Patient specific based simulation of blood flows in arteries has been proposed as a future approach for better diagnostics and treatment of arterial diseases. The outcome of theoretical simulations strongly depends on the accuracy in describing the problem (the geometry, material properties of the artery and of the blood, flow conditions and the boundary conditions). In this study, the uncertainties associated with the approach for a priori assessment of reconstructive surgery of stenoted arteries are investigated. It is shown that strong curvature in the reconstructed artery leads to large spatial- and temporal-peaks in the wall shear-stress. Such peaks can be removed by appropriate reconstruction that also handles the post-stenotic dilatation of the artery. Moreover, it is shown that the effects of the segmentation approach can be equally important as the effects of using advanced rheological models. This fact has not been recognized in the literature up to this point, making patient specific simulations potentially less reliable.