About the Project
Location: UCL, London UK
Supervisors: Marta Betcke (Primary, CMIC/CIP/CS);
Ben Cox (Secondary, PIG/BUG/MedPhys);
Bradly Treeby (Secondary, BUG/MedPhys);
UCL Department of Computer Science (CS),
UCL Centre for Medical Image Computing (CMIC),
UCL Centre for Inverse Problems (CIP),
UCL Department of Medical Physics and Biomedical Engineering (MedPhys)
Start date: 28th September 2020 (in exceptional circumstances may be possible to delay)
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. This is especially important when propagating the waves through acoustically distorting tissues such as skull or regions of fat. 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 [Jaros2016], 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 in this project 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 builds on our prior work on geometric optics based solution for linear wave propagation in ultrasonic modalities [Rullan2018].
Treatment planning (inverse problem) can be mathematically formulated as an optimisation problem in treatment parameters. The cost function promotes delivering the estimated dose in the target while not exceeding the safety dose in organs at risk. Such problems are usually non-convex and as such require a large number of iterations of an optimisation method each involving a forward solve. Thus, efficient HIFU simulations are crucial to feasibility of the approach
Delivery of therapeutic focused ultrasound usually requires real-time image guidance and treatment monitoring most frequently with ultrasound imaging. The so collected images could be used to inform the treatment. For instance, near real-time HIFU simulations would in principle allow continuous assessment of the validity of the current treatment plan (e.g. via monitoring of the error of the current plan applied to the updated image parameters) and if they could be performed fast enough it could even lead to adaptive treatment (re)planning by solution of a warm started and possibly simplified inverse problem.
Machine Learning can be used for HIFU treatment planning to speed-up both the forward and the inverse problem. A fast approximate forward solver could be trained on data from forward simulations using the proposed linear ray / non-linear amplitude model prior to treatment. Promising hybrid model and data based approaches for fast inverse problem solvers are built on the idea of learnt iterative schemes [Hauptmann2018].
This is a fundamental research project which has different aspects: mathematical modelling, numerical analysis and scientific computing. The successful applicant will have a lot of freedom to steer the direction towards their interests and strengths. The ideal candidate will have
• A BSc or MSc degree in Mathematics, Scientific Computing, Computer Science or related field with top marks
• Strong mathematical background
• Experience with numerical simulations, scientific computing
• Programming skills, knowledge of at least one of Matlab, Python or C++
• Previous experience with numerical simulation of wave propagation would be beneficial but not essential
• Previous experience with machine learning and optimization would be beneficial but not essential
• Good communication skills; especially in written English
• Strong work ethic and the ability to think creatively and independently
Interested candidates please get in contact with Marta Betcke ([Email Address Removed])
Application deadline: 14 July 2020
Interviews will be held virtually on morning of 17 July 2020 please ensure availability for a call. We will contact the shortlisted candidates with precise instructions by 16 July 2020.
[Rullan2018] F. Rullan and M. M. Betcke. “Hamilton-Green solver for the forward and adjoint problems in photoacoustic tomography” arXiv1810.13196 [math.NA] 2018.
[Hauptmann2018] A. Hauptmann et al., "Model-Based Learning for Accelerated, Limited-View 3-D Photoacoustic Tomography," IEEE Transactions on Medical Imaging, vol. 37, no. 6, pp. 1382-1393, June 2018, doi:10.1109/TMI.2018.2820382
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