When a substance is pressure-injected from a micropipette into the extracellular space of the brain it may either form a cavity or it may infiltrate the extracellular space. In either case subsequent diffusion is governed by the volume fraction and tortuosity of the brain tissue as well as the diffusion coefficient of the substance itself. Appropriate equations, solutions and approximations to these problems are discussed. The results are relevant to the interpretation of studies on neuropharmacology and in situ electrochemistry.