Chaotic indices and canonical ensemble of heart rate patterns in small-for-gestational age fetuses

Aims: We studied how linear and nonlinear heart rate dynamics differ between normal fetuses (n=135) and uncomplicated small-for-gestational age (SGA) fetuses (n=65), aged 32-40 weeks' gestation. Methods: We analyzed each fetal heart rate time series for 20 min. We quantified the complexity (nonlinear dynamics) of each fetal heart rate (FHR) time series by approximate entropy (ApEn) and correlation dimension (CD). The linear dynamics were analyzed by canonical correlation analysis (CCA). Results: The ApEn and CD of the uncomplicated SGA fetuses were significantly lower than that of the normal fetuses in all three gestational periods (32-34, 35-37, 38-40 weeks). Canonical correlation ensemble in SGA fetuses is slightly higher than normal ones in all three gestational periods, especially at 35-37 weeks. Conclusions: Irregularity and complexity of the heart rate dynamics of SGA fetuses are lower than that of normal ones. Also, canonical ensemble in SGA fetuses is higher than in normal ones, suggesting that the FHR control system has multiple complex interactions. Along with the clear difference between the two groups' non-linear chaotic dynamics in FHR patterns, we clarified the hidden subtle differences in linearity (e.g., canonical ensemble). The decrease in non-linear dynamics may contribute to the increase in linear dynamics. The present statistical methodology can be readily and routinely utilized in obstetrics and gynecologic fields.