Effect of porosity distribution in a propagation direction on ultrasound waves through cancellous bone

Ultrasound propagation in clusters of elliptic (two-dimensional) or ellipsoidal (three-dimensional) scatterers randomly distributed in a fluid is investigated numerically. The essential motivation for the present work is to gain a better understanding of ultrasound propagation in trabecular bone. Bone microstructure exhibits structural anisotropy and multiple wave scattering. Some phenomena remain partially unexplained, such as the propagation of two longitudinal waves. The objective of this study was to shed more light on the occurrence of these two waves, using finite-difference simulations on a model medium simpler than bone. Slabs of anisotropic, scattering media were randomly generated. The coherent wave was obtained through spatial and ensemble-averaging of the transmitted wavefields. When varying relevant medium parameters, four of them appeared to play a significant role for the observation of two waves: (i) the solid fraction, (ii) the direction of propagation relatively to the scatterers orientation, (iii) the ability of scatterers to support shear waves, and (iv) a continuity of the solid matrix along the propagation. These observations are consistent with the hypothesis that fast waves are guided by the locally plate/bar-like solid matrix. If confirmed, this interpretation could significantly help developing approaches for a better understanding of trabecular bone micro-architecture using ultrasound.

Section: Resultssupporting

confidence: 91%

Simulations of ultrasound propagation in random arrangements of elliptic scatterers: Occurrence of two longitudinal waves

Mézière

Müller

Dobigny

et al. 2013

“…[4][5][6][7][8][9][10] In some experimental situations, the two waves are separated in the time-domain data, whereas in other circumstances the two waves substantially overlap and may appear as only a single wave. The degree to which the fast waves and slow waves overlap depends on a number of factors including porosity, structural anisotropy, ultrasonic path length, and the angle of insonification relative to the predominant trabecular orientation.…”

Section: Introductionmentioning

confidence: 99%

Determining attenuation properties of interfering fast and slow ultrasonic waves in cancellous bone

Nelson

Hoffman

Anderson

et al. 2011

Previous studies have shown that interference between fast waves and slow waves can lead to observed negative dispersion in cancellous bone. In this study, the effects of overlapping fast and slow waves on measurements of the apparent attenuation as a function of propagation distance are investigated along with methods of analysis used to determine the attenuation properties. Two methods are applied to simulated data that were generated based on experimentally acquired signals taken from a bovine specimen. The first method uses a time-domain approach that was dictated by constraints imposed by the partial overlap of fast and slow waves. The second method uses a frequency-domain log-spectral subtraction technique on the separated fast and slow waves. Applying the time-domain analysis to the broadband data yields apparent attenuation behavior that is larger in the early stages of propagation and decreases as the wave travels deeper. In contrast, performing frequency-domain analysis on the separated fast waves and slow waves results in attenuation coefficients that are independent of propagation distance. Results suggest that features arising from the analysis of overlapping two-mode data may represent an alternate explanation for the previously reported apparent dependence on propagation distance of the attenuation coefficient of cancellous bone.

“…The complicated microstructure is known to support the propagation of multiple compressional ultrasonic wave modes, often referred to as fast waves and slow waves. [13][14][15][16][17][18][19] When cancellous bone samples are insonified in through-transmission studies, the two waves occasionally are separated and clearly distinct in the radiofrequency ͑rf͒ data. However, in some circumstances, the two waves can strongly overlap during the time period over which the rf data are acquired, resulting in interference and difficulties in distinguishing between the two waves.…”

Section: Introductionmentioning

confidence: 99%

Inverse problems in cancellous bone: Estimation of the ultrasonic properties of fast and slow waves using Bayesian probability theory

Anderson

Bauer

Holland

et al. 2010

Quantitative ultrasonic characterization of cancellous bone can be complicated by artifacts introduced by analyzing acquired data consisting of two propagating waves ͑a fast wave and a slow wave͒ as if only one wave were present. Recovering the ultrasonic properties of overlapping fast and slow waves could therefore lead to enhancement of bone quality assessment. The current study uses Bayesian probability theory to estimate phase velocity and normalized broadband ultrasonic attenuation ͑nBUA͒ parameters in a model of fast and slow wave propagation. Calculations are carried out using Markov chain Monte Carlo with simulated annealing to approximate the marginal posterior probability densities for parameters in the model. The technique is applied to simulated data, to data acquired on two phantoms capable of generating two waves in acquired signals, and to data acquired on a human femur condyle specimen. The models are in good agreement with both the simulated and experimental data, and the values of the estimated ultrasonic parameters fall within expected ranges.