A mathematical model of the fetal cardiovascular system based on genetic algorithms as identification technique

Abstract

The development of fetal cardiac surgery, considered the ultimate goal in the treatment of congenital cardiac malformations, needs to be supported by detailed knowledge of the blood circulation in the fetal cardiovascular system. The hemodynamic behavior in distal territories is usually inferred from vessel resistance indices, which give limited physiological information. This study presents a mathematical model of the human fetal global cardiovascular system, developed to clarify the relationships and differences existing between upper and lower body circulation. We modelled the heart with two time-varying capacitances, each representing the respective ventricle's pressure-volume relationship. The fetal vascular system was represented using two six-element Windkessel models, for the upper and lower body respectively. We obtained the identification of the set of circuital and elastance function parameters of the model using Genetic Algorithms (GAs), which follow the laws of evolutionary theory. We compared the results of our numerical study on the model identified with data collected from measurements and literature, to validate the proposed global cardiovascular system model of the human fetus. This model is intended as an instrument to investigate the differences in blood distribution between the different vascular districts in the upper and lower fetal body and the role of the aortic isthmus, the small tract of vessel connecting upper and lower fetal vascular beds; it may also represent a useful tool in the assessment of dynamic balance during mechanical assistance of circulation.