Ultrasound propagation in trabecular bone: a numerical study of the influence of microcracks

Numerical parametric study of Nonlinear Coda Wave Interferometry sensitivity to microcrack size in a multiple scattering medium

This paper reports a numerical study of the sensitivity and applicability of the Nonlinear Coda Wave Interferometry (NCWI) method in a heterogeneous material with a localized microcracked zone. We model the influence of a strong pump wave on the localized microcracked zone as a small average increase in the length of each crack. Further probing of this microcracked zone with a multiply scattered ultrasonic wave induces small changes to the coda-type signal, which are quantified with coda wave interferometry. A parametric sensitivity study of the CWI observables with respect to the changes in crack length is established via numerical simulations of the problem using a 2D spectral element method (SEM2D). The stretching of the signal, proportional to the relative variation in effective velocity, is found to be linearly proportional to the global change in crack length, while the other CWI parameter, the remnant decorrelation coefficient, is found to be quadratically proportional to the crack length change. The NCWI method is shown to be relevant for the detection of different damaged material states in complex solids. The reported numerical results are especially significant in the context of quantitative nondestructive evaluation of micro-damage level of a heterogeneous materials using nonlinear ultrasound signals.

Mechanisms of Interaction of Ultrasound With Cancellous Bone: A Review

Ultrasound is now a clinically accepted modality in the management of osteoporosis. The most common commercial clinical devices assess fracture risk from measurements of attenuation and sound speed in cancellous bone. This review discusses fundamental mechanisms underlying the interaction between ultrasound and cancellous bone. Because of its two-phase structure (mineralized trabecular network embedded in soft tissue-marrow), its anisotropy, and its inhomogeneity, cancellous bone is more difficult to characterize than most soft tissues. Experimental data for the dependencies of attenuation, sound speed, dispersion, and scattering on ultrasound frequency, bone mineral density, composition, microstructure, and mechanical properties are presented. The relative roles of absorption, scattering, and phase cancellation in determining attenuation measurements in vitro and in vivo are delineated. Common speed of sound metrics, which entail measurements of transit times of pulse leading edges (to avoid multipath interference), are greatly influenced by attenuation, dispersion, and system properties, including center frequency and bandwidth. However, a theoretical model has been shown to be effective for correction for these confounding factors in vitro and in vivo. Theoretical and phantom models are presented to elucidate why cancellous bone exhibits negative dispersion, unlike soft tissue, which exhibits positive dispersion. Signal processing methods are presented for separating "fast" and "slow" waves (predicted by poroelasticity theory and supported in cancellous bone) even when the two waves overlap in time and frequency domains. Models to explain dependencies of scattering on frequency and mean trabecular thickness are presented and compared with measurements. Anisotropy, the effect of the fluid filler medium (marrow in vivo or water in vitro), phantoms, computational modeling of ultrasound propagation, acoustic microscopy, and nonlinear properties in cancellous bone are also discussed.

Dynamic acousto-elastic test using continuous probe wave and transient vibration to investigate material nonlinearity

This study demonstrates the feasibility of the dynamic acousto-elastic effect of a continuous high frequency wave for investigating the material nonlinearity upon transient vibration. The approach is demonstrated on a concrete sample measuring 15×15×60cm(3). Two ultrasonic transducers (emitter and receiver) are placed at its middle span. A continuous high frequency wave of 500kHz propagates through the material and is modulated with a hammer blow. The position of the hammer blow on the sample is configured to promote the first bending mode of vibration. The use of a continuous wave allows discrete time extraction of the nonlinear behavior by a short-time Fourier transform approach, through the simultaneous comparison of a reference non-modulated signal and an impact-modulated signal. The hammer blow results in phase shifts and variations of signal amplitude between reference and perturbed signals, which are driven by the resonant frequency of the sample. Finally, a comprehensive analysis of the relaxation mechanisms (modulus and attenuation recovery) is conducted to untangle the coupled fast and slow hysteretic effects.