Time-domain simulation of ultrasound propagation with fractional Laplacians for lossy-medium biological tissues with complicated geometries

Simulations of ultrasound wave propagation inside biological tissues have a wide range of practical applications. In previous studies, wave propagation equations in lossy biological media are solved either with convolutions, which consume a large amount of memory, or with pseudo-spectral methods, which cannot handle complicated geometries effectively. The approach described in the paper employed a fractional central difference method (FCD), combined with the immersed boundary (IB) method for the finite-difference, time-domain simulation. The FCD method can solve the fractional Laplace terms in Chen and Holm's lossy-medium equations directly in the physical domain without integral transforms. It also works naturally with the IB method, which enables a simple Cartesian-type grid mesh to be used to solve problems with complicated geometries. The numerical results agree very well with the analytical solutions for frequency power-law attenuation lossy media.