Mathematical model of the human fetal and neonatal circulation with pulmonary atresia

Important changes in the circulatory system happen at the time of birth when the gas-exchange function is transferred from the placenta to the lungs. At this time, modifications of the system come about for the adaptation and survival of newborns. However, patients with cyanotic congenital heart diseases (CHDs), such as pulmonary atresia (PA) are at risk, as they may fail to make an adequate transition to postnatal life. Objective: We propose a mathematical model, simplifying the human-fetal and -neonatal circulatory system of healthy and PA infants, in order to solve the hemodynamic steady conditions of each circulation and evaluate the hemodynamic effects of the adaptations required at the moment of transition between them. Methods: Fetal and neonatal circulations of both healthy and PA infants were simplified and modeled as electrical circuit analogs. In the pursuance of solving the hemodynamic steady conditions of each circulation, the main assumption between models was the maintenance of oxygen supply and blood flow rate to vital regions. Additionally, in the interest of modeling the transition between healthy fetal and PA fetal circulations, blood flow rate through the pulmonary valve was decreased, simulating the in-womb progressive development of an obstruction at this level. Results: The resulting hemodynamic steady conditions were validated with the variables of healthy newborns found in the literature. The models estimated pressures, blood flow rates and resistance values for all the modeled structures in all four conditions, which are parameters that cannot be assessed from clinical measurements. Results confirmed the fetal right-heart and newborn left-heart dominance in the healthy models and the importance of the patency of the DA and FO in PA infants. They furthermore allowed to simulate the distinctive parameter variation related to the physiological events that happen during the fetal development of PA. Conclusion: This study is the first step in the understanding of distinctive hemodynamics of the healthy and pathological fetal and neonatal circulations. Moreover, the proposed models provide a basis for a more in-depth study of the natural transitions between circulations and for the assessment of CHD, thereby broadening our understanding of the distinctive hemodynamic phenomena that govern them.