This paper considers numerical simulations of fluid-structure interaction (FSI) problems in hemodynamics for idealized geometries of healthy cerebral arteries modeled by both nonlinear isotropic and anisotropic material constitutive laws. In particular, it focuses on an anisotropic model initially proposed for cerebral arteries to characterize the activation of collagen fibers at finite strains. In the current work, this constitutive model is implemented for the first time in the context of an FSI formulation. In this framework, we investigate the influence of the material model on the numerical results and, in the case of the anisotropic laws, the importance of the collagen fibers on the overall mechanical behavior of the tissue. With this aim, we compare our numerical results by analyzing fluid dynamic indicators, vessel wall displacement, Von Mises stress, and deformations of the collagen fibers. Specifically, for an anisotropic model with collagen fiber recruitment at finite strains, we highlight the progressive activation and deactivation processes of the fibrous component of the tissue throughout the wall thickness during the cardiac cycle. The inclusion of collagen recruitment is found to have a substantial impact on the intramural stress, which will in turn impact the biological response of the intramural cells. Hence, the methodology presented here will be particularly useful for studies of mechanobiological processes in the healthy and diseased vascular wall.