Fast-pressure field calculations applied to large spherical ultrasound phased arrays designed for thermal therapy

Abstract

Large spherical ultrasound phased arrays are ideal for simulation studies of thermal therapy devices designed for noninvasive breast cancer treatments. In a spherical array, circular sources packed in a dense hexagonal arrangement facilitate the most efficient use of the available aperture. Circular sources are also preferred for simulations of large phased arrays because pressure fields are computed more rapidly for circular pistons than for any other transducer geometry. The computation time is further reduced for circular transducers with grid sectoring. With this approach, the grid of computed pressures is divided into several regions, and then grid sectoring applies more abscissas in regions where the pressure integral converges slowly and fewer abscissas where the integral converges rapidly. As a result, the peak value of the numerical error is roughly the same in each sector, so the maximum numerical error in the computed field is maintained while the computation time is significantly reduced. The grid sectoring approach is extended to three dimensions (3D) for pressure field calculations with spherical arrays. In 3D calculations, the sectors are represented by cones, and the intersections between the computational grid and these cones define the boundaries required for grid sectoring. When these cone structures are applied to spherical phased arrays, 3D grid sectoring calculations rapidly compute the pressure fields so that the time required for array design and evaluation is substantially reduced.