Perivascular spaces (PVSs) are defined as anatomical structures surrounding blood vessels. Within the central nervous system, these cerebrospinal fluid filled compartments act as drainage pathways, and play a key role in maintaining brain homeostasis. The perivascular spaces also come to be a “second way in” for drug delivery to the brain, such as in intrathecal chemotherapy used for treating leukemia and lymphoma. Despite extensive research on brain clearance mechanisms and neurological diseases treatments, dosing of potentially neurotoxic intrathecal drugs is still not tailored at the individual level. Data-driven biomedical models, investigating potential drug pathways and predicting drug concentrations in various brain compartments, come as an innovative shift towards personalized adjustment of chemotherapy dosage. These models must tackle the complexity and multi-scale aspect of the brain, and are based on diverse numerical approaches from pharmacokinetic ODE-based models to fluid flow and solute transport models in the PVSs. Yet, these raise multiple challenges with respect to patient-specific parameterization, multi-scale couplings, performance and scalability. This talk introduces some of the models we have been developing in this context, from macro-scale (organ) to meso-scale (vasculature), with particular emphasis on numerical approaches and performances.