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

Abstract

Ultrasound signals that pass through cancellous bone may be considered to consist of two longitudinal waves, which are called fast and slow waves. Accurate decomposition of these fast and slow waves is considered to be highly beneficial in determination of the characteristics of cancellous bone. In the present study, a fast decomposition method using a wave transfer function with a phase rotation parameter was applied to received signals that have passed through bovine bone specimens with various bone volume to total volume (BV/TV) ratios in a simulation study, where the elastic finite-difference time-domain method is used and the ultrasound wave propagated parallel to the bone axes. The proposed method succeeded to decompose both fast and slow waves accurately; the normalized residual intensity was less than -19.5 dB when the specimen thickness ranged from 4 to 7 mm and the BV/TV value ranged from 0.144 to 0.226. There was a strong relationship between the phase rotation value and the BV/TV value. The ratio of the peak envelope amplitude of the decomposed fast wave to that of the slow wave increased monotonically with increasing BV/TV ratio, indicating the high performance of the proposed method in estimation of the BV/TV value in cancellous bone.

Mechanisms of Interaction of Ultrasound With Cancellous Bone: A Review

“…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…”

“…First, initial estimates of fast and slow waves are performed using frequency-domain interferometry. Second, final estimates are obtained by performing least-squares fitting in the time domain [229,230].…”