Doppler waveform pulsatility index and resistance, pressure and flow in the umbilical placental circulation: an investigation using a mathematical model

A mathematical model of the umbilical placental circulation was used to examine the effect of different physiological variables on the pulsatility index (PI) of the umbilical artery Doppler waveform. The variables include the umbilical and placental resistances, the volume flow rate and the pressure. In the model the branching structure of the placental villous tree is considered in detail, while each arterial branch is itself represented simply using a resistor and a capacitor. Placental vascular disease is modelled as obliteration of a fraction of the terminal branches of the tree. The model umbilical artery PI depends on the ratio of the placental resistance to the umbilical artery resistance. The PI increases with vascular disease, but the rate of increase is not uniform. Initially, the placental resistance and the PI increase very slowly with vessel obliteration. Once the level of vessel obliteration has reached a large enough value--typically between 60% and 90% obliteration--the PI begins to rise sharply. A larger placental vascular bed can accommodate a greater level of vessel obliteration before this rapid PI rise begins. The umbilical artery PI also depends on the pulsatility of the input (aortic bifurcation) pressure waveform, but blood pressure variations in the physically attainable range cannot account for the very high PI values associated with fetal compromise. Physically attainable pressure waveform changes would, however, enable the fetus with substantial placental vascular disease to maintain umbilical volume flow rate, and at the same time exhibit a raised umbilical artery PI value.