Federica Caforio

Federica Caforio, Francesco Regazzoni, Stefano Pagani et al.

The development of biophysical models for clinical applications is rapidly advancing in the research community, thanks to their predictive nature and their ability to assist the interpretation of clinical data. However, high-resolution and accurate multi-physics computational models are computationally expensive and their personalisation involves fine calibration of a large number of parameters, which may be space-dependent, challenging their clinical translation. In this work, we propose a new approach which relies on the combination of physics-informed neural networks (PINNs) with three-dimensional soft tissue nonlinear biomechanical models, capable of reconstructing displacement fields and estimating heterogeneous patient-specific biophysical properties. The proposed learning algorithm encodes information from a limited amount of displacement and, in some cases, strain data, that can be routinely acquired in the clinical setting, and combines it with the physics of the problem, represented by a mathematical model based on partial differential equations, to regularise the problem and improve its convergence properties. Several benchmarks are presented to show the accuracy and robustness of the proposed method and its great potential to enable the robust and effective identification of patient-specific, heterogeneous physical properties, s.a. tissue stiffness properties. In particular, we demonstrate the capability of the PINN to detect the presence, location and severity of scar tissue, which is beneficial to develop personalised simulation models for disease diagnosis, especially for cardiac applications.

Matthias Höfler, Francesco Regazzoni, Stefano Pagani et al.

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.

Francesco C. Mantegazza, Federica Caforio, Christoph Augustin et al.

Personalized cardiac diagnostics require accurate reconstruction of myocardial displacement fields from sparse clinical imaging data, yet current methods often demand intrusive access to computational models. In this work, we apply the non-intrusive Parametrized-Background Data-Weak (PBDW) approach to three-dimensional (3D) cardiac displacement field reconstruction from limited Magnetic Resonance Image (MRI)-like observations. Our implementation requires only solution snapshots -- no governing equations, assembly routines, or solver access -- enabling immediate deployment across commercial and research codes using different constitutive models. Additionally, we introduce two enhancements: an H-size minibatch worst-case Orthogonal Matching Pursuit (wOMP) algorithm that improves Sensor Selection (SS) computational efficiency while maintaining reconstruction accuracy, and memory optimization techniques exploiting block matrix structures in vectorial problems. We demonstrate the effectiveness of the method through validation on a 3D left ventricular model with simulated scar tissue. Starting with noise-free reconstruction, we systematically incorporate Gaussian noise and spatial sparsity mimicking realistic MRI acquisition protocols. Results show exceptional accuracy in noise-free conditions (relative L2 error of order O(1e-5)), robust performance with 10% noise (relative L2 error of order O(1e-2)), and effective reconstruction from sparse measurements (relative L2 error of order O(1e-2)). The online reconstruction achieves four-order-of-magnitude computational speed-up compared to full Finite Element (FE) simulations, with reconstruction times under one tenth of second for sparse scenarios, demonstrating significant potential for integration into clinical cardiac modeling workflows.