Fractal noises and motions in time series of presympathetic and sympathetic neural activities.

We used Allan factor analysis to classify time series of the discharges of single presympathetic neurons in the cat medullary lateral tegmental field (LTF) and rostral ventrolateral medulla (RVLM) and of the postganglionic vertebral sympathetic nerve. These time series fell into two classes of fractal-based point processes characterized by statistically self-similar behavior reflecting long-range correlations among data points. Classification of a time series as either a fractional Gaussian noise (fGn)-or fractional Brownian motion (fBm)-based point process depended on the scaling exponent, alpha, of the power law in the Allan factor curve. fGn is defined as 0 < alpha < 1 and fBm as 1 < alpha < 3. The process responsible for the fractal spike trains of 11 of 12 classifiable LTF neurons with sympathetic nerve-related activity was fGn. In contrast, the process responsible for the fractal spike trains of eight of nine classifiable RVLM presympathetic neurons was fBm. The time series of simultaneously recorded vertebral sympathetic nerve discharge and the arterial pulse also were fBm-based signals. Because a fBm signal is the cumulative sum of the elements comprising the corresponding fGn signal, these results show smoothing of fractal time series in a feedforward direction from medullary presympathetic neurons to postganglionic sympathetic neurons. This may involve integration by RVLM neurons of their LTF inputs or independent fractal processes acting at different levels of the network controlling sympathetic nerve discharge. Whether feedforward smoothing of fractal signals is a feature in other neural systems is open to investigation.