Turbulence in globus pallidum neurons in patients with Parkinson's disease: exponential decay of the power spectrum.

Exponential decay of the power spectrum is typically observed in turbulent flow patterns, as evidenced both in experiments and in the Navier-Stokes equations describing fluid dynamics. In this study, we present evidence on the exponential decay of power spectra belonging to interspike interval time series, registered in pallidal neurons from patients with Parkinson's disease. Extracellular neuronal recordings were obtained during functional neurosurgery and processed off-line. Interspike interval power spectra were calculated for single unit recordings. All power spectra analyzed were similar, presenting rapid decay of power with frequency. Regression coefficient (adjusted R squared) for exponential function fit was very high, over 0.99 (p<0.001) in every case. We therefore suggest that the neurons studied here show turbulent-like behavior from a spectral point of view, and theorize that Navier-Stokes-like equations may be potentially useful tools to model spectral patterns of firing activity in neurons of this type. We propose to classify neural systems according to the general form of their power spectrum into two major groups of physical systems: systems with scale invariance and a power-law behavior of the power spectrum, and systems with critical scale and an exponential decay of the power spectrum.