Ultrasound beam simulations in inhomogeneous tissue geometries using the hybrid angular spectrum method

The angular spectrum method is a fast, accurate and computationally efficient method for modeling wave propagation. However, the traditional angular spectrum method assumes that the region of propagation has homogenous properties. In this paper, the angular spectrum method is extended to calculate ultrasound wave propagation in inhomogeneous tissue geometries, important for clinical efficacy, patient safety, and treatment reliability in MR-guided focused ultrasound surgery. The inhomogeneous tissue region to be modeled is segmented into voxels, each voxel having a unique speed of sound, attenuation coefficient, and density. The pressure pattern in the 3-D model is calculated by alternating between the space domain and the spatial-frequency domain for each plane of voxels in the model. The new technique was compared with the finite-difference time-domain technique for a model containing attenuation, refraction, and reflection and for a segmented human breast model; although yielding essentially the same pattern, it results in a reduction in calculation times of at least two orders of magnitude.