Non-Invasive Reconstruction of Cardiac Activation Dynamics Using Physics-Informed Neural Networks

Nathan Dermul; Hans Dierckx

physics.med-phMar 4, 2026

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.

Abstract

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 $f_{n}(\mathbf{r})$ are then calculated as a preprocessing step and serve as the input coordinates for the PINN. The spatial-temporal fields of the deformation vector $\mathbf{U}(\mathbf{r},t)$ , active tension $T_{a}(\mathbf{r},t)$ and hydrostatic pressure $p(\mathbf{r},t)$ 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 $N_{d}$ data points and the physics loss enforced on $N_{c}$ collocation points.

Panel of Figure 2 — 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.

Panel of Figure 3 — Figure 3: PINN results for the estimated active tension $T_{a}$ , 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 $T_{a}$ -field, the last column shows the corresponding LAT map for the activation wave.

Panel of Figure 4 — Figure 4: PINN results for the estimated active tension $T_{a}$ , 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.

Panel of Figure 5 — Figure 5: PINN results for the estimated active tension $T_{a}$ 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.

Panel of Figure 6 — Figure 6: PINN results for the estimated active tension $T_{a}$ 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	$\alpha$	RMSE $T_{a}$ (kPa)	RMSE $U$ (mm)	RMSE $p$ (kPa)
Reference	$10^{-1}$	$0.333\pm 0.013$	$(705.3\pm 4.6)\cdot 10^{-5}$	$0.1811\pm 0.0031$
5 $\%$ noise	$10^{0}$	$0.3445\pm 0.0045$	$0.0127\pm 0.0014$	$0.2161\pm 0.0025$
10 $\%$ noise	$10^{0}$	$0.388\pm 0.028$	$0.0156\pm 0.0018$	$0.2204\pm 0.0053$
0.50 resolution	$10^{-1}$	$0.400\pm 0.048$	$0.00863\pm 0.00052$	$0.2248\pm 0.0024$
0.25 resolution	$10^{-2}$	$0.491\pm 0.023$	$0.00130\pm 0.00022$	$0.2799\pm 0.0058$

Table 1: Summarization of the chosen

\alpha

values for each dataset and the resulting PINN accuracies for the active tension

T_{a}

, 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.

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