Effect of bone cortical thickness on velocity measurements using ultrasonic axial transmission: A 2D simulation study

In recent years, quantitative ultrasound (QUS) has played an increasing role in the assessment of bone status. The axial transmission technique allows to investigate skeletal sites such as the cortical layer of long bones (radius, tibia), inadequate to through-transmission techniques. Nevertheless, the type of propagation involved along bone specimens has not been clearly elucidated. Axial transmission is investigated here by means of two-dimensional simulations at 1 MHz. We focus our interest on the apparent speed of sound (SOS) of the first arriving signal (FAS). Its dependence on the thickness of the plate is discussed and compared to previous work. Different time criteria are used to derive the apparent SOS of the FAS as a function of source–receiver distance. Frequency-wave number analysis is performed in order to understand the type of propagation involved. For thick plates $(\mathrm{thickness}{\mathrm{>\lambda }}_{\mathrm{bone}},$ longitudinal wavelength in bone), and for a limited range of source–receiver distances, the FAS corresponds to the lateral wave. Its velocity equals the longitudinal bulk velocity of the bone. For plate thickness less than ${\lambda }_{\mathrm{bone}},$ some plate modes contribute to the FAS, and the apparent SOS decreases with the thickness in a way that depends on both the time criterion and on the source–receiver distance. The FAS corresponds neither to the lateral wave nor to a single plate mode. For very thin plates $(\mathrm{thickness}{\mathrm{<\lambda }}_{\mathrm{bone}}\text{/4),}$ the apparent SOS tends towards the velocity of the lowest order symmetrical vibration mode ${\mathrm{(S}}_0$ Lamb mode).