Nonlinear analysis of neuronal firing modulated by sinusoidal stimulation at axons in rat hippocampus

Abstract

Introduction: Electrical stimulation of the brain has shown promising prospects in treating various brain diseases. Although biphasic pulse stimulation remains the predominant clinical approach, there has been increasing interest in exploring alternative stimulation waveforms, such as sinusoidal stimulation, to improve the effectiveness of brain stimulation and to expand its application to a wider range of brain disorders. Despite this growing attention, the effects of sinusoidal stimulation on neurons, especially on their nonlinear firing characteristics, remains unclear.

Methods: To address the question, 50 Hz sinusoidal stimulation was applied on Schaffer collaterals of the rat hippocampal CA1 region in vivo. Single unit activity of both pyramidal cells and interneurons in the downstream CA1 region was recorded and analyzed. Two fractal indexes, namely the Fano factor and Hurst exponent, were used to evaluate changes in the long-range correlations, a manifestation of nonlinear dynamics, in spike sequences of neuronal firing.

Results: The results demonstrate that sinusoidal electrical stimulation increased the firing rates of both pyramidal cells and interneurons, as well as altered their firing to stimulation-related patterns. Importantly, the sinusoidal stimulation increased, rather than decreased the scaling exponents of both Fano factor and Hurst exponent, indicating an increase in the long-range correlations of both pyramidal cells and interneurons.

Discussion: The results firstly reported that periodic sinusoidal stimulation without long-range correlations can increase the long-range correlations of neurons in the downstream post-synaptic area. These results provide new nonlinear mechanisms of brain sinusoidal stimulation and facilitate the development of new stimulation modes.

Keywords: Fano factor; Hurst exponents; fractal; hippocampus; long-range correlations; sinusoidal stimulation; unit spike.

Figure 1

Increase of neuronal firing during the period of 50 Hz sinusoidal stimulation of Schaffer collaterals in the hippocampal CA1 region. (A) Workflow of the animal experiments and data acquisition, including schematic diagram of the implant positions of the recording electrode (RE) in the pyramidal layer and the stimulation electrode (SE) in the Schaffer collaterals of CA1 region. (B) A typical example of neuronal responses to 1-min 50 Hz sinusoidal stimulation. The shadow denotes the stimulation period. The red curves denote the sinusoidal waveforms applied at the Schaffer collaterals. Superposition traces of spike waveforms with an average waveform denoted by the black color of a typical pyramidal cell and an interneuron were shown on the left. Triangles and dots mark the firing of pyramidal cells and interneurons, respectively. (C) Comparison of the mean MUA firing rates between the baseline recordings and the recordings during stimulation. (D,E) Comparison of the firing rates of pyramidal cells and interneurons between the baseline recordings and the recordings during stimulation. Baseline recordings were obtained 1-min before the sinusoidal stimulation. **p < 0.01, paired t-test.

Figure 2

Sinusoidal stimulation induced changes of firing patterns of both pyramidal cells and interneurons. (A) A typical example of unit spike recording of pyramidal cells before and during stimulation. (B) The average inter-spike-interval (ISI) curve of 25 pyramidal cells. (C,D) Corresponding plots as panels (A,B) for interneurons with a same order in panels (A,B) but neuronal types changed from pyramidal cells to interneurons. On the recording signals, red and blue dots denote unit spikes at baseline and during stimulation, respectively.

Figure 3

Fano factor analyses of the firing of pyramidal cells and interneurons. (A) Left: The average Fano factor plots of the total 25 pyramidal cells. Fano factors were expressed as function of the time lags (in seconds, double logarithmic scales). Right: The comparison of scaling exponent of Fano factor curve between the baseline recordings of pre-stimulation and the recordings during stimulation. (B) The Fano factor plots and comparison of scaling exponent of interneurons. **p < 0.01, paired t-test.

Figure 4

Hurst exponents analyses of the firing of pyramidal cells and interneurons. (A) Left: Examples of rescale range (Hurst exponents) analyses of a pyramidal cell. The image shows a linear relationship between (R/S)_d and the ISI number d, when plotted in double-logarithmic representation. Right: Comparison of the Hurst exponent of pyramidal cells between the baseline recordings of pre-stimulation and the recordings during stimulation. (B) Corresponding plots as panel (A) for interneurons. **p < 0.01, paired t-test.