Nonlinear acoustic assessment of the human calcaneus

Abstract

Elastic properties of bone, especially those that are linear, have been examined extensively in the past. These mechanical properties have been assessed as a function of age, gender, anatomical site and various skeletal pathologies. Acoustical nonlinearity is one of the most sensitive and at the same time least investigated parameters of bone characterizing its structural integrity. The present work describes preliminary results of several nonlinear acoustic methods for assessing the calcaneus in males and females covering the range of 44 to 93 years of age.We have tested the following methods of bone nonlinearity assessment: A novel nonlinear Time Reversal Acoustic (TRA) method based on the concentration of acoustic energy of two signals with different frequencies in a small volume of bone and the measurements of a generated signal with sum frequency. In this study, we used two 5 channel synchronized TRA systems to focus ultrasonic waves with different frequencies (f1 = 460 kHz and f2 = 610 kHz) in a coinciding focal spot. The level of measured signal of the summed frequency was significantly different for tested bone specimens. The sum frequency signal measured on two specimens obtained from two human calcanei (female, 93 and 83 years) was 10-14 dB higher than that for the specimens taken from younger people. Our attempt of using Nonlinear Resonant Ultrasound Spectroscopy (NRUS) method was unsuccessful. Signals detected from the bone appeared to be too weak for quantitative assessment of bone nonlinearity. We used Single tone method of nonlinear measurements based on measurements of the amplitude dependence of the recorded bone vibration on the applied signal. We used a high power acoustic transducer operating at frequencies 67 and 145 kHz for bone excitation and a laser Doppler vibrometer for measurement of the bone response. The amplitude dependencies of bone vibrations were clearly nonlinear and normalized amplitude dropped to 80% for the specimen ta