Researcher have disclosed changes of alpha power in each cerebral-cortex region under different states. These studies show that spontaneous alpha exhibits different distributions owing to the variation of alpha sources or the propagation ways. Most substantially, alpha distribution might be related to the states of alertness. In these studies, alpha power was calculated by short-time spectral analysis based on Fourier-transformation method within a specific time window. Notice that Fourier approach is restricted by the piecewise stationary property that requires a narrow window of analysis and the frequency resolution that desires a wide window. In general, the window width is in the range from 1 to 5 seconds. However, from the viewpoint of the microscopic neural activities, the message is transmitted on the time scale of mini-second. The traditional FFT method is restricted to the window length and is difficult to explore the cerebral microstate.
In the research of Lehmann [16,17], he considered that the consistent neural activities would results in higher Global Field Power (GFP). The GFP is defined as the sum of the powers of all recoding channels at a specific sampling moment. The activity of each neuron could be considered as an electrical dipole vector including magnitude and direction. If each vector is uncorrelated with others, the activities would be canceled each other. In some
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conditions, neurons are driven by the same source that leads to a large GFP. As larger GFP often infers better signal-to-noise ratio (SNR), the driven response can be more significant with less noise interference. The appearance of local maximal GFP’s is thus an appropriate reference for choosing representative brain mappings (landscapes) to be utilized in the spatial microstate analysis. The sites of extremes (maximum and minimum) of a particular brain mapping compose a current dipole model generating the brain potential distribution recorded on the scalp.
We analyzed the brain microstates for a given time period ‘segment’. A segment is a continuous time duration within which the electrode sites of maximal and minimal potential are almost immobile (staying in a small region). Alternatively speaking, dipole vectors within a segment are stationary in a sense. A spatial segmentation algorithm was developed to separate different segments of brain topographical activities. Each particular segment class contains brain mappings with two sites of extremes appearing most frequently at a given region. As a consequence, the method adopted in this thesis provides rather local and subtle temporal information which cannot be accessible based on conventional Fourier analysis.
Lehmann [16,17] used the raw EEG data (potentials on the recording sites) to extract the brain landscapes of interest. His method is not practicable for our aim on the analysis of alpha-rhythmic behaviors. We applied the alpha-power for the brain landscape for the microstate analyzing.
A number of approaches and methods have been developed to analyze the EEG signals in time, frequency, and spatial domains. A number of methods have been proposed to explore various EEG features, in either macroscopic or microscopic aspects. Each particular method calls for different lengths of EEG segments and different numbers of channels. In our study, we firstly performed feature clustering for 20 minutes EEG signals based on the spatial characteristics. Then those 4-second EEG epochs with particular topographic features were extracted for microstate analysis. We will demonstrate that, based on a short EEG epoch of only a few seconds, the microstates method provides a way of exploring the brain
topographical behaviors under Zen meditation.
2.4.1 Global Field Power (GFP)
Global field power (GFP) at a given time instant represents the summation of EEG powers of all channels at that particular time t. A high GFP stands for a potential distribution with many peaks and troughs. According to [18], brain mappings with maximal GFP’s normally have better SNR (signal-noise-ration) performance. Hence, GFP provides a reference for us to select the appropriate time instants for microstates analysis. Assume a series Ak represents the data of channel-k. GFP is a function of time as shown below:
Where i represents the time point of discrete time signal and is number of channel. In this thesis, the is defined as 30.
nch
nch
Figure 2.5 displays the GFP of a one-second EEG epoch. Apparently, GFP oscillates at a rhythm twice the EEG frequency due to the rectification effect.
Figure 2.5 The GFP of 1 second EEG epoch.
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Since alpha activity was our major focus, we applied wavelet decomposition to raw EEG to extract alpha-band (8-12Hz) patterns before the GFP evaluation. As a consequence, we could reduce the contamination from other rhythmic bands, for example, delta (0-4Hz), theta (4-8Hz), and beta (>20Hz). We then computed the GFP of alpha-dominated EEG.
2.4.2 Segmentation Method
A brain microstate is defined as the constant landscape (brain topographical mapping) that lasts for a momentarily continuous time segment. The landscape was obtained by a 131msec moving window. Compute the power in the window and it results a 30 dimensional map. Note that we recorded 30-channel EEG in our experiment with a sampling rate of 1,000 Hz. Within a 4-second EEG epoch, we can obtain almost 4,000 maps. Previous study [18] has demonstrated that maximum GFP normally resulted in a good signal-to-noise ratio. This is accordingly a moderate clue for choosing the representative maps. We thus focused on the locations of extremes (maximum and minimum power value) of brain mappings.
In our study, brain microstates are characterized by the current dipole vector pointing from the minimum to the maximum potential of the multichannel EEG mapping on the scalp.
As a consequence, it becomes important to determine the appropriate locations (EEG channels) where extremes occur. Sometimes the extremes might be influenced by the noise. To deal with
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at
e class es.
the noise problem, we developed an approach for better extracting the extremes.
First, we employed the spherical-coordinate model of the EEG electrodes to compute the average distance DRnR between Cz and each of the rest 29 electrode sites. We then computed the local average power (LAP) of brain potentials within the DRnR-radius circle centered on each channel. From the set of 30 local average powers (LAP’s), extremes (maximum and minimum) could be determined in a sense of better statistical significance. Finally, the centered electrode of maximal and minimal LAP forms the dipole vector of the brain microstate.
In order to obtain the data with an optimal SNR, only the maps at the peaks (local maxima) of GFP temporal sequence were selected for brain microstates analysis. These brain mappings were reduced to the locations of the extremes (maximum and minimum power value).
The so-called segment of a microstate begins with a particular brain potential map BPMR1R characterized by a given dipole vector, and continues as long as the succeeding maps the GFP peaks come up with the same dipole vector. That is, minimal and maximal LAP locates at the same sites as those of the beginning dipole vector obtained from BPMR1R. The
segment ends if the extreme LAP sites are out of range and continues if the sites are in the
pre-defined range. The duration of a segment can be obtained straightforwardly. And th of a segment is defined by the extreme LAP sites whose have the highest occurrence tim
In each group, we analyzed four parameters: a) number of maximum GFPs per seconds,
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b) average duration of a segment, c) number of segments per second, and d) maximum duration of the segments.
2.4.3 Selection of the Window of Extreme LAP Site
In the microstates analysis, we need to designate a circular window for justifying whether the extreme LAPs belong to the same microstate. Table 2.2 lists the results of an experimental subject with frontal alpha obtained by different threshold ( DRnR : same as the DRnR
before, ie, average of 29 distances from Cz to others). The threshold is used as the radius of the circular window.
A larger threshold could cause the different microstates as the same state, and on the other hand, a smaller threshold could separate one microstate into several segments. Either a small or a large threshold may not reliably reflect the evolution of microstates, so we had to find a suitable range for this threshold. According to our experiment, the threshold in the range of 0.7DRnR ~ 1.5DRnR provides obviously different dipole vectors with the range of 0.5DRnR
and 2DRnR ; while the locations of dipole vectors in range of 0.7DRnR ~ 1.5DRnR are about the same as the frontal alpha, so it represent that the efficacy of segmentation are quiet the same in this region. Hence the threshold in this range (0.7DRnR ~ 1.5DRnR) is feasible. This study adopted DRnR
as the threshold
Table 2.2 Results of microstate analysis with different thresholds
Threshold 0.5 Dn 0.7Dn Dn 1.5Dn 2Dn
Dipole strength
(mv^2)
96.5 200 197 173 67 Dipole
location
CPZ – O1 FCZ – P8 FCZ – P8 FZ – P8 O1 – TP8