We present a mathematical model that describes the initial stages of placental development during which trophoblast cells begin to invade the uterine tissue. We then carry out a mathematical analysis of a simpler submodel that describes the final stages of normal embryo implantation and suggests that as the timescale of interest increases, the dominant migratory mechanism of the trophoblasts switches from chemotaxis to nonlinear random motion. © 2001 Elsevier Science Ltd. All rights reserved.
Byrne, H. M., Chaplain, M. A. J., Pettet, G. J., & McElwain, D. L. S. (2001). An analysis of a mathematical model of trophoblast invasion. Applied Mathematics Letters, 14(8), 1005–1010. https://doi.org/10.1016/S0893-9659(01)00079-9