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Cardiovascular diseases are among the most common diseases with high mortality, including aortic valve stenosis and insufficiency. Minimally invasive implantation of transcatheter aortic valve prosthesis (TAVI) has become the standard procedure for patients with increased risk for open surgery. It is commonly accepted that the long-term outcome of aortic valve replacement depends on hemodynamic performance. This motivates the analysis of the velocity field in the vicinity of the TAVI. Computational fluid dynamics (CFD) methods have been established in the past, but show limitations in terms of computational effort when rapid design optimization or patient-specific decision making in real time is required. In this study we show the usage of PINNs for predicting fluid flow through a TAVI device. We also show a method of enforcing boundary conditions for this specific problem. Due to the physics involved in the training process, this principle does in theory not require additional training data. To validate the method, we performed CFD simulations that solved the Navier-Stokes equations be means of finite volume methods. Besides the good estimation of the main flow components, discrepancies between CFD and PINN results are present. Nevertheless, the flow structures have certain similarities in the coarse spatial localization of the vortex patterns occurring in flow around the TAVI device.

Computation of flow through TAVI device by means of physics informed neural networks