ИСТИНА

Background: Multi-element focused phased arrays have been successfully used in clinics for thermal lesioning in deep brain structures. Despite undoubted advantages of the existing hemispherical transducers, several limitations in their surgical application have been revealed. For example, overheating of non-targeted tissues and skull bones may occur due to thermal spread. Furthermore, hemispherical array geometry restricts mechanical displacement of the transducer, thus the treatment envelope of the existing systems is limited to the central part of the head. This study is aimed at evaluating the potential of a new design of less focused fully populated array (Fig. 1) for mechanical tissue ablation using boiling histotripsy (BH) method. The proposed approach could potentially enlarge the treatment region and expand the range of bioeffects. The possibility of tight transskull focusing at different depths with aberration correction was examined using linear and nonlinear field modeling. Material and Methods: Three models of 1 MHz 256-, 512-, and 1024-element arrays (Fig. 1a) with 200 mm aperture and 60° focusing angle were developed. A novel algorithm based on the capacity-constrained tessellation was used to develop a fully populated random pattern of equal area elements (Fig. 1b). A realistic 3D acoustical model of the head was built using MRI open database and included in simulations (Fig. 1c). A combination of different approaches was used in the acoustic field modeling and aberration correction. For linear simulations, the Rayleigh integral was used for propagation in water outside the head and pseudo-spectral time domain simulation (k-Wave software) based on the Kelvin–Voigt rheological model for propagation through the skin, skull, and brain (Fig. 2a). Aberration correction was based on the phase-conjugation method. A spherically divergent wave propagating from the focal point to the “Boundary 1” was simulated. Then the phase delays were defined at the array elements by calculating backpropagation using the Rayleigh integral (Fig. 2b). Nonlinear simulations were similar to the linear ones, but the Westervelt equation was used inside the homogeneous brain tissue and outside the head to account for strong nonlinear effects and a linear Kelvin–Voigt model was applied inside the skull and adjacent tissues (Fig. 2c). It was assumed that only the 1-MHz fundamental harmonic passes through the skull because bones induce strong frequency-growing ultrasound transmission losses. Results: Linear simulations with aberration correction were performed at 5 focal depths, 25–65 mm from the inner skull surface (Fig. 2a). Pressure distributions for the deepest (a), central (b) and outer (c) positions of the focus are presented in Fig. 3 for the 256-element array showing that aberration correction provides the tight focal lobe for all cases. For deeper focusing (Fig. 3a, b), the acoustic intensity near skull bones is relatively low (7–15%) compared to the focal intensity. For shallow focusing (Fig. 3c), the increased intensity near skull (40%) could be compensated in pulsed BH exposures by using low pulse repetition rates. To demonstrate the feasibility of nonlinear focusing through the skull, the central position of the focus (red circle in Fig. 2a) was simulated for the intensity at the array elements of 30 W/cm2 and 40 W/cm2 (typical technical limitations). The resulting focal waveforms contain developed shocks of >60 MPa (Fig. 4) and thus can be used to realize a BH method. Conclusions: This study demonstrates that the proposed new type of fully populated multi-element phased arrays can provide tight focusing through an intact skull at least over a 40 mm range of depths. Future work is planned to develop BH pulsing schemes for transskull sonication, evaluate electronic steering capabilities of the arrays with aberration correction, and determine safe levels of nonlinear pressure fields near skull bones. Acknowledgements/Funding Sources: This study was funded by RSF 19-12-00148, RFBR 19-02-00035, the Ph.D. student stipend from “Basis” Foundation, the stipend of the President of Russia SP-2644.2018.4, and FUSF summer 2020 Internship Program.