Speaker
Description
Personalized cardiac diagnostics require accurate reconstruction of myocardial displacement fields from limited clinical imaging data. In this work, we propose an enhanced Parametrized-Background Data-Weak [1] framework for the recovery of 3D cardiac displacement fields from sparse, MRI-like observations, designed for fast and robust online application. The main contribution is the introduction of an $H$-size minibatch worst-orthogonal matching pursuit [2] strategy that accelerates sensor selection while maintaining reconstruction fidelity, together with memory optimizations that leverage block-matrix structures in vector-valued formulations to improve computational performance.
The methodology is assessed on a high-fidelity 3D left-ventricular model including simulated scar regions. Beginning with noise-free measurements, we gradually add Gaussian noise and increase spatial sparsity to mimic realistic MRI acquisition conditions. In noise-free settings, the proposed framework achieves a relative $L^2$-error of about 1e-5. Introducing Gaussian noise with a signal-to-noise ratio equals $10$, the relative $L^2$-error remains around 1e-2, and similar accuracy is obtained for sparse and noisy observation scenarios. Importantly, the online phase yields a speed-up of approximately four orders of magnitude compared to full finite element simulations, with reconstruction times below $0.1$ seconds.
These results indicate that the proposed strategy provides a computationally efficient and robst approach for reconstructing myocardial displacement fields from low-resolution sparse imaging data. Although further validation on clinical datasets and across a wider range of anatomical and pathological configurations is necessary, the current findings highlight its potential for integration into cardiac digital twinning workflows.
[1] Maday Y., Patera A. T., Penn J. D., Yano M., A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics, International Journal for Numerical Methods in Engineering, Vol. 102(5), pp. 933--965, 2014.
[2] Aretz N., Data assimilation and sensor selection for configurable forward models: challenges and opportunities for model order reduction methods, Dissertation, RWTH Aachen University, 2022.