Simulation in Correlation Dimension Circuit

Fig. 4-20 shows the waves of correlation dimension circuit for the first state.

The state READ_IN takes 2306 (for embedding dimension=11)/2308 (for embedding dimension=13) cycles, and we can see the calculation time of standard deviation overlaps the READ_IN state.

Fig. 4-20 Correlation dimension simulation for the first state

Fig. 4-21 Correlation dimension simulation results

READ_IN 2306 cycles

VECTOR_REF_SEL

Standard deviation overlaps READ_IN

Chapter 5 Experimental Results

In this chapter, we will show the experiment results of the algorithms, and the comparison with other important algorithms in recent years.

5.1 EEG Data and Patient Characteristics

The EEG data that we use are invasive EEG recordings of 11 patients suffering from medically intractable temporal lobe epilepsy. The data were recorded during an invasive pre-surgical epilepsy monitoring at the Epilepsy Center of the University Hospital of Freiburg, Germany (http://www.fdm.uni-freiburg.de/EpilepsyData/).

In eight patients, the epileptic focus was located in neocortical brain structures, in two patients in the hippocampus, and in one patient in both. In order to obtain a high signal-to-noise ratio, fewer artifacts, and to record directly from focal areas, intracranial grid-, strip-, and depth-electrodes were utilized. The EEG data were acquired using a Neurofile NT digital video EEG system with 128 channels, 256 Hz sampling rate, and a 16 bit analogue-to-digital converter. Notch or band pass filters have not been applied.

For each of the patients, there are datasets called "ictal" and "interictal", the former containing files with epileptic seizures and at least 50 min pre-ictal data. the latter containing approximately 24 hours of EEG-recordings without seizure activity.

At least 24 h of continuous interictal recordings are available for eight patients. For the remaining patients interictal invasive EEG data consisting of less than 24 h were joined together, to end up with at least 24 hours per patient (Table 5-1).

Table 5-1 Patient characteristics

Patient Sex Age Seizure type H/NC Origin Electrodes #Seizures Interictal (h)

1 f 15 SP, CP NC Frontal g, s 4 24

Seizure types and location: simple partial (SP), complex partial (CP), generalized tonic-clonic (GTC), hippocampal (H), neocortical (NC).

Electrodes: grid (g), strip (s), depth (d).

5.2 Seizure Prediction Statistics 5.2.1 Terminology

A seizure prediction method has to forecast an impending epileptic seizure by raising an alarm in advance of the seizure onset. A perfect prediction method indicates the exact point in time when a seizure occurs. This ideal behavior is not expected for current prediction methods that analyze EEG data. The uncertainty can be considered by use of the seizure occurrence period, SOP, which is defined as a time period during which the seizure is to be expected (Fig. 5-1). In addition, to permit a therapeutic intervention, a minimum window of time between the alarm raised by the prediction method and the beginning of SOP is essential. This window of time is called the seizure prediction horizon, SPH.

Taking into account the two time periods SPH and SOP, a correct prediction is

defined as follows: after the alarm signal, during SPH, no seizure has occurred yet.

During SOP, a seizure occurs.

Fig. 5-1 Defining the SPH and SOP

Thus, the sensitivity was defined as the number of seizures predicted divided by the total number of seizures recorded.

the number of seizures predicted Sensitivity

total number of seizure recorded

= (5.1)

The False Positive Rate (FPR) was defined as the average number of warnings that no seizure occurs within SOP after SPH per hour.

the number of warnings that no seizure occurs

FPR= EEG recording length (h) (5.2)

5.2.2 Seizure Prediction Results

To evaluate the WCDSP, a prediction was considered to be true if a seizure occurred within 1 h after a warning was observed and false otherwise. That is, a time horizon of 1-h period was chosen for the evaluation of the prediction results of the algorithm. Long time horizons obviously improve the sensitivity of the algorithm but also increase the uncertainty about the exact time of the next seizure. Short time horizons decrease the sensitivity and specificity.

Seizure Prediction

Horizon (SPH) Seizure Occurrence Period (SOP)

Alarm Seizure onset

time

Table 5-2 Performance of WCDSP for the optimal setting over all patients (SPH = 1h, SOP = 18s, p1 = 11, p2 = 13, threshold1 = 0.95, threshold2 = 0.85,

interval = 33)

Sensitivity False Positive Rate Average Prediction Time Patient

The algorithm was tested under two cases. In the first case, we evaluated a range of parameter settings (threshold1, threshold2, interval) to find the optimal result, when applied to all eleven patients (see Table 5-2). Under this condition, we obtain the parameter settings with p1 = 11, p2 = 13, threshold1 = 0.95, threshold2 = 0.85, and interval = 33. The sensitivity ranged from 66% (patient 3) to 100% (patient 2, etc.), with an average of 87% sensitivity overall. For example, the algorithm correctly predicted 75% (3/4) of seizures in patient 7 with FPR = 0.1/h, and 100% (4/4) of seizures in patient 1 with FPR = 0.3/h. On average, the algorithm gives alarms approximate 27 minutes before each seizure.

In the other case, we have the optimal parameter settings for each individual patient.

5.3 Comparison with other Prediction Methods

There have been few studies about seizure prediction algorithm. In the thesis, we will discuss with the difference between our proposed and others in Table 5-3.

In 2008, Bruno Direito1 [12] proposed an algorithm based on energy-wavelet with a sensitivity of 40% and false prediction rate of 0.4/h. V. Navarro’s [13] and Le van Quyen’s [1] algorithms using similar index achieve sensitivities of 83% and false prediction rates of 0.3/h in 2002 and 1999, respectively. In 2003, F. Mormann proposed an algorithm [2] based on synchronization decrease with a sensitivity of 81%. Maryann D’Alessandro et al. [14] presented a method of hybrid-feature with a sensitivity of 62.5% and false prediction rate of 0.27/h. Leon D. Iasemidis [7]

proposed an algorithm by using short-term Lyapunov exponential to estimate the LLE, called ASPA, with a sensitivity of 84% and false prediction rate of 0.12/h.

Table 5-3 Comparison with other algorithms

2008[12]

Our proposed algorithm achieves a higher sensitivity of 86.69% with a slightly larger false prediction rate of 0.254 than others. Moreover we have the prediction time of 27 minutes witch is much longer than most of the others for a therapeutic intervention.

Fig. 5-2 Sensitivity and FPR comparisons with other algorithms

In Fig. 5-2, we show the comparison results of sensitivity and FPR. The bars of the chart represent the result of sensitivity and the line represents the one of FPR.

Chapter 6

Conclusions and Future Works

In this thesis, we have proposed the WCDSP algorithm based on wavelet analysis, and chaos theory. The experiment results for several patients were shown with a high sensitivity with respect to prediction of epileptic seizures. The time horizon for a seizure prediction was set at 1 h and the average prediction time over all patients was about 27 min/seizure. The interval is sufficient for a therapeutic intervention. Not only a more reliable algorithm is presented, a VLSI implementation of the seizure analysis IP is also made for applications in portable device, such as VNS.

In the future, we may improve the prediction sensitivity and lower the false positive rate (FPR) by the two approaches:

(1) Hilbert-Huang transform:

The Hilbert-Huang transform (HHT) is NASA's designated name for the combination of the empirical mode decomposition (EMD) and the Hilbert spectral analysis (HSA).

It is an adaptive data analysis method, which improves accuracy by using an adaptive basis to preserve intrinsic properties of data, designed specifically for analyzing data from nonlinear and non-stationary processes, e.g. EEG signals. It yields results with more physical meaning and a different perspective than existing transforms.

Table 6-1 Comparison between Fourier, wavelet, and HHT

Fourier Wavelet Hilbert

Basis a priori a priori adaptive

energy-frequency energy-time- frequency

Base theory complete theory complete empirical

By HHT, we may obtain more important information to enhance the prediction results.

(2) Independent Component Analysis (ICA) :

In recent years, Independent Component Analysis (ICA) has been proved as a powerful algorithm to solve blind source separation (BSS) problems in a variety of signal processing applications such as speech, image, or biomedical signal processing.

The EEG is composed of electrical potentials arising from several sources.

Each source (including separate neural clusters, blink artifact, or pulse artifact) projects a unique topography onto the scalp, called "scalp maps." These maps are mixed according to the principle of linear superposition.

Independent component analysis (ICA) attempts to reverse the superposition by separating the EEG into mutually independent scalp maps, or components.

Fig. 6-1 ICA decomposition

We can apply ICA to multi-channel EEG recordings and remove a wide variety of artifacts from EEG records by eliminating the contributions of artifactual sources onto the scalp maps. It may lead to noiseless signals and we could more easily extract useful features to increase the sensitivity.

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