Direct interstitial infusion is a technique capable of delivering agents over both small and large dimensions of brain tissue. However, at a sufficiently high volumetric inflow rate, backflow along the catheter shaft may occur and compromise delivery. A scaling relationship for the finite backflow distance along this catheter in pure gray matter (x_m) has been determined from a mathematical model based on Stokes flow, Darcy flow in porous media, and elastic deformation of the brain tissue: x_m = constant Q_o³R⁴r_c⁴G³µ¹ (Q_o = volumetric inflow rate, R = tissue hydraulic resistance, r_c = catheter radius, G = shear modulus, and µ = viscosity). This implies that backflow is minimized by the use of small diameter catheters and that a fixed (minimal) backflow distance may be maintained by offsetting an increase in flow rate with a similar decrease in catheter radius. Generally, backflow is avoided in rat gray matter with a 32-gauge catheter operating below 0.5 µl/min. An extension of the scaling relationship to include brain size in the resistance term leads to the finding that absolute backflow distance obtained with a given catheter and inflow rate is weakly affected by the depth of catheter tip placement and, thus, brain size. Finally, an extension of the model to describe catheter passage through a white matter layer before terminating in the gray has been shown to account for observed percentages of albumin in the corpus callosum after a 4-µl infusion of the compound to rat striatum over a range of volumetric inflow rates.