blacksimo/eeg-analysis

EEG-Analysis

The complete report can be found HERE

Introduction

Electroencephalography (EEG) is an electrophysiological monitoring method to record electrical activity of the brain. The EEG signals used in this paper, recorded during subject’s resting state, have been deeply analysed in order to allow us to study how information flows through different brain regions and understand the network activity organization, quantifying brain connectivity properties. The aim of this analysis is a biological interpretation of the above-mentioned signals and further predictions for a potential engineering application. In this work will be shown a comparison between results obtained from EEG of the subject with open and closed eyes. The analysis will compare and reason on results obtained through the application of methods and study algorithms on two different dataset.

Development Environment and Tools

The programming language Matlab has been chosen due to its easy management of huge data as EEG signals and due to several specific available tools. The following list shows all the tools and libraries that have been used in this work:

• Bioinformatics Tools Matlab

• Brain Connectivity Toolbox

• eMVAR - Extended Multivariate Autoregressive Modelling Toolbox

• edfRead - Read European Data Format file into MATLAB

The dataset processed by our algorithms refer to Subject 070 of the dataset available at EEG Motor Movement / Imagery Dataset . Only the first two runs (S070R01 and S070R02) have bben used for this project: R01 is recorded during eyes-open (EO) resting state; R02 is recorded during eyes-closed (EC) resting state.

Analysis of the results

In the following section will be presented and analyzed the results of the tests are described in Table [tab:task_and_classes], according to the project requests. The analysis of the results has been divided into various study topics presented below.

Connectivity Graphs

In order to gain a better understanding of the brain we choose the analysis method that fall into the category of frequency domain. In particular thanks to the use of the use of the framework edfRead , we are able to access the data structure containing values that defines the frequency curve of 64 electrodes placed on different regions of the brain. In the frequency domain we can make use of the spectral estimators, based on Multi-Variant Autoregressive Models, Partial Directed Coeherence and Direct Transfer Function. The application of these two algorithms is shown in Fig.[fig:OpenEYE1.1e1.2] and Fig.[fig:ClosedEYE1.1e1.2], in which we see the mean of Adjacency Matrix and Coherence Matrix of all the 64 channels, from both PDC and DTF. This give us an idea of the strength of a connection between a couple of channels. The results have been obtained with while loop to make the network density equal to 20% through the search of a proper threshold. From a quick look of the two images we can conclude that, for both closed and open eyes, the brain activity comes from the same regions, under the same stimulus. In Fig.[fig:OpenEYE1.3] and Fig.[fig:ClosedEYE1.3] are shown results obtained by the application of PDC algorithm with several densities: starting leftmost the percentages are: 1%, 5%, 10%, 20% 30%, 50%. It can be noticed how the increasing density brings the network to a more dense connection status between brain regions. Comparing instead the open and closed eyes version, we can again notice that regions involved during stimulus are mostly the same. PDC application is then compared to the Asymptotic PDC algorithm Fig.[fig:OpenEYE1.4] on a selection of 19 channels, shown in Fig.[fig:List19Channels], with a density value of 5%. Through the use of this particular algorithm, which makes the sample growing to infinite, we can see where the connections between channels totally disappear. Moreover, Fig.[fig:OpenEYE1.5] and Fig.[fig:ClosedEYE1.5] are a topological representation of the above-mentioned network in which we can graphically visualize nodes, edges and directions of the filtered signals. This is obtained through the extraction of the adjacency matrix output from PDC filtering. All the tests and analysis above-mentioned are made on a frequency range between 8Hz and 13Hz, which corresponds to the Alpha Waves of signal. The same algorithms mentioned before has been applied on a frequency range between 14Hz and 30Hz, which is relative to the Beta Waves. This is shown in Fig.[fig:OpenEYE1.6] and Fig.[fig:ClosedEYE1.6], were we can see that our brain regions are frequency-specific.

Graph Theory Indices

From now on, if not specifically mentioned, we are gonna make use of signals from 64 channels in the range of alpha waves and a network density of 3%. The use of graph theory allow us to transform a complex network like our brain, into a mathematical model from which it is possible to extract useful information. By modeling the structure of the brain as nodes (i.e. brain areas) and edges (i.e. anatomical and functional connections) it is possible to understand the organization of the network and quantify the connectivity properties of the brain in order to study how information flows between different regions of the brain. Through the use of the adjacency matrix mentioned in the previous section, we analyzed the Clustering Coefficient data shown in Fig.[fig:OpenEYE2_1_cc] and Fig.[fig:ClosedEYE2_1_cc]. Those values represents the tendency of a graph to be divided into cluster and moreover the modular nature of the brain in terms of activities and organization. From the comparison between open and closed eyes we can notice that this nature is amplified when we keep our eyes opened. The following table shows, during the various tests performed, the average path length obtained for both weighted and unweighted network. In all the four case we can notice such a small number, that makes us sense the easiness of nodes to communicate between each other.

	WEIGHTED	UNWEIGHTED
Closed Eye	0.000825043345541398	0.006660772178014
Open Eye	0.00720517771579775	0.000754489076568139

Average Best Path Length

The use of graphs allows us to analyze other important features of the connections that are established in a network, such as the in-degrees, out-degree that correspond respectively to the quantity of output and input connections in a directed graph. In Fig.[fig:OpenEYE2_3PDC], Fig.[fig:ClosedEYE2_3PDC], Fig.[fig:OpenEYE2_3DTF] and Fig.[fig:ClosedEYE2_3DTF] the 10 highest channels of the network in terms of in-degree, out-degree and total degree for PDC and DTF application. It is possible to notice how in both datasets and in both study methods the nodes that establish greater and their neighbors in-going connections are always the same. This makes it possible to notice that some brain regions are mostly used in receiving stimuli for both conditions of open and closed eyes. The same method of study and the same data gathering algorithm was then applied to the weighted version of the graph coming from PDC method. In Fig.[fig:OpenEYE2_7_cc] and Fig.[fig:ClosedEYE2_7_cc] are shown results of clustering coefficients for both dataset.

Motif Analysis

Another aspect of the representation of the neural network, that can be deducted from the graph, concern the presence of Motif. It represents sub-sequences of nodes and edges of the network that occur with high frequency. In particular they can be divided into 13 main isomorphism for patterns composed of 3 nodes, as shown in Fig.[fig:MOTIF]. In Fig.[fig:OpenEYE3_1] and Fig.[fig:ClosedEYE3_1] are shown those classes and their frequency in the analyzed network. Is, therefore, particularly important the repetition of the first isomorphism shown in Fig.[fig:MOTIF], which is composed of the sequence A(\xrightarrow{})B(\xleftarrow{})C and appears in both datasets over 900 times and 600 times respectively which make us think that more than one signal are combined by some nodes to reach its goal. For this recurrent Pattern is shown a topological representation in Fig.[fig:OpenEYE3_2] and Fig.[fig:ClosedEYE3_2]. In Fig.[fig:OpenEYE3_3] and Fig.[fig:ClosedEYE3_3] are shown the main motifs concerning the node relative to the "PO3" channel, which is located in the parieto-occipital scalp region. It has to be noticed that the type 1 isomorphis, in the situation of receiving stimuli with open eyes is almost twice as often than the situation of closed eyes probably due to a greater number of input to process. The same analysis made to find motifs composed of 3 nodes, was then proposed again with the aim to look for patterns that include 4 nodes. In this case the possible isomorphisms are 199 and in Fig.[fig:OpenEYE3_4] and Fig.[fig:ClosedEYE3_4] are shown the results obtained on the 64 channels network.

Community Detection

Finally in Fig.[fig:OpenEYE4_1] and Fig.[fig:ClosedEYE4_1] are shown, respectively for open and closed eyes, different regions of channel interactions, called Community Detection. They are subsets of vertices with denser connections within them and sparser connections between them. We can notice that in the open eyes condition, bigger cluster of nodes are grouped together in the same community. In Tab.[tab:community_detection] are listed the nodes quantity of the above mentioned images regarding brain connections.

	Open Eyes	Closed Eyes
Group 1	39	11
Group 2	10	20
Group 3	25	13
Group 4	-	20

Number of the communities and nodes

Conclusion

To conclude, the brain studies through the use of graph theory allow us to unearth useful information about data flow and its distribution within various brain regions. It has been possible to analyze several different interactions happening in different regions of the brain of a subject exposed to a series of stimuli with open and closed eyes in rest conditions. We understood and qualified similarities and differences within active nodes connections. The used algorithms let us transform merely electric signals recorded from EEG channels into mathematical data to model and visually represent a cerebral map of our beautiful brain.