Nonlinear elastodynamics in micro-inhomogeneous solids observed by head-wave based dynamic acoustoelastic testing

Dynamic acoustoelastic testing provides a more complete insight into the acoustic nonlinearity exhibited by micro-inhomogeneous media like granular and cracked materials. This method consists of measuring time of flight and energy modulations of pulsed ultrasonic waves induced by a low-frequency standing wave. Here pulsed ultrasonic head waves were employed to assess elastic and dissipative nonlinearities in a region near the surface of a solid. Synchronization of the ultrasound pulse sequence with the low-frequency excitation provided instantaneous variations in the elastic modulus and the attenuation as functions of the instantaneous low-frequency strain. Weak quadratic elastic nonlinearity and no dissipative nonlinearity were detected in duralumin. In limestone, distinction between tensile and compressive behaviors revealed an asymmetry in the acoustic nonlinearity and hysteresis in both the elastic modulus and the attenuation variations. Measured nonlinear acoustical parameters are in good agreement with values obtained by different techniques. Reversible acoustically induced conditioning modified the acoustic nonlinearity both quantitatively and qualitatively. It reduced tension-compression asymmetry, suggesting a nonequilibrium modification of the sources of acoustic nonlinearity. Additionally to the metrology of the acoustic nonlinearity, head wave based dynamic acoustoelastic testing may be a useful tool to monitor changes in the microstructure or the accumulation of damage in solids.

Young’s modulus repeatability assessment using cycling compression loading on cancellous bone

For various applications, precision of the Young’s modulus of cancellous bone specimens is needed. However, measurement variability is rarely given. The aim of this study was to assess the Young’s modulus repeatability using a uniaxial cyclic compression protocol on embedded specimens of human cancellous bone. Twelve specimens from 12 human calcanei were considered. The specimens were first defatted and then 1 or 2 mm at the ends were embedded in an epoxy resin. The compression experiment consists in applying 20 compressive cycles between 0.2 per cent and 0.6 per cent strain with a 2 Hz loading frequency. The coefficient of variation of the current protocol was found to be 1.2 per cent. This protocol showed variability similar to the end-cap technique (considered as a reference). It can be applied on porous specimen (especially human bone) and requires minimal bone length to limit end-artifact variability. The current method could be applied in association with noninvasive measurements (such as ultrasound) with full compatibility. This possibility opens the way for bone damage follow-up based on Young’s modulus monitoring.

Monitoring trabecular bone microdamage using a dynamic acousto-elastic testing method

Dynamic acousto-elastic testing (DAET) is based on the coupling of a low-frequency (LF) acoustic wave and high-frequency ultrasound (US) pulses (probing wave). It was developed to measure US viscoelastic and dissipative non-linearity in trabecular bone. It is well known that this complex biphasic medium contains microdamage, even when tissues are healthy. The purpose of the present study was to assess the sensitivity of DAET to monitor microdamage in human calcanei. Three protocols were therefore performed to investigate the regional heterogeneity of the calcaneus, the correlation between DAET measurements and microdamage revealed by histology, and DAET sensitivity to mechanically induced fatigue microdamage. The non-linear elastic parameter beta was computed for all these protocols. The study demonstrated the presence of high viscoelastic and dissipative non-linearity only in the region of the calcaneus close to the anterior talocalcaneal articulation (region of high bone density). Protocols 1 and 2 also showed that most unsorted calcanei did not naturally exhibit high non-linearity, which is correlated with a low level of microcracks. Nevertheless, when microdamage was actually present, high levels of US non-linearity were always found, with characteristic non-linear signatures such as hysteresis and tension/compression asymmetry. Finally, protocol 3 demonstrated the high sensitivity of DAET measurement to fatigue-induced microdamage.

Exploration of trabecular bone nonlinear elasticity using time-of-flight modulation

Bone tissue contains microcracks that may affect its mechanical properties as well as the whole trabecular structure. The relationship between crack density and bone strength is nevertheless poorly understood. Linear ultrasound techniques being almost insensitive to the level of damage, we propose a method to measure acoustic non- linearity in trabecular bone using time-of-flight modulation (TOFM) measurements. Ultrasonic short bursts times-of- flight (TOF) are modulated as a result of nonlinear interaction with a low-frequency (LF) wave in the medium. TOF variations are directly related to elastic modulus variations. Classical and nonclassical nonlinear parameters beta, delta, and alpha can be derived from these measurements. The method was validated in materials with classical, quadratic, nonlinear elasticity. In dense trabecular bone region, TOFM related to classical, quadratic, nonlinear elasticity as a function of the LF pressure exhibits tension-compression asymmetry. The TOFM amplitude measured in dense areas of trabecular bone is almost one order of magnitude higher than in a low-density area, but the linear parameters show much smaller variations: 5% for ultrasound propagation velocity and 100% for broadband ultrasonic attenuation (BUA). In high-density trabecular bone regions, beta depends on the LF pressure amplitude and can reach 400 at 50 kPa.

[Assessment of a matrix-based quantitative ultrasound imaging device (Beam scanner): reproducibility]

PURPOSE

A new matrix-based quantitative ultrasound (QUS) device was developed for the assessment of two parameters: BUA (Broadband Ultrasound Attenuation) and SOS (Speed Of Sound). This device, called Beam scanner, is a contact imaging device designed to evaluate the calcaneus. The aim of this preliminary study was to evaluate the reproducibility of results in a sample of patient with heterogeneous age distribution.

MATERIALS AND METHODS

Seventy-six subjects were included: 18 healthy young males, 18 healthy young women and 40 women aged over 50 years old, including 19 osteoporotic patients according to WHO criteria. Five measurements were made for each patient after foot repositioning. Short-term precision was estimated using the coefficient of variation (CV), standardized CV (SCV) and intra-class correlation coefficient (ICC).

RESULTS

SCV varied with the group of subjects between 2.0 and 4.3% for BUA, and between 3.1 and 4.5% for SOS. Mean values of BUA and SOS were statistically lower for osteoporotic women compared with healthy young women or healthy young males (p<0.001). For BUA, only SCV and ICC were better for women aged over 50 years old but without statistical difference.

CONCLUSION

This study shows that the heterogeneity of the studied sample population is not a significant factor when assessing precision. This new device has a precision similar to others QUS devices.

2D arrays device for calcaneus bone transmission: an alternative technological solution using crossed beam forming

In the context of manned space flight with the European Space Agency, a quantitative ultrasound device for transmission imaging through the calcaneus bone has been developed. It includes two matrix transducers of 576 elements each in order to electronically perform the scanning and the focusing of the 500 kHz ultrasonic beam. This device called the BEAM scanner, provides two parametric images of attenuation (BUA, broadband ultrasonic attenuation) and velocity (SOS, speed of sound) of the investigated skeletal site. The cost and complexity of such a device has motivated the study of an alternative solution, less demanding in terms of technology, based on a crossed beam former [H. Ermert et al., A new concept for a real-time ultrasound transmission camera, in: IEEE Ultrasonics Symposium Proceedings, 2000, pp. 1611-1614]. It consists in forming two perpendicular cylindrically focused planes, one in emission, one in reception, instead of two spherically focused apertures. The crossing line of the two planes replaces the focused beam. The 2D beam forming technological challenge is moved to a 1D simpler and cheaper architecture. In this work the two solutions have been compared for in vivo measurements. Data sets have been acquired using all spatial combinations of emission and reception single elements of the matrix. Then signals have been processed using either the cylindrical or the spherical focussing mode. For cylindrical focussing, the increased level of the side lobes caused severe artefacts. Several apodization techniques have been implemented to reduce these artefacts, resulting in encouraging results. After a brief description of this new ultrasonic method for bone quantitative assessment, several reconstructed images using both processing schemes are presented. Corresponding statistical results obtained in 29 subjects are also provided.

In vivo performance of a matrix-based quantitative ultrasound imaging device dedicated to calcaneus investigation

We developed a prototype of an ultrasound (US) bone matrix densitometer, the BEAM scanner, in the context of a European Space Agency research program. This device, which is a contact imaging device, was designed to overcome the limitations of immersion devices in space. Broadband US attenuation (BUA) and speed of sound (SOS) parameters were calculated from the radiofrequency (RF) signal. The principle aim of this study was to evaluate in vivo performance in direct comparison with a currently available device (UBIS 3000, DMS, France). The short-term precision of the BEAM scanner for BUA was estimated at 2.8%, whereas it was 2.3% with UBIS 3000. The short-term precision for SOS was 0.3%, and this was the same as the coefficient of variation (CV) of the UBIS 3000. CVs of 3.4% and 0.6% for midterm precision were found for BUA and SOS, respectively, and UBIS 3000 scores were 3% and 0.4%, respectively. This preliminary study demonstrates the high performance of the BEAM scanner and its new concept offers a wide range of improvements and new applications.