Virtual ultrasound transducers in the human brain

We aim to construct the signal between two points inside a model of the human skull as if there were virtual transducers located inside the skull. We show how this can be achieved through the use of time-reversed Green's functions that are measured on opposite sides of the skull. We then demonstrate how to achieve similar results using special wavefields named focusing functions, which are designed to work specifically when injected from a single-side of the medium of interest. We show two ways to obtain these focusing functions, through the use of the iterative Marchenko method and by inversion of a measured Green's function. The inversion of the Green's function shows potential benefits over the use of the Marchenko method, however, this approach requires further studies. We demonstrate how these wavefields function on 2D acoustic in silico data by injecting the time-reversed Green's functions and focusing functions into the model. We also demonstrate how the response between virtual transducers can be obtained directly through use of the homogeneous Green's function representation.