Origin, structure, and role of background EEG activity. Part 1. Analytic amplitude.

TL;DR: Derivation and interpretation of unit data in studies of perception might benefit from using multichannel EEG recordings to define distinctive epochs that are demarcated by state transitions of neocortical dynamics in the CS-CR intervals, particularly in consideration of the possibility that EEG may reveal recurring episodes of exchange and sharing of perceptual information among multiple sensory cortices.

About: This article is published in Clinical Neurophysiology.The article was published on 2004-09-01 and is currently open access. It has received 253 citations till now. The article focuses on the topics: Primary sensory areas & Electroencephalography.

Summary

1. Introduction

• By this measure, EEG signals from arrays showed a high degree of synchrony.
• Each transmitting neuron broadcasts its activity by axonal branching.

2.1. Experimental animals and EEG recording

• The experimental procedures by which the electrode arrays were surgically implanted, the rabbits were trained, and the EEG signals were recorded and stored have been documented elsewhere (Barrie, Freeman and Lenhart, 1996).
• Each subject was trained in an aversive classical conditioning paradigm with 20 trials using a reinforced conditioned stimulus (CS+) and 20 trials of an unreinforced conditioned stimulus (CS-) in each session, all with correct conditioned responses.
• The analysis was done with MATLAB software, which has excellent graphics capabilities but is slow in computation; hence analysis was restricted to an adequate subset of the available data.

2.2. Derivation of analytic amplitude and phase

• The 64 EEG signals in each trial were preprocessed first by de-meaning to remove channel bias (Fig. A1.01).
• A spatial low pass filter was applied to remove channel noise (defined in Fig. A1.02, B).
• The spatial ensemble average, v’(t), is shown by the red curve in Fig. A1.03, A, which also approximated the negative rate of change of v(t) in blue.
• The waveform of the average analytic amplitude, A(t), over the 64 channels is shown in Fig. A1.03, C. The analytic phase, Pj(t), for the j-th channel was given by the arctangent of the ratio of the imaginary part to the real part .
• The unwrapped phase, pj(t) on each channel, j, or the average p(t) was marked by repeated jumps known as “phase slip” above or below the mean difference.

2.3. Estimation of synchrony using the analytic amplitude

• In the present study the EEG data from up to 40 6-s trials from 6 subjects were normalized, lowpass filtered at 0.32 c/cm, and band-pass filtered at 20-80 Hz.
• The spatial ensemble average, AT(t), of the 64 time series of Aj(t) in the window was computed to get its SDT.
• In order to compare the time relations of Re to the other measure of synchrony, SDX, the ratio was inverted, 1/Re.
• B. The time course is shown for the Euclidean distance, De(t), serving as a measure of pattern stability.
• This separated the measure of frame amplitude into the 65-th dimension of N+1 space.

3. Results

• Comparison of the variation across channels in phase differences, SDX(t), and the mean analytic amplitude across 64 channels, A(t), at each time point confirmed prior results (Freeman and Rogers, 2003; Freeman, Burke and Holmes, 2003) by showing the strong tendency for troughs in A(t) (light [blue] curve in Fig. 1.01, A) to accompany peaks in SDX(t) black curve).
• Comparison between SDx and 1/Re (Fig. 1.02, A, light [red] curve) showed that the spikes in SDX usually occurred in conjunction with spikes in 1/Re (light curve), but they also were seen during epochs of low 1/Re (high synchrony) as indicated by (*).
• C. Qualifying epochs are illustrated by the black bars when 1/Re(t) and De(t) were both below the thresholds.
• A, B. Histograms are shown of the durations and intervals between starting times of all qualifying epochs.

4. Discussion

• Two new measures of EEG, one of temporal synchrony, Re, and the other of spatial pattern stability, De, have been compared with prior indices SDX and q that were derived from the analytic phase given by the Hilbert method.
• Therefore, optimal cortical transmission of output occurs when (i) the beta or gamma oscillations are synchronous, (ii) when a stable spatial pattern of amplitude modulation emerges at high amplitude, and (iii) when the state lasts at least 3 cycles of the carrier oscillation (Freeman, Part http://sulcus.berkeley.edu/wjf/EG_EEGPart1AnalyticAmplitude.pdf 2).
• These conditions are met intermittently by state transitions that occur in four steps.
• Globally it appears that the state transition is triggered by a few long axons having the highest conduction velocities, which are sufficient in number to initiate widespread seeds of locally spreading cortical activity.
• D. The blue sawtooth curve shows the average analytic phase, P(t), given by equation (3).

4.2. Implications of the hypothesis

• Three lines of further investigation open from this conclusion.
• This question should be thoroughly explored in preparation for studies correlating EEG with human cognition (Fig. A1.12) to search for AM patterns in phase plateaus.
• The sum of squares of the real and imaginary parts, A2(t), when integrated over the window used to measure the SDx of A2(t), gives an index of the free energy dissipation rate, E(t).
• Third, the analytic amplitude might provide an index of the amount of information available for transmission.
• An “order parameter” (Haken, 1983) can be defined as the intensity of the intracortical synaptic interactions by which action potentials are synchronized.

Figures

Table 1. Symbol List for Part 1 and Part 2

Fig. 1.03. A. De(t) and Re(t). B. De(t) and A(t).

Fig. 1.03. A. De(t) and Re(t). B. De(t) and A(t).

Fig. 1.03. A. De(t) and Re(t). B. De(t) and A(t).

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Origin, structure, and role of background eeg activity. part 1. analytic amplitude" ?

In this paper, the authors measured the phase of EEG signals with respect to the phase at a shared frequency and calculated the standard deviation ( SDX ) of the spatial distribution of the phase. 

Q2. What is the order parameter in dynamic models of neuron populations?

In dynamic models of neuron populations expressed in differential equations, the order parameter is represented by a feedback gain coefficient, k (Freeman, 1975). 

Q3. What is the synchronization index based on Shannon entropy?

The index based on Shannon entropy defined phase locking as a peak in the distribution of the phase differences between pairs of traces within a sliding window:e(t) = ! pj j=1N" ln pj (4)where pj was the relative frequency of finding the phase mod 2π within the j-th bin, and e varied between zero and ê = ln N, the number of bins (e.g. 100 bins of 0.06 radians between -π and +π radians). 

Q4. What software was used to analyze the EEG signals?

The analysis was done with MATLAB software, which has excellent graphics capabilities but is slow in computation; hence analysis was restricted to an adequate subset of the available data. 

Q5. What was the synchronization index for the EEG?

The index was generalized to multiple channels by calculating the distribution of phase differences over all pairs of channels, after subtracting the means for each pair within the sliding window. 

Q6. What is the phase slip that was revealed by upward or downward deviations from the mean differences?

The phase slip that was revealed by upward or downward deviations from the mean differences, Δpj(t), tended to occur synchronously across the entire 8x8 array, here plotted in a compressed display of Δpj(t) in the order of channel number. 

Q7. What was the synchronization index as a function of time?

This synchronization index as a function of time was normalized, q(t) = ( ê-e(t))/ê, (5) so that q(t) was zero for a uniform distribution, and one for a delta distribution of phase values. 

Q8. What was the level of covariance among the EEG signals from arrays up to 1?

the level of covariance among the EEG signals from arrays up to 1 cm in width was high; the fraction of the variance in the first component of principal components analysis (PCA) usually exceeded 95%. 

Q9. How long did the lag between phase changes between the two measurements be?

The combined mean lag of 28 ms lay within the range of three estimates previously derived from the Fourier method for the delay between formation of a spatial pattern of phase modulation and establishment of the spatial pattern of amplitude modulation: 24-34 ms (Freeman, 2003b). 

Q10. What was the average analytic amplitude for each channel?

The analytic amplitude for each channel, Aj(t), was the length of the vector, which was given by the square root of the sums of squares of the real and the imaginary parts for each channel. 

Q11. What is the phase gradient of the array?

When they form lines that deviate from the direction of the right abscissa (as most clearly at about -250 ms) there is a phase gradient across the array. 

Q12. How can the authors estimate the phase of multiple EEG records?

The synchrony among multiple EEG records can be estimated by measuring the phase of each signal with respect to the phase of the spatial ensemble average at a shared frequency and calculating the standard deviation (SDX) of the spatial distribution of the phase (Freeman, Burke and Holmes, 2003; Part 2). 

Q13. What is the amplitude of the component of the shared wave form?

Yet the amplitude of that component, however chaotic the wave form might be, varied with electrode location in the array so as to constitute a spatial pattern of amplitude modulation (AM) of the shared wave form.