Oxygen exchange mechanisms in the human placenta: mathematical modelling and simulation.

An exact knowledge of the human fetus's respiratory mechanisms is still lacking; in particular, the role of human placental anatomy in oxygen exchange has not yet been studied satisfactorily. In this paper, a mathematical model of placenta as O2 exchanger between maternal and fetal blood was developed; it led to the solution of equations based upon diffusion laws and the haemoglobin dissociation curve. Particular care was taken to represent the regimen of laminar motion or whirling into the capillaries. Theoretical results were compared, under physiological conditions, with clinical data relating to fetal oxygenated blood p O2 during the second half of gestation (20th-38th weeks), and a theoretical confirmation of the decreasing effectiveness of placental O2 exchange during gestation was found. The result was able to describe oxygen exchange during a period in which clinical data are scanty (23rd-30th weeks). The effects of some pathological events on O2 exchange were then simulated. Model parameters were changed to simulate the effects on oxygen exchange of some typical pathological variations of placental anatomical features: exchange surface thickness and capillary length. The curves obtained for different gestational ages can easily be correlated with echographic measures of placental volume and dimensions of placental capillaries. The results also show that the human placenta is more sensitive to pathologies when it is young than at term of gestation.