Spectral element methods for fractional differential equations, with applications in applied analysis and medical imaging
Lead Research Organisation:
University College London
Department Name: Medical Physics and Biomedical Eng
Abstract
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Organisations
Publications
Miscouridou M
(2022)
Classical and Learned MR to Pseudo-CT Mappings for Accurate Transcranial Ultrasound Simulation.
in IEEE transactions on ultrasonics, ferroelectrics, and frequency control
Stanziola A
(2022)
j-Wave: An open-source differentiable wave simulator
Stanziola A
(2023)
A learned Born series for highly-scattering media
in JASA Express Letters
Stanziola A
(2023)
Transcranial ultrasound simulation with uncertainty estimation.
in JASA express letters
Stanziola A
(2021)
A Helmholtz equation solver using unsupervised learning: Application to transcranial ultrasound
in Journal of Computational Physics
Stanziola A
(2023)
j-Wave: An open-source differentiable wave simulator
in SoftwareX
Stanziola A
(2022)
A Learned Born Series for Highly-Scattering Media
Stanziola, A
(2022)
A Learned Born Series for Highly-Scattering Media
in arXiv
| Description | Ultrasound absorption in human tissue (the loss of energy as a wave propagates through the body) is known from experiments to depend on the frequency of the ultrasound, increasing with frequency according to a power law. Modelling this using computers has typically been challenging, as conventional approaches often require a lot of computer memory to model realistic problems. Building on work developed by the other project partners, we incorporated a new type of absorption model, that uses a fixed or static amount of memory, into a widely-used open source acoustic software package called k-Wave. This will allow other researchers to model absorption in the body, particularly in scenarios where the absorption follows different power laws in different regions. |
| Exploitation Route | The new models may be particularly useful for modelling absorption through heterogeneous tissue where the absorption power laws can be quite different, for example, when modelling photoacoustic wave propagation through the breast for the purpose of diagnosing breast cancer. |
| Sectors | Healthcare |
| Title | j-Wave: Differentiable acoustic simulations in JAX |
| Description | j-Wave is a library of simulators for acoustic applications. Is heavily inspired by k-Wave (a big portion of j-Wave is a port of k-Wave in JAX), and its intended to be used as a collection of modular blocks that can be easily included into any machine learning pipeline. Following the philosophy of JAX, j-Wave is developed with the following principles in mind: to be differentiable, to be fast via jit compilation, easy to run on GPUs, easy to customize. |
| Type Of Technology | Software |
| Year Produced | 2022 |
| Open Source License? | Yes |
| Impact | j-Wave was used in a recent modelling intercomparison, and to study uncertainty in transcranial ultrasound simulation. |
| URL | https://github.com/ucl-bug/jwave |
| Title | jaxdf - JAX-based Discretization Framework |
| Description | jaxdf is a JAX-based package defining a coding framework for writing differentiable numerical simulators with arbitrary discretizations. The intended use is to build numerical models of physical systems, such as wave propagation, or the numerical solution of partial differential equations, that are easy to customize to the user's research needs. Such models are pure functions that can be included into arbitrary differentiable programs written in JAX: for example, they can be used as layers of neural networks, or to build a physics loss function. |
| Type Of Technology | Software |
| Year Produced | 2022 |
| Open Source License? | Yes |
| Impact | jaxdf is being used by researchers interested in differentiable models, and forms the basis for the j-Wave acoustic simulation software. |
| URL | https://github.com/ucl-bug/jaxdf |