A transfer function-based mathematical model of the fetal-placental circulation

The circulation of a human fetus has been modeled using a transfer function that is based on the arterial dimensions at 28 weeks gestational age (GA). These dimensions have then been adapted for growth between 28 and 40 weeks GA. The input to the model is a series of current pulses at the fetal heart rate, where current in the model is analogous to volume blood flow in the fetus. The arterial system is divided into short segments that are cascaded together. The respective transfer functions are based on the dimensions, wall properties and fluid characteristics at each frequency and GA. Bleed off conductances distribute current to circuits representing the various anatomical regions. In particular, the placenta is simplified to a symmetrically distributed network of branching vessels, each represented by a transfer function. All calculations are performed in the frequency domain, after which the inverse Fourier transform is used to calculate the currents that represent the time-domain blood flow waveforms. Simulated flow waveform resistance index and pulsatility index values are within 8% of those reported for human clinical studies, at all gestational ages.