Modelling nonlinear ultrasound propagation in bone

Simulations have been carried out to assess the possibility for detecting the nonlinear properties of bone in vivo. We employed a time domain solution to the KZK equation to determine the nonlinear field generated by an unfocussed circular transducer in both cancellous and cortical bone. The results indicate that determining nonlinear properties from the generation of higher harmonics is challenging in both bone types (for propagation distances and source amplitudes appropriate in the body). In cancellous bone this is because the attenuation length scale is very short (about 5 mm) and in cortical bone because the high sound speed and density result in long nonlinear length scales (hundreds of millimeters). An alternative approach to determine the nonlinear properties was considered using self-demodulation of sound. For cancellous bone this may result in a detectable signal although the predicted amplitude of the self-demodulation signal was almost 90 dB below the source level (1 MPa). In cortical bone the self-demodulated signal was even weaker that in cancellous bone (similar to 110 dB down) and, for a practical length signal, was not easy to separate from the components associated with the source