# A Study on Electroencephalograph and the Brain

EEG or Electroencephalograph is a technique to measure the constant electrical activity taking place inside our brain. It is basically the diagnosis of our brain and it gives a clear picture of the minute activities that are taking place inside our highly complex brain. Doctors usually follow the 10/20 convention, in which electrodes are placed on our scalp which pick up the minute potentials that are generated by the neurons inside our brain. Sometimes an electrode may also be placed on our forehead or maybe our earlobe. This electrode is the reference electrode. With the help of amplifiers, these potentials are magnified to a level that can be reproduced on paper. The main aim or in other words, the main use of performing an EEG is to diagnose the various diseases which occur and which are related to the brain. One of them is Epilepsy, which affects millions of people in the world.

Epilepsy or commonly known as Convulsion or fits is a disorder of the brain in which the neurons fail to communicate with each other. The main reason for getting these unpredictable seizures or fits is a sudden rush in the electrical activity of the brain, which takes place due to the firing and interaction of neurons inside our brain.The main aim of this thesis is to analyze the three different Nonlinear methods to predict Epilepsy. The three methods are:-

1-Dynamical Similarity Index:-This method is a very dynamical method in the sense that it takes into account the reference electrode which is sometimes placed on the forehead or on the earlobe. The functioning is similar to that employed in the effective correlation dimension with the exception that in this method the values of electrode potentials are subtracted from the value of the reference electrode. Standard Deviation is calculated which acts as an indicator or a threshold which gives an accurate prediction of the onset of Epilepsy.

2-Increments of Accumulated Energy:- In this method, individual accumulated energy levels from the values or the various potentials that have been picked up by the electrodes that have been attached to a person’s skull are calculated. After plotting the graph, the mean of the Energy levels is calculated which gives an indication or in other words, it acts as a threshold value to predict the onset of epilepsy.

3- Effective Correlation Dimension:-In this method, value of the correlation dimension is determined from the values that have been picked up by the electrode potentials. Equation 4.4 gives the formula to calculate correlation dimension. Hence, a graph is plotted and from that the exact value of standard deviation is obtained which helps us to determine the exact onset of the epileptical activity.

Analyzation of the three different methods to predict epilepsy,gives us a clear understanding of what exactly is the electroencephalograph and how useful it can be in our lives. The methods have been studied in detail and they give us a clear picture of how to determine or predict correctly the onset of epilepsy. Also it becomes extremely important to discuss a very important phenomenon in today’s time that has a great impact. This is nothing but Neuromarketing.

Neuromarketing is nothing but applying the concepts of electroencephalograph in the field of marketing. Now the question arises to as to how are the concepts applied. Taking for example two different products or brands of pizza say, dominoes and pizza hut. Electrodes are placed on a person’s head and he is readied for Electroencephalograph. Marketing strategies of the two different firms are presented in front of him and his EEG is recorded. A fluctuation seen in the EEG for the two different products gives a fair amount of an idea to the examiner.

## Chapter 2

## Electroencephalograph

Electroencephalograph or commonly known as EEG is a technique that continuously monitors and records the electrical activity , taking place due to the continuous interaction and firing of neurons in the brain, by carefully placing electrodes on the scalp. It basically defines brain activity quantitatively, since it sums up the neuron activity which is operating in an unsynchronized and a completely random manner inside the brain [1,3,5].The diagnosis or prediction of many diseases related to the functioning of the brain, commonly known as neurological disorders, can be done by the continuous monitoring of EEG. It is an extremely effective way of predicting and diagnosing Epilepsy, a disease which affects nearly 1-5% of the world’s population. The main function of the EEG machine is to detect and record the countless signals produced by the brain cells and somehow reproduce the activity on paper. EEG is a harmless test and it does not induce any kind of physical pain on the person who is taking the test.

The EEG test report generally shows two types of results, which are:

NORMAL RESULT:-A normal result generally has a sort of predefined or in other words it is a typical electrical activity. Most of the people in the world, irrespective of the fact that whether or not they suffer from epilepsy, show a positive result. The reason being that the EEG test records the activity only during the time the test is done. Abnormal behavior or Abnormal EEG is observed only when the test is conducted when the epileptical activity begins.

The EEG on the next page is of a person who shows normal results.

Fig 2.1- Normal EEG [21]

ABNORMAL RESULT:- Abnormal patterns of EEG which largely deviate from the normal pattern are observed. Cases have been observed worldwide wherein, a person with no history of previous seizures and who does not suffer from Epilepsy, has got EEG results which have shown abnormal patterns. Therefore, to conclude it is perfectly alright to say that a normal result cannot rule out epilepsy and an abnormal result cannot simply conclude that a person suffers from epilepsy.

The figure on the next page is of a person who suffers from epilepsy the time the EEG recording took place.

It is very easy to differentiate between a normal EEG and an Abnormal EEG. As seen from figure 2.1 on the previous page, the normal EEG stays well in the limits that are predefined. On the other hand, t the EEG of a person who suffers from epilepsy at the time when the EEG is being recorded, it looks very different from that of a normal one which can be observed from figure 2.2 .

Electrodes C4-P4, P4-O2, F7-T3, P3-O1 and C6-P6 are seen to cross the threshold value in the case of the person suffering from epilepsy [7].

Fig 2.2- Abnormal EEG [21]

## 2.1 Clinical Recording Of EEG

EEG recording is done by placing electrodes on the scalp which pick up the potentials arising due to the continuous interaction and firing of neurons which take place inside our brain. The electric potentials generated by the neurons are extremely small to be picked up by the EEG. EEG, is therefore the summation of all the interaction of the millions and millions of neurons taking place inside our brain [4].

EEG electrodes are placed on the scalp, by a traditional standard known as the 10/20 system which is universally accepted. It consists of 21 electrodes, i.e. 21 electrodes are placed on different locations on the scalp.

FIG 2.3- Use of electrodes on a person to perform EEG [16]

From Fig 2.3 it is quite clear that the electrodes are placed on different locations of the scalp to record and pick up the EEG signals. EEG electrodes are generally much smaller in size compared to the ECG electrodes. The electrodes can usually be applied separately to the scalp and electrode jelly or some kind of electrode paste is used to improve the electrical contact. As we all know that technology is advancing rapidly in today’s world. We now have something which is known as the Needle Electrodes. In the case of needle electrodes, the electrodes are placed or pierced under the scalp to help record and monitor the neuron firing/potentials more carefully. Another very good advantage of needle electrodes is that they help in reducing the movement artefacts. The main disadvantage of needle electrodes is that the chances of infection increases considerably if they are employed .EEG electrodes should also offer good contact impedance. The general standard worldwide for good contact impedance is 5Kilo Ohm.

Other than the electrodes placed on the scalp, a reference electrode maybe placed on the forehead or any other part of the body. Collecting the Voltage difference between an electrode placed on a scalp with respect to a reference electrode is known as Monopolar Recording, whereas Bipolar Recording is when Voltage difference between two electrodes placed on the scalp is collected. Electrodes are generally located according to their position on the scalp.

FP- Frontpolar

F-Front

C-Central

O-Occipital

T-Temporal

P-Parietal

As the convention stands, Odd numbers which are subscripted with the Alphabet refer to those electrodes which are placed on the left hand side of the cranium and even

numbers denote those electrodes which are placed on the right hand side of the cranium. The Electrodes which are placed exactly on the middle of the cranium are represented by the alphabet Z.

A standard use of EEG or one of the main applications of it is in the diagnosis of Epilepsy.

Being a neurological disorder, Epilepsy is generally related to frequent and Unexpected seizures. The main aim of the EEG is to find any interictal activity or seizure and to determine the exact region of it. EEG’s are also used in the vital process of recording brain waves. They are :-

Alpha Waves:- 8.5-12 Hz. Associated with relaxed alertness.

Fig 2.4- spectrum of alpha waves [16]

Beta Waves:- 12Hz and above. Associated with active/anxious concentration.

Fig 2.5 – Spectrum Of beta waves [16]

3- Delta Waves:- Upto 4 Hz. Associated with sleep.

Fig 2.6 – Spectrum of Delta waves [16]

4- Theta Waves:- 4.5-8 Hz. Associated with light sleep. Prior to and waking up

after sleep.

Fig 2.7 – Spectrum of Theta waves [16]

## Chapter-3

## EPILEPSY

Epilepsy can be broadly defined as repeated occurrence of seizures(Commonly known as fits or convulsions).The main reason for getting these unpredictable seizures is a sudden rush in the electrical activity of the brain, which has been discussed earlier (due to the firing and interaction of neurons).In simple words, our brain is a complex structure where the neurons communicate with one another i.e transfer information by means of electrical impulses takes place but during a convulsion, this contact or communication is disrupted and this causes “FITS”[2].

Since it is a well known fact that our brain is the Mecca or the region for all the main functions of which are performed inside our body. Therefore, it becomes extremely important that the exact location of the seizure is found. Due to this particular reason, there are different types of seizures. But the reason that epilepsy occurs is still very unclear.

The two different types of seizures are:-

1- Partial Seizure:- Partial seizure is said to occur when the neurons, which are not functioning properly, that is , the neurons which are not able to transmit electrical impulses in a way that they should, are located in a particular region of the cranium and are not distributed uniformly.

2-Distributed Seizure:- Distributed seizure is said to occur when the neurons, which are not functioning properly, that is , the neurons which are not able to transmit electrical impulses in a way that they should, are distributed uniformly on the cranium. That means, it is not a particular region that is contributing towards the seizure but it is the entire region that is involved.

Epilepsy can be broadly classified in to three main categories. They are:-

Symptomatic:- In this kind of Epilepsy, the symptoms are generally because of a grave damage to the brain. It can be from birth, that is, a person is born with a slight defect or damage in his brain or the damage can be incurred during the course of his life time.

Cryptogenic:- In this kind of Epilepsy, damage to the brain has occurred but we generally have no evidence to support our conclusion. The symptoms, such as having difficulties to learn, difficulties in responding etc can suggest that damage to the brain has occurred.

Idiopathic:- In this kind of Epilepsy, there is no evidence or case which suggests that damage has been done and it cannot be found.

As of today, there is no reason which has been identified and which can be solely singled out which exactly determines the cause of epilepsy. For proper diagnosis of epilepsy, we would normally expect or want seizures to occur as frequently as they can so that they can be easily monitored [8]. There is no well defined cure for epilepsy and it requires proper monitoring by a well qualified doctor. In the coming sections, three methods, which are quite useful in predicting epilepsy, will be discussed in detail.

Fig 3.1- Epilepsy Study [23]

## Chapter -4

## Non Linear Analysis of EEG

There have been extensive studies on EEG which have employed signal processing techniques which are based on the assumption that EEG is a linear process or in other words it is a Gaussian process. Linear analysis techniques are very useful and efficient computationally as well as theoretically, but they use information which is retained in the second order function [14,16]. The major drawback of Linear Analysis is that the major chunk of information, which is stored in higher order functions, is ignored by it.

There has been ample evidence which proves that the amplitude distribution of the EEG very often tends to deviate from the Linear or the Gaussian behavior. A prime example to prove this would be that a person who is doing mental mathematics will have an EEG that deviates from the Gaussian behavior, that is, it exhibits Non-Gaussian states. Therefore Non-Linear Analysis of the EEG becomes extremely important to address the non-linear behavior of the EEG.

The three Nonlinear seizure prediction methods which will be analyzed are:-

1- Increments of Accumulated Energy:- The purpose of this method is to distinguish the preictal (before seizure) states from the Interictal (during seizure) states.

2- Dynamical Similarity Index:- Basic idea is to make a comparison of the sliding windowwith a fixed reference window, in a seizure free period.

3- Effective Correlation Dimension:- In this method, the correlation Dimension, D2, acts as a threshold and maximum deviation is calculated occurring under the threshold.

4.1 Increments of Accumulated Energy

The purpose of this method is to distinguish preictal states from interictal statems. The total Accumulated energy is based on average energy which is given by:-

For a time window kN

The Accumulated energy and its increments are given by:-

where m=1,2…,

The threshold value is said to be the mean of the accumulated energy levels. On the next page, a figure has been plotted on the software MatLab where, the electrode potential values where known. 4000 samples were taken into account and the time window was 1 second. The first figure is the MatLab plot of a normal patient, the second plot is of a patient who suffers from Epilepsy and finally, the third plot on the software MatLab is of the accumulated energy levels, which tells us to find the mean of the accumulated energies so that the threshold value can be calculated and an alarm can be buzzed whenever it crosses the mean.

Normal EEG

Fig 4.1- Normal EEG Plot

Epileptic EEG

Fig 4.2- Epileptic EEG plot

Accumulated Energy Levels

Fig 4.3- Accumulated Energy

Fig 4.4-Combined plot 1

Fig 4.5- Accumulated Energy of Combined plot 1

Fig 4.6- Combined Plot 2

Fig 4.7- Accumulated Energy of Combined plot 2

Fig 4.8- Combined Plot 3

Fig 4.9- Accumulated Energy of Combined plot 3

Fig 4.10- Combined Plot 4

Fig 4.11- Accumulated Energy of Combined plot 4

Fig 4.12- Combined Plot 5

Fig 4.13- Accumulated Energy of Combined plot 5

4.2 Effective Correlation Dimension

Before starting the discussion on Effective Correlation Dimension, it becomes extremely important to understand as to what exactly correlation dimension is.

As it is clear, any object (strictly speaking a geometrical object), can be represented with the help of points in the Geometrical or Euclidean space provided that the dimension, m, is quite large enough to be able to locate all the points individually. Therefore, a single point in space will have a dimension of 0, a line will have a dimension of 1, a plane surface will have a dimension of 2 and a solid will have a dimension of 3.

A fractal dimension is one in which it is not necessary to have real dimensions but fractional dimensions can also exist[11,13].

Fig 4.14- Fractal Dimension [14]

The above figures give a great amount of insight on the concept of fractal dimension. In the first part of the figure, there is only one square with size “d”. Therefore, €=d and M(€)=1. In the second figure, there are eight squares of size d/3. Therefore, €=d/3 and M(€)=8. In the third figure, there are 64 squares. Therefore, €=d/9 and M(€)=64. In general it follows that, for any division p, fractal dimension is:

## 4.3 Grassberger-Procaccia Algorithm

Grassberger-Procaccia Algorithm is based or relies on the approximation that the probability of two specific points in a set of similar size “r” is approximately or almost same to the probability that the same two points are differentiated by a distance ρ which is less than or almost equal to “r” [9,10].

(j) ||)--- Eq 4.4

Where the Heavyside function, θ is defined as:-

Θ(s)={ 1 if s>= 0 , 0 if s<0

The correlation sum is generally calculated for a wide variety of the range of radius. The mean of D or it follows that the average of the correlation Dimension serves or is an indicator for the threshold value. For any value of the electrode potential, dropping below this threshold, the time is measured and the maximum deviation is also measured.

Correlation Dimension – Normal Sample

Fig 4.15- Correlation Dimension of a Normal Sample

Correlation Dimension of Epileptic Sample

Fig 4.16- Correlation Dimension Of Epileptic Sample

Correlation Dimension for Combined Sample

Fig 4.17- Correlation Dimension for combined sample

4.3 Dynamical Similarity Index

Dynamical Similarity Index is the third and the last non-linear method which will be analyzed to predict the onset of epilepsy. This method is similar to the method studied before which is Effective Correlation Dimension. As discussed before, while performing an Electroencephalograph, the electrodes are placed on the person’s scalp. These electrodes then pick up the minute electric potentials which are naturally generated inside our brain [6,7,8].

In some of the cases, a reference electrode is generally placed on a person’s forehead or earlobe. Therefore or as a result of which, when the final output is observed, it is in terms of the difference of the potentials picked up by the electrodes placed on the person’s scalp and the reference electrode [6,7]. Instead of the Correlation Dimension, which was calculated in the previous method, In this method the aim is to find the similarity index, which is given by:-

() ||)--- Eq 4.5

Where the Heavyside function, θ is defined as:-

Θ(s)={ 1 if s>= 0 , 0 if s<0

From the above equation ,the main point which is interpreted is that the value of the electrode potential is subtracted from that of the reference electrode which gives a clear idea about how the dynamic similarity index is calculated.

Dynamic Similarity Index for Combined Sample

Fig 4.18- Dynamic Similarity Index for Combined sample

## Chapter 5

## Results

After having gone through the concepts regarding the Electroencephalograph, it becomes extremely to discuss a vital and important application of EEG which has come into prominence a lot in today’s world.

The application is nothing but Neuromarketing.

Now the question arises to as to what exactly is neuromarketing. Neuromarketing is nothing but applying the concepts of electroencephalograph in the field of marketing. In recent years, there was a strategy that was employed by many in the field of marketing comparing two products. The two products being in the car business, Toyota and Mercedes. People were subjected to different strategies by both the companies and simultaneously there brain activities were being monitored with the help of EEG. By monitoring it, the examiners were able to draw conclusions about the more powerful strategy and the strategy which had a greater impact on the people present.

It is very clear that our brain is the center or in other words the mecca of everything. It has a role to play in even the smallest of decision that we take. Therefore, it becomes very important to monitor it. Another application or in other words a deviation from the normal Electroencephalograph is the Narco analysis test which is performed on convicts to get the truth out. In simpler words, it is the Lie detector test. Electrodes are placed on the person’s head and after giving him a truth medication. Questions are asked and the fluctuations in the potentials in noted which is used to determine the authenticity of the answer.

The three different Non-Linear methods to predict the onset of epilepsy are very crucial in today’s time. Even though none of them give a 100 % accurate and precise result, but they bring with them a level of accuracy which can help us to predict epilepsy.The level of precedence in the accuracy levels of the three methods according to the simulations are as follows:-

1- Increments of Accumulated Energy

2- Effective Correlation Dimension

3- Dynamic Similarity Index

## Chapter 6

## Conclusion

This paper has presented a thorough analysis of the three different Non-linear methods to predict the onset of Epilepsy. Mathematical techniques and formulae were employed to get a clear picture. The concept of calculating the mean was used in Increments of Accumulated Energy, whereas the concept of Standard Deviation was employed for Effective Correlation Dimension and Dynamic Similarity Index.

A completely new study called the Magnetic Resonance Imaging (MRI) has also come up which also studies the functioning of the brain. Some of the advantages of EEG compared to MRI are:-

EEG machine hardware costs, which include various type of sensors are comparatively cheap when compared to those of MRI sensors.

EEG hardware (sensors) can also be used for various other applications, whereas the MRI sensors are used only for the heavy MRI machine

Some of the drawbacks of EEG compared to MRI are:-

EEG has a much lower resolution than compared to a MRI machine.

EEG sometimes aggravates claustrophobic conditions, which sometimes acts as a deterrent.

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