Understanding the mechanisms behind solute transport and waste clearance in the brain is crucial for understanding the pathophysiology of neurodegenerative disorders. Previous studies of brain-scale tracer transport based on glymphatic magnetic resonance imaging conclude that tracer influx and efflux rates from brain tissue are faster than predicted from a single-continuum diffusion process. This chapter describes a two-compartment diffusion–dispersion model for the transport of gadobutrol in the whole brain. The brain tissue is modeled as two interacting continua representing perivascular spaces (PVSs) and extracellular spaces (ECSs) in brain tissue, where transport in PVS is faster than in ECS. The model equations are solved using the finite element method to simulate tracer transport in the brain tissue following the intrathecal injection of gadobutrol. The simulation results show that, for the relevant parameter regime, an equilibrium is quickly attained between the ECSs and PVSs. Moreover, tracer dynamics are significantly influenced by perivascular diffusion/dispersion and solute transfer rates between PVSs and blood.