Rapid cardiac activation prediction for cardiac resynchronization therapy planning using geometric deep learning

Introduction: : Cardiac resynchronization therapy (CRT) is used to treat patients with dyssynchronous heart failure. Identifying optimal pacing sites, however, remains a key challenge due to patient anatomical variability and the limitations of individualized lead placement strategies, with nearly one-third of CRT recipients classified as non-responders. Although the importance of pacing site selection is emphasized in numerous experimental and clinical studies, its optimization in clinical practice remains difficult.

Physics-based computational modeling, based on differential equations, has offered valuable insights into the mechanisms of CRT and the optimization of pacing sites. Their applicability in clinical settings, however, is limited by lengthy computation times. While recent advances in deep learning (DL) have led to the development of surrogate models that rapidly predict cardiac behavior, few are specifically tailored to CRT optimization. A major challenge lies in developing DL surrogates that can accommodate patient-specific heart geometries.

Here, we developed and compared two physics-based DL models using a graph neural network (GNN) architecture (Graph-UNet) [1] and a geometry-informed neural operator (GINO) framework [2] to predict cardiac activation time and patterns in the left ventricle (LV). Operating directly on point cloud representations of LV geometries, we showed that the trained DL models can rapidly and accurately predict activation patterns across arbitrary LV geometries, tissue conductivity, and pacing sites. An interactive web-based GUI (https://dcsim.egr.msu.edu) was also developed to demonstrate how the DL models can serve as a clinical decision-support tool for personalized CRT optimization.

Materials and

Methods: : The physics-based DL models were developed from a large set of paired input-output data generated through numerical simulations. First, we created 17,500 synthetic LV geometries using the methodology adapted by Buoso et al. [3]. These geometries were then utilized in finite element (FE) simulations of cardiac electrophysiology using the Aliev-Panfilov model [4] to compute activation patterns associated with randomly selected pacing sites. Single pacing-site simulations represented intrinsic activation associated with left branch bundle block (LBBB) [5], while dual pacing-site simulations modeled post-CRT scenarios, in which the second pacing site represents the placed lead. Additionally, tissue electrical conductivity values were varied to reflect inter-subject variability.

The 17,500 simulation cases were split into three sets: 8,700 cases for training and 4,400 cases for development (hyperparameter optimization) and testing. Furthermore, the trained models’ discretization invariance was evaluated using a set of 100 cases with refined discretization.

Based on the trained DL models, we developed a workflow for CRT planning to optimize pacing site selection. The workflow begins with user input of an LV geometry and a measured activation map associated with LBBB (simulated here but clinically measurable). An inverse problem is first solved to estimate the intrinsic source and tissue conductivity, which is followed by an optimization problem to identify the optimal CRT pacing site that minimizes the maximum activation time.

Results, Conclusions, and Discussions:: Table 1 summarizes the performance of the optimized GNN and GINO models, showing consistently lower errors in the GINO model across all datasets. Fig. 1 shows that the GINO model consistently captured the overall activation patterns accurately, with the largest errors primarily localized near the pacing sites, even in cases with high global error. The error values are comparable to prior physics-based DL models on arbitrary geometries, which reported mean test errors ranging from 2% to 10% [1,2, 6-8].

The computational efficiency of the trained GINO model, which predicts activation maps in just a few milliseconds (compared to approximately 12 minutes in FE simulations), makes it feasible to be used for the CRT optimization workflow, where numerous pacing sites are evaluated to identify the optimal lead position. To demonstrate its potential, we analyzed a case with a single intrinsic pacing site and a prolonged maximum activation time of 147 ms, reflecting pathological conditions associated with LBBB. Fig. 2 demonstrates that pacing at the optimized site reduced the maximum activation time by 20% (from 147 ms to 118 ms). In contrast, pacing at a randomly chosen site resulted in only an 8% reduction (to 135 ms). The entire workflow, including thousands of evaluations using evolutionary optimization, was completed in under two minutes.

There are, however, several limitations associated with this work. First, the LV geometries used to train the DL models were synthesized based on a POD model of 75 LV geometries, which may not capture the full spectrum found in patients with LBBB and other heart diseases. Second, the DL models focus only on cardiac electrophysiology and do not consider mechanical deformation, which is also an important aspect in optimizing CRT. Third, we assumed that the activation time map associated with LBBB can be reproduced from a single pacing site along with homogeneous tissue conductivity. The DL models can be refined further by evaluating them on geometries from other sources, incorporating cardiac electromechanics, including more pacing locations, and accounting for local variation in tissue conductivity.

Acknowledgements and/or References (Optional):: This work is supported by NIH R01HL166508, R43HL174177 and NSF 2406029.

[1] H. Gao and S. Ji, “Graph U-Nets,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 44, no. 9, pp. 4948–4960, 2022.
[2] Z. Li, N. B. Kovachki, C. Choy, B. Li, J. Kossaifi, S. P. Otta, M. A. Nabian, M. Stadler, C. Hundt, K. Azizzadenesheli, and A. Anandkumar, “Geometry-informed neural operator for large-scale 3d PDEs,” in Thirty-seventh Conference on Neural Information Processing Systems, 2023.
[3] S. Buoso, T. Joyce, and S. Kozerke, “Personalising left-ventricular biophysical models of the heart using parametric physics-informed neural networks,” Medical Image Analysis, vol. 71, p. 102066, 2021.
[4] R. R. Aliev and A. V. Panfilov, “A simple two-variable model of cardiac excitation,” Chaos, Solitons & Fractals, vol. 7, no. 3, pp. 293–301, 1996.
[5] E. Surkova, L. P. Badano, R. Bellu, P. Aruta, F. Sambugaro, G. Romeo, F. Migliore, D. Muraru, Left bundle branch block: from cardiac mechanics to clinical and diagnostic challenges, EP Europace, vol, 19, no. 8, pp. 1251–1271, 2017.
[6] H. Wu, H. Luo, H. Wang, J. Wang, and M. Long, “Transolver: A fast transformer solver for PDEs on general geometries,” in Proceedings of the 41st International Conference on Machine Learning, ser. ICML’24, Vienna, Austria: JMLR.org, 2024.
[7] M. Elrefaie, A. Dai, and F. Ahmed, “DrivAerNet: A parametric car dataset for data-driven aerodynamic design and graph-based drag prediction,” in Volume 3A: 50th Design Automation Conference (DAC), International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Aug. 2024, V03AT03A019.
[8] M. Yin, N. Charon, R. Brody, L. Lu, N. Trayanova, and M. Maggioni, “A scalable framework for learning the geometry-dependent solution operators of partial differential equations,” Nature Computational Science, vol. 4, no. 12, pp. 928–940, 2024.