Scaling approach to study the changes through the gestation of human fetal cardiac and circulatory behaviors.

During human gestation, fetal body size increases considerably and important transformations occur to hemodynamics of the cardiovascular system of the fetus. Vascular compliances and resistances as well as the cardiac function show important changes. In order to investigate these modifications, a mathematical approach based on scaling techniques was developed. Vascular and cardiac parameters of the human fetus were related by allometric equations to the anatomical dimensions of vessels that, in turn, depend on the fetal body weight and the gestational age. A scaling factor (b) was identified for each parameter under study: vascular resistances and flow inertances decrease with gestational age (b= -0.33 for flow inertances) whereas vascular compliances remarkably increase (b= 1.33). Scaling factors were also adopted for the fetal cardiac parameters, according to experimental data on the development of fetal myocardium. Parameter values calculated for each week of the last trimester of the fetal gestation, were tested using a mathematical lumped parameter model, previously developed for a human fetus near the term of the gestation. The validation of the scaling method adopted for the parameters was performed by comparing the results of the simulations with a group of data obtained by Doppler velocimetry at different stages of fetal normal gestation. The adopted allometric equations were appropriate in describing the development of the human fetal circulatory system. The ductus venosus, the ductus arteriosus, and the foramen ovale, that conclude their function at the birth moment, as well as the lungs and the brain, do not follow the general growth rate and require different scaling factors.