Large Bone Vibration: Modeling and Experimental Measurements

A model for vibration of large bones, such as a femur, is presented. Using this model, the resonance frequencies of an intact, partially fractured, and bonded (healed) bone are determined. To measure bone resonance frequencies experimentally, a non-contact method for bone excitation and motion detection is developed. This method uses the radiation force of focused amplitude-modulated ultrasound to exert a vibrating force directly, and remotely, on excised bone. The vibration frequency is varied in the range of interest to induce resonances in the bone. The resulting bone motion is detected by a laser vibrometer and the resonance frequencies are determined. Experiments are conducted on excised rat femurs and resonance frequencies of intact, fractured, and bonded (simulating healed) bones are measured. The experiments demonstrate that the fractured bone exhibits a lower resonance frequency than the intact bone, and the resonance frequency of the bonded bone approaches that of the intact bone. These results are in agreement with the predictions of the model. It is concluded that the resonance frequencies of bone can be used as markers of its integrity, and the radiation force method may be used as a remote and noninvasive tool for studying one fracture.