Comparison of two theoretical models for predicting non-linear propagation in medical ultrasound fields

Non-linear propagation models are required to predict the fields from medical ultrasonic equipment, particularly diagnostic devices and lithotripters. This need arises because of the requirement to know the safety and effectiveness of these instruments. Several theoretical models have been developed to take account of non-linear propagation as well as diffraction, focusing and attenuation, but little work has been done to validate them. This paper compares two theoretical models with each other and with measurements in the field of a 3.5 MHz focused transducer. One model uses an approximation based on modelling the beam profile with a Gaussian function, whereas the other utilises a full three-dimensional finite difference method, using a uniform transducer excitation function. Comparisons are made in the time and frequency domain at the focus for four different source levels and in general the results agree to within about 10%. However, an important conclusion is that the finite amplitude field of a real transducer may differ significantly from that of an ideal piston source, particularly for the weakly focused beams used in diagnostic ultrasound.