AJP - Regulatory, Integrative and Comparative Physiology, Vol 235, Issue 3 181-R199, Copyright © 1978 by American Physiological Society
Water exchange in the placenta: a mathematical model
W. J. Wilbur, G. G. Power and L. D. Longo
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.
