Modelling the feto-placental circulation: 1. A distributed network predicting umbilical haemodynamics throughout pregnancy.

The modifications of the Doppler flow velocity parameters occurring in the feto-placental circulation throughout pregnancy have been reproduced on the basis of a mathematical model. Some simple assumptions were made, such as the progressive development of a dichotomous villous vessel network and the increase of the perfusion pressure and of the umbilical arteries dimensions throughout pregnancy. Moreover, both the viscous and capacitive characteristics of the vascular bed were taken into consideration in order to predict the mean values of blood volume, flow and velocity and the pulsatility index. Their value is shown to depend on few parameters, and mainly on the cross-sectional area ratio between the vessels belonging to two succeeding generations.