Noninvasive determination of bone mechanical properties using vibration response: a refined model and validation in vivo

Abstract

Accurate non-invasive mechanical measurement of long bones is made difficult by the masking effect of surrounding soft tissues. Mechanical response tissue analysis (MRTA) offers a method for separating the effects of the soft tissue and bone; however, a direct validation has been lacking. A theoretical analysis of wave propagation through the compressed tissue revealed a strong mass effect dependent on the relative accelerations of the probe and bone. The previous mathematical model of the bone and overlying tissue system was reconfigured to incorporate the theoretical finding. This newer model (six-parameter) was used to interpret results using MRTA to determine bone cross-sectional bending stiffness, EIMRTA. The relationship between EIMRTA and theoretical EI values for padded aluminum rods was R2 = 0.999. A biological validation followed using monkey tibias. Each bone was tested in vivo with the MRTA instrument. Postmortem, the same tibias were excised and tested to failure in three-point bending to determine EI3-PT and maximum load. Diaphyseal bone mineral density (BMD) measurements were also made. The relationship between EI3-PT and in vivo EIMRTA using the six-parameter model is strong (R2 = 0.947) and better than that using the older model (R2 = 0.645). EIMRTA and BMD are also highly correlated (R2 = 0.853). MRTA measurements in vivo and BMD ex vivo are both good predictors of scaled maximum strength (R2 = 0.915 and R2 = 0.894, respectively). This is the first biological validation of a non-invasive mechanical measurement of bone by comparison to actual values. The MRTA technique has potential clinical value for assessing long-bone mechanical properties.