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 signals characterized by statistically self‐similar behavior reflecting long‐range correlations among data points. Classification of a time series as either fractional Gaussian noise (fGn) or fractional Brownian motion (fBm) was based 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. All but one of the spike trains of 12 classifiable LTF neurons with sympathetic nerve‐related activity were fGn. In contrast, the spike trains of 8 of 9 RVLM presympathetic neurons that could be classified were fBm. The time series of simultaneously recorded vertebral sympathetic nerve discharge and heart period fell into the fBm class. Because a fBm signal is the cumulative sum of the elements comprising the corresponding fGn signal, these results demonstrate smoothing of fractal time series in a feedforward direction from medullary presympathetic neurons to postganglionic sympathetic neurons. Whether this involves integration by RVLM neurons of their LTF inputs or independent fractal processes acting at different levels of the network controlling sympathetic nerve discharge remains to be determined. (Supported by NIH HL‐33266.)