High intensity focussed ultrasound (HIFU) treatment planning with geometrical optics acoustics

聚焦超声越来越多地被用于治疗应用，例如肿瘤的热消融和泌尿系结石的碎石术。精确的治疗计划需要声学模型来预测超声波将集中在哪里。在这些治疗所需的高声压区，声波以非线性方式传播--换句话说，它们使能量变陡，并将能量推向更高的谐波，有时高出基频一个数量级。这会显著改变热沉积的速度或声波的形状，从而对治疗产生影响。因此，有必要对非线性模型进行精确建模。声传播的主要数值模型是基于网格或网格的，并且需要比最高波长的一半更近的节点(实际上更近一些)，因此产生的谐波导致需要非常大的网格，并且计算量变得非常大。因此，HIFU模拟(正问题)需要一种不同的方法。对于这些应用中的大多数，在靠近焦点之前，传播是线性的，因此焦点位置不会从线性区域改变，而只是场的幅度。基于这一观测结果，我们建议设计一种方法，利用快速线性几何光学计算射线的轨迹，然后通过求解非线性声学方程来计算沿这些射线的声压幅度。Burgers方程或Westvelt方程，或它们的导数，沿着射线。然后，该方法可以用作优化治疗计划(反问题)的正解算器。

Focussed ultrasound is increasingly being exploited in therapeutic applications, for example for thermal ablation of tumours and lithotriptic destruction of urological stones. Accurate planning of the treatment requires acoustic modelling to predict where the ultrasound waves will focus. In the high acoustic pressure regimes required for these treatments, the acoustic waves propagate nonlinearly - in other words they steepen and push energy into higher harmonics, sometimes as much as an order of magnitude higher than the fundamental frequency. This can significantly alter the rate of heat deposition, or the shape of the acoustic wave, and thereby have an effect on the treatment. It is therefore necessary to model the nonlinearity accurately. The leading numerical models of acoustic propagation are grid or mesh-based, and require nodes spaced closer than half-the-highest-wavelength (in practice quite a bit closer) and so the generation of harmonics leads to a requirement for very large grids, and the computations become impractically large. HIFU simulations (forward problem) therefore call for a different approach. As for most of these applications, the propagation is linear until close to the focus, and so the focal position does not change from the linear regime, just the amplitude of the field. Based on this observation we propose to devise a method that calculates the ray trajectories using fast linear geometric optics, and then computes the acoustic pressure amplitude along these rays by solving nonlinear acoustic equations, eg. Burgers equation or Westervelt equation, or a derivative from them, along the rays. This method can then be used as a forward solver in the optimisation of the treatment plan (inverse problem).