Mathematical model for nutrient exchange across the placenta
Abstract
This study presents a new mathematical model for nutrient exchange across the placenta which
include nutrient exchange from foetus to mother to provide a system of equations in the form,
Y ሶ ൌ AY rԦሺtሻ and whose solution was analyzed for equilibrium and stability. This model introduces
another parameter that takes care of waste elimination from foetus to mother. It was established that
the final model is stable compared to the existing models, that is, the eigenvalues of the coefficient
matrix are negative real number and complex numbers with negative real parts. This shows that the
new model provides one straight line of solutions tending to the origin and a plane of solutions which
spiral towards the origin. This gives a more accurate mathematical model for nutrient exchange in the
placenta. This model would create a lot of insight into nutrient exchange in the placenta, the
elimination of waste from the foetus and open room for further research from the mathematical
concept developed.
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