Tomás Banduc | Searcharxiv

arXiv2026

iLogMap: Geodesic Polar Coordinates Parameterization with the Magnetic Laplacian

Geodesic polar coordinates (GPCs) provide an intrinsic parameterization over curved surfaces, but their accurate estimation remains challenging, particularly in the presence of anisotropic metrics, high curvature and complex topology. We introduce iLogMap, a method for computing GPCs in curved domains that recasts the angular component of the logarithmic map to a ground-state magnetic eigenproblem over the circumferential direction field of geodesic distance. Our method effortlessly extends to anisotropic metric tensors and solid volumes, enabling cylindrical and spherical parameterizations in tetrahedral meshes. Experiments on diverse shapes with varying genus confirm competitive angular accuracy and reduced metric distortion relative to heat-based methods, with improved performance on surfaces with boundary and domains with anisotropy. We demonstrate the utility of iLogMap in computational cardiology applications, where we use it to initialize spiral phases on atrial surfaces and estimate local activation patterns in ventricular models.

cs.CG↗

arXiv2025

WarpPINN-fibers: improved cardiac strain estimation from cine-MR with physics-informed neural networks

The contractile motion of the heart is strongly determined by the distribution of the fibers that constitute cardiac tissue. Strain analysis informed with the orientation of fibers allows to describe several pathologies that are typically associated with impaired mechanics of the myocardium, such as cardiovascular disease. Several methods have been developed to estimate strain-derived metrics from traditional imaging techniques. However, the physical models underlying these methods do not include fiber mechanics, restricting their capacity to accurately explain cardiac function. In this work, we introduce WarpPINN-fibers, a physics-informed neural network framework to accurately obtain cardiac motion and strains enhanced by fiber information. We train our neural network to satisfy a hyper-elastic model and promote fiber contraction with the goal to predict the deformation field of the heart from cine magnetic resonance images. For this purpose, we build a loss function composed of three terms: a data-similarity loss between the reference and the warped template images, a regularizer enforcing near-incompressibility of cardiac tissue and a fiber-stretch penalization that controls strain in the direction of synthetically produced fibers. We show that our neural network improves the former WarpPINN model and effectively controls fiber stretch in a synthetic phantom experiment. Then, we demonstrate that WarpPINN-fibers outperforms alternative methodologies in landmark-tracking and strain curve prediction for a cine-MRI benchmark with a cohort of 15 healthy volunteers. We expect that our method will enable a more precise quantification of cardiac strains through accurate deformation fields that are consistent with fiber physiology, without requiring imaging techniques more sophisticated than MRI.

eess.IV↗