Gestational age dependency of umbilical flow waveforms: an investigation using a lumped parameter model

A lumped parameter electrical analogue model has been used to investigate the umbilical arterial flow waveform from 28 weeks to 40 weeks of gestational age. The model splits the foetal circulation into small segments and represents each segment with an equivalent electrical circuit which uses frequency dependent components. The dimensions of the segments are varied with gestational age using a clinical study of the foetal mass versus gestational age as a reference. As a simple approximation, the segment dimensions are varied with the cube root of the estimated mass. Two port analysis is then used to mathematically represent each segment, and transfer the input flow pulses from the heart to an output flow waveform at the umbilical arteries. The analysis is performed in the frequency domain, and the flow waveforms are obtained using the inverse Fourier transform. The shape of the umbilical flow waveform has been described by the RI and PI which are commonly used indices in obstetric practice. It is shown that the variation of these indices along the cord decreases with increasing gestational age. It is also shown that these indices decrease in value with increasing gestational age, due to the increase in the arterial dimensions with age. This work shows the importance of taking foetal growth and hence gestational age into account when interpreting Doppler umbilical flow waveform indices. It also provides insight into the effect of arterial dimensions on the waveform indices.