Image Velocimetry using Direct Displacement Field estimation with Neural Networks for Fluids

An important tool for experimental fluids mechanics research is Particle Image Velocimetry (PIV). Several robust methodologies have been proposed to perform the estimation of velocity field from the images, however, alternative methods are still needed to increase the spatial resolution of the results. This work presents a novel approach for estimating fluid flow fields using neural networks and the optical flow equation to predict displacement vectors between sequential images. The result is a continuous representation of the displacement, that can be evaluated on the full spatial resolution of the image. The methodology was validated on synthetic and experimental images. Accurate results were obtained in terms of the estimation of instantaneous velocity fields, and of the determined time average turbulence quantities and power spectral density. The methodology proposed differs of previous attempts of using machine learning for this task: it does not require any previous training, and could be directly used in any pair of images.

Ensemble learning of the atrial fiber orientation with physics-informed neural networks

The anisotropic structure of the myocardium is a key determinant of the cardiac function. To date, there is no imaging modality to assess in-vivo the cardiac fiber structure. We recently proposed Fibernet, a method for the automatic identification of the anisotropic conduction -- and thus fibers -- in the atria from local electrical recordings. Fibernet uses cardiac activation as recorded during electroanatomical mappings to infer local conduction properties using physics-informed neural networks. In this work, we extend Fibernet to cope with the uncertainty in the estimated fiber field. Specifically, we use an ensemble of neural networks to produce multiple samples, all fitting the observed data, and compute posterior statistics. We also introduce a methodology to select the best fiber orientation members and define the input of the neural networks directly on the atrial surface. With these improvements, we outperform the previous methodology in terms of fiber orientation error in 8 different atrial anatomies. Currently, our approach can estimate the fiber orientation and conduction velocities in under 7 minutes with quantified uncertainty, which opens the door to its application in clinical practice. We hope the proposed methodology will enable further personalization of cardiac digital twins for precision medicine.