POTENCOR: a program to calculate power and correlation spectra of EEG signals

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Abstract

This work describes a computer program (POTENCOR) that applying the Fast Fourier Transform and Pearson product-moment correlation, can calculate easily, fast and accurately the absolute and relative power as well as the inter- and intrahemispheric correlation between every pair of EEG signals for narrow bands and for broad bands. POTENCOR has three main advantages: (1) it allows calculation of inter- and intrahemispheric correlation spectra, for which to our knowledge, there is no commercial program available; (2) the absolute and relative power values are not affected by the number of points that constitutes the signal segment; and (3) in case of making the analysis by each segment the temporal evolution for each EEG parameter can be graphically represented. The utility and flexibility of this program has been confirmed in many clinical and experimental researches.

Introduction

The need for quantitative methods in the analysis of an electroencephalogram (EEG) trace that allows extract more information than the one available by visual inspection, has led to the application of mathematical methods, originally employed in physics and engineering fields for oscillatory phenomena and time series analysis [1] since early stages of the EEG age. Quantitative EEG analysis has proved to be useful for identifying EEG activity related to cognitive functions, behavior and pathology. Currently, quantitative EEG analysis has reached a high level of development with sophisticated methods allowing the construction of cortical maps and current source location [2].

Various methods have been employed for dealing with automatic computer processing of EEG. One of the most common quantitative EEG analyses employed, is the spectral power analysis using Fourier Transform (FT). FT calculates the frequency components contained in the EEG signal. There are many commercially available programs, most of them however, have to be used with specific hardware including amplifiers, computer equipment or both, which makes them very expensive. In addition, some of these programs have been developed for specific purposes and therefore, they are restricted to a special kind of analysis that not always fits experimental and/or clinical needs.

In recent years, there has been an increasing interest in obtaining linear relationships, between unitary activity as well as between field potentials, to understand functional and temporal relationships within and between the cortex and subcortical structures involved in the generation of electrical activity and information processing [3], [4], [5], [6]. Two main approaches have been used, coherence analysis and cross-correlation function. Both methods are often considered as equivalents and although this is generally true, there are important differences between them, in the calculation procedures as well as in the results obtained. Each analysis has its own advantages depending on the experimental issue addressed. Coherence is obtained from the FT by dividing the numerical square of the cross-spectrum by the product of the autospectra, therefore, it gives a coherence value from 0 to 1 as a function of frequency; polarity is lost however, and it is sensitive to changes in power as well as to changes in phase relationship. The value of coherence for a single segment always equals one, regardless of the true phase relationship. Therefore, it has to be calculated for several segments and it does not give the true phase relationship but rather the co-variation and stability of the relationship for the segments that have entered the analysis. If the same relationship is maintained, even if it is 0, coherence will equals 1. Correlation, on the other hand, is calculated in time domain and, although it also gives the average phase or time relationship over a certain time, it can be calculated for a single segment. Since it is based on Pearson product-moment correlation, polarity information is preserved (correlation values rank from −1 to 1) and it is independent from amplitude [7].

Since it has been demonstrated that time relationships between two brain regions are not the same for every band, it is important to obtain the correlation for each narrow or broad band; there are no commercial programs available though, combining frequency and time domain analysis that calculate correlation spectra. The main shortcoming for calculating correlation comes from computer problems rather than from mathematical or theoretical issues. The commercial programs available for calculating correlation or cross-correlation function don't separate by frequencies the two time series that are going to be correlated so that a single correlation value is obtained. In order to obtain a correlation value for a particular frequency, the two time series need to be filtered previously to calculations. Calculations have to be repeated as many times as frequencies are desired, provided previous filtering resulting in a high computer time consumption, i.e. if the time relationships for each frequency from 1 to 50 Hz (which is equivalent to a correlation spectra) is desired, the program has to be run 50 times.

This report describes a computer program, POTENCOR, that has been developed to obtain at the same time absolute power (AP) relative power (RP) and the correlation spectra among each pair of channels for narrow bands as well as for broad bands in a very short time. In this program Fourier analysis is used to separate the frequency components mean while Pearson product-moment coefficients are used to calculate the similarity among these components. Additionally, since these three EEG variables need to be normalized before statistical analysis, the program also calculates the normalized data for AP, RP and correlation.

Section snippets

Computational methods and theory

The program calculates the Fast Fourier Transform, based on the algorithm of the Discrete Fourier Transform (DFT) [8] which is indicated in the , , for all epochs of every file name contained in the two main files.Frex=n=0N−1fncos2πnx/NFimx=−n=0N−1fnsen2πnx/NPot(x)={Fre(x)}2+{Fim(x)}2

Fre(x), x=0, 1, 2, . . ., N−1represent the N values of the real part of the signal spectrum f(n).
f(n), n=0, 1, 2, . . ., N−1N points that represent the signal segment during the time.
Fim(x), x=0, 1, 2, . . ., N−1represent the N

Program description

The use of the program is very simple. It requires two main files in ASCII format containing the names of the EEG files for all derivations to be processed, one containing the names of the files from one hemisphere and the other, the names of the files of the other hemisphere. Each individual file needs eight digits with the last pair indicating the derivation; for example, in the file name ‘moc1oaF3’, the first two digits indicate the subject name, the following four digits indicate the

System performance and examples

POTENCOR creates separate files with the average spectral values of all the epochs for each frequency and derivation, for bands and for frequency values, for absolute power, relative power, inter- and intrahemispheric correlation and for the corresponding transformed values (18 files in total). In the case of frequency values, the results are contained in two files, one from 1 to 25 and the other from 35 to 55 Hz. The files are identified by different append, i.e. POTENCOR.ABF for absolute

Hardware and software specifications

The program has been written in Delphi and runs in a Window environment in every PC compatible computer fulfilling the following minimal requirements: a 386DX processor and 32 Mb RAM. Output files are in ASCII format needing very short memory. Memory requirements or limitations are determined by the amount of data to be processed (i.e. number of channels and length of the time series that in turn depends on the length of the time segment and sampling frequency).

POTENCOR requires digitized

Lessons learned and availability

The program described here offers a simple way for obtaining complex quantitative analysis combining frequency and time domain analyses. It has been developed to obtain at absolute power (AP), relative power (RP) and correlation spectra simultaneously, among every pair of signals for narrow bands and for broad bands in a very short time.

POTENCOR offers many advantages. It does not require a complex equipment, it runs on every PC and the output is stored in independent ASCII files, facilitating

Acknowledgements

Authors wish to Christel Ketzer for the correction of the English version of the manuscript.

References (21)

There are more references available in the full text version of this article.

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