Lattice Boltzmann simulations have been carried out in order to study the flow of blood in normal and constricted blood channels using Newtonian and non-Newtonian rheological models. Instead of using parameters from previous works as is usually done, we propose a new optimization methodology that provides in a consistent manner the complete set of parameters for the studied models, namely Newtonian, Carreau-Yassuda and Kuang-Luo. The optimization was performed simultaneously using experimental data from several sources. Physical observables such as velocity profiles, shear rate profiles and pressure fields were evaluated. For the normal channel case, it was found that the Newtonian model predicts both the highest velocity and shear rates profiles followed by the Carreau-Yassuda and the Kuang-Luo models. For a constricted channel, important differences were found in the velocity profiles among the studied models. First, the Newtonian model was observed to predict the velocity profile maximum at different channel width positions compared to the non-Newtonian ones. Second, the obtained recirculation region was found to be longer for the Newtonian models. Finally, concerning the constriction shape, the global velocity was found to be lower for a rectangular geometry than for a semi-circular one.