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              <p>Most network models describing solute transport in the brain microcirculation usethe well-mixed hypothesis and assume that radial gradients inside the blood vesselsare negligible. Recent experimental data suggest that these gradients, which mayresult from heterogeneities in the velocity field or consumption in the tissue, mayin fact be important. Here, we study the validity of the well-mixed hypothesis innetwork models of solute transport using theoretical and computational approaches.We focus on regimes of weak coupling where the transport problem inside thevasculature is independent of the concentration field in the tissue. In these regimes,the boundary condition between vessels and tissue can be modelled by a Robinboundary condition. For this boundary condition and for a single cylindrical capillary,we derive a one-dimensional cross-section average transport problem with dispersionand exchange coefficients capturing the effects of radial gradients. We then extendthis model to a network of connected tubes and solve the problem in a complexanatomical network. By comparing with results based on the well-mixed hypothesis,we find that dispersive effects are a fundamental component of transport in transientsituations with relatively rapid injections, i.e. frequencies above one Hertz. For slowlyvarying signals and steady states, radial gradients also significantly impact the spatialdistribution of vessel/tissue exchange for molecules that easily cross the blood brainbarrier. This suggests that radial gradients cannot be systematically neglected and thatthere is a crucial need to determine the impact of spatio-temporal heterogeneities ontransport in the brain microcirculation.</p>
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