M. H. Byrne, M. A. J. Chaplain, G. J. Pettet, D. L. S. McElwain, "A Mathematical Model of Trophoblast Invasion", Computational and Mathematical Methods in Medicine, vol. 1, Article ID 908460, 12 pages, 1999. https://doi.org/10.1080/10273669908833026
A Mathematical Model of Trophoblast Invasion
In this paper we present a simple mathematical model to describe the initial phase of placental development during which trophoblast cells invade the uterine tissue as a cells invade the uterine tissue as a continuous mass of cells.The key physical variables involved in this crucial stage of mammalian development are assumed to be the invading trophoblast cells, the uterine tissue trophoblast derived proteases that degrade the uterine tissue, and protease inhibitors that neutralise the action of the protease.Numerical simulations presented here are in good qualitative agreement with experimental observations and show how changes in the system parameters influence the rate and degree of trophoblast invasion.In particular we suggest that chemotactic migration is a key feature of trophoblast invasion and that the rate at which proteases are produced is crucial to the successful implantation of the embryo.For example both insufficient and excess production of the proteases may result in premature halting of the trophoblasts. Such behaviour may represent the pathological condition of failed trophoblast implantation and subsequent spontaneous abortion.
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