##
Trond Varslot, Svein-Erik Måsøy

### Forward propagation of acoustic pressure pulses in 3D soft biological tissue

A simulation method for forward propagation of acoustic pressure pulses in a medium with spatially variable acoustic properties is presented. The intended application is to study aspects of ultrasound imaging of soft biological tissue.Ideally the ultrasonic pulse would pass undistorted from the transducer array, through the body, until it reaches the organ to be imaged. The pulse should be reflected by this organ, and then pass undistorted back through the body to the transducer array. Most ultrasound imaging techniques are based on this assumption. However, in many situations this is not the case, leading to degraded image quality. The aim for the method presented here is to perform simulations of the forward wave propagation. To this end a one-way wave equation is used. The equation describes tissue exhibiting nonlinear elasticity and arbitrary frequency-dependent attenuation, and is a good approximation of the full wave equation when all acoustically-important quantities are sufficiently smooth.A numerical solution to this equation is found by means of first-order accurate operator splitting and propagation along the spatial depth coordinate. Thus diffraction, nonlinearity and attenuation are solved independently at each propagation step, making their relative importance easy to monitor. The method is seen to yield an accurate simulation of the wave propagation when compared to numerical solutions of the full wave equation and experiments in a water tank.By this approach it is possible to simulate wave propagation over relatively large distances - typically 300 wavelengths - at a modest computational complexity compared to solution of the full wave equation. It furthermore facilitates a high degree of parallelism, thus enabling efficient distribution of the required computations over multiple processors. The method is implemented using MPI under Matlab.