Mathematical modeling of the human fetal arterial blood circulation.

A mathematical model of the human fetal arterial circulation based on mass and momentum conservation for one-dimensional flow is presented. We simplified the fetal arterial vascular system from the heart to the placenta, defined 16 anatomical segments and studied the characteristics of the vascular system in relation to changes in morphology and hemodynamics. The two-step Lax-Wendroff finite difference scheme was used to solve the system of equations, after introducing the rheological constants, the diameter and length of the segments measured by two-dimensional imaging and the mean arterial velocity at the inlet segments obtained by pulsed Doppler. The model was validated by comparing the numerical results to our non-invasive ultrasound direct measurements and to previous published data.