Solute transport in the brain is essential for metabolic waste clearance and is strongly influenced by cerebrospinal fluid (CSF) motion driven by vascular and tissue pulsations. CSF oscillations within the subarachnoid space around the brain (cSAS) and perivascular spaces along blood vessels (PVS) have been shown to enhance transport by dispersion effect. However, the mechanisms by which spatially heterogeneous tissue deformations and propagating waves enhance solute mixing in those spaces remain poorly understood. In particular, the existence of optimal pulsation patterns maximizing transport efficiency, and the relative contributions of cSAS and PVS transport, have not been systematically investigated in models accounting for tissue poroelasticity. We develop a coupled modelling framework combining a poroelastic description of brain tissue with an analytical representation of the CSF flow in cSAS to study pressure-driven transport at the brain boundary. We quantify transport efficiency for spatially heterogeneous tissue displacements and propagating waves, exploring a range of frequencies and wavelengths. In addition, transport in the cSAS is compared with that in PVS by coupling the poroelastic model to a one dimensional PVS network model using flow boundary conditions derived from the poroelastic simulations. The model enables a systematic comparison of tracer transport efficiency for different pulsation patterns and allows to interpret in vivo measurements of vascular pulsations. The coupled cSAS–PVS framework highlights distinct transport regimes and clarifies the relative contributions of cSAS and PVS to brain solute transport. This work shows how computational models can help identify the physical processes underlying solute transport in the brain and improve our understanding of how it varies across physiological states, anaesthetic conditions and species.