Modeling Oxygen Transport in the Human Placenta

Abstract : The efficient functioning of the human placenta is crucial for the favorable outcome of the pregnancy. This thesis aims at developing a mathematical model of respiratory gas exchange in the human placenta, which would improve our understanding of the relation between the structure and the function of the organ. Taking advantage of the precise 2D placental structure provided by the placental histology, we construct a 3D model of oxygen transport in the placenta by extending 2D histological cross-sections along the third dimension. The model simultaneously accounts for both diffusion and convention of oxygen in the intervillous space and allows us to predict the oxygen uptake of a placentone. In the first part of the thesis, the diffusion-convection equation governing oxygen exchange is numerically solved for different densities of circular fetal villi in a placentone. These calculations provide estimations of the oxygen uptake of a placentone with an arbitrary villi density and demonstrate the existence of an optimal villi density maximizing the uptake. This optimality is explained as a trade-off between the incoming oxygen flow and the absorbing villous surface. As a next step, the assumption of circular villi is relaxed and an approximate analytical solution is proposed for the diffusion-convection equation. It is shown that only two geometrical characteristics — the villi density and the effective villi radius — are required to predict the fetal oxygen uptake. Two combinations of physiological parameters that determine oxygen uptake in a given placenta are also identified: (i) the maximal oxygen inflow of a placentone, and (ii) the Damköhler number defined as the ratio of the transit time of the maternal blood through the intervillous space to a characteristic oxygen extraction time in a cross-section. Analytical formulas for fast and simple calculation of oxygen uptake are derived, and two diagrams of oxygen transport efficiency in an arbitrary placental cross-section are provided. The theory also suggests a method of how the results of artificial placenta perfusion experiments performed with no-hemoglobin blood can be recalculated to account for oxygen-hemoglobin dissociation. Finally, an automatic image analysis method is developed allowing one to analyze large histological human placenta cross-sections and to determine areas, perimeters and shapes of villous, intervillous space and fetal capillary compartments. These data can then be used as input data for the model. This method is applied to 25 cross-sections from 22 healthy and 3 pathological pregnancies. By combination of the obtained data with the described efficiency diagrams, it is demonstrated that the villi density of a healthy human placenta lies within 10% of the optimal value. The overall geometry efficiency of a healthy placenta was found to be rather low (around 30–40 %). In a perspective, the presented model can constitute the base of a reliable tool of assessment of oxygen exchange efficiency in the human placenta from histological measurements post partum, or, in a longer term, from non-invasive in utero measurements.
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Contributor : Alexander S. Serov <>
Submitted on : Friday, September 25, 2015 - 10:40:25 AM
Last modification on : Wednesday, January 23, 2019 - 10:29:31 AM
Long-term archiving on : Tuesday, December 29, 2015 - 9:59:48 AM

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  • HAL Id : tel-01205237, version 1

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Alexander S. Serov. Modeling Oxygen Transport in the Human Placenta. Biological Physics [physics.bio-ph]. Ecole Polytechnique, 2015. English. ⟨tel-01205237⟩

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