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• Model order reduction for blood flows to enhance computational efficiency (real time). • Patient specific numerical simulations. • Efficient Haemodynamic simulations. Left ventricular assist devices (LVADs) are used to provide haemodynamic support to patients with critical cardiac failure. Severe complications can occur because of the modifications of the blood flow in the aortic region. In this work, the effect of a continuous flow LVAD device on the aortic flow is investigated by means of a non-intrusive reduced order model (ROM) built using the proper orthogonal decomposition with interpolation (PODI) method based on radial basis functions (RBF). The full order model (FOM) is represented by the incompressible Navier-Stokes equations discretized by using a Finite Volume (FV) technique, coupled with three-element Windkessel models to enforce outlet boundary conditions in a multi-scale approach. A patient-specific framework is proposed: a personalized geometry reconstructed from Computed Tomography (CT) images is used and the individualization of the coefficients of the three-element Windkessel models is based on experimental data provided by the Right Heart Catheterization (RHC) and Echocardiography (ECHO) tests. At FOM level, we also consider the pre-surgery configuration in order to further validate the predictive capabilities of the model in several contexts. The ROM has been tested by considering a parametric setting with respect to the LVAD flow, which is a crucial parameter of the problem. We consider a parameter range that covers typical clinical values. The accuracy of the ROM is assessed against results obtained with the FOM both for primal, velocity and pressure, and derived quantities, wall shear stress (WSS). Finally, we briefly discuss the efficiency of our ROM approach. [ABSTRACT FROM AUTHOR]