Water exchange in the placenta: a mathematical model

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Abstract
To better understand the complicated interplay of forces affecting human placental water exchange, we developed a system of differential equations describing the flows of water, glucose, bicarbonate ion, amino acids, CO2, O2, passive cations (such as Na+ and K+), and chloride ion transplacentally and across the erythrocytes. The equations are based largely on the flux equations of irreversible thermodynamics, although Goldman's hypothesis and equation are employed to treat the ionic currents across the erythrocyte membrane. Bicarbonate ion and dissolved carbon dioxide were found to be major forces acting early in capillary transit to produce a large flow of water toward the fetus. Near the end of the capillary an almost equal amount of water returns to the mother, an effect due predominantly to the effect of glucose. For small deviations from accepted normal values, water transfer is most sensitive to changes in passive cations and chloride, followed by bicarbonate and CO2, plasma solutes (including lactate and glucose), hydrostatic pressure, and amino acids. A simple equation is given to summarize the model's results for water transfer when many factors change simultaneously. Uneven distribution of maternal-to-fetal blood flows tends to favor fetal water acquisition.

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