Wavelet Coherence and Its Application in Analyzing Auditory and Motor Task Event-Related Potentials

WU Jie，ZHANG Ning，YANG Zhuo，ZHANG Tao, Wavelet coherence and its application in analyzing auditory and motor task event-related potentials.

This paper has been accepted by ACTA BIOPYSICA SINICA，here is its abstract.

Related links:Tips about Wavelet , Wavelet Coherence Method,A Vivid Example to Show How Wavelet Coherence Works, Some Concepts about ERP signals ,Wavelet and EEG Signals. These links can help to gain further information about this paper.

Abstract:
Wavelet coherence method is applied in analyzing single trial of ERP (event-related potential). There are three groups of experiments: auditory single task, motor single task 1 and motor single task 2. Data from 12 participants is analyzed around 40 Hz by wavelet coherence method and the coherence values between prefrontal area and other areas in the brain are calculated. It is found that the coherence values in motor tasks are larger than those in auditory task and there are significantly differences. Furthermore, in different tasks, the distributions of the coherence values are obviously different, and the values are changing in particularly ways according the varying of the time. This analysis indicates that wavelet coherence method has its advantages in investigating short time EEG signals.

Brief descriptions:


The coherence values, around 40Hz between prefrontal area and other areas in the cerebral cortex, were measured. It was found that the coherence values in the MST (Motor Single Task) are larger than that in the AST (Auditory Single Task) with significant differences.Brain dealing with complicated tasks can have more information to process, and there should be more information communication between different areas of the brain. This can be denoted by coherence values.


Wavelet Coherence Values along the time axis. The colors in the images indicate the coherence values between prefrontal area and other areas in the cerebral cortex around 40Hz(the relationship between the color and the value is shown in the color-bar).large coherence values exactly locate in Auditory Cortex at temporal lobe in AST conditions, whilst in MST conditions, the big values are in motor cortex which is in parietal area.

The data show that the wavelet methods calculations of non-stationary signals, compared to the Fourier methods, can characterize the time-frequency features of neural mechanisms underlying cognitive control. Furthermore, wavelet approach can provide higher resolution in both temporal and spatial scales and can be applied in analyzing other physiological signals.

Main reference:
Lachaux, J.-P., et al., Estimating the time-course of coherence between single-trial brain signals: an introduction to wavelet coherence. Neurophysiol Clin., 2002. 32: p. 157-174.

A Vivid Example to Show How Wavelet Coherence Works

Some formulas have been given in previous article, but they are not friendly to understand. Now there is a vivid example to show what Wavelet Coherence analysis looks like.

Please pay attention to the differences of the two pictures below. The description following the pictures will tell you the details.

a

b

Two signals in experiments were randomly chosen and a synchronization in 2~3 s and 10~40Hz was created between them. Then the Wavelet Coherence values were calculated. (a) result of the signals without artificial synchronization, (b) result of the signals with artificial synchronization. The color-bar in the right shows the relationship between coherence values and the colors. High coherence values can be seen in area with designed synchronization (2~3 s and 10~40Hz).

References of this article:
Lachaux J-P, Lutz A, Rudrauf D, Cosmelli D, Quyen MLV, Martinerie J,Varela F. Estimating the time-course of coherence between single-trial brain signals: an introduction to wavelet coherence. Neurophysiol Clin., 2002, 32: 157-174.

Wavelet Analysis of ERP Recordings for Dual Tasks in Man

WU J, YANG Z, ZHANG T, Wavelet analysis of ERP recordings for dual tasks in man.

This paper has been accepted by ICCN'07 & SICPB'07 which will be held in Shanghai, China during November 17-21, 2007. The abstract is shown as below.

Click Wavelet Packet Transform, Relative Wavelet Energy, ERP for more relevant information.

Abstract:
The study was to examine the application of wavelet packet method to electrophysiological responses recorded during single and dual task performance. Relative energies of both EEG alpha and beta frequency bands were significantly higher in the single task conditions compared with that of the dual task condition (P is less than 0.05). The data demonstrated that relative energy measurements based on wavelet transform could be a useful alternative approach to analyzing short duration EEG signals on a time scale of seconds.

It is impossible and unnecessary to show the details of this paper in a single short article, so only the abstract is shown here.

The most important point is that, compared to the Fourier methods, wavelet method can be an alternative and much better method to deal with short time EEG signals. Accordingly, wavelet method can be used in analyzing other data in our lab, those data include EEG, ERP and RSNA signals. They are all complicated signals and represent nonlinear dynamic systems with high dimensionality.

There will be other artcles in this blog to illustrate the advantages of Wavelet method compared to regular frequency analysis methods.

Relative Wavelet Energy

It is only a short introduction about Relative Wavelet Energy. Click here for some basic information about wavelet.

The energy of a discrete signal s(k) is defined as

and the relative energy is defined as

where is the total energy, which is calculated by adding here(Rosso, et al., 2006).

Rosso, O.A., Martin, M.T., Figliola, A., Keller, K. and Plastino, A. (2006) EEG analysis using wavelet-based information tools, Journal of Neuroscience Methods, 153, 163-182.

Wavelet Packet Transform

The wavelet packet transform (WPT) represents a generalization of the wavelet methods and it has recently been applied to various science and engineering fields with great success. Here are some tips about WPT from Matlab tutorial.

From WT to WPT:

In wavelet analysis, a signal is split into an approximation and a detail. The approximation is then itself split into a second-level approximation and detail, and the process is repeated. For an n-level decomposition, there are n+1 possible ways to decompose or encode the signal. More basic information about wavelet can be got here.

In wavelet packet analysis, the details as well as the approximations can be split.


The wavelet decomposition tree is a part of this complete binary tree. For instance, wavelet packet analysis allows the signal S to be represented as A1 + AAD3 + DAD3 + DD2.

Here is a sample transform of an EEG signal in our lab. The original waveform was decomposed into five waveforms in WPT method, db5 mother wavelet was employed and 7 levels decomposition was taken. We can see DELTA, THETA, ALPHA, BETA, GAMMA waves in this figure.

Wavelet and EEG Signals

EEG signals are wildly studied to determine how patterns contained within them might reflect control by the nervous system. Generally, they are investigated with frequency analysis based on FFT. However, EEG data sets (including signals in ERP experiments) are non-stationary in both time and space. And FFT is not good at analyzing waveforms with this feature，see this article.

The main advantage of wavelet transform (WT) in the analysis of EEG signals is that it allows accurate decomposition of a neuro-electrical record into a set of component waveforms (detail functions). These detail functions can isolate all scales of waveform structure, from the largest to smallest pattern of variation in time and space that is available in the signal. Consequently WT provides flexible control over the resolution with which different activities and events contained in the neuroelctrical signal can be localized in time, space and scale. This leads to several important applications like(Samar, et al., 1999): (a) noise filtering and signal separation; (b) preprocessing neuroelectric data; (c) neuroelectric signal compressions; (d) spike and transients detections; (e) component and event detection; (f) time-scale and space-scale analysis of neuroelectric waveforms; among others(Rosso, et al., 2006).

Many details have been reviewed by Samar(Samar, et al., 1999).


Rosso, O.A., Martin, M.T., Figliola, A., Keller, K. and Plastino, A. (2006) EEG analysis using wavelet-based information tools, Journal of Neuroscience Methods, 153, 163-182.
Samar, V.J., Bopardikar, A., Rao, R. and Swartz, K. (1999) Wavelet analysis of neuroelectric waveforms: a conceptual tutorial, Brain Lang, 66, 7-60.

Some Concepts about ERP signals

Enterprise Resource Planning is usually recognized as ERP for common people, but the "ERP" here means Event related Potential. For brain scientists, it is a common way to investigate the brain. Event-related potential is the measurement of the brain's electrical activity in response to different types of events, such as attention, words, thinking or sounds. By measuring the brain's response to such events we can learn how different types of information are processed.

In an Event related Potential experiment, signals together with the events are recorded. The events (for example, auditory stimulus, vibrative stimulus, human actions) are designed according to the purpose. Thus, ERP experiments provide a possibility to learn how the events are processed in the brain.


Normally, dozens of individual raw ERP experiment signals are averaged together to gain the ERP, this method allow us to cancels out the noise and make the responses clearly. There are three measurable aspects of the ERP waveform, i.e., amplitude, latency, and scalp distribution. Component amplitude provides index of neural activation extent (how the component responds functionally to experimental variables); component latency (the point in time at which the peak occurs) reveals the timing of this activation; and a component’s scalp distribution (the pattern of voltage gradient over the scalp at any point in time) provides information on the overall pattern of activated brain areas.

Note: some contents above comes from Wikipedia


A sample from http://www.city.ac.uk/psychology/research/CNRU/eegintro.html,This is an averaged ERP signal, in which you can see the responses (positive and negative components).Basic research are based on the measurements of this type of components.

Wavelet Coherence Method

The coherence function is a direct measure of thecorrelation between the spectra of two random processes. Fourier method can provide accurate estimates of stationary signals. However, Most signals ( including our signals from brains) are non-stationary waveforms.

Wavelet coherence method was first used in physics to estimate interactions among non-stationary signals, now it has been applied in investigating neuroelectric waveforms such as EEG signals.

First of all, signals are decomposed along the Morlet wavelet family, the advantage of which is that it is simple and well suited for spectral estimations. It is defined for frequency f and time τ by:

The wavelet transform of a signal x(u) is a function of time (τ) and frequency ( f ) given by the convolution of x with this wavelet family:


From the wavelet transforms of two signals x and y, we can define the wavelet cross-spectrum between x and y around time t and frequency f

Whereδis an important parameter which depends on the frequency

Finally, analogous to the Fourier-based coherence, the wavelet coherence WCo(t, f) is defined at time t and frequency f by:

WCo(t, f) takes its values between 0 and 1, the bigger this value, the more dependence between x and y around time t and frequency f.

NOTE: It is a brief introduction of Wavelet Coherence Method. For further information about this method, please refer to relevant papers.

References of this article:
Lachaux J-P, Lutz A, Rudrauf D, Cosmelli D, Quyen MLV, Martinerie J,Varela F. Estimating the time-course of coherence between single-trial brain signals: an introduction to wavelet coherence. Neurophysiol Clin., 2002, 32: 157-174.
Li X, Yao X, G J, Jefferys,Fox J. Interaction Dynamics of Neuronal Oscillations Analysed Using Wavelet Transforms. J. Neurosci. Methods, 2007, 160(1): 178-185.

In the 20th International CODATA Conference

The 20th International CODATA Conference: Scientific Data and Knowledge within the Information Society, was held during October 23-25th 2006 in Peking. We had two posters there. Some photos and our posters are shown as below.


Welcome Reception


Palace Convention Hall


Wonderful presentations


Our posters and me


Our poster

Our poster

Cocktails

Tips about Wavelet

This introduction about Wavelet is summarized from matlab wavelet tutorial, for this tutorial, in my opinion, is concise and easy to understand.

From Fourier to Wavelet

Fourier method is the most well-known method for signal analysis. It breaks down a signal into constituent sinusoids of different frequencies, in other words, it transforms the signals from time-based to frequency-based.

Fig.1 Fourier Transform

Although this useful technique has been wildly used by people for a long time, it has a serious drawback: time information is lost during the transform, thus Fourier is not suited to detecting nonstatinary signals, such as EEG.

In an effort to correct this deficiency, Dennis Gabor (1946) adapted the Fourier transform to analyze only a small section of the signal at a time -- a technique called windowing the signal. Gabor's adaptation, called the Short-Time Fourier Transform (STFT), maps a signal into a two-dimensional function of time and frequency.

Fig.2 Short Time Fourier Transform

However, in STFT a particular size for time window should be chosen, the drawback is that this window can not provide a flexible analysis for all frequencies.

Wavelet analysis represents the next logical step: a windowing technique with variable-sized regions. Wavelet analysis allows the use of long time intervals where we want more precise low-frequency information, and shorter regions where we want high-frequency information.

Fig.2 Wavelet Transform

NOTE: Most of the information in this article comes from MATLAB tutorial, many thanks for MATLAB! The knowledge here are only basic tips, so if you want more details, see relevant books or papers please!

What is EEG?

Electroencephalography is the neurophysiologic measurement of the electrical activity of the brain by recording from electrodes placed on the scalp or, in special cases, subdurally or in the cerebral cortex. The resulting traces are known as an electroencephalogram (EEG) and represent a summation of post-synaptic potentials from a large number of neurons. These are sometimes called brainwaves, though this use is discouraged, because the brain does not broadcast electrical waves.The EEG is a brain function test, but in clinical use it is a "gross correlate of brain activity". Electrical currents are not measured, but rather voltage differences between different parts of the brain.

The basic knowledge above comes from Wikipedia. It can give you a concept: EEG is a kind of signal from brain.

There are some details about the EEG data in our lab in Nankai University.

Some of the EEG data come from brains of human beings, including epileptic EEG signals from patients in hospitals, EEG from healthy people and ERP (Event Related Potentials) raw data from cognization research centers. Most of these signals have been collected in a database, you can see the articles with the tag database for more introduction.

Some EEG data were obtained from rats, which were healthy or in ill condition (ischemia model or epilepsy model). Signals from animals may be much more easier for us to detect the things happening in the brain. We recorded the data from the hippocampus and also the cortex.

Obviously, our purpose of calculating these data is to investigate the brain and to find out different features in the nerve systems in different physiology conditions. The analysis methods will be discussed in other articles.

ERPDB: a Database of ERP Data for Neuroinformatics Research

Event-related potential (ERP) is the measurement of the brain's electrical activity in response to different types of events. These signals are useful for learning how information is processed in the human brain. Being a neuroinformatics laboratory, we deal with lots of ERP signals, which come from various research programs. Different programs have different experiment designs, different parameters settings, and different data formats. These could be big problems for our study. For this reason, arranging the data and constructing a database to store them is quite necessary.

ERPDB contains the information of the participants and the rearranged signals.The data have been transformed into more organized data, which are more convenient for further computation and analysis. Also, new data can be easily added into the database according to our standard. This database is available on the web.



Publications:
Qinghong Yan, Ning Zhang, Jie Wu. The Constitution of ERP Database Based on SQL Server2000. The 20th International CODATA Conference (CODATA2006 ABSTRACT，China，Beijing):2006, 308
QingHong Yan, Ning Zhang, Jie Wu, Tao Zhang. ERPDB: an integrated database of ERP datafor neuroinformatics research, Data science journal, 2007

SheetsPair: a Database of Amino Acids Pairs in Protein Sheet Structures

Sheet is a basic secondary structural element of proteins. To provide a data resource for further analysis on "Sheet", a database which contains a large number of sheet structures was constructed.


The protein dataset utilized to populate the database was obtained from PDB, excluding those that have no sheet structure and those with modified residues, that is, the database is rigorous, precise and faithworthy, with no uncertain residues or modified residues or uncertain structures. The database now contains a total of 756,897 amino acids pairs in sheet structures of 10,704 proteins. There are more details in the publications.

The website interface is shown below:

Publication:

Ning Zhang, Jie Wu, Tao Zhang. SheetsPair: a database of amino acids pairs in protein sheetstructures. The 20th International CODATA Conference (CODATA2006 ABSTRACT，China，Beijing): 295

Ning Zhang, Jishou Ruan, Jie Wu, Tao Zhang. SheetsPair: a database of amino acids pairs inprotein sheet structures, Data science journal, 2007

An Epilepsy EEG Database

Research on Epilepsy EEG is a big part in our lab-- Biocomputation and Neuroinformatics Laboratory. By analyzing the EEG signals in rat models, we aim to find some way to predict seizures before they begin, which could be helpful for treatment of epilepsy. Some samples of human epilepsy EEG were also collected from hospitals and research centers. For the data formats are distinctive, there was some problems to analyze them together.

Being a preparation for a further investigation, an EEG database was constituted. EEG signals from healthy and epilepsy humans together with the annotations were collected and standardized in this database.

The website of this database is shown as below.



Publication: Zhang Ning,Wu Jie,Yang Zhuo,et al,Constitution of an EEG database based on SQL server. Chinese Chinese High Technology Letters,2006,16(12): 48-52.

Overview of the Databases

Several databases were constituted, including Sheetspair Database, ERPDB, epileptic EEG Database, and a database for Prediction of Protein Secondary Structures. These databases are created to make the data more effecient and simpler for further investigation. The data had been carefully parsed and standardized before they were stored into the databases, thus accurate and convenient sequences can be easily retrieved for further analysis. Also, the reorganized data can be shared in the web, and fresh data can be added in a simple way.

The databases above were constituted in Nankai University, all of them were based on SQL Server and websites were built for each database, providing friendly interfaces.

The details of these databases will be introduced in other articles of this blog.