A mathematical model for analyzing beat-to-beat difference in the human fetal heart rate during gestation and labor

We devised a model suitable for mathematical analysis of beat-to-beat differences (BBDs) in fetal heart rates (FHRs). Factor analysis was applied, using a computer system, on a specially devised model of an FHR matrix. This matrix was arranged with FHRs and BBDs at 1-beat/min intervals by rows and columns, respectively. After obtaining the BBD by subtracting the antecedent FHR from the following FHR in a given pair of two consecutive FHRs, both variables of the antecedent FHR and BBD were crossed and the number of one was recorded at the corresponding element of the matrix. This procedure was done for all pairs of FHR and BBD yielding a matrix containing the cumulative incidences. Investigated was a total of 225,282 FHRs obtained from 20 fetuses between 37 and 41 weeks of gestation, by means of a scalp-lead electrocardiograph taken during labor. As shown by clusters of BBDs in units of beats/min, three different factors become evident: fluctuation around zero bpm, plus deviations and minus deviations. The first is considered to play a role in maintaining so-called baseline FHRs, and the second and the third indicate accelerating and decelerating actions on FHRs, respectively. This analytical model is discussed with reference to the findings obtained.