Computer simulation of forward wave propagation in non-linear, heterogeneous, absorbing tissue

A method is proposed for simulating forward wavefront propagation in heterogeneous tissue. The propagation is done in the spatial variable, and allows for tissue exhibiting non-linear elasticity and arbitrary relaxation. Spatial variation in all important material parameters is also permitted. A brief introduction to the use of operator splitting is given before showing how this will lead to a simple solution method for the wave equation at hand. The numerical solution is found to be accurate when compared to known exact solutions for special cases of the equation in homogeneous media. Models of body walls, constructed from digital images of pork, are used to show how phenomena experienced in practical medical ultrasound imaging are reproduced. These include phase aberration and generation of harmonic frequencies.