Ultrasound fields in an attenuating medium

Ultrasound fields propagating in tissue will undergo changes in shape not only due to diffraction, but also due to the frequency dependent attenuation. Linear fields can be fairly well predicted for a non-attenuating medium like water by using the Tupholme-Stepanishen method for calculating the spatial impulse response, whereas the field cannot readily be found for an attenuating medium. In this paper we present a simulation program capable of calculating the field in a homogeneous attenuating medium. The program splits the aperture into rectangles and uses a far-field approximation for each of the rectangles and sums all contributions to arrive at the spatial impulse response for the aperture and field point. This approach makes it possible to model all transducer apertures, and the program can readily calculate the emitted, pulse-echo and continuous wave field. Attenuation is included by splitting it into a frequency dependent part and frequency independent part. The latter results in an attenuation factor that is multiplied onto the responses from the individual elements, and the frequency dependent part is handled by attenuating the basic one-dimensional pulse. The approach taken is very fast, and point spread functions can usually be generated within 10 seconds on commercially available workstations. The influence on ultrasound fields from attenuation is demonstrated.