Analysis of the most energetic late arrival in axially transmitted signals in cortical bone

Axial transmission techniques are particularly suitable for the ultrasonic assessment of cortical bone. The generic term "axial transmission technique" indicates a measurement configuration in which emitters and receivers are placed on the same side of the skeletal site, along the bone axis. Whereas axially transmitted signals are composed of several contributions, only the first arriving signal was shown to be a robust indicator of bone status, because its velocity discriminates osteoporotic from healthy patients in clinical studies. Later arrivals may provide additional bone indicators enhancing diagnostic value, but the precise determination of their velocities is challenging. In this paper, we focus on the most energetic contribution and we applied a singular-value decomposition-based extraction method not yet employed in the domain of bone assessment with the aim of determining the velocity of this contribution. Signals acquired in vitro on human radii, together with academic models, were used to reveal the relationship between the velocity of the most energetic component and bone properties. The velocity of the most energetic component is highly correlated to cortical layer thickness in the in vitro database (R² = 0.6, P < 10^-5; compared with R² = 0.20, P < 10-² for the first arriving signal), consistent with a flexural type of wave on regular tubes or plates. Conclusions are in agreement with published papers based on other axial transmission and signal processing approaches.