Modelling the feto-placental circulation: 2. A continuous approach to explain normal and abnormal flow velocity waveforms in the umbilical arteries.

A mathematical model of the feto-placental circulation which describes the development of the placental vasculature throughout pregnancy on the basis of simple assumptions is used to simulate some abnormalities of the villous vascular tree which may affect the values of Doppler indices. In normal cases, the model shows a decreasing trend of the pulsatility index (PI) throughout pregnancy which is comparable to that observed in vivo. When a pathological interruption of the villous growth is simulated, the PI does not decrease any further, unless the input pressure keeps increasing. When various degrees of obliteration of the villous tree are simulated, either through an occlusive process or a reduction of the lumen of the vessels, the PI values increase and the volume flow decreases to a greater extent. The data predicted by the model are compared to those obtained in clinical studies and in experimental animal models.