The perception that high cerebral arterial concentrations transiently achieved by arterial injections will lead to greater drug uptake and efficacy is an exceedingly misleading oversimplification. In 1986, Dedrick proposed a conceptual arterial drug delivery model that is widely cited in the literature. This chapter reviews the Dedrick model and its updated version. It discusses the limitations and the scope of these and future models. The compelling conclusion of these simulations is that retention of the drug by the target tissue is the critical parameter in improving drug delivery. These models show that dramatic improvements in intra-arterial drug delivery are possible when the blood flow is transiently reduced during arterial injections and when drugs and carriers with high target tissue uptake and affinity are used.