Feto-maternal circulation: mathematical model and comparison with Doppler measurements.

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.