Fractal character of the auditory neural spike train

Abstract

Long-counting-time pulse-number distributions (PNDs) were measured in cat primary auditory fibers using a broad range of fibers, stimuli, counting times T, and number of repetitions NT. Short-counting-time PNDs readily exhibit the existence of spike pairs, whereas PNDs with T≳100 ms exhibit irregular shapes in all cases, indicating the presence of spike clusters in the underlying auditory neural spike train. The count variance-to-mean ratio (or Fano factor) F(T) was relatively constant over a broad range of stimulus levels for all units measured, but increased substantially as T or NT increased. A normalized coincidence rate [g(τ) versus delay time τ], based on three physiologically plausible factors, is in accord with the Fano-factor versus counting-time function. The observed power-law growth for the Fano factor for large T[F(T) ∝ Tα] implies that g(τ) ∝ τα 1 and that the spectral density of the spike train S(f) ∝ f−α, where 0⩽α⩽1. This suggests that the auditory events exhibit fractal behavior for sufficiently large times (sufficiently low frequencies) [M. C. Teich, IEEE Trans. Biomed. Eng., in press (1989)]. This behavior leads to spike clusters in the PND. The fractal dimension for the process is D = α≈12 in the range 0.1 s⩽T⩽10 s. The firings of vestibular fibers do not exhibit fractal behavior, suggesting that the form of the auditory neural-firing pattern serves to effectively sample fractal natural noises. [Work supported by NIH and NSF.]