Conventional, Bayesian, and Modified Prony's methods for characterizing fast and slow waves in equine cancellous bone

Abstract

Conventional, Bayesian, and the modified least-squares Prony's plus curve-fitting (MLSP þ CF) methods were applied to data acquired using 1 MHz center frequency, broadband transducers on a single equine cancellous bone specimen that was systematically shortened from 11.8 mm down to 0.5 mm for a total of 24 sample thicknesses. Due to overlapping fast and slow waves, conventional analysis methods were restricted to data from sample thicknesses ranging from 11.8 mm to 6.0 mm. In contrast, Bayesian and MLSP þ CF methods successfully separated fast and slow waves and provided reliable estimates of the ultrasonic properties of fast and slow waves for sample thicknesses ranging from 11.8 mm down to 3.5 mm. Comparisons of the three methods were carried out for phase velocity at the center frequency and the slope of the attenuation coefficient for the fast and slow waves. Good agreement among the three methods was also observed for average signal loss at the center frequency. The Bayesian and MLSP þ CF approaches were able to separate the fast and slow waves and provide good estimates of the fast and slow wave properties even when the two wave modes overlapped in both time and frequency domains making conventional analysis methods unreliable.

Mechanisms of Interaction of Ultrasound With Cancellous Bone: A Review

“…However, bandlimited deconvolution, MLSP+CF, and Bayesian methods gave similar results in bovine cancellous femur samples [228]. In addition, the Bayesian and MLSP+CF algorithms gave similar results in equine cancellous radius [146].…”

“…(That is, phase velocity increases with frequency). For media with attenuation coefficients that vary linearly with frequency, the Kramers-Kronig relations (which are required for causal systems) imply that [145][146][147] c f = c f 0 + c f 0 2 β π 2 ln f f 0…”

“…Separate reconstruction of individual fast and slow waves is challenging when the two waves overlap in time and frequency domains. Several methods proposed for this decomposition, including Bayesian [146,[222][223][224], modified least-squares Prony's (MLSP) [225], space alternating generalized expectation maximization (SAGE) [226], MLSP plus curve fitting (MLSP+CF) [227,228], and adaptive beamforming [229,230] algorithms, are predicated on a model for the transfer function of the bone specimen that contains terms for fast and slow waves [156,222] Y f = X f H fast f + H slow f (7) where Y(f) and X(f) are complex amplitude spectra of the signals passing through bone and water-path-only respectively. For the Bayesian and MLSP+CF algorithms, the fast and slow wave transfer functions are…”

A Prony-Based Curve-Fitting Method for Characterization of RF Pulses From Optoelectronic Devices

“…Future work will be focused on automated processing of repeated measurements to accurately fit undersampled signals. Additionally, upgrades to the algorithm to deal with higher-order oscillations in the signal tail will be investigated [39], [40]. Finally, while the current technique can only process uniformly sampled data, techniques to process non-uniformly sampled data will be developed [41].…”

Fast decomposition of two ultrasound longitudinal waves in cancellous bone using a phase rotation parameter for bone quality assessment: Simulation study

“…Accurate decomposition of the fast and slow waves would be highly beneficial for determination of the characteristics of cancellous bone. One strategy that has been used to decompose these waves is application of a Bayesian method that uses a Markov chain Monte Carlo method with simulated annealing (Marutyan et al, 2007;Anderson et al, 2010;Nelson et al, 2011;Hoffman et al, 2012;Groopman et al, 2015). The Bayesian decomposition method has a) Electronic mail: hirofumi.taki.a1@tohoku.ac.jp demonstrated high performance in accurately characterizing the fast and slow waves, but at the cost of a high computational load.…”