Structural and material mechanical properties of human vertebral cancellous bone

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Abstract

The structural Young's modulus (i.e. that of the cancellous framework) was determined by non-destructive compressive mechanical testing in the three orthogonal axes of 48 vertebral bone cubes. In addition, the material Young's modulus (i.e. of the trabeculae themselves) was estimated using an ultrasonic technique. Apparent and true density were determined by direct physical measurements. Significant mechanical anisotropy was observed: mean structural Young's modulus varied from 165 MPa in the supero-inferior direction to 43 MPa in the lateral direction. Structural Young's modulus correlated with apparent density, with power-law regression models giving the best correlations (r2=0.52–0.88). Mechanical anisotropy increased as a function of decreasing apparent density (p<0.001). Material Young's modulus was 10.0±1.3 GPa, and was negatively correlated with apparent density (p<0.001). In multiple regression models, material Young's modulus was a significant independent predictor of structural Young's modulus only in the supero-inferior direction. The data suggest the presence of two effects in vertebral bone associated with decreasing apparent density and, by implication, bone loss in general: (a) increased mechanical anisotropy, such that there is relative conservation of stiffness in the axial direction compared with the transverse directions; and (b) increased stiffness of the trabeculae themselves.

Introduction

Osteoporotic fracture of the vertebra, and consequent spinal deformity, pain and disability, constitute a major clinical problem amongst the elderly. In addition to their medical and social impact, these fractures, along with other osteoporotic fractures at the forearm and, most seriously, the proximal femur, are imposing increasing economic demands on our healthcare systems. The annual direct costs alone of treating these fractures have been estimated at 614 million pounds in the U.K., and $6 billion in the U.S.A.[1]

Osteoporotic vertebral fractures are frequently associated with low or minimal trauma, clearly indicating that a pathological reduction in bone mechanical competence has occurred prior to the fracture event. Of major importance is the reduction in the quantity of solid bone tissue present in a given volume that occurs in osteoporosis, and which is detected in clinical measurements of areal (projectional) bone mineral density (BMD) using dual energy X-ray absorptiometry (DXA) and volumetric BMD using quantitative computed tomography (QCT). This reduction in apparent bone density leads to a reduction in the mechanical properties of the bone. However, other factors may be significant in defining the mechanical properties of cancellous bone. In discussing such factors it is convenient to clearly distinguish between the properties at a structural level (i.e. those of the cancellous framework, including both the bone and the interstitial spaces) and at a material level (i.e. those of the trabeculae that make up the framework). It is clear that the material properties may significantly affect structural properties but there are relatively few published data on this point2, 3, and it is still unclear whether osteoporotic bone loss is associated with changes in the material properties of the trabeculae that remain. The microstructure of the cancellous framework is another potentially very important determinant of the overall mechanical properties of cancellous bone, although it has yet to be demonstrated that, for bone from a given site studied in a given direction, microstructural information is an independent additional predictor of mechanical properties beyond that of apparent density alone. The importance of trabecular structure can be assessed by quantifying the changes in mechanical properties seen when the direction of the measurement is changed, for example, from parallel to the dominant direction of trabecular alignment to perpendicular to that direction. Such measurements allow the quantification of the anisotropy of cancellous bone, which represents an important feature of the structural adaptation of the bone to the physiological loads imposed upon it. Anecdotal evidence suggests that osteoporotic vertebral fractures are often associated with actions, such as rising from bed, which involve twisting the spine and which may lead to forces in the vertebra different from the predominantly axial compressive regime. It may be hypothesised that such loading regimes cause many osteoporotic vertebral fractures, and that studying the anisotropy of vertebral bone could help us understand the particular vulnerability of the osteoporotic vertebra to collapse under moderate loads.

Biomechanical studies of the structural behaviour of human cancellous bone are extensive, dating from the early 1960s, and have been reviewed in depth elsewhere[4]. The mechanical properties of cancellous bone correlate well with ash density and apparent density5, 6and are moderately strain rate dependent[6]. In addition, it is known that the mechanical properties vary within the vertebral body[7], and demonstrate anisotropy8, 9, 10.

Rather less is known about the mechanical properties of the trabeculae themselves. Wolff[11]speculated that the trabecular material modulus was similar to that of cortical bone, and this assumption is common in many more recent studies12, 13, 14, 15. In fact, direct assessement of the mechanical properties of the trabecular material poses some problems, and several different approaches have been reported in the literature. Carter and Hayes[6]observed a cubic relationship between structural Young's modulus and apparent density in trabecular bone, and observed that extrapolating to higher densities allowed cortical bone to be placed within the same relationship. This implied that the solid trabecular material essentially had the same mechanical properties as cortical bone, i.e. Young's modulus of approximately 20 GPa. However, other workers have reported that the mechanical properties of the trabecular tissue to be much lower than those of cortical bone. Williams and Lewis[16]used a two-dimensional finite element model to determine the modulus of trabecular material, obtaining estimates of as low as 1.3 GPa. These values are unlikely to be correct, since structural Young's moduli in excess of 4 GPa are observed in dense cancellous bone4, 17. In a later study, Williams and Johnson[18]extrapolated from the mechanical behaviour of cancellous bone/PMMA composites to obtain an estimate of the trabecular tissue modulus of 8.9 GPa. Another approach has been to devise micro-mechanical tests for directly assessing the properties of individual trabeculae. Buckling loads have been measured in single trabeculae14, 19, giving average Young's modulus values of approximately 10 GPa, but some workers using similar methods[20]have obtained much lower values. Ryan and Williams[21]used tensile testing and also obtained very low values of approximately 1 GPa. Rho et al.[22]performed tensile tests on individual trabecular struts from the human tibia, and obtained Young's moduli values of 10.4 GPa. This compared with Young's modulus of 18.6 GPa obtained for cortical bone micro-specimens.

Yet another method for determination of trabecular material Young's modulus has been the use of ultrasound. Ultrasonic determination of Young's modulus (E) relies on the fact that when longitudinal ultrasonic waves propagate along rod or bar-like structures whose typical cross-sectional dimensions are much less than the wavelength of the ultrasound, the velocity, c, is given byc=Eρwhere ρ is the density of the rod material[23]. Whilst it is theoretically possible to propagate ultrasound through an individual trabecula, there are problems in specimen preparation and handling, similar to those encountered in conventional micromechanical tests. Nevertheless, ultrasonic measurements in single trabeculae have been reported by Rho et al.[22], who obtained an average trabecular material modulus of 14.8 GPa. However, ultrasonic assessment of this type is most valuable when it can be applied to larger specimens of trabecular bone, and there is evidence that this can be achieved when the trabecular structure is highly orientated in a single direction, such as is found in the vertebra, femur and tibia. Ashman and Rho[24]argued that ultrasonic velocity measurements along the main axis of trabecular orientation in human femoral and bovine bone samples corresponded to bar velocities through individual trabeculae, and could therefore be used to determine trabecular material modulus. Using 2.25 MHz transducers, velocities of 2200–2700 m/s were obtained, and the calculated material moduli ranged from 10.9 to 13.1 GPa. Williams[25]challenged the validity of this approach, suggesting that the velocities were consistent with those of a compressional (bulk) wave predicted using Biot's theory, a phenomenological theory describing wave propagation in fluid-saturated porous solids. However, data supporting the hypothesis of bar wave propagation in individual trabeculae have come from work with water-saturated vertebral bone. Nicholson et al.[26]reported that broadband ultrasonic pulses propagating in the axial direction separated into a fast (2000–2500 m/s) lower frequency wave and a slow (1500 m/s) higher frequency wave. Repeating the measurements in air, only the fast wave was observed, confirming that this wave was travelling directly through the bone (air is highly attenuating). Furthermore, this fast wave was only present in measurements in the cranio-caudal direction, strongly suggesting that it was associated with the orientation of trabeculae parallel to the axis of measurement: a bulk wave would have been expected to have been present in the other two measurement axes. Similar phenomena have been observed in highly orientated cancellous bone from the calcaneus (Nicholson, data in preparation).

This present study aimed to investigate the structural Young's modulus of vertebral bone concentrating, in particular, on (a) relationships with apparent bone density; (b) quantification of anisotropy; and (c) the influence of trabecular material properties. It represents the first substantial study of human vertebral bone to make use of non-destructive multi-axial mechanical testing, and also the first use of ultrasound to estimate the material Young's modulus of bone from this site. The work was principally directed towards understanding osteoporotic vertebral fracture, but the non-destructive techniques described could prove to be useful in other areas.

Section snippets

Bone specimens

Lumbar spine segments consisting of vertebrae L2 to L4 were excised from 50 adult cadavers. These 50 subjects were a subset of a larger group of 70 subjects comprising the study material for the EC BIOMED1 Concerted Action “Assessment of Quality of Bone in Osteoporosis”, whose clinical characteristics have been described elsewhere[27]. Twenty subjects were excluded because the bone samples were unavailable at the time of the present work. In brief, this was an unscreened group of subjects—no

Results

Table 1 summarises the measured values. The specimens were very porous, with a mean bone volume fraction of only 7.6% and a mean apparent density of 0.149 g/cm3. The true density of the trabecular material was relatively constant, at 1.962±0.056 g/cm3.

There were significant differences in structural Young's modulus (Es) between all three axes: Es was greatest in the supero-inferior direction and least in the lateral direction (Table 1). There was a small but significant difference between Es in

Discussion

The values we report for structural Young's moduli of cancellous bone are quite comparable with previously published data for the vertebra12, 32, 33. It should be noted that Odgaard and Linde[33]have shown that Young's modulus of cubical specimens of trabecular bone determined by conventional compressive testing may be underestimated by approximately 20%. The error appears to arise from the uneven strain distribution due to the lack of support of cut vertical trabeculae at the interface with

Conclusions

This study presents initial data suggestive of two effects accompanying reduced vertebral bone apparent density, and, by implication, longitudinal bone loss. Firstly, we found an increase in mechanical anisotropy with decreasing apparent density, such that there was a relative conservation of Young's modulus in the axial (supero-inferior) direction compared with the transverse directions. Secondly, there was evidence for an increase in the material Young's modulus of the trabeculae, such that

Acknowledgements

This work was performed within the framework of the EC BIOMED1 Concerted Action “Assessment of Quality of Bone in Osteoporosis”, contract number BMH1-CT92-0296. One of us (PHFN) is grateful for fellowships from the Royal Society, London, and the Academic Board of the Katholieke Universiteit Leuven, Belgium.

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