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HEIndividual fellowship2023–2025

NIOT · Network Inpainting via Optimal Transport

Horizon Europe — Marie Skłodowska-Curie Actions

Duration
2023-04-01 → 2025-03-31
EU contribution
€210,911
Participants
1
Scheme
HORIZON-TMA-MSCA-PF-EF

Lines connect the coordinator with its partners.

Results in brief

Network Inpainting via Optimal Transport

Current State and Challenges in Vascular Imaging Medical imaging techniques like Magnetic Resonance Imaging (MRI) allow for non-invasive visualization of blood vessel networks. While valuable for diagnostics and research, MRI data can present challenges, such as noise and artifacts, sometimes leading to incomplete or seemingly disconnected representations of the vascular system, especially for smaller vessels. These fragmented vascular network models can complicate accurate medical diagnosis and treatment planning. They also pose difficulties for researchers using computational models to simulate blood flow, as incomplete data can reduce the reliability of simulation outcomes. Addressing the Needs of Clinicians and Mathematicians Clinicians require reliable methods to obtain accurate vascular models from scans, while mathematicians work on developing algorithms to process imaging data and reconstruct these networks. The NIOT (Numerical challenges in Optimal Transport) project aims to contribute to this area by applying Optimal Transport (OT) theory, a branch of Mathematics studying the optimal strategy for moving resources at the least cost possible. Project Goals and Approach The project's goal is to develop computational tools for improved reconstruction of blood vessel networks from medical imaging. Leveraging OT principles, which are well-suited for analyzing branched structures and pathways in graph-based systems, the project will adapt existing expertise in OT solvers to address the specific challenges of vascular network reconstruction. This work is supported by the host institution's capabilities in processing vascular data. Long-Term Contributions and Collaborative Benefits In the longer term, the tools developed aim to streamline the process of converting raw MRI scan data into formats suitable for numerical simulations. This could enable more routine use of patient-specific models in computational studies. By providing improved data for medical assessment and computational modeling, this research seeks to foster closer interaction between medical practitioners and mathematical scientists. More reliable data can lead to better predictions, which in turn can support the clinical use of mathematical tools, creating a positive feedback loop for continued development.

Data: CORDIS, © European Union

Project objective

The precise digital reconstruction of natural networks such as blood vessels or plant roots is crucial to ensure the quality ofsimulation-driven predictions. However, these structures can often be accessed only via noninvasive techniques, leading to artifactsthat compromise the reliability of the data and the derived simulations. No technological solution is currently able to recover digitalreconstructions of ""real"" networks from corrupted images.The NIOT (Network Inpainting via Optimal Transport) project aims to fill this technological gap by defining for the first time a robustmathematical formulation of the image network reconstruction problem. Thanks to the most recent advances of the optimaltransport theory, we will finally encode into equations the well-known fact that several natural networks are designed to transportresources with the least effort possible. We will adopt a variational image processing method, where the reconstructed network isobtained as the density minimizing the sum of the discrepancy with the observed data and a branch inducing functional. As such, ourproposed methodology builds a bridge between the image regularization and optimal transport communities.A major ambition of the project is to pair the theoretical analysis with robust simulation tools that are capable of handling real dataarising from MRI acquisition techniques. This will require exploitation and development of dedicated components to handle largedatasets, both from a data handling and a multiscale simulation perspective. Our algorithm will be tested on a sequence ofincreasingly channeling problems. We will start from simple synthetic networks, then we will use an high-quality map of the bloodvessel network of a mouse brain. The final benchmark will be to reconstruct of corrupted vascular networks in MRI scans of humanpatients.""

Original text from CORDIS.

Participants

  • UNIVERSITETET I BERGEN · BergenCoordinatorNorway

Links

Data: CORDIS, © European Union