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Journal of Theoretical Medicine
Volume 1 (1999), Issue 4, Pages 275-286
http://dx.doi.org/10.1080/10273669908833026

A Mathematical Model of Trophoblast Invasion

1Department of Mathematics, UMIST, PO Box 88, Manchester M60 1QD, UK
2Centre for Nonlinear Systems in Biology, Department of Mathematics, University of Dundee, Dundee DD1 4HN
3Centre in Statistical Science and Industrial Mathematics, School fo Mathematical Sciences, Queensland University of Technology, Brisbane Qld 4001, Australia

Received 30 April 1998; Accepted 30 April 1998

Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.