A discrete source model for simulating bowl-shaped focused ultrasound transducers on regular grids: Design and experimental validation

Accurately representing the behaviour of acoustic sources is an important part of ultrasound simulation. This is particularly challenging in ultrasound therapy where multi-element arrays are often used. Typically, sources are defined as a boundary condition over a 2D plane within the computational model. However, this approach is difficult to apply to arrays with multiple elements distributed over a non-planar surface. In this work, a grid-based discrete source model for single and multi-element bowl-shaped transducers is developed. The source model is defined as a symmetric, simply-connected surface with a single grid point thickness. Simulations using the source model with the open-source k-Wave toolbox are validated using the Rayleigh model and experimental measurements of a focused bowl transducer. The results show good agreement, even at very low grid resolutions. As the model only requires the geometry and drive signal, it allows modelling of multi-element transducers where measuring an input plane is not possible. This may be particularly useful for modelling hemispherical ultrasound arrays often used in transcranial applications.