Objectives: Clinicians are more and more frequently studying fetal blood flow velocity curves recorded by Doppler ultrasound in vital organs such as the placenta and fetal brain to evaluate fetal well-being. We have therefore developed a mathematical model of the utero-placental and fetal circulations which could be used for teaching and for a better understanding of regulatory mechanisms.
Methods: The model is based on two basic elements-an arterial segment and a bifurcation-and we have reproduced the major arteries of the feto-maternal circulation combining these basic elements. The mathematical model of the system is based on the Navier-Stokes equations. The peripheral areas such as the brain, kidneys and placenta are modeled by a simple Windkessel model and the model computes instantaneous flow and pressure at any point in the fetal arterial tree and the uterine arteries.
Results: We have compared the computed instantaneous flow curves and pressure with in vivo data and our results agree with the findings in physiological situations and in gravidic hypertension.
Conclusions: Our model provides new interesting insights into fetal hemodynamics such as a better understanding of the mismatch impedance phenomena and is a promising model for the study of blood redistribution mechanisms in hypoxic situations.
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