Formation of functional associations across time scales in the fetal autonomic control system — A multifractal analysis

• Properties of fetal heart rate variability are assessed using multiscale multifractal analysis.
• A model predicting gestational age based only on fetal heart rate variability is discussed.
• Correlations of heart rate variability properties occur at specific scale ranges.
• Persistency of heart rate variability increases with age in connection with sleep changes.

During fetal development, different control systems mediated by the autonomic nervous system form functional connections over a wide range of time scales. Using multiscale multifractal analysis (MMA) of fetal heart rate variability (HRV), we describe fundamental relationships in the developing scale-wide adjustments within fetal behavior states as well as across state changes.MMA yields the local Hurst exponent surface h(q,s) with q as the multifractal parameter and s as the scale. In 30-minute recordings of healthy fetuses between 24 and 36 weeks of gestation (n = 25 in quiet sleep, n = 29 in active sleep, n = 30 changing sleep state) we investigated the dependency of h(q,s) on gestation age.In univariate models, we found a decreasing persistence for short scales and small amplitudes in the quiet (s1 = 39, q1 = − 0.7, R2 = 0.52) and in the active (s1 = 69, q1 = − 1.4, R2 = 0.23) sleep in contrast to an increasing persistency for long scales and large amplitudes (s1 = 147, q1 = 2.4, R2 = 0.29) in the mixed state. Bivariate models (additional scales considered) presented increased coefficients of determination R2 = 0.56, 0.4, and 0.43, respectively. Persistency increasing with age in connection with the sleep state changes (independent of the age related short range dependencies within the separate homogeneous sleep states) is reported here for the first time. The MMA indices obtained for the fetal HRV represent characteristics of the maturating scale-wide cardiovascular control in the context of the evolving sleep state dynamics, which have so far not been considered. They should be incorporated in the search for HRV indices for prenatal diagnosis of developmental disorders and risk assessment.