On the prediction of Young's modulus in calcaneal cancellous bone by ultrasonic bulk and bar velocity measurements.

Abstract

This study evaluated two different approaches to the prediction of Young's modulus (E) from ultrasonic velocity and density measurements in 23 cubes of cancellous bone from human calcaneae. The first approach used clinically applicable measurements of bulk velocity and bone mineral density (BMD), whilst the second involved bar velocity and apparent density, which are strictly in vitro measurements. Bulk velocities were measured with an immersion technique with 1 MHz transducers using three different transit time markers (first arrival, thresholding, zero-crossing). Bar velocities were measured in the defatted specimens using a contact technique with 37 kHz transducers in air. Volumetric BMD was derived from dual-energy X-ray absorptiometry measurements, and apparent density was measured directly. Compressive mechanical testing was used to determine E. Bulk velocity, bar velocity and E all displayed significant anisotropy, being greatest in the proximo-distal (PD) axis and least in the medio-lateral (ML) axis. Bulk velocity was dependent on the transit time marker used, with velocity differences of up to 20% observed between different markers. Bar velocities were significantly lower than bulk velocities in all directions. Both bulk and bar velocities correlated with E (r2 = 0.26-0.83, r = 0.36-0.81, respectively) with stronger relationships obtained when the data for the three axes were pooled. The predictive ability of bulk velocities determined using different markers was similar. In general, combining velocity and density measurements yielded improved correlations with E. Thus, strong correlations were observed between E and the product of BMD and bulk velocity2 (r2 = 0.58-0.89), and the product of apparent density and bar velocity2 (r2 = 0.58-0.89). These results demonstrate that clinically applicable measurements of bulk velocity and BMD are good predictors of the elastic modulus of calcaneal bone, and that bulk and bar velocity, both alone and when combined with density measurements, have a similar predictive ability for mechanical properties.