Towards Reduced Order Models via Robust Proper Orthogonal Decomposition to Capture Personalised Aortic Haemodynamics

Abstract

Data driven, reduced order modelling has shown promise in tackling the challenges associated with computational and experimental hemodynamic models. In this work, we explore the use of Reduced Order Models (ROMs) to capture the main flow features in a patient-specific dissected aorta. We apply Proper Orthogonal Decomposition (POD) and Robust Principle Component Analysis (RPCA) on in vitro, hemodynamic data acquired by Particle Image Velocimetry and compare the decomposed flows to those derived from Computational Fluid Dynamics (CFD) data for the same geometry and flow conditions. The flow is reconstructed using different numbers of POD modes and the flow features obtained throughout the cardiac cycle are compared to the original Full Order Models (FOMs). RPCA has been found to enhance the quality of PIV data and to capture most of the kinetic energy of the flow in just two modes similar to the numerical data that are free from measurement noise. The reconstruction errors differ along the cardiac cycle with diastolic flows requiring more modes for accurate reconstruction. In general, modes{Phi} 1-10 are found sufficient to represent the flow field. The results demonstrate that the coherent structures that characterise this aortic dissection flow are described by the first few POD modes suggesting that it is possible to represent the macroscale behaviour of aortic flow in a low-dimensional space; thus significantly simplifying the problem, and allowing for more computationally efficient flow simulations that can pave the way for translation of such models to the clinic.