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 work investigates, through an in-silico study, the application of physics-informed neural networks (PINNs) for inferring active contractility parameters in time-dependent cardiac biomechanical models from these types of imaging data. In particular, by parametrising the sought state and parameter field with two neural networks, respectively, and formulating an energy minimisation problem to search for the optimal network parameters, we are able to reconstruct in various settings active stress fields in the presence of noise and with a high spatial resolution. To this end, we also advance the vanilla PINN learning algorithm with the use of adaptive weighting schemes, ad-hoc regularisation strategies, Fourier features, and suitable network architectures. In addition, we thoroughly analyse 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 approach opens a new pathway to significantly improve the diagnosis, treatment planning, and management of heart conditions associated with cardiac fibrosis.

Dynamic computed tomography (CT) reconstruction faces significant challenges in addressing motion artifacts, particularly for nonperiodic rapid movements such as cardiac imaging with fast heart rates. Traditional methods struggle with the extreme limited-angle problems inherent in nonperiodic cases. Deep learning methods have improved performance but face generalization challenges. Recent implicit neural representation (INR) techniques show promise through self-supervised deep learning, but have critical limitations: computational inefficiency due to forward-warping modeling, difficulty balancing DVF complexity with anatomical plausibility, and challenges in preserving fine details without additional patient-specific pre-scans. This paper presents a novel INR-based framework, BIRD, for nonperiodic dynamic CT reconstruction. It addresses these challenges through four key contributions: (1) backward-warping deformation that enables direct computation of each dynamic voxel with significantly reduced computational cost, (2) diffeomorphism-based DVF regularization that ensures anatomically plausible deformations while maintaining representational capacity, (3) motion-compensated analytical reconstruction that enhances fine details without requiring additional pre-scans, and (4) dimensional-reduction design for efficient 4D coordinate encoding. Through various simulations and practical studies, including digital and physical phantoms and retrospective patient data, we demonstrate the effectiveness of our approach for nonperiodic dynamic CT reconstruction with enhanced details and reduced motion artifacts. The proposed framework enables more accurate dynamic CT reconstruction with potential clinical applications, such as one-beat cardiac reconstruction, cinematic image sequences for functional imaging, and motion artifact reduction in conventional CT scans.