A Walsh—Fourier Analysis of the Effects of Moderate Maternal Alcohol Consumption on Neonatal Sleep-State Cycling

Recent discussions of the functional significance of ultradian rhythms emphasize their importance to human physiology. Over the past 25 years, electroencephalographic (EEG) sleep patterns have been used in assessing the cerebral and central nervous system maturation of neonates. Through an interdisciplinary effort, spectral (Fourier) methods have been developed to discriminate between the various stages of sleep based on EEG recordings. Nevertheless, there has been little effort to develop methods for the statistical analysis of sleep-state cycling. In particular, attention has primarily been focused on the ultradian rhythm of sleep as it cycles between two states, active or rapid eye movement (REM) and quiet or non-REM sleep. There are, however, several components of REM and non-REM sleep, as well as a transitional state (indeterminate sleep) and abrupt alterations of state (arousal). Moreover, few studies have investigated the effects of prenatal alcohol exposure on the neurophysiological development of infants as assessed through sleep or EEG patterns. In this article the theory of Walsh—Fourier analysis for discrete-valued (categorical) time series is used to investigate the spectral components of EEG sleep-state patterns of infants whose mothers abstained from drinking during pregnancy, and infants of mothers who used moderate amounts of alcohol continuously during pregnancy. The sample for this study is part of a larger cohort of women participating in a longitudinal study of substance use during pregnancy. The analysis is based on the finite Walsh—Fourier transform that is defined in terms of the Walsh functions. The square-wave Walsh functions form a complete orthonormal sequence on (0, 1) and take on only two values, +1 and –1 (“on” and “off”). This allows correlation of per-minute infant sleep-state records with square waveforms, and analysis of sleep-state cycles relative to per-minute switches from one sleep stage to another (termed sequency). The analysis consists of two parts. First, the article considers the problem of detecting whether a common sleep pattern exists in the unexposed and exposed groups of neonates separately. As expected, it is concluded that a common signal does exist in each group. Next, the spectral components of the sleep-state signals of the two groups are compared, and the differences between the two groups are discussed.