  Starting from full-dimensional models of solute transport, we derive and
analyze multi-dimensional models of time-dependent convection, diffusion, and
exchange in and around pulsating vascular and perivascular networks. These
models are widely applicable for modelling transport in vascularized tissue,
brain perivascular spaces, vascular plants and similar environments. We show
the existence and uniqueness of solutions to both the full- and the
multi-dimensional equations under suitable assumptions on the domain velocity.
Moreover, we quantify the associated modelling errors by establishing a-priori
estimates in evolving Bochner spaces. In particular, we show that the modelling
error decreases with the characteristic vessel diameter and thus vanishes for
infinitely slender vessels. Numerical tests in idealized geometries corroborate
and extend upon our theoretical findings.
