Computer and Experimental Simulation of a Cortical End-plate Phase Cancellation Artefact in the Measurement of BUA at the Calcaneus

It has been experimentally demonstrated that for the measurement of broadband ultrasound attenuation (BUA) at the human calcaneus the cortical end-plate creates a measurement artefact of the order of 7 dB MHz(-1). It has been suggested that the origin of this artefact may be a phase cancellation of the ultrasound pulse resulting from inconsistencies in propagation time across the ultrasound beam. Experimental and computer simulations were performed on samples of varying degrees of curvature and hence varying propagation times across the ultrasound beam. The experimental simulation incorporated Perspex samples of 35, 50 and 75 mm radius. The computer simulation was implemented using Matlab and Simulink, with the propagation time represented by a transport delay. The wavelet-based simulation incorporated a digitized transmitted ultrasound pulse derived from the experimental simulation. The experimental and computer-derived frequency spectra for the varying radii samples were comparable, demonstrating, firstly, that there is a significant dependence of measured BUA upon radius of curvature and, secondly, that the response in measured BUA to radius of curvature is similar in magnitude and trend for both experimental and computer simulations. The current study suggests that the BUA artefact observed in vitro corresponds to a radius of approximately 58 mm. Although the radius of curvature was not recorded in the original in vitro study, this value appears to be reasonable. This study indicates that the assumptions within the computer simulation were manifested within the experimental validation, and, hence, the observed BUA measurement artefact is related to the presence of the calcaneal cortical end-plate and is due to phase cancellation of the propagating ultrasound pulse.