The central nervous system is a very challenging target for drug delivery due to the presence of the blood brain barrier. To bypass the blood brain barrier, the infusion of therapeutic molecules into the cerebrospinal fluid through intrathecal administration is a frequently used clinical modality. The goal of this thesis is to build a predictive model that computes the biodistribution and biochemical reactions of an intrathecally infused drug. This main goal was accomplished by the computation of drug biotransport, the investigation of factors influencing drug distribution such as anatomical structures and pulse frequency, the subject-specific reconstruction of the human central nervous system, and the biochemical reactions of the drug at the cellular scale. The integration of imaging data with bio-fluid mechanics and reaction kinetics leads to an adaptable, multi-scale computational model that can predict drug fate inside the central nervous system after an intrathecal infusion. After validation, this model can facilitate the translation of bench-top results towards clinical infusion therapies.