We present a careful evaluation of non-Newtonian blood rheology effects in arterial flow simulations. We achieve that by comparing the converged solutions obtained a) from a Casson viscoplastic modeling of blood rheology using a recently developed parametrization [Apostolidis and Beris, J. Rheol., 58: 607-633 (2014)], and b) from a Newtonian model. We emphasize on the proper implementation of outlet boundary conditions (OBCs) in a way that ensures consistency with the pressure flow predictions of the downstream network, which is modeled approximately using a 1D model [Johnson et al., Comp. Chem. Eng., 35: 1304-1316 (2011)]. We further improve and validate the iterative scheme proposed by [Johnson et al., Int. J. Num. Meth. Fluids, 66: 1383-1408 (2011)] for the implementation of the OBCs, by employing it in conjunction with a) Casson-derived simulation data, b) a more accurate geometrical model and c) an accelerated convergence iterative scheme through application of Shanks transformation. Finally, we performed a rigorous analysis to ensure appropriately converged solutions. Our investigation shows significant differences (up to 50%) between the simulation output of Newtonian and non-Newtonian models. The differences are attributed to the coupling that exists between low and high shear rate areas in the flow. They show the significance of non-Newtonian blood rheology and motivate further work towards an even more accurate modeling of the thixoropic and three-dimensional characteristics of the blood flow rheology that go beyond the Casson model utilized in the present work. (C) 2016 Elsevier B.V. All rights reserved.