基于K-wave的经颅超声聚焦仿真研究

由于颅骨形状不规则，声速、密度等声学参数分布不均匀，使用传统相控聚焦的方法进行经颅超声精确聚焦时会出现焦点偏移、焦点形状畸变、散焦的现象，时间反转法被认为是能够克服颅骨非均匀特性，实现经颅聚焦的有效手段。而利用传统有限元，有限差分法进行数值仿真时，往往需要划分十分精密的网格进行计算，耗费大量的时间。K空间伪谱法通过在空间域上进行傅里叶变换，时间域上进行有限差分的方法求解声波方程，能够在降低计算网格密度的同时保证计算精度。为了克服颅骨对聚焦超声造成的焦移影响，同时避免声学模型计算量过大的问题，本文使用Matlab K-wave开源工具箱，对食蟹猴颅骨CT数据进行三维声学建模，实现了基于时间反转法的经颅超声聚焦，讨论了时间反转法对于颅骨不规则形状及非均匀声速造成的焦移的补偿。仿真结果表明，K-wave在提高计算速度的同时能够服务于精准经颅超声聚焦，且相较于传统基于声时差法的相控聚焦方法，时间反转法在预设焦点位置，焦点强度更高，焦斑形状更为规则，聚焦效果更好。

Simulation study of K-wave based transcranial ultrasound focusing simulation

Due to the non-uniform distribution of acoustic parameters, such as sound velocity and density, caused by the irregular shape of the skull, focus shift could happen while using the traditional phase-controlled focusing method for transcranial ultrasound focusing. The time reversal method is considered to be able to overcome the difficulty of skull nonuniformity, and can be an effective means to achieve transcranial focusing. However, when the traditional finite element and finite difference methods are used for numerical simulation of transcranial ultrasound focusing, very precise grids need to be divided for calculation, which consumes a lot of time. The K-space pseudo-spectrum method is used to solve the acoustic wave equation by performing the Fourier transform in the space domain and the finite difference in the time domain, which can greatly reduce the grid density required for calculation while ensuring the accuracy of calculation. In this article, the Matlab K-wave open source toolbox and the CT data of cynomolgus monkey skulls are used to realize transcranial ultrasound focusing based on the time reversal method, and the problem using the time reversal method to compensate the focus shift caused by the irregular skull shape and the non-uniform sound velocity is discussed. The simulation results show that K-wave can serve accurate transcranial ultrasound focusing while improving the computing speed. Compared to traditional phased focusing methods based on acoustic time difference method, the time reversal method has higher focus intensity, more regular focal spot shape, and better focusing effect at preset focus positions.