Keywords: trabecular bone, bone damage assessment, non-linear ultrasound, non-linear acoustic dissipation, non-destructive evaluation, wave modulation.

Microdamage in bone accumulated by repetitive loading and its effect on bone fragility has received considerable attention in recent years. Several studies have revealed a strong correlation between damage and bone fragility. The precise role, however, of microdamage in bone fragility is as yet unclear and has to be further investigated. Therefore, non-invasive techniques to access bone damage quantitatively are important.

In this paper a method for assessing microdamage in human bone based on non-linear ultrasound is presented. It is based on the non-linear modulation of a high-frequency wave by low-frequency vibration. The non-linear behavior of human bone samples was investigated experimentally. The experiments were carried out on human femoral bone specimens approximately 40x40x40mm with marrow and soft tissues removed. Care was taken to exclude mixing of the signals in electrical circuits and transducers. A high-frequency wave was modulated using low-frequency vibration applied directly on the bone samples. The modulation appeared as side frequencies around the high-frequency corresponding to low-frequency vibration revealing the non-linear nature of human bone. In a series of well controlled experiments it was shown that the amplitude of modulation increases with progressively increasing damage induced by identation and can be used as an effective indicator of damage.

To explain the non-linear phenomena observed during the experiments, a non-linear dissipation mechanism was considered. This additional damping for the high-frequency wave under the action of the low-frequency vibration is attributed to the thermoelastic losses in the vicinity of the microdamage. In contrast to conventionally considered hysteritic non-linearity, it seems that non-linear acoustic dissipation of the HF wave plays a significant role in the modulation process. The insight into the underlying physical mechanisms for modulation could contribute to a quantitative correlation of microdamage to measure non-linear parameters. The results suggest that non-linear ultrasound can be an efficient tool for microdamage assessment in human bone.

The proposed approach is superior compared to existing methods because the size and shape of bone samples are not important. Furthermore, it is non-invasive, easy to implement and appropriate for in vivo application. Further work on the development of in vivo bone microdamage characterization is already under way.

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