Quantification of seizures

tions in epileptology like how the propagating ictal discharges affect the ongoing electrical activity of the brain or why seizures terminate. Seizure dynamics have been investigated using many different mathematical methods, both linear and non-linear. Time course of seizure is a non-stationary process typically evolving from higher to lower frequencies; therefore the methods of time-frequency analysis are appropriate to estimate the seizure dynamics.

The most advanced method of time-frequency analysis—matching pursuit (Sect. 2.4.2.2.7) was used by [Franaszczuk and Bergey, 1999] to evaluate seizures originat- ing from the mesial temporal lobe. Periods of seizure initiation, transitional rhyth- mic bursting activity, organized bursting activity, and intermittent bursting activity were identified (Figure 4.15).The authors showed in a subsequent study [Bergey and Franaszczuk, 2001] that the complexity of the EEG signal registered from the location closest to the epileptic focus increases during a seizure.

The non-linear method based on the computation of the correlation dimension D2 was applied by [Pijn et al., 1991] for analysis of the time course of EEG recorded from different sites of the limbic cortex of rats. A comparison of the evolution of a seizure analyzed by means of correlation integral [Pijn et al., 1997] and matching pursuit1_{is shown inFigure 4.16[Blinowska, 2002].}

1_{Matching pursuit is a method in which no assumption about linearity or non-linearity of the signals is}

FIGURE 4.15: (SEE COLOR INSERT) From the bottom: signal, 2D time- frequency energy distribution obtained by means of MP, the same distribution in 3D. Courtesy of P. Durka, from [Durka, 2003].

At the beginning of the seizure (20–40 s) the occurrence of epileptic spikes re- sulted in a low value of D2; in time-frequency energy distribution it was reflected by very broad-band structures of short duration. During the period of chaotic behav- ior (60–80 s) characterized by flatness of the plot we can see random distribution of time-frequency structures. Interesting is the period (150–170s) when the system tends toward limit cycle, which is accompanied by a low value of D2. We can con- clude that time-frequency distribution obtained by MP algorithm reveals the dynam- ics of the signal and explains the behavior of D2preventing its misinterpretation.

The problem of spatial synchronization in the pre-ictal and ictal periods has at- tracted a lot of attention. It is usually approached by assessing the correlation struc- ture of multichannel EEG. Schindler [Schindler et al., 2007] found that the zero-lag correlations of multichannel EEG either remain approximately unchanged or, espe- cially in the case of secondary generalization, decrease during the first half of the seizure, then gradually increase before seizure termination. However, zero-lag cor- relation doesn’t give the full information on synchronization phenomena since there are phase differences between channels connected with the propagation of epileptic activity.

In [Schiff et al., 2005] canonical multivariate discrimination analysis based on sin- gular value decomposition was applied to search for dynamically distinct stages of epileptic seizures. The input values were: total power, total correlation at both zero

FIGURE 4.16: A comparison of the evolution of a seizure analyzed by means of correlation integral and matching pursuit. Top panel: the time sequence of plots of the correlation integral logC(ε,m) vs log(ε) (Sect. 2.5.2) obtained from 10-s epochs of the signal from rat hippocampus in the peri-ictal time. Adapted from [Pijn et al., 1997]. Bottom panel: Time frequency representation obtained by means of MP from the HCR signal shown in top panel and repeated at the bottom of the figure. From [Blinowska, 2002].

and arbitrary time lag, average phase amplitude (calculated by Hilbert transform), phase angle, and amplitude dispersion. The authors distinguished rhythmic partial onset, tonic middle and clonic terminal activity. In respect to the postulated hyper- synchronous character of seizures they reported that synchronization was a promi- nent feature only once the seizure had passed through its initiation phase and was a variable feature of seizure termination depending on the subject. We have to distin- guish here local synchronous activity of neurons which leads to the high amplitude of epileptic activity and hyper-synchronization in the larger spatial scale.

An interesting methodological approach to the assessment of synchronization of interictal and ictal EEG signals was presented by [Franaszczuk and Bergey, 1999]. They have used the multichannel autoregressive method of analysis that can be inter- preted in stochastic and deterministic framework. As a measure of synchronization they have used a value connected with the goodness of fit of MVAR model:

SY= logdet( ˆV) (4.3)

where det( ˆV)) is a determinant of the residual matrix ˆV of MVAR (Sect. 3.2). For a purely uncorrelated Gaussian normalized white noise, ˆV is a diagonal identity ma-

trix2, and SY = 1 setting the upper bound value for SY. For a purely deterministic linear system or a dynamical system of a periodic or quasi-periodic trajectory the ma- trix ˆV represents a covariance matrix of measurement errors, setting the lower bound value of SY . For chaotic or stochastic colored-noise systems the value of SY will be between these bounds. The quantity SY can be interpreted as a measure of order in the system. There is a close relationship between Shannon entropy and residual variance of an autoregressive process [Serio, 1992]. In case of multichannel process, high correlation between channels increases predictability. If channels are highly correlated, one channel can be predicted using other channels, the number of vari- ables necessary to describe dynamics of the system is lower, and the MVAR is better fitted, resulting in smaller values of SY . The changes to lower values of SY reflect higher spatiotemporal synchronization. The method was tested on a limited number of patients, however the results were very coherent. The relatively high and station- ary level of SY in the interictal EEG remote from seizure onset reflected much less synchronization. The minimum of SY always occurred shortly after the onset of a seizure, reflecting high regional synchrony. The level of synchronization remained high after a seizure for prolonged periods which may explain in part the phenomena of seizure temporal clustering often observed in patients. It seems that the method has a high potential for explaining the evolution of seizures and can be helpful in seizure detection [Jouny et al., 2005].

4.1.6.4.2 Seizure detection and prediction The study of epileptic EEG dynam-