Reconstruction of 4D Mitral Regurgitation Hemodynamics from Sparse Planar Data using Deep Operator Networks with Test-Time Adaptation
Abstract
Quantifying mitral regurgitation severity remains limited by the assumptions of clinical flow convergence methods, while high-fidelity simulation and volumetric velocimetry are too slow for routine use. We investigate whether a learned solution operator can reconstruct transient three-dimensional transvalvular hemodynamics from the sparse observation an in-vitro experiment actually provides: a single planar velocity slice and two boundary pressure traces. A Deep Operator Network is pretrained on an experimentally benchmarked URANS database spanning eleven mitral regurgitation orifice phantoms, learning a mapping from a masked two-component planar velocity snapshot to the surrounding volumetric field, and is subsequently adapted to unseen target cases by fine-tuning on their sparse measurements. Adaptation reliably corrects the flow topology within the supervised plane, reorienting a strongly eccentric jet that the pretrained operator predicts as straight, and yields full-field predictions in minutes rather than the days required by the underlying simulations. Its influence decays sharply with distance from that plane, however: measured against phase-resolved particle image velocimetry, the reconstruction error rises from 24.6% at 2mm to 52.6% at 6mm, and the resulting mismatch between corrected and uncorrected layers degrades physical consistency. Single-plane supervision thus constrains the observed plane far more effectively than the surrounding volume, which we identify as the principal obstacle to coherent 4D reconstruction from sparse planar data.
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BibTeX
@misc{hoffmann2026reconstruction,
title = {{Reconstruction of 4D Mitral Regurgitation Hemodynamics from Sparse Planar Data using Deep Operator Networks with Test-Time Adaptation}},
author = {Jakob Marcel Hoffmann and Yosuke Hasegawa and Alexander Stroh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20857},
eprint = {2609.20857},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20857},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Reconstruction of 4D Mitral Regurgitation Hemodynamics from Sparse Planar Data using Deep Operator Networks with Test-Time Adaptation
AU - Jakob Marcel Hoffmann
AU - Yosuke Hasegawa
AU - Alexander Stroh
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.20857
UR - https://arxiv.org/abs/2609.20857
AB - Quantifying mitral regurgitation severity remains limited by the assumptions of clinical flow convergence methods, while high-fidelity simulation and volumetric velocimetry are too slow for routine use. We investigate whether a learned solution operator can reconstruct transient three-dimensional transvalvular hemodynamics from the sparse observation an in-vitro experiment actually provides: a single planar velocity slice and two boundary pressure traces. A Deep Operator Network is pretrained on an experimentally benchmarked URANS database spanning eleven mitral regurgitation orifice phantoms, learning a mapping from a masked two-component planar velocity snapshot to the surrounding volumetric field, and is subsequently adapted to unseen target cases by fine-tuning on their sparse measurements. Adaptation reliably corrects the flow topology within the supervised plane, reorienting a strongly eccentric jet that the pretrained operator predicts as straight, and yields full-field predictions in minutes rather than the days required by the underlying simulations. Its influence decays sharply with distance from that plane, however: measured against phase-resolved particle image velocimetry, the reconstruction error rises from 24.6% at 2mm to 52.6% at 6mm, and the resulting mismatch between corrected and uncorrected layers degrades physical consistency. Single-plane supervision thus constrains the observed plane far more effectively than the surrounding volume, which we identify as the principal obstacle to coherent 4D reconstruction from sparse planar data.
ER -