A transmission line model of the human foetal circulatory system

A transmission line model of the human foetal circulatory system is presented. The model has been developed in the frequency domain with the cardiac input modeled as a flow rather than as a pressure pulse and is structured upon electrical transmission line analogies. The model is formed by cascading solutions to the two-dimensional Navier-Stokes equations for both oscillatory and steady, laminar viscous fluid flow in isotropic visco-elastic tubes with thick walls, which are constrained by surrounding tissues. Simulations allow for representation of both forward and retrograde travelling flow and pressure waves in all of the main foetal arterial vessels. The solution is verified by a comparison of model generated Doppler indices in the thoracic aorta, abdominal aorta, iliac artery and both ends of the umbilical arteries with previously published indices obtained by clinical measurements in these arteries. For simulations of blood flow in a healthy foetus, the model generated Pulsatility and Resistance indices were on average within 8% of the corresponding clinical measurements. The model results also demonstrates that placental resistance must increase by a factor of three, corresponding to a 60% decrease in flow to the placenta, before umbilical arterial absent end diastolic flow is observed. Differences between indices obtained from simulations at opposite ends of the umbilical arteries increase with increasing placental resistance.