Modeling Oxygen Transport in the Human Placenta

Efficient functioning of the human placenta is crucial for the favorable pregnancy outcome. We construct a 3D~model of oxygen transport in the placenta based on its histological cross-sections. The model accounts for both diffusion and convention of oxygen in the intervillous space and allows one to estimate oxygen uptake of a placentone. We demonstrate the existence of an optimal villi density maximizing the uptake and explain it as a trade-off between the incoming oxygen flow and the absorbing villous surface. Calculations performed for arbitrary shapes of fetal villi show that only two geometrical characteristics~- villi density and the effective villi radius~- are required to predict fetal oxygen uptake. Two combinations of physiological parameters that determine oxygen uptake are also identified: maximal oxygen inflow of a placentone and the Damk\"ohler number. An automatic image analysis method is developed and applied to 22~healthy placental cross-sections demonstrating that villi density of a healthy human placenta lies within~10\% of the optimal value, while overall geometry efficiency is rather low~(around~30-40\%). In a perspective, the model can constitute the base of a reliable tool of post partum oxygen exchange efficiency assessment in the human placenta.