A single-pole model for the propagation of ultrasound in soft tissue

A minimum-phase function, which characterizes the velocity dispersion in tissue was calculated from measured attenuation. This function was incorporated into a causal tissue model. Predictions of attenuation using the minimum-phase function with just a single pole matched measured attenuation in the 1- to 10-MHz range within a few percent. Dispersion of phase velocity predicted by the single-pole model was comparable to measured dispersion. The frequency associated with the single pole, which is a relaxation frequency, decreased with hemoglobin concentration and collagen content but increased with temperature. The electrical equivalent circuit for this model is a delay coupled with a low-pass filter which can be configured as a resistance in series with a parallel combination of resistance and capacitance.