  We derive a reduced model of solute transport in blood based on the center
manifold theory. The derivation is carried out on a convection diffusion
equation with general axial and radial velocity profiles in a blood vessel of
varying cross section. We couple the resulting one dimensional equation to a
reduced model for blood flow in a compliant vessel. In the special case of a
no--slip axial velocity profile, we study the dependence of the diffusion
coefficient and corresponding numerical solutions on the shape of the profile.
