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.

Fetal heart modelling based on a pressure-volume relationship

Study of the cardiovascular system of the human fetus is based on non-invasive measurement methods such as Doppler echography systems. The circulation conditions in fetal vessels are usually evaluated by resistance indices, giving limited physiological information on distal territories such as the placenta or the brain. To enhance the understanding of human fetal haemodynamics, a numerical model of the fetal heart has been developed, using the hydraulic-electric analogy. The model is based on a mechanical hypothesis of parallel functioning of the right and left ventricles, considered to have analogue elastance properties. Their behaviour is equivalent to that of a single ventricle ejecting an equivalent blood volume of 7 ml in the aorta. The characterisation of the equivalent ventricle is based on the determination of a set of four parameters (Emax, Vo, kv and Po) representing the maximum ventricle contractility, a reference volume, and volume and pressure constants, respectively. The model proposed is validated by studying the effects of preload and afterload variations on the fetal heart work, and by comparing the numerical results with literature and measured data. The model constitutes the first step towards a global model of the cardiovascular system of the human fetus.

[Influence of treatment on the chemotaxis of polymorphonuclear neutrophils in rheumatoid arthritis]

The chemotaxis of neutrophil polymorphonuclear cells was measured in 56 patients with rheumatoid arthritis classified according to the treatment received. The presence of D-penicillamine in the serum affected the migration of the neutrophil polymorphonuclear cells in both the control subjects and the patients. In the patient group, the chemotaxis of the neutrophil polymorphonuclear cells was corrected non-significantly in the presence of control AB serum.