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.