This paper proposes the use of a k-space method to obtain the correction for transcranial ultrasound beam focusing. Mirroring past approaches, a synthetic point source at the focal point is numerically excited, and propagated through the skull, using acoustic properties acquired from registered computed tomography of the skull being studied. The received data outside the skull contain the correction information and can be phase conjugated (time reversed) and then physically generated to achieve a tight focusing inside the skull, by assuming quasi-plane transmission where shear waves are not present or their contribution can be neglected. Compared with the conventional finite-difference time-domain method for wave propagation simulation, it will be shown that the k-space method is significantly more accurate even for a relatively coarse spatial resolution, leading to a dramatically reduced computation time. Both numerical simulations and experiments conducted on an ex vivo human skull demonstrate that precise focusing can be realized using the k-space method with a spatial resolution as low as only 2.56 grid points per wavelength, thus allowing treatment planning computation on the order of minutes.
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