Time-Domain Simulation of Ultrasound Propagation With Fractional Laplacian

The simulation is developed for the purpose of simulating ultrasound propagation through biological tissues. The simulation is based on the time-domain conservation laws with the governing equations for acoustic pressure and velocity, with frequency dependent absorption and dispersion effects. We use forward differencing for velocity and backward differencing for pressure on the non-fractional derivative operator terms in spatial discretization. The fractional Laplacian operators are treated as Riesz derivatives. The shifted standard Grunwald approximation method is used to solve fractional derivative operator terms. To accommodate complicated biological tissue geometries, an immersed boundary method is developed that enables a Cartesian computational grid mesh to be used. The results are compared with those for a non-absorption homogeneous medium to discuss absorption and dispersion effects of biological material.