Assessment of trabecular bone tissue elasticity with resonant ultrasound spectroscopy.

The material properties of the trabeculae (tissue-level properties), together with the trabecular architecture and the bone volume fraction determine the apparent millimetre-scale bone mechanical properties. We present a novel method to measure trabecular tissue elastic modulus Et using resonant ultrasound spectroscopy (RUS). The first mechanical resonance frequency fe of a freestanding cuboid specimen is measured and used to back-calculate Et. The steps of the back-calculation are (1) the apparent stiffness tensors C(Et˜) is computed using micro-finite elements for a set of trial values of tissue Young's modulus Et˜ based on the computed tomography image of the specimen; (2) the modeled free-vibration resonance frequencies fm(Et˜) of the specimen is calculated with the Rayleigh-Ritz method using C(Et˜); (3) finally, Et is obtained by interpolation using fe and fm(Et˜). Four bovine bone specimens were tested (nominal size 5×6 ×6mm3). Average (standard deviation) of Et was 13.12 (1.06)GPa. The measurement of a single resonance frequency enabled an estimation of tissue elasticity in line with available data. RUS is a non destructive technique relatively easy to implement compared to traditional mechanical testing. The novel method could contribute to a better documentation of bone tissue elasticity which is an important parameter of micro-finite element analyses for the clinical assessment of bone strength.

Cortical bone elasticity measured by resonant ultrasound spectroscopy is not altered by defatting and synchrotron X-ray imaging.

In the study of mechanical properties of human bone, specimens may be defatted before experiments to prevent contamination and the risk of infections. High energy synchrotron radiation micro-computed tomography (SR-µCT) is a popular technique to study bone microstructure. However, little is known about the effects of defatting or irradiation during SR-µCT imaging on different elastic coefficients including shear and longitudinal moduli in different anatomical directions. In this work, these effects are evaluated on a set of 24 samples using resonant ultrasound spectroscopy (RUS), which allows one to accurately measure the complete set of elastic coefficients of cortical bone non destructively. The results show that defatting with diethylether and methanol and irradiation up to 2.5kGy has no detectable effect on any of the elastic coefficients of human cortical bone.

A critical assessment of the in-vitro measurement of cortical bone stiffness with ultrasound.

Elasticity assessment based on bulk wave velocity (BWV) measurements is the most popular technique to characterize the anisotropic stiffness tensor in cortical bone. Typically, a cuboid bone specimen is cut with its sides along the different anatomical directions. Then, the velocity of shear and longitudinal waves propagating along different directions are assessed, from which stiffness coefficients are calculated. Despite the importance of obtaining accurate elasticity values for bone research, there is no generally accepted protocol to measure BWV and the precision of the technique has been seldom investigated. The purpose of this work is to critically assess the method to measure BWV on cuboid specimens in terms of ultrasound frequency, specimen size and signal processing technique. In this study, we measured polycarbonate specimens of different dimensions and 55 human bone specimens with different transducers using frequencies ranging from 2.25 to 10MHz and 1-5MHz for longitudinal and shear waves, respectively. We compared four signal processing methods to detect the wave arrival time. The main results are that, (1) the measurement of shear waves is more complex than that of longitudinal wave, being less precise and more sensitive to sample size; (2) the estimated stiffness depends on the signal processing technique used (up to 10% variation for shear coefficients of bone); and (3) bone stiffness assessed from BWV using the first arrival of the signal to determine the time-of-flight is not different from stiffness assessed using resonant ultrasound spectroscopy (RUS). These results evidence that the measurement method can have an effect on the stiffness values estimates and hence, a well-defined protocol is needed to accurately measure bone stiffness coefficients based on BWV.

Can a continuous mineral foam explain the stiffening of aged bone tissue? A micromechanical approach to mineral fusion in musculoskeletal tissues.

UNLABELLED: Recent experimental data revealed a stiffening of aged cortical bone tissue, which could not be explained by common multiscale elastic material models. We explain this data by incorporating the role of mineral fusion via a new hierarchical modeling approach exploiting the asymptotic (periodic) homogenization (AH) technique for three-dimensional linear elastic composites. We quantify for the first time the stiffening that is obtained by considering a fused mineral structure in a softer matrix in comparison with a composite having non-fused cubic mineral inclusions. We integrate the AH approach in the Eshelby-based hierarchical mineralized turkey leg tendon model (Tiburtius et al 2014 Biomech. MODEL: Mechanobiol. 13 1003-23), which can be considered as a base for musculoskeletal mineralized tissue modeling. We model the finest scale compartments, i.e. the extrafibrillar space and the mineralized collagen fibril, by replacing the self-consistent scheme with our AH approach. This way, we perform a parametric analysis at increasing mineral volume fraction, by varying the amount of mineral that is fusing in the axial and transverse tissue directions in both compartments. Our effective stiffness results are in good agreement with those reported for aged human radius and support the argument that the axial stiffening in aged bone tissue is caused by the formation of a continuous mineral foam. Moreover, the proposed theoretical and computational approach supports the design of biomimetic materials which require an overall composite stiffening without increasing the amount of the reinforcing material.

Analytical methods to determine the effective mesoscopic and macroscopic elastic properties of cortical bone.

We compare theoretical predictions of the effective elastic moduli of cortical bone at both the meso- and macroscales. We consider the efficacy of three alternative approaches: the method of asymptotic homogenization, the Mori-Tanaka scheme and the Hashin-Rosen bounds. The methods concur for specific engineering moduli such as the axial Young's modulus but can vary for others. In a past study, the effect of porosity alone on mesoscopic properties of cortical bone was considered, taking the matrix to be isotropic. Here, we consider the additional influence of the transverse isotropy of the matrix. We make the point that micromechanical approaches can be used in two alternative ways to predict either the macroscopic (size of cortical bone sample) or mesoscopic (in between micro- and macroscales) effective moduli, depending upon the choice of representative volume element size. It is widely accepted that the mesoscale behaviour is an important aspect of the mechanical behaviour of bone but models incorporating its effect have started to appear only relatively recently. Before this only macroscopic behaviour was addressed. Comparisons are drawn with experimental data and simulations from the literature for macroscale predictions with particularly good agreement in the case of dry bone. Finally, we show how predictions of the effective mesoscopic elastic moduli can be made which retain dependence on the well-known porosity gradient across the thickness of cortical bone.

Simultaneous determination of acoustic velocity and density of a cortical bone slab: ultrasonic model-based approach.

An ultrasonic setup coupled to a 1-D mathematical model of wave propagation is used to determine the material properties of elastic solids. A maximum likelihood fit of the acoustic response with the model response in the frequency domain enables the simultaneous determination of acoustic velocity, mass density, damping, and sample thickness. The method, previously tested with homogeneous materials, has been applied to compact bone despite the fact that it is a highly attenuating material.