Simulation and Analysis of Umbilical Blood Flow using Markov-based Mathematical Model

The intra-uterine development of the fetus depends on various factors, one such critical factor is umbilical blood flow because the quantity of oxygen delivered to the placenta and to the fetus is directly limited by umbilical blood flow rate. Since the measurement of the hemodynamic quantities such as blood pressure and blood flow rate is not possible in utero hence the use of patient-specific mathematical modeling is beneficial for the assessment of feto-maternal wellbeing. A Markov model based mathematical model of fetal circulation is developed by taking three node concept. The fetus, the umbilical cord, and the placenta represent the 3 nodes of Markov model. A LabVIEWbased virtual instrument is designed to simulate the mathematical model which results in waveform similar to Doppler blood flow velocimetry of umbilical artery. The model is simulated at various degree of conductivity of the umbilical cord to the oxygenated blood. Simulation results show that the umbilical artery blood flow velocity waveform depends on gestation age, fetal heart rate, uterine contraction and placental insufficiency. The Doppler indices calculated from simulation helps in predicting both fetal and maternal abnormalities at various degrees of the conductivity to the blood flow passage. Therefore, integrating patient-specific models along with established medical equipments will be helpful in identifying true intra-uterine growth restricted fetuses from normal fetuses and helps clinicians to take timely interventions.