  We present a stream-tube model of oxygen exchange inside a human placenta
functional unit (a placentone). The effect of villi density on oxygen transfer
efficiency is assessed by numerically solving the diffusion-convection equation
in a 2D+1D geometry for a wide range of villi densities. For each set of
physiological parameters, we observe the existence of an optimal villi density
providing a maximal oxygen uptake as a trade-off between the incoming oxygen
flow and the absorbing villus surface. The predicted optimal villi density
$0.47\pm0.06$ is compatible to previous experimental measurements. Several
other ways to experimentally validate the model are also proposed. The proposed
stream-tube model can serve as a basis for analyzing the efficiency of human
placentas, detecting possible pathologies and diagnosing placental health risks
for newborns by using routine histology sections collected after birth.
