  We propose an analytical approach to solving the diffusion-convection
equations governing oxygen transport in the human placenta. We show that only
two geometrical characteristics of a placental cross-section, villi density and
the effective villi radius, are needed to predict fetal oxygen uptake. We also
identify two combinations of physiological parameters that determine oxygen
uptake in a given placenta: (i) the maximal oxygen inflow of a placentone if
there were no tissue blocking the flow, and (ii) the ratio of transit time of
maternal blood through the intervillous space to oxygen extraction time. We
derive analytical formulas for fast and simple calculation of oxygen uptake and
provide two diagrams of efficiency of oxygen transport in an arbitrary
placental cross-section. We finally show that artificial perfusion experiments
with no-hemoglobin blood tend to give a two-orders-of-magnitude underestimation
of the in vivo oxygen uptake and that the optimal geometry for such setup
alters significantly. The theory allows one to adjust the results of artificial
placenta perfusion experiments to account for oxygen-hemoglobin dissociation.
Combined with image analysis techniques, the presented model can give an
easy-to-use tool for prediction of the human placenta efficiency.
