Estimation of Active Stress Parameters in Cardiac Models Using Physics-Informed Neural Networks
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Active stress models in cardiac biomechanics play a crucial role in capturing the mechanical deformation induced by muscle activity, thereby bridging the electrophysiological and mechanical properties of myocardial tissue. Accurate estimation of active stress parameters is essential for a comprehensive understanding of myocardial function. However, achieving this in clinical settings remains challenging, particularly when only displacement and strain data from medical imaging modalities are available. In this work [1], we present a novel framework based on physics-informed neural networks (PINNs) [2] for inferring active contractility in time-dependent cardiac biomechanics using only these types of data. By incorporating adaptive weighting schemes, residual-based attention mechanisms, ad-hoc regularisation strategies, and Fourier features, the proposed method demonstrates robust and accurate reconstruction of active stress fields across various scenarios, even in the presence of noise and with high spatial resolution. Additionally, we conduct a detailed Pareto front analysis to investigate the impact of loss weights on the reconstruction of active stress parameters. The framework is further applied to characterise tissue inhomogeneities and detect fibrotic scars in myocardial tissue. This work represents a significant methodological advancement in addressing inverse problems in computational biomechanics. It offers a promising pathway to enhance the diagnosis, treatment planning, and management of cardiac conditions associated with tissue heterogeneity, such as cardiac fibrosis and myocardial infarction. REFERENCES [1] Höfler M., Regazzoni F., Pagani S., Karabelas E., Augustin C., Haase G., Plank G. and Caforio F., 2025. Physics-informed neural network estimation of active material properties in time-dependent cardiac biomechanical models. arXiv preprint arXiv:2505.03382. [2] Raissi M., Perdikaris P. , and Karniadakis G.E., Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comp. Phys., 2019. 378: 686–707.
