Physics-informed neural network estimation of active material properties in time-dependent cardiac biomechanical models

Active stress models in cardiac biomechanics account for the mechanical deformation caused by muscle activity, thus providing a link between the electrophysiological and mechanical properties of the tissue. The accurate assessment of active stress parameters is fundamental for a precise understanding of myocardial function but remains difficult to achieve in a clinical setting, especially when only displacement and strain data from medical imaging modalities are available. This study introduces a novel physics-informed neural networks (PINNs) framework for inferring active contractility in time-dependent cardiac biomechanics from these types of imaging data. By leveraging adaptive weighting schemes, residual-based attention mechanisms, ad-hoc regularisation strategies, Fourier Features, the proposed method achieves robust and accurate reconstruction of active stress fields in various settings, in the presence of noise and with a high spatial resolution. In addition, we perform a thorough Pareto front analysis to study the influence of the loss weights in the reconstruction of active stress parameters. Finally, we apply the method to the characterisation of tissue inhomogeneities and detection of fibrotic scars in myocardial tissue. This work represents a significant methodological advancement, addressing key challenges in inverse problems for computational biomechanics and it opens a new pathway to significantly improve the diagnosis, treatment planning, and management of heart conditions associated with cardiac diseases and conditions associated with tissue heterogeneity, such as cardiac fibrosis or myocardial infarction.