Simulation of ultrasound pulse propagation in lossy media obeying a frequency power law

A method is proposed to simulate the propagation of a broadband ultrasound pulse in a lossy medium whose attenuation exhibits a power law frequency dependence. Using a bank of Gaussian filters, the broadband pulse is first decomposed into narrowband components. The effects of the attenuation and dispersion are then applied to each component based on the superposition principle. When the bandwidth of each component is narrow enough, these effects can be evaluated at the center frequency of the component, resulting in a magnitude reduction, a constant phase angle lag, and a relative time delay. The accuracy of the proposed method is tested by comparing the model-produced pulses with the experimentally measured pulses using two different phantoms. The first phantom has an attenuation function which exhibits a nearly linear frequency dependence. The second phantom has an attenuation function which exhibits a nearly quadratic frequency dependence. In deriving the dispersion from the measured attenuation, a nearly local model and a time causal model are used. For linear attenuation, the two models converge and both predict accurately the waveform of the transmitted pulse. For nonlinear attenuation, the time causal model is found more accurate than the nearly local model in predicting the waveform of the transmitted pulse.