Estimation of shear wave 3D velocity fields from echocardiographic time-of-flight data using physics-informed neural networks.

Ultrasound shear wave elastography offers a promising non-invasive method to measure cardiac stiffness, providing valuable insights into an individual's heart condition. The technique uses high-frame-rate imaging to capture shear wave propagation along the cardiac wall, originating from mechanical events such as valve closure. The speed of these waves correlates with myocardial stiffness, enabling quantitative evaluation of cardiac tissue properties. While current implementations primarily rely on two-dimensional imaging, three-dimensional imaging has also been explored. In this case, shear wave velocity reconstruction is performed along the short- and long-axis direction of the heart or in regions traversed by the wave. We here demonstrate a novel method to reconstruct the shear wave velocity field throughout the left ventricle, by means of physics-informed neural networks. In this framework, neural networks are used as general function approximators for both the time-of-flight map and the shear wave propagation velocity, subjected to physics regularization, i.e. the waves follow eikonal propagation. This approach was validated both in silico and in vitro, where ground truth stiffness measures were available, and further demonstrated on 6 healthy volunteers. Compared to current reported methods, our approach showed better robustness to noisy and incomplete data. Furthermore, it has the potential to allow shear wave velocity reconstruction in multiple orthogonal directions. These improvements pave the way for more robust and clinically applicable cardiac stiffness measurements.