THE RELATION BETWEEN RESONANT FREQUENCIES AND TORSIONAL STIFFNESS OF LONG BONES INVITRO - VALIDATION OF A SIMPLE BEAM MODEL

The results of vibration analysis experiments and impact torsion tests performed on excised animal long bones were used to validate a simple beam model for the prediction of torsional stiffness from resonant fr equencies. Resonant frequency data on two mutually perpendicular bendi ng vibration modes of 142 excised long bones were evaluated. Torsional stiffness of the same bones had been determined by an impact torsion test. Using a simple beam model, a theoretical relation between resona nt frequencies and torsional stiffness was derived. If total bone mass and bone length are known, the formula thus derived allows one to cal culate torsional stiffness from resonant frequencies. Linear regressio n analysis shows a strong correlation between the measured and the cal culated torsional stiffness for sheep femora (r2 = 0.63, n = 24), dog femora (r2 = 0.94, n = 34), dog tibiae (r2 = 0.79, n = 18) and monkey radii (r2 = 0.77, n = 66). It was found that this linear relation was valid not within one bone type alone. Linear regression analysis on th e combined data of all bones demonstrated that all bones obeyed the sa me global linear relation between measured and the calculated torsiona l stiffness (r2 = 0.98, n = 142). This implies that one and the same b eam model is valid for the different bone types investigated. The calc ulation of stiffness from resonant frequencies, however, requires tota l bone mass, m, and length to be known. In view of in vivo application s, the feasibility of using total bone mineral content (TBMC) as a mea sure for m was investigated. A good linear correlation was found betwe en total bone mass and total bone mineral content. The correlation bet ween torsional stiffness using TBMC data and measured torsional stiffn ess was still highly satisfying. Finally, a good linear correlation wa s observed between the properties of left and right bone from a single specimen. These results demonstrate a simple relation between resonan t frequencies and bone mechanical properties in vitro. Under the condi tion that in vivo effects (muscles, skin, joints, etc.) on the vibrati onal behaviour can be accounted for properly, the results are promisin g as to the feasibility of the resonant frequency technique for fractu re healing monitoring and osteoporosis evaluation.