Enhancing blood clot simulations by Deep Learning and Model Order Reduction techniques

Thrombus formation in blood vessels is a medical problem which manifests itself both spontaneously and after the insertion of medical devices inside human bodies. Around 500000 people die in the EU each year because of it, it is thus crucial to develop robust computational methods to predict its formation. This work shows how Deep Learning and Model Order Reduction techniques can be applied in order to enhance physical simulations of blood clots formation. A few simulations were carried out with the software OpenFoam, to solve the Navier-Stokes equations for the blood flow and a set of parametrized PDEs, which couple the concentrations of the biochemical species with the velocity field of blood. Our aim is finding a method which allows to predict the evolution in time and space of some selected biochemical species giving as input the parameters on which the PDEs depend, without solving numerically the biochemical and mechanics equations. At this regard, we show how Proper Orthogonal Decomposition (POD) and a Neural Network (NN) architecture that combines a Convolutional Autoencoder (CAE) and a Deep Feed-Forward Neural Network (DFNN) can be exploited to give a good approximation of the PDEs solution. We then analyze some limitations of the method, such as the difficulty at making good predictions in time when the blood flow changes rapidly, and we propose some modifications to overcome these drawbacks.