Physics-informed neural network estimation of material properties in soft tissue nonlinear biomechanical models

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 and secondary variables such as stresses and strains. 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 with respect to noise and model uncertainty and its great potential to enable the effective identification of patient-specific, heterogeneous physical properties, e.g. tissue stiffness properties. In particular, we demonstrate the capability of PINNs 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.