Abstract
4D-flow magnetic resonance imaging (MRI) provides non-invasive blood flow reconstructions in the heart. However, low spatio-temporal resolution and significant noise artefacts hamper the accuracy of derived haemodynamic quantities. We propose a physics-informed super-resolution approach to address these shortcomings and uncover hidden solution fields. We demonstrate the feasibility of the model through two synthetic studies generated using computational fluid dynamics. The Navier-Stokes equations and no-slip boundary condition on the endocardium are weakly enforced, regularising model predictions to accommodate network training without high-resolution labels. We show robustness to each type of data degradation, achieving normalised velocity RMSE values of under 16% at extreme spatial and temporal upsampling rates of 16\(\times \) and 10\(\times \) respectively, using a signal-to-noise ratio of 7.
Erica Dall’Armellina and Alejandro F Frangi: Joint senior authors.
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References
Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C., G.S, Corrado.: TensorFlow: large-scale machine learning on heterogeneous distributed systems. In: 12th USENIX Symposium on OSDI (2016)
Bergstra, J., Yamins, D., Cox, D.D.: Making a science of model search: hyperparameter optimization in hundreds of dimensions for vision architectures. Comput. Sci. Discov. 8 (2015)
Fathi, M.F., et al.: Super-resolution and denoising of 4D-flow MRI using physics-informed deep neural nets. Compu.t Methods Programs Biomed. 197, 105729 (2020)
Ferdian, E., et al.: 4DFlowNet: super-resolution 4D flow MRI using deep learning and computational fluid dynamics. Front. Phys. 8(183) (2020)
Jin, X., Cai, S., Li, H., Karniadakis, G.E.: NSFnets (Navier-Stokes flow nets): physics-informed neural networks for the incompressible Navier-Stokes equations. J. Comput. Phys. 426, 109951 (2021)
Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. 3rd ICLR (2015)
Kissas, G., Yang, Y., Hwuang, E., Witschey, W.R., Detre, J.A., Perdikaris, P.: Machine learning in cardiovascular flows modeling: predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks. Comput. Methods Appl. Mech. Eng. 358, 112623 (2020)
Markl, M., Frydrychowicz, A., Kozerke, S., Hope, M., Wieben, O.: 4D flow MRI. J. Magn. Reson. Imaging 36(5), 1015–1036 (2012)
Pelc, N.J., Bernstein, M.A., Shimakawa, A., Glover, G.H.: Encoding strategies for three-direction phase-contrast MR imaging of flow. J. Magn. Reson. Imaging 1, 405–413 (1991)
Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378, 686–707 (2019)
Shit, S., Zimmermann, J.: SRflow: Deep learning based super-resolution of 4D-flow MRI data. Front. Artif. Intell. (2022)
Sitzmann, V., Martel, J.N.P., Bergman, A.W., Lindell, D.B., Wetzstein, G.: Implicit neural representations with periodic activation functions. In: 34th Conference on NeurIPS (2020)
Xia, Y., et al.: Automatic 3D+t four-chamber CMR quantification of the UK biobank: integrating imaging and non-imaging data priors at scale. Med. Image Anal. 80, 102498 (2022)
Acknowledgements
This work was partially supported by the EPSRC Centre for Doctoral Training in Fluid Dynamics (EP/L01615X/1) and the Royal Academy of Engineering Chair in Emerging Technologies (CiET1919/19). The computational work was undertaken on the UK National Tier-2 high performance computing service JADE-2 (EP/T022205/1).
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Shone, F. et al. (2023). Deep Physics-Informed Super-Resolution of Cardiac 4D-Flow MRI. In: Frangi, A., de Bruijne, M., Wassermann, D., Navab, N. (eds) Information Processing in Medical Imaging. IPMI 2023. Lecture Notes in Computer Science, vol 13939. Springer, Cham. https://doi.org/10.1007/978-3-031-34048-2_39
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DOI: https://doi.org/10.1007/978-3-031-34048-2_39
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