authors wish to thank M. Brown, J. Boura, K. Burrell, K. Kendig, O. Renaud, B. Riemer-McCreadie and M. Stock for their respective contributions. References Amprino, R., 1958. Investigations on some physical properties of bone tissue. Acta Anatomica 34, 161}186. Ascenzi, A., 1988. The micromechanics versus the macromechanics of cortical bone-A comprehensive presentation. Journal of Biomechanical Engineering 110, 357}363. Ascenzi, A., Baschieri, P., Benvenuti, A., 1990. The bending properties of single osteons. Journal of Biomechanics 23, 763}771. Ascenzi, A., Baschieri, P., Benvenuti, A., 1994. The torsional properties of single selected osteons. Journal of Biomechanics 27, 875}884. Ascenzi, A., Bonucci, E., 1967. The tensile properties of single osteons. The Anatomical Record 158, 375}386. Ascenzi, A., Bonucci, E., 1968. The compressive properties of single osteons. The Anatomical Record 161, 377}391. Ascenzi, A., Bonucci, E., 1972. The shearing properties of single osteons. The Anatomical Record 172, 499}510. Ashman, R.B., Cowin, S.C., Buskirk, W.C.V., Rice, J.C., 1984. A continuous wave technique for the measurement of the elastic properties of cortical bone. Journal of Biomechanics 17, 349}361. Bundy, K.J., 1989. Composite material models for bone. In: Cowin, S.C. (Ed.), Bone Mechanics. CRC Press, Boca Raton, FL, pp. 197}210. Carter, D.R., Hayes, W.C., 1977. The compressive behaviour of bone as a two phase porous structure. Journal of Bone and Joint Surgery 59 A, 954}962. Crolet, J.M., Aoubiza, B., Meunier, A., 1993. Compact bone: numerical simulation of mechanical characteristics. Journal of Biomechanics 26, 677}687. Currey, J.D., 1969. The mechanical consequences of variation in the mineral content of bone. Journal of Biomechanics 2, 1}11. Currey, J.D., 1988. The e!ect of porosity and mineral content on the Young's modulus of elasticity of compact bone. Journal of Biomechanics 21, 131}139. Evans, G.P., Behiri, J.C., Currey, J.D., Bon"eld, W., 1990. Microhardness and Young's modulus in cortical bone exhibiting a wide range of mineral volume fractions, and in bone analogue. Journal of Material Science: Materials in Medicine 1, 38}43. Gardner, T.N., Elliott, J.C., Sklar, Z., Briggs, G.A.D., 1992. Acoustic microscope study of the elastic properties of #uorapatite and hydroxyapatite, tooth enamel and bone. Journal of Biomechanics 25, 1265}1277.
Guo, X.E., Goldstein, S.A., 1997. Is trabecular bone tissue di!erent from cortical bone tissue?. FORMA 12, 185}196. Hodgskinson, R., Currey, J.D., Evans, G.P., 1989. Hardness, an indicator of the mechanical competence of cancellous bone. Journal of Orthopaedic Research 7, 754}758. Ho%er, C.E. Guo, X.E. Zysset, P.K. Moore, K.E., Goldstein, S.A., 1997. Evaluation of bone microstructural properties: e!ect of testing conditions, depth, repetition, time delay and displacement rate. In: Proceedings of the Bioengineering Conference of the ASME. Sunriver, OR. Katz, J.L., 1980. Anisotropy of Young's modulus of bone. Nature 283, 106}107. Katz, J.L., Meunier, A., 1993. Scanning acoustic microscope studies of the elastic properties of osteons and osteon lamellae. Journal of Biomechanical Engineering 115, 543}548. Martin, R.B., Ishida, J., 1989. The relative e!ects of collagen "ber orientation, porosity, density, and mineralization of bone strength. Journal of Biomechanics 22, 419}426. Meunier, A., Katz, J.L., Christel, P., Sedel, L., 1988. A re#ection scanning acoustic microscope for bone and bone-biomaterials interface studies. Journal of Orthopaedic Research 6, 770}775. Miller, R.G., 1986. Beyond Anova, Basics of Applied Statistics. Wiley, New York. Oliver, W.C., Pharr, G.M., 1992. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. Journal of Materials Research 7, 1564}1583. Reilly, D.T., Burstein, A.H., 1975. The elastic and ultimate properties of compact bone tissue. Journal of Biomechanics 393}405. Rho, J., Tsui, T., Pharr, O., 1997. Elastic properties of human cortical and trabecular lamellar bone measured by nanoindentation. Biomaterials 18, 1325}1330. Sasaki, N., Ikawa, T., Fukuda, A., 1991. Orientation of mineral in bovine bone and the anisotropic mechanical properties of plexiform bone. Journal of Biomechanics 24, 57}61. Scha%er, M.B., Burr, D.B., 1988. Sti!ness of compact bone: e!ects of porosity and density. Journal of Biomechanics 21, 13}16. Sneddon, I.N., 1965. The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary pro"le. International Journal of Engineering Science 3, 47}57. Vlassak, J.J., Nix, W.D., 1994. Measuring the elastic properties of anisotropic materials by means of indentation experiments. Journal of Mechanics and Physics of Solids 42, 1123}1245. Wagner, H.D., Weiner, S., 1992. On the relationship between the microstructure of bone and its mechanical sti!ness. Journal of Biomechanics 25, 1311}1320. Weaver, J.K., 1966. The microscopic hardness of bone. Journal of Bone and Joint Surgery A 48, 273}288. Wol!, J., 1892. Das Gesetz der Transformation der Knochen. A. Hirchwild, Berlin.
Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur Philippe K. Zysset*, X. Edward Guo, C. Edward Ho%er, Kristin E. Moore, Steven A. Goldstein Orthopaedic Research Laboratories, University of Michigan, USA Received 29 July 1998; accepted 31 May 1999
Abstract The mechanical properties of bone tissue are determined by composition as well as structural, microstructural and nanostructural organization. The aim of this study was to quantify the elastic properties of bone at the lamellar level and compare these properties among osteonal, interstitial and trabecular microstructures from the diaphysis and the neck of the human femur. A nanoindentation technique with a custom irrigation system was used for simultaneously measuring force and displacement of a diamond tip pressed 500 nm into the moist bone tissue. An isotropic elastic modulus was calculated from the unloading curve with an assumed Poisson ratio of 0.3, while hardness was de"ned as the maximal force divided by the corresponding contact area. The elastic moduli ranged from 6.9$4.3 GPa in trabecular tissue from the femoral neck of a 74 yr old female up to 25.0$4.3 GPa in interstitial tissue from the diaphyseal cortex of a 69 yr old female. The mean elastic modulus was found to be signi"cantly in#uenced by the type of lamella (p(10\) and by donor (p(10\). The interaction between the type of lamella and the donor was also highly signi"cant (p(10\). Hardness followed a similar distribution as elastic modulus among types of lamellae and donor, but with lower statistical contrast. It is concluded that the nanostructure of bone tissue must di!er substantially among lamellar types, anatomical sites and individuals and suggests that tissue heterogeneity is of potential importance in bone fragility and adaptation. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Bone lamella; Elastic modulus; Femur; Hardness; Nanoindentation
1. Introduction Improved preventive and therapeutic strategies for skeletal diseases such as osteoporosis rely on a better understanding of the lamellar mechanical properties of bone and their in#uence on cell-mediated adaptation processes. The macroscopic mechanical properties of bones are determined by composition as well as nanostructural (lamella), microstructural (osteon/trabecular packet) and structural (compacta/trabecula) organization (Ascenzi, 1988; Currey, 1988; Martin and Ishida, 1989).
* Corresponding author. Laboratoire de MeH canique AppliqueH e et d'Analyse de FiabiliteH (LMAF), Ecole Polytechnique FeH deH rale de Lausanne, ME-Ecublens, CH-1015 Lausanne, Switzerland. Tel.: #4121-693-59-73; fax: #41-21-693-35-09. E-mail address: Philippe.Zysset@ep#.ch (P.K. Zysset)
While water content, mineral content, microstructure and porosity have all been found to in#uence the elastic behavior of bone or bone microstructural elements, little is known about the intrinsic elastic properties of the bone lamella, namely the anisotropic type I collagen "ber and hydroxyapatite crystal composite. Most of the previous work devoted to the local mechanical quality of bone tissue quanti"ed microhardness or acoustic impedance, which correlate to some extent, but remain physically distinct properties from elasticity constants such as Young's modulus (Amprino, 1958; Evans et al., 1990; Gardner et al., 1992; Hodgskinson et al., 1989; Katz and Meunier, 1993; Meunier et al., 1988; Weaver, 1966). In addition, available experimental results on elastic properties of bone tissue di!er highly according to the adopted technique because the representative volume elements and the deformation mechanisms do not coincide (Guo and Goldstein, 1997). For instance, the reported elastic moduli of trabecular tissue range from
0021-9290/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 1 - 9 2 9 0 ( 9 9 ) 0 0 1 1 1 - 6
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1.3 to 14.8 GPa, which extends beyond the standard deviation of a speci"c experimental technique. A number of micromechanical models with increasing sophistication have been proposed to quantify the relationship between composition, hierarchical organization and selected macroscopic mechanical properties such as anisotropic elasticity (Crolet et al., 1993; Katz, 1980; Sasaki et al., 1991; Wagner and Weiner, 1992). Unfortunately, the elastic properties of bone tissue lamellae used by these models often remain speculative and lack experimental support (Bundy, 1989). Consequently, the objective of this work was to quantify elastic modulus and hardness of human bone at the lamellar level and test the hypothesis that these properties are identical in osteonal, interstitial and trabecular microstructures.
2. Materials and methods Eight fresh frozen, unembalmed human femurs were obtained through the University of Michigan Anatomical Donations Program with no prior history of fracture or osteosarcoma. Donors included four females and four males ranging from 53 to 93 yr old. Mean age and standard deviation were 75.3$11.7 yr, and the partial means of females and males were not statistically di!erent as calculated by an independent t-test (p'0.05). Bone specimens were sectioned into 3 mm slices along a transverse plane from the posterior mid-diaphysis and the neck of the femurs with an Exakt precision diamond band saw (Exakt Medical Instruments Inc., Oklahoma City, OK) under constant water irrigation. An Isomet diamond blade saw (Buehler Ltd, Lake Blu!, IL) was used to cut a small sector, approximately one-eighth of the circumference, from the posterior and lateral aspects of the mid-diaphysis and the neck, respectively. The specimens from the neck including trabecular tissue had their marrow removed using a soft water jet followed by an ultrasonic bath. All specimens were then embedded in a weakly exothermal liquid plastic (Measurements Group Inc., Raleigh, NC) and allowed to cure overnight at room temperature (&233C). After rehydration, the samples were polished with progressive grades of silicon carbide paper and "nished manually on a soft cloth with a 0.25 lm diamond slurry. Finally, the samples were cleaned in a distilled water ultrasonic bath for 5 min. Prior to mechanical testing, preparation of the samples was controlled under the optical microscope where the lamellar microstructure of the bone had to appear as clear as in Fig. 1. Nanoindentation is an evolution of the conventional hardness test for assessment of the mechanical properties of thin "lms and surface layers. In particular, this recent technique reduces the depth of indentation to submicron range, extends the spatial resolution to about 1 lm and
allows for estimation of the elastic modulus under speci"c assumptions and careful calibration. The theoretical basis of the method relies on the Boussinesq solution of indentation of an elastic half-space by a rigid, axisymmetric indenter derived by Sneddon (1965). The relationship between contact sti!ness and the elastic properties of the sample is the following: dP 2 E , " (A (1) dh (p (1!l) where P is the load, h is the depth, A is the projected contact area of the indenter as a function of depth h, E is Q the elastic modulus and l is the Poisson ratio of the sample. Application of this solution to the unloading procedure of nanoindentation with a deformable pyramidal Berkovich tip was then proposed by Oliver and Pharr (1992). The relationship between contact sti!ness and the elastic properties of the sample becomes dP 2 "b (AE , dh (p
(2)
where b is an empirical indenter shape factor and the reduced modulus E is given by 1 (1!l) (1!l) # " (3) E E E with the indices i and s corresponding to the indenter and the sample, respectively. In addition, critical assumptions of this derivation are 1. The constitutive behavior of the sample is elastic with time-independent plasticity. 2. The solution for the elastic deformation of an irreversibly indented surface geometry is similar to the one of a #at semi-in"nite half space. 3. The Poisson ratio l of the sample is known. These assumptions have been examined in experimental and numerical studies and found to be acceptable for a range of materials such as aluminum, quartz, sapphire, fused silica, soda lime glass and tungsten (Oliver and Pharr, 1992). Recently, this technique has also been applied to bone tissue (Ho%er et al., 1997; Rho et al., 1997). In this study, a Nanoindenter II (Nano Instruments Inc., Oak Ridge, TN) was used to assess elastic properties of the bone samples at room temperature (&233C). The system has force and displacement resolutions of 0.3 lN and 0.16 nm, respectively. The calibration procedure provided an average elastic modulus of 75.1 GPa for fused silica to be compared with the 72 MPa value provided by the manufacturer of the calibration sample (#4.3%). An irrigation system was developed to maintain moisture of
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Fig. 1. Bone specimens were retrieved from the diaphysis and the neck of eight human femurs and embedded in plastic. Indentation locations were de"ned in 30 lm squares in osteonal, interstitial or trabecular lamellae.
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the wet specimens with a physiological saline solution during the few hours of testing (Fig. 2). In addition, bacterial degradation of bone collagen was inhibited by adding 0.5 mg/ml of gentamicin (Life Technologies, Grand Island, NY). For the mid-diaphysis specimens, nine osteonal and nine interstitial regions were selected randomly under the microscope. For the neck specimens, nine osteonal, nine interstitial and nine trabecular regions were selected. Each region covered a square of 30 lm and an indentation was programmed at each corner contributing to a total of 180 indents per donor (Fig. 1). Following the "ndings of our former validation study, the indentation depth and rate were 500 nm and 10 nm/s, respectively (Ho%er et al., 1997). After removing 85% of the maximal load, constant load was held for 1 min to measure drifting of the displacement transducer due to both the thermal e!ect on the transducers capacitor and the viscous e!ect of the bone tissue behavior. In subsequent analysis, the measured drift was then subtracted from the original displacement}time data. Hardness and elastic moduli were computed from the unloading force-displacement curves with the Nanoindenter II soft-
ware, according to Eqs. (2) and (3). The de"nition of hardness was the mean pressure under the indenter at maximal depth. Following the method of Oliver and Pharr (1992), a window (for instance 20}95%) of the unloading curve is "tted to a power function and the slope used in Eq. (2) is then calculated analytically for the maximal depth (Fig. 3). Calculation of the elastic moduli with Eq. (3) assumed a Berkovich diamond tip with an elastic modulus of 1141 GPa, a Poisson ratio of 0.07 and an isotropic, elasto-plastic bone sample property with a Poisson ratio of 0.3. Statistical analysis was started by calculating a table of means and standard deviations of both elastic moduli and hardness for all combinations of microstructures (MICRO) and donors (BODY). Then, a linear regression between hardness and elastic modulus was done. Finally, a mixed model with microstructure (MICRO) as "xed e!ect, donor (BODY) and interaction (MICRO*BODY) as random e!ects was analyzed with the robust Winsor method (Miller, 1986). Tukey post-hoc tests were run for multiple comparisons of means (S-Plus, Mathsoft, Seattle, WA).
Fig. 2. Scheme of the experimental setup including the Nanoindenter II system mounted on an air pressurized table and the custom saline irrigation system. The indentation tip is suspended by elastic springs. Displacements of the tip are measured by a capacitor, while forces are recorded by an induction transducer. An xyz table allows for selection of the indentation locations under a light microscope and for positioning the sample under the indentation tip with a micron accuracy. The 3 mm thick bone specimens is mounted on an aluminum cylinder and irrigated from a central hole with a connection to the periphery for out#ow.
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Fig. 3. Force}displacement curves obtained by indentation of osteonal and trabecular lamellae. Hardness is the average pressure under the tip at maximal depth, while the elastic modulus is calculated from the bold portion of the unloading curve. The constant load period towards the end of the unloading phase allows to estimate the e!ect of drifting of the displacement transducer. However, this e!ect was found to be negligible in the calculation of the mechanical properties.
3. Results Typical force-displacement curves from which the elastic moduli and hardness of wet bone tissue were calculated are shown in Fig. 3, indicating a di!erent response of cortical and trabecular tissue. The correction procedure to account for drifting of the displacement transducer was found to have a negligible e!ect on our results since both hardness and elastic modulus di!ered by less than 1% from those calculated from the uncorrected data. A total of 39 indentations failed probably due to invasion of water on the surface of the tissue and were attributed zero values for both elastic modulus and hardness. The remaining 1401 indentations were used for preliminary statistical analysis. As expected, elastic modulus correlated with hardness (n"1401, r"0.75, p(10\). In diaphyseal femoral bone, the average elastic moduli were 19.1$5.4 GPa in osteonal and 21.2$5.3 GPa in interstitial lamellae. In the neck, the average moduli were 15.8$5.3 GPa in osteonal, 17.5$5.3 GPa in interstitial and 11.4$5.6 GPa in trabecular lamellae. As shown in Fig. 4, the error on these elastic moduli by varying Poisson s ratio between 0.2 and 0.4 remains within $10%. Average hardness ranged from 0.234 to 0.760 GPa and followed a similar distribution among the di!erent microstructures. The distributions of elastic modulus and hardness for the eight individuals are detailed in Figs. 5a and b. The mixed model analysis required the use of the full set of 1440 observations, but robustness of the Winsor method prevents the estimations and related tests from being in#uenced by the zero values. The model provided a very
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Fig. 4. The e!ect of Poisson ratio on the calculation of elastic modulus for an isotropic material as compared to the selected value of 0.3. It is likely that the actual Poisson s ratio of bone tissue is positive and that the error associated with its estimation in the nanoindentation technique ranges between #9.9%. and !8.2%.
high signi"cance for both the MICRO and BODY factors (p(10\), con"rming that both microstructure and donor a!ect the mechanical properties of bone tissue. The null hypothesis that the interaction factors MICRO*BODY are all zero was also rejected (p(10\), suggesting that the microstructural di!erences vary from one individual to another. The multiple comparisons with Tukey post hoc tests for the e!ect of MICRO revealed that the mechanical properties of trabecular bone were signi"cantly lower than those of compact bone from the neck and the diaphysis (p(0.05), except for hardness of the osteonal bone from the neck (p'0.05). The mechanical properties of the neck were also signi"cantly lower than those from the diaphysis (p(0.05), except for the elastic modulus of osteonal tissue (p'0.05). Due to the random e!ects, the null hypotheses that the mechanical properties in osteonal and interstitial bone are identical could not be rejected in both diaphysis and neck (p'0.05).
4. Discussion The "rst attempts to quantify the mechanical properties of bone microstructure were microhardness tests with indentation sizes on the order of 50 lm and weights on the order of 100 g (Amprino, 1958; Weaver, 1966). In particular, the extensive study by Weaver provided hardness values between 0.049 and 0.579 GPa for fresh human bone as well as a number of interesting conclusions: 1. Microhardness of dry bone is increased by 30}40% as compared to fresh bone, while microhardness of bone subjected to natural protein degradation over 24 h at 43C is decreased by 20%.
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Fig. 5. (a) Means and standard deviations of elastic moduli measured in "ve microstructures and eight individuals. There is evidence of the in#uence of both MICRO and BODY factors but also of the MICRO*BODY interaction term, since the e!ect of MICRO is di!erent in each individual. (b) Means and standard deviations of hardness for the same factors.
2. Microhardness was found to be an accurate and reliable measure of the degree of mineralization. In particular, the progression of mineralization that accompanies skeletal maturation was re#ected by an increase in the microscopic hardness. 3. Microhardness of cortical bone taken from selected sites within an individual varied widely, but there was little variability in the hardness of the same bone taken from standard sites in di!erent individuals. 4. On the one hand, microhardness of cortical bone is quite uniform after skeletal maturity and is not signi"cantly a!ected by osteoporosis. On the other hand,
bone from patients with Paget's disease, renal rickets and osteogenesis imperfecta showed highly reduced hardness. The average hardness range obtained with nanoindentation compares favorably with the results obtained by Weaver, especially when the 6 orders of magnitude di!erence in indentation force is recalled. Weaver's "rst conclusion motivated the need for an irrigation system and an antibacterial treatment for our specimens when the measurement period exceeds a few hours. In addition, we demonstrated in a preliminary study that the embedded
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and rewet specimens provided statistically equivalent indentation results to the wet specimens (Ho%er et al., 1997). The di!erence we noticed between diaphyseal and neck bone hardness corroborates Weaver's measurements in the "bula, but the importance of the BODY factor and the MICRO*BODY interaction revealed by our analysis diverges with his third conclusion that seemingly lacks of statistical support. In contrast with Weaver's fourth conclusion, we observed signi"cant di!erences between individuals of similar age, but did not investigate yet the e!ect of disease. A recent nanoindentation study examined the mechanical properties of dry human vertebral and tibial bone (Rho et al., 1997). As expected from Weaver's work, the elastic moduli and hardness values of dry bone were higher than in the present study, but a signi"cant di!erence between osteonal and interstitial bone properties was found. Another technique allowing for investigation of bone elasticity at the lamellar level is scanning acoustic microscopy (Meunier et al., 1988; Gardner et al., 1992; Katz and Meunier, 1993). While the GHz frequency range of this technique provides resolution on the order of a micron, calculation of elastic moduli from the acoustic impedance which contains information on both density and wave velocity seems to remain a major di$culty that does not appear with nanoindentation. In agreement with previous studies (Hodgskinson et al., 1989; Evans et al., 1990), elastic modulus correlates with hardness. Evans et al. (1990) found higher correlations (r"0.96) between elastic modulus and hardness that we attribute to the wider range of species, anatomical locations and therefore mineral content of their data. The average elastic modulus of diaphyseal cortical bone measured by nanoindentation was 20.1$5.4 GPa as compared to 17.0$1.7 GPa and 20.0$1.3 GPa measured in the longitudinal direction by mechanical and ultrasonic testing, respectively (Reilly and Burstein, 1975; Ashman et al., 1984). This coincidence has to be moderated by the fact that the isotropic nanoindentation modulus represents some weighted average of anisotropic moduli and the longitudinal elastic modulus of bone lamellae is therefore likely to be larger (Vlassak and Nix, 1994). Given this perspective, haversian porosity and cement line interface e!ects could then reconcile the macroscopic and lamellar elastic properties. The average elastic modulus of trabecular bone measured by nanoindentation was 11.4$5.6 GPa as compared to the 1.3 to 14.8 GPa range reported in a review paper by Guo and Goldstein (1997). The nanoindentation results are consistent with the upper part of this range, because they do not account for local strain heterogeneities due to lacunae or cement lines that become of signi"cant importance when testing microspecimens.
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The elastic modulus of human bone tissue was found to depend strongly on tissue type, anatomical location and individual. The di!erence in elastic modulus obtained between compact and trabecular tissue contradicts the original assumption by Wol! (1892) and the suggestion by Carter and Hayes (1977) that compact and trabecular bone are made of the same tissue. These di!erences may be attributed to variations in canalicular porosity or mineralization of the extracellular matrix (Currey, 1969; Scha%er and Burr, 1988). Collagen orientation distribution, however, may have in#uenced the interpretation of the average elastic properties of trabecular bone, since trabecular packets were tested randomly along multiple orientations, while Haversian bone was tested exclusively along its longitudinal axis. The di!erence in elastic properties found between anatomical locations may involve turnover rate and osteon type. A higher turnover rate reduces the mean age of the osteons and therefore reduces mineralization and the associated elastic properties. According to the work by Ascenzi et al., a di!erent distribution of osteon types, distinguished by predominant collagen "ber orientation, may be present in the neck as compared to the diaphysis which may also lead to distinct average mechanical properties (Ascenzi and Bonucci, 1967,1968,1972; Ascenzi et al., 1990,1994). Interestingly, the cortical shell of the neck exhibits intermediate elastic properties when compared to diaphyseal and trabecular femoral bone, which may prevent deleterious local deformation mismatches with the trabecular microstructure that could reduce the strength of the femoral neck. The distinct distributions of lamellar properties found among individuals provide a new perspective in the understanding of bone fragility. Failure may be strongly a!ected by heterogeneity of the tissue, allowing for strain concentration, damage accumulation and crack propagation. Undoubtedly, extensive studies and careful statistical analysis will be required to gain more insight in the distribution of these lamellar properties in human populations and in their potential relationship with aging and disease. In conclusion, a nanoindentation technique has been utilized to quantify hardness and elastic moduli of wet human femoral bone at the lamellar level of organization. Extending the "ndings of previous studies on hardness, signi"cant di!erences in elastic properties have been found among tissue types, anatomical sites and individuals. In the future, multiple experimental techniques will be needed to clarify the origin of these variations, to provide input for micromechanical models of bone tissue and to improve our understanding of the consequences of aging and disease on the mechanical integrity of human bone. We believe nanoindentation will continue to be an important experimental method supporting these studies.
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Acknowledgements This work was funded by NIH grant no. AR34399. The authors wish to thank M. Brown, J. Boura, K. Burrell, K. Kendig, O. Renaud, B. Riemer-McCreadie and M. Stock for their respective contributions. References Amprino, R., 1958. Investigations on some physical properties of bone tissue. Acta Anatomica 34, 161}186. Ascenzi, A., 1988. The micromechanics versus the macromechanics of cortical bone-A comprehensive presentation. Journal of Biomechanical Engineering 110, 357}363. Ascenzi, A., Baschieri, P., Benvenuti, A., 1990. The bending properties of single osteons. Journal of Biomechanics 23, 763}771. Ascenzi, A., Baschieri, P., Benvenuti, A., 1994. The torsional properties of single selected osteons. Journal of Biomechanics 27, 875}884. Ascenzi, A., Bonucci, E., 1967. The tensile properties of single osteons. The Anatomical Record 158, 375}386. Ascenzi, A., Bonucci, E., 1968. The compressive properties of single osteons. The Anatomical Record 161, 377}391. Ascenzi, A., Bonucci, E., 1972. The shearing properties of single osteons. The Anatomical Record 172, 499}510. Ashman, R.B., Cowin, S.C., Buskirk, W.C.V., Rice, J.C., 1984. A continuous wave technique for the measurement of the elastic properties of cortical bone. Journal of Biomechanics 17, 349}361. Bundy, K.J., 1989. Composite material models for bone. In: Cowin, S.C. (Ed.), Bone Mechanics. CRC Press, Boca Raton, FL, pp. 197}210. Carter, D.R., Hayes, W.C., 1977. The compressive behaviour of bone as a two phase porous structure. Journal of Bone and Joint Surgery 59 A, 954}962. Crolet, J.M., Aoubiza, B., Meunier, A., 1993. Compact bone: numerical simulation of mechanical characteristics. Journal of Biomechanics 26, 677}687. Currey, J.D., 1969. The mechanical consequences of variation in the mineral content of bone. Journal of Biomechanics 2, 1}11. Currey, J.D., 1988. The e!ect of porosity and mineral content on the Young's modulus of elasticity of compact bone. Journal of Biomechanics 21, 131}139. Evans, G.P., Behiri, J.C., Currey, J.D., Bon"eld, W., 1990. Microhardness and Young's modulus in cortical bone exhibiting a wide range of mineral volume fractions, and in bone analogue. Journal of Material Science: Materials in Medicine 1, 38}43. Gardner, T.N., Elliott, J.C., Sklar, Z., Briggs, G.A.D., 1992. Acoustic microscope study of the elastic properties of #uorapatite and hydroxyapatite, tooth enamel and bone. Journal of Biomechanics 25, 1265}1277.
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