In this paper, we utilize micro-computed tomography (micro-CT) to obtain micro-CT images with a resolution of 60 μm and establish a micro-CT model based on the k-wave toolbox, which can visualize the microstructures in trabecular bone, including pores and bone layers. The transcranial ultrasound phased array focusing field characteristics in the micro-CT model are investigated. The ultrasonic waves are multiply scattered in skull and time delays calculations from the transducer to the focusing point are difficult. For this reason, we adopt the pulse compression method and the linear frequency modulation Barker code to compute the time delay and implement phased array focusing in the micro-CT model. It is shown by the simulation results that ultrasonic loss is mainly caused by scattering from the microstructures of the trabecular bone. The ratio of main and side lobes of the cross-correlation calculation is improved by 5.53 dB using the pulse compression method. The focusing quality and the calculation accuracy of time delay are improved. Meanwhile, the beamwidth at the focal point and the sound pressure amplitude decrease with the increase in the signal frequency. Focusing at different depths indicates that the beamwidth broadens with the increase in the focusing depth, and beam deflection focusing maintains good consistency in the focusing effect at a distance of 9 mm from the focal point. This indicates that the phased-array method has good focusing results and focus tunability in deep cranial brain. In addition, the sound pressure at the focal point can be increased by 8.2% through amplitude regulation, thereby enhancing focusing efficiency. The preliminary experiment verification is conducted with an ex vivo skull. It is shown by the experimental results that the phased array focusing method using pulse compression to calculate the time delay can significantly improve the sound field focusing effect and is a very effective transcranial ultrasound focusing method.

This paper explores the propagation of nonlinear elastic waves in a two-dimensional isotropic medium. The analytical expressions of first-order potentials corresponding to second harmonic acoustic components are obtained and discussed by using the perturbation method. Based on the careful theoretical analysis, it is shown that the first-order P wave always has a resonant term, which is proportional to the propagation distance in the condition of simultaneous excitation of the P wave. On the contrary, the first-order SV wave does not have any cumulative effect. Moreover, the nonlinear interactions between the P wave and SV are also presented.

Transcranial acoustoelectric brain imaging (tABI) is a potential brain activity imaging technique with high spatiotemporal resolution. Precise focus of transcranial ultrasound is critical for realizing millimeter-level spatial resolution in tABI. In this study, a precise focusing simulation platform is proposed by constructing a high-precision 3D skull model from Bama pig computed tomography data and a mathematical model equation by considering the skull’s heterogeneous properties. Then, the delay parameters derived from the simulation platform improve the precision of transcranial ultrasound focusing, enabling precise localization of brain activation sources with tABI. Phantom experimental results demonstrate that the transcranial ultrasound field is precisely focused at the target with a 0.20 mm deviation when delay parameters are obtained from the proposed simulation platform, whereas it exhibits divergence when using delay parameters derived from pure water or homogeneous skull models. Furthermore, using the proposed simulation platform, tABI can accurately identify intracranial electrical signals of distinct frequencies and precisely locate the corresponding activation sources with a spatial deviation of 0.50 mm. These results demonstrate that the proposed simulation platform is a powerful tool for the precise focusing of tABI.