Finite Element Simulation of the MRTA Test of a Human Tibia

The mechanical response tissue analyzer (MRTA) tests long bone quality through low frequency, low amplitude vibration in vivo. The MRTA measures complex stiffness over a range of low frequencies, offering a wealth of information on bone composition. Previous MRTA interpretation used lumped parameter algorithms focused on reliably estimating the bone's bending stiffness (EI). To interpret the stiffness response, the first finite element (FE) simulation of the MRTA test of a human tibia was developed to identify dominant parameters that will possibly make linear prediction algorithms more suitable for estimating bone quality.

Five FE models were developed in stages by adding complexity. Starting with a solid mesh of the diaphysis, each model was created from its predecessor by sequentially adding: a medullary canal, linear elastic (LE) cancellous epiphyses, linear viscoelastic (LVE) cancellous and cortical bone, and a LVE skin layer. The models were simulated in vibration using a direct steady-state dynamics procedure in ABAQUS to calculate the complex stiffness response.

Natural frequency analysis (ABAQUS) verified that the FE models accurately reproduced previous experimental and computational resonances for human tibiae. A solid, LE cortex roughly matched the dominant frequency from experimental MRTA raw data. Adding the medullary canal and LVE properties to bone did not greatly spread the peak or shift the resonant frequency. Adding the skin layer broadened the peak response to better match the MRTA experimental response. These results demonstrate a simulation of the MRTA response based upon published geometries and material data that captures the essence of the instrument.