An analysis of the regulatory mechanisms in fetal heart rate changes, using a mathematical analysis-model

To elucidate the effects of regulatory mechanisms on heart rate changes in the human fetus in utero, we devised a mathematical model involving factor analysis, a type of multivariate analysis. From the viewpoint of mathematics, a set of fetal heart rate (FHR) values has two different properties, scalar and vector. We studied the instantaneous FHR values for 96, 704 beats in sequence, obtained from a normal fetus at 33 weeks of gestation. The scalar components of the FHR changes appear to be composed of around 4,000 beats, among which a few isolated properties may be present. These findings indicate the underlying baseline heart rates, which differ in biological origin. The distribution of the beat-to-beat differences included the "core fluctuation" ranging up to +/- 3 beats per minute. According to the factor analysis for the vectorial components, it has also become evident that there were at least two different characteristics in FHR changes, indicating the existence of acceleration and deceleration mechanisms.