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

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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).