**4. Epileptic seizure prediction based on Fourier-Bessel function**

Any signal can be represented in terms of Fourier Bessel series due to its decaying nature. An EEG signal is expanded into a Fourier Bessel series [2]. In this way, an EEG signal can be segmented and periods interictal and ictal are classified to predict the occurrence of seizure.

*First plot shows original signal followed by segmented EEG seizure signal of inter ictal period.*

A 1–1 mapping exists between the frequencies and the coefficients. *fs* = 256 and n = 128 (number of Fourier Bessel Coefficients).

All the **Figures 5**–**7** show the segmented bands of a seizure signal.

The five features energy in each sub band, fmean, IQR and MAD are extracted from each sub band.

The **Figure 8** shows the sum of all Bessel coefficients the preictal and interictal features are discriminating.

#### *Epilepsy - Update on Classification, Etiologies, Instrumental Diagnosis and Treatment*

**Figure 7.** *First plot shows original signal followed by segmented EEG seizure signal of pre-ictal period.*

**Figure 8.** *Absolute sum of Bessel coefficients with red being Preictal and blue being Interictal EEG signals.*

**Figure 9.** *MAD of coefficients with red being Preictal and blue being Interictal EEG signals.*

From the **Figure 9** it can be observed that the feature, Median absolute deviation of Fourier Bessel coefficients for the Interictal and preictal are discriminating.

The inter ictal and pre ictal data is prepared as per the information in **Table 7**. The calculated Fourier-Bessel Coefficients from inter ictal and pre ictal data is given to Neural Network with 64 input neurons, one output neuron and one hidden layer. The Feed Forward Back propagation algorithm was used as shown in **Figure 10**. The network is trained 1 as target for inter -ictal and + 1 for pre-ictal.

The trained network is simulated with Inter-ictal and Pre-ictal data. There was one epoch as false negative and zero epochs as false positives. The simulation results had garnered 150 epochs of inter -ictal and 150 epochs of pre-ictal data. Inter ictal period is used to study sensitivity where as the pre ictal data is used for specificity.

The number of false negative values should be low so that it should have high sensitivity. The specificity must be high with lower false positive values. From **Table 8**, it is observed that sensitivity, specificity and accuracy of the


#### **Table 7.**

*Mapping of frequencies to the Fourier-Bessel coefficients.*

#### **Figure 10.**

*The neural network architecture used above contains three layers: 64 neuron input layer, 1 neuron output layer and a hidden layer in the middle which also has 64 neurons.*


#### **Table 8.**

*Seizure information of Subject-1 with timing in seconds.*


#### **Table 9.**

*Sensitivity, specificity and classification accuracy.*


#### **Table 10.**

*Seizure information of Subject-2 with timing in seconds.*


#### **Table 11.**

*Sensitivity, specificity and classification accuracy.*

proposed method is superior and the seizure is predicted before 5 minutes for subject 1 (**Table 9**).

The inter-ictal and pre ictal data is prepared as per the information in **Table 10**. The trained network is simulated with inter-ictal and pre-ictal data. There were zero epochs as false negative and zero epochs as false positives.

The simulation results of 150 epochs of inter-ictal and 150 epochs of pre-ictal data have been tabulated as above in **Table 11**.

The number of false negative and false positive values was minimum due to the fact that the testing was done for shorter periods.

From **Table 11** it is observed that for shorter periods under consideration seizure is predicted before 5 minutes for subject 2 with 100% accuracy.

#### **5. Epileptic seizure prediction based on localization**

The selection of data was done a bit different from the previous works. Care has been taken to reduce the effects of post seizure by taking a minimum gap of 2 hours in the inter-ictal period.

Using the EEG data as compiled from above, IMF's are extracted using the EMD technique. Using these IMF's, features such as Kurtosis, Inter-quartile range and Median Absolute Deviation are extracted. The following **Figure 11** shows the steps involved in the study for prediction. The extracted features are used for training the Neural network and the results are tabulated.

For patient 8, source has been localized as discussed in the topic of source localization. It has been observed that 4 channels 6,8,20 and 21 have been the most significant channels. These channels are decomposed into 4 IMF's out of which 3 significant features are extracted thus a total of 4x4x3 = 48 features are extracted.

600 preictal and interictal epochs of 2 second duration are considered respectively, which means 1200 epochs (600 + 600 = 1200) with 48 features add up to a total input vector of 1200x48 to the neural network. This is tabulated as shown below in **Table 12**.

#### **Figure 11.**

*Steps involved in epileptic seizure prediction using epileptic zone. It is divided into three parts. 1) the first part extracted the IMF's while in the second part 2) features are extracted from these IMF's. These features are given as 3) input to the neural network in the third part.*


#### **Table 12.**

*An overview of the input vector to neural network.*

The following results were obtained in this method (**Table 13**):

The concept is extended to all the patients whose source has been localized as shown in below **Table 14**.

The prediction method is run on the entire channels localized from the source as derived from **Table 14**. The results are as shown in the **Table 13**. The above results are obtained for data of short intervals (**Table 15**). A testing has been run for continues data whose results are as shown in the figures below.

When a seizure free data is considered, there is a chance for false alarm. Consider the **Figure 12** where the result of testing of continuous seizure free data is shown.


#### **Table 13.**

*Sensitivity, specificity and classification accuracy using epileptic zone for prediction.*
