The capabilities and limitations of various molecular viscosity models, in the left coronary arterial tree, were analyzed via: molecular viscosity, local and global non-Newtonian importance factors, wall shear stress (WSS) and wall shear stress gradient (WSSG). The vessel geometry was acquired using geometrically correct 3D intravascular ultrasound (3D IVUS). Seven non-Newtonian molecular viscosity models, plus the Newtonian one, were compared. The WSS distribution yielded a consistent LCA pattern for nearly all non-Newtonian models. High molecular viscosity, low WSS and low WSSG values occurred at the outer walls of the major bifurcation in proximal LCA regions. The Newtonian blood flow was found to be a good approximation at mid- and high-strain rates. The non-Newtonian Power Law, Generalized Power Law, Carreau and Casson and Modified Cross blood viscosity models gave comparable molecular viscosity, WSS and WSSG values. The Power Law and Walburn-Schneck models over-estimated the non-Newtonian global importance factor I(G) and under-estimated the area averaged WSS and WSSG values. The non-Newtonian Power Law and the Generalized Power Law blood viscosity models were found to approximate the molecular viscosity and WSS calculations in a more satisfactory way.