  The primary exchange units in the human placenta are terminal villi, in which
fetal capillary networks are surrounded by a thin layer of villous tissue,
separating fetal from maternal blood. To understand how the complex spatial
structure of villi influences their function, we use an image-based theoretical
model to study the effect of tissue metabolism on the transport of solutes from
maternal blood into the fetal circulation. For solute that is taken up under
first-order kinetics, we show that the transition between flow-limited and
diffusion-limited transport depends on two new dimensionless parameters defined
in terms of key geometric quantities, with strong solute uptake promoting
flow-limited transport conditions. We present a simple algebraic approximation
for solute uptake rate as a function of flow conditions, metabolic rate and
villous geometry. For oxygen, accounting for nonlinear kinetics using
physiological parameter values, our model predicts that villous metabolism does
not significantly impact oxygen transfer to fetal blood, although the
partitioning of fluxes between the villous tissue and the capillary network
depends strongly on the flow regime.
