Time series analysis of brain potentials preceding voluntary movements

Area of Science:

• Neuroscience
• Biomedical Engineering
• Signal Processing

Background:

• Voluntary movements are preceded by distinct brain potential shifts.
• Understanding the characteristics of these slow potentials shifts (SPS) is crucial for motor control research.
• Existing models may not fully capture the complex nature of pre-movement brain activity.

Purpose of the Study:

• To test hypotheses regarding the mathematical structure of slow potentials shifts (SPS) preceding voluntary movements.
• To determine if SPS can be decomposed into a smooth trend and stationary residuals.
• To assess if autoregressive (AR) or autoregressive moving average (ARMA) models can describe these components and ongoing EEG activity.

Main Methods:

• Averaging single-trial EEG records synchronized with voluntary button presses.
• Estimating the trend component of SPS using least mean square error minimization with various approximating functions.
• Applying AR and ARMA models to analyze SPS residuals and preceding ongoing EEG activity.

Main Results:

• The hypotheses were not rejected, supporting the proposed model of SPS.
• A hyperbolic function or Chebyshev's second-order polynomial provided the best fit for the trend component.
• AR models demonstrated a good fit for both SPS residuals and ongoing EEG activity.

Conclusions:

• SPS preceding voluntary movements can be characterized by a smooth function (trend) and stationary residuals.
• The trend is well-approximated by specific mathematical functions.
• AR models adequately describe the dynamic properties of both SPS residuals and background EEG activity.