Non-Invasive Reconstruction of Cardiac Activation Dynamics Using Physics-Informed Neural Networks
Authors: Nathan Dermul, Hans Dierckx
Organizations: Department of Cardiovascular Sciences, Cardiovascular Imaging and Dynamics, KU Leuven, Belgium. · Department of Cardiology, Leiden University Medical Centre, Albinusdreef 2, Leiden, 2333 ZA, the Netherlands. · Mathematical Institute, Leiden University, Einsteinweg 55, Leiden, 2333 CC, the Netherlands. · Leiden Institute of Physics, Leiden University, Niels Bohrweg 2, Leiden, 2333 CA, the Netherlands.
Cardiac arrhythmogenesis is governed by complex electromechanical interactions that are not directly observable in vivo, motivating the development of non-invasive computational approaches for reconstructing three-dimensional activation dynamics. We present a physics-informed neural network framework for recovering cardiac activation patterns, active tension propagation, deformation fields, and hydrostatic pressure from measurable deformation data in simplified left ventricular geometries. Our approach integrates nonlinear anisotropic constitutive modeling, heterogeneous fiber orientation, weak formulations of the governing mechanics, and finite-element-based loss functions to embed physical constraints directly into training. We demonstrate that the proposed framework accurately reconstructs spatiotemporal activation dynamics under varying levels of measurement noise and reduced spatial resolution, while preserving global propagation patterns and activation timing. By coupling mechanistic modeling with data-driven inference, this method establishes a pathway toward patient-specific, non-invasive reconstruction of cardiac activation, with potential applications in digital phenotyping and computational support for arrhythmia assessment.
Figures & tables
Figure 1: Schematic overview of the PINN framework. The input consists of a 3D volumetric mesh together with available deformation data defined on the vertices. Laplacian eigenfunctions fn(r) are then calculated as a preprocessing step and serve as the input coordinates for the PINN. The spatial-temporal fields of the deformation vector U(r,t) , active tension Ta(r,t) and hydrostatic pressure p(r,t) are represented by three fully connected NNs. The optimization is done by minimizing two terms that make up the total loss function: the data loss which is evaluated on Nd data points and the physics loss enforced on Nc collocation points.
Figure 2: PINN results for the estimated deformation field U and hydrostatic pressure p , optimized on all available data points. The fields are visualized by slicing the 3D volumetric mesh with the x=0 mm plane (longitudinal, left) and the z=−5 mm plane (radial, right). Both planes slice through the source point, see Fig. 5 for the 3D orientation. Panels (a) and (b) show the y-component of the deformation, while panels (c) and (d) consist of the hydrostatic pressure p , used in the forward simulation to satisfy the incompressibility constraint.
Figure 3: PINN results for the estimated active tension Ta , optimized on all available data points. The fields are visualized by slicing the 3D volumetric mesh with the x=0 mm plane (longitudinal, panel (a) ) and the z=−5 mm plane (radial, panel (b) ). Both planes slice through the source point, see Fig. 5 for the 3D orientation. In addition to the Ta -field, the last column shows the corresponding LAT map for the activation wave.
Figure 4: PINN results for the estimated active tension Ta , optimized on all available data points. Panel (a) shows polar maps of the endo- and epicardial surfaces, calculated from the longitudinal and circumferential coordinates. The continuous field is visualized by linearly interpolating the vertex values in the new space. Panel (b) presents a cross-section of the volume by slicing the 3D volumetric mesh with the x=−5 mm plane which, unlike other figures, does not go through the source point, revealing the transmural differences in wave propagation.
Figure 5: PINN results for the estimated active tension Ta and corresponding LAT map, optimized on all available data points with Gaussian noise levels of 5% and 10% of the maximum values. The datasets are illustrated in the first column by the y-component of the deformation at one timestep. The plane in the first row indicates the 3D orientation of the cross-sections, panel ( a ) for the longitudinal view (( x=0 mm) and panel ( b ) for the radial ( z=−5 mm). Both planes go through the source point.
Figure 6: PINN results for the estimated active tension Ta and corresponding LAT map, optimized on data with reduced spatial resolution. The data was first smoothed with a discrete Gaussian before randomly subsampled to mimic reduced resolution in the data. This was done for 50% and 25% of all points, see Section 2.1 for details. The datasets are illustrated in the first column by the y-component of the deformation at one timestep. The plane in the first row indicates the 3D orientation of the cross-sections, panel ( a ) for the longitudinal view (( x=0 mm) and panel ( b ) for the radial ( z=−5 mm). Both planes go through the source point.
Dataset
α
RMSE Ta (kPa)
RMSE U (mm)
RMSE p (kPa)
Reference
10−1
0.333±0.013
(705.3±4.6)⋅10−5
0.1811±0.0031
5 % noise
100
0.3445±0.0045
0.0127±0.0014
0.2161±0.0025
10 % noise
100
0.388±0.028
0.0156±0.0018
0.2204±0.0053
0.50 resolution
10−1
0.400±0.048
0.00863±0.00052
0.2248±0.0024
0.25 resolution
10−2
0.491±0.023
0.00130±0.00022
0.2799±0.0058
Table 1: Summarization of the chosen α values for each dataset and the resulting PINN accuracies for the active tension Ta , the deformation U and pressure p . The optimization is repeated 3 times where the initialization of the NN weights, the mini-batch sampling and the gaussian noise if applicable is different. Average values over the runs and standard deviation are shown. The RMSE value of one run is calculated by taking the average over the full spatial and temporal domain, while all three components of U are averaged jointly.
Accurate forward modelling is essential for non-invasive cardiac electrophysiology, particularly in atrial fibrillation, where electrical activation is highly disorganised. Conventional physics-based forward models require explicit specification of intracellular conductivity tensors, which are not directly measurable in clinical practice and introduce structural modelling errors. This proof-of-concept study presents a deep learning approach that learns a direct mapping from left atrial intracellular electrical potentials to far-field ECGs without requiring explicit intracellular conductivity inputs at inference time. Despite training only on 74 subjects, the model achieved an R2 of 0.949 \pm 0.037, highlighting potential to reduce structural uncertainty and improve non-invasive AF assessment.
Shaheim Ogbomo-Harmitt, Cesare Magnetti, Jakub Grzelak +1
King’s College London, Floor 3, Lambeth Wing St Thomas’ Hospital Westminster Bridge Road, London, SE1 7EH · Floor 3, Lambeth Wing St Thomas’ Hospital Westminster Bridge Road, London, SE1 7EH · PhysicsX, 1 Leonard Circus, London EC2A 4DQ
Quantifying myocardial perfusion from cardiac magnetic resonance (CMR) can be achieved by fitting tracer-kinetic models to the dynamic contrast-enhanced MR data. However, fitting the observed data with multi-compartment exchange models, which describe the evolution of the contrast agent in the tissue, to estimate perfusion parameters is a challenging inverse problem that is sensitive to noise and acquisition variability. Previously, physics-informed neural networks (PINNs) have been proposed as an alternative to conventional non-linear least squares fitting methods with promising results for quantitative perfusion CMR. In this work, we extend the previously proposed PINN framework with spatiotemporal implicit neural representations (INRs) to represent the MR signal as a continuous spatiotemporal function and to improve the accuracy, smoothness, and physical consistency of the PINN model. In realistic simulated CMR datasets, our proposed PINN with INRs demonstrates improved robustness and parameter estimation accuracy over the previously established methods. The code is available at https://github.com/q-cardIA/pinn-inr.
Christos Tsepas, Chang Yan, Maximilian Fuetterer +2
Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, the Netherlands · Institute for Biomedical Engineering, University and ETH Zurich, Zurich, Switzerland
Accurate localization of myocardial infarction is essential for risk stratification. While LGE-MRI remains the gold standard, it is resource-intensive. Integrating cine MRI with ECG enables a more detailed representation of infarct properties. Existing inverse MI inference methods overlook realistic scar morphology and cardiac repolarization, reducing sensitivity to subtle ECG variations and interpretability of infarct-induced electrophysiological changes. In this paper, we propose a novel framework for noninvasive MI localization using cardiac digital twins. To bridge the domain gap between simulation and reality, we introduce an anatomy-aware stochastic infarct synthesis strategy to synthesize realistic, irregular scars with border zones, mimicking ischemic transmural progression. We then construct a virtual cohort to simulate QRS-T waveforms, capturing both depolarization and repolarization dynamics. Furthermore, we design a Physiology and Anatomy Aware Network (PAA-Net) that jointly encodes 3D myocardial geometry and multi-lead ECGs to infer infarct areas with varying localizations, sizes, spatial extents, and transmuralities. Experimental results demonstrate that our framework significantly outperforms existing methods in inverse inference, achieving Dice scores of 0.7391 and 0.5503 for scar and border zone segmentation, respectively, while further enhancing the interpretability of the ECG-infarct relationship. Our code will be released upon acceptance.
Mengxiao Wang, Yilin Lyu, Julia Camps +6
Shanghai Jiao Tong University, Shanghai, China · National University of Singapore, Singapore · Universitat Pompeu Fabra, Barcelona, Spain