Given the effects of nonlinear propagation, it is difficult to model the ultrasound beams from a scanner or other ultrasound source. My research in this area focuses on methods of computationally modeling ultrasound beams and interactions with tissue. If ultrasound were linear, this would be very similar to modeling optical beams and diffraction. The method often used is to evaluate the "Rayleigh Integral". This integral adds up the contribution of sound or light at a particular location in space from all infitesimal areas on the source. With significant nonlinear effects, this is not possible, since in a nonlinear situation, the sum of the parts does not equal the whole. Other processes have removed or added to the situation.
In practice, these situation require finite difference and finite element methods. We model the ultrasound beam as it propagates through tissue by first calculating the pressure right next to the source. Then the pressure at this location becomes the source for the region right next to it. We continue this throughout the beam until we have reached the areas we are interested in. At each step, we account for diffraction, attenuation, and nonlinear effects.