Effects of non-optimal focusing on dual-frequency ultrasound measurements of bone

In pulse-echo (PE) ultrasound measurements, the use of focused transducers is desirable for quantitative assessment of bone characteristics because of the attenuation in the overlying soft tissues. However, the variable thickness and composition of the soft tissue overlying bone affect the focal depth of the ultrasound beam and induce errors into the measurements. To compensate for the attenuation-related effects caused by the interfering soft tissue (i.e., fat and lean tissue), a dual-frequency ultrasound (DFUS) technique was recently introduced. The aim of this study was to investigate the effect of non-optimal focal depth of the ultrasound beam on the determination of the integrated reflection coefficient (IRC) of bone when overlaid by an interfering layer composed of oil and water. The feasibility of the DFUS-based correction of the IRC was evaluated through numerical simulations and experimental measurements. Even when the interfering layer-bone interface was out of focus, the total thickness of the interfering layer could be accurately determined with the technique. However, based on the simulations, the errors in the determination of the composition of the interfering layer increased (0.004 to 113.8%) with the increase in distance between the interfering layer-bone interface and the focus of the ultrasound beam. Attenuation compensation, based on the true composition of the interfering layer, resulted in an average relative error of 22.3% in the IRC values calculated from the simulations. Interestingly, the attenuation compensation with the interfering layer composition estimated using the DFUS technique resulted in a smaller average relative error of 14.9% in the IRC values. The simulations suggest that DFUS can reduce the errors induced by soft tissue in bone PE ultrasound measurements. The experimental measurements indicate that the accuracy of the IRC measurements is rather similar when using DFUS correction or correction based on the true composition of the interfering layer. However, the results suggest that accurate determination of soft tissue composition may be difficult without optimal focusing of the ultrasound beam on the soft tissue-bone interface.