A novel numerical model was developed to simulate three-dimensional nonlinear fields generated by high intensity focused ultrasound (HIFU) arrays. The model is based on the solution to the Westervelt equation; the developed algorithm makes it possible to model nonlinear pressure fields of periodic waves in the presence of shock fronts localized near the focus. The role of nonlinear effects in a focused beam of a two-dimensional array was investigated in a numerical experiment in water. The array consisting of 256 elements and intensity range on the array elements of up to 10 W/cm² was considered. The results of simulations have shown that for characteristic intensity outputs of modern HIFU arrays, nonlinear effects play an important role and shock fronts develop in the pressure waveforms at the focus.

中文翻译：

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超声治疗阵列三维非线性场的模拟。


开发了一种新颖的数值模型来模拟高强度聚焦超声（HIFU）阵列产生的三维非线性场。该模型基于 Westervelt 方程的解；所开发的算法使得在焦点附近存在激波锋面的情况下模拟周期波的非线性压力场成为可能。在水中的数值实验中研究了二维阵列聚焦光束中非线性效应的作用。考虑由256个元件组成的阵列以及阵列元件上高达10W/cm ²的强度范围。模拟结果表明，对于现代 HIFU 阵列的特征强度输出，非线性效应起着重要作用，并且冲击锋在焦点处的压力波形中形成。