Identification of In-Vivo Vibration Modes of Human Tibiae by Modal Analysis

Abstract

When attempting to evaluate the mechanical properties of human bones in vivo by mechanical vibration analysis, some essential requirements must be met. A quantitative relation between measured vibration parameters (e.g., natural frequency) and mechanical bone properties must be available, in-vivo vibration modes should correctly be identified and the associated natural frequencies reproducibly and accurately measured, the influence of joints and soft tissues must be known. These problems were addressed by modal analysis (i.e., experimental determination of natural frequencies, mode shapes and damping ratios) of human tibiae in the following situations: 1) dry excised tibiae, 2) fresh excised tibiae, 3) in-vivo tibiae, 4) tibiae in an amputated leg, in different steps of dissection. In the in-vivo measuring conditions used by the authors, the tibia vibration is practically free-free. Two single bending modes (at ± 270 Hz and ± 340 Hz, respectively), each of them corresponding with one principal direction for bending, were identified. The difference between the natural frequencies observed in vivo and those of fresh excised tibiae is almost completely caused by the effect of muscles (added mass and damping), whereas joints and skin play only a minor role. Frequency differences between fresh and dry excised tibiae are largely accounted for by the absence of bone marrow in the latter.