# Spatiotemporal dynamics of interictal spikes.

INTRODUCTIONEpilepsy is a widely prevalent neurological disorder affecting around 50 million people worldwide and has been classified as the third most common neurological disorder next to stroke and Alzheimer's. There are two distinct neuronal hallmarks that characterize epilepsy: epileptic seizures and epileptic spikes. Epileptic spikes are high amplitude (>50 V) fast electrographic activity, sometimes followed by a slow wave, and last for only a couple of hundreds of milliseconds when recorded at the brain surface (e.g. via scalp electroencephalography--scalp EEG). Although spikes have been recognized as a diagnostic tool for epilepsy, the cause of their occurrence is still unknown. Spiking may occur interictally, preictally (before seizures) and postictally (after seizures), and the neural networks generating seizures and spikes may be different from each other. A quantitative analysis of spiking in patients with temporal lobe epilepsy by Lieb et al [1] has revealed that the epileptogenic focus (the region of the brain that triggers a seizure) generates spikes at maximum mean spiking rate and minimum coefficient of variation, and minimum variance in inter-spike intervals. The study suggested that spikes can be used as biomarkers for identification of the epileptogenic focus. Also, spatiotemporal changes in preictal spike activity in human temporal lobe epilepsy [2] revealed that the degree of bilateral interdependence in medial temporal lobe spike activity increased prior to onset of a seizure, thus indicating that spikes may herald the interictal to ictal transition. Contrary to the notion that epileptic spikes are precursors to seizures, postictal increase in spike rate in human focal epilepsy was reported independently by Gotman [3] and Katz et al. [4]. Most of the studies relating epileptic spikes and seizures have been quantitative in nature but limited to analysis of either spike rate or spike location. Herein we investigate the spatiotemporal evolution of epileptic spikes themselves and its predictive value for an impending seizure.

METHODS

Spike Synchronization Measure (SSM)

SSM is a normalized measure of spike synchrony that is parameter-free, time-scale adaptive and sensitive to both spike rate and the number of coincident spikes [5]. The measure is computationally fast and relies on the differences between spike times in two spike trains under consideration and their interspike intervals. Consider two point process x and y containing [M.sub.x] and [M.sub.y] spikes respectively. Let [t.sup.x.sub.i] and [t.sup.y.sub.j] denote the occurrence times of spikes in process x and y respectively. Let {[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]} be the time series containing the spike times of x and y respectively. We define [e.sup.i](x|y) for spike i in process x as

[e.sup.i] (x|y) = 0.5 exp (-[d.sup.x,min.sub.i]/([t.sup.x.sub.i+1]-[t.sup.x.sub.i])) i [member of] [1, 2, ... .. [M.sub.x]]

Where [d.sup.x,min.sub.i] = min ([t.sup.y.sub.j] - [t.sup.x.sub.i]) for j [member of] [1, 2, ... .. [M.sub.y]], that is, the difference in spike time [t.sub.i] of process x from the time of the next occurring spike in process y. Similarly we estimate [e.sup.i] (y|x) for spike i in process y. Now we combine e(x|y) and e(y|x) in one symmetric measure as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The SSM measure Q takes values in [0, 1], with 0 when spike trains are desynchronized and 1 when there is perfect coincidence of spikes. By using the interspike interval [t.sup.x.sub.i+1] - [t.sup.x.sub.i] of the point process under consideration in the exponential decay function, we normalize SSM with respect to the firing rate of the process making it robust to dynamical changes of spike rate. (1)

RESULTS

Long-term (days) continuous intracranial EEG recordings from two patients, who underwent presurgical evaluation for localization of their epileptogenic focus at the epilepsy monitoring unit (EMU) of Shands Hospital in Gainesville, Florida, were analyzed (see Table 1). Informed consent for participation in this study was obtained from the patients. The EEG was recorded by a Nicolet BMSI 4000 EEG machine at sampling rate of 200 Hz and with an average common reference and band-pass analog filter settings of 0.1 Hz -70 Hz. Depth electrodes were placed in the right and left hippocampi, two subdural strips were placed at right and left orbitofrontal lobes, and two subdural strips were placed at right and left subtemporal lobes.

Per electrode site, epileptic spikes were detected for the entire duration of the EEG recordings using improved morphological filtering with adaptive structure elements as described in [5]. The SSM measure of spike synchronization was estimated for each patient from successive EEG segments of 30.72 seconds duration and overlapped by 10.24 seconds per pair of electrodes for the whole EEG recording. Figure 1 shows the average synchronization profile across all pairs of electrodes and across all seizures for the two patients. For both patients, increased synchronization in the preictal and desynchronization in the postictal periods can be observed. These results are similar to our previous synchronization studies where we observed preictal synchronization and postictal desynchronization between pairs of electrodes in terms of their Lyapunov exponents [6-7].

Finally, to quantify the dynamical changes around seizures, we developed a measure of resetting similar to the method discussed in [8]. Given the set of profiles and for a time point t, for each pair of sites (i,j) we define as [Q.sup.pre.sub.ij] (t) the vector that has components the spike synchronization values within a preictal window [w.sub.pre](t) = {t--60 * 10.24, ..., t}, and [Q.sup.post.sub.ij] (t) the vector of spike synchronization values in the postictal window [w.sub.post](t) = (t + [d.sub.sz], ..., t + [d.sub.sz] + 60 * 10.24], where [d.sub.sz] = 5 min is taken as the maximum duration of a seizure. Mann-Whitney's U test is employed to compare the distribution of [Q.sup.pre.sub.ij](t) and [Q.sup.post.sub.ij] (t). Since Mann-Whitneys U test can only suggest that the distributions are different, we performed a Z-test to test whether the mean of one distribution is larger than the other. We define the resetting power ([RP.sub.q] (t)) at time t as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where [THETA] (A) is the Heaviside step function and is equal to 1 when A is true and is equal to 0 when it is false, and [Q.sup.pre.sub.ij] (t) [not equal to] [Q.sup.post.sub.ij] (t) denotes the result of the U-test. [Z.sub.thr], the statistical threshold for the Z-score, was set to 4 (corresponding to a significance level of p < 0.001), and [N.sub.e] is the number of available electrode sites. By using a high Z-score threshold we ascertained that only pairs of sites that have significant change in [Q.sub.ij] were selected. The distribution of [RP.sub.Q] at interictal and during seizures for the two patients is shown in Figure 2.

To statistically validate the significance of resetting at seizures compared to interictal, we defined the resetting score ([SRP.sub.Q] ([t.sub.0])) at time [t.sub.0] as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [N.sub.rec] is the recording length of the EEG. The resetting score quantifies how unlikely it is to observe large resetting power at random times t anywhere in the entire EEG recording compared to those at time [t.sub.0] (seizure times). Since [SRP.sub.Q] is an independent measure of overall resetting power, we can compare the values of [SRP.sub.Q] across patients. Each [SRP.sub.Q] can be perceived as the p value of testing if "resetting at time [t.sub.0] is significantly different than any time in the interictal period". Finally we estimated the combined p value for each patient by using Fischer's method for combining p. The method has been previously described [8]. For the two patients, these combined p values were found to be less than 0.001 and hence we can state that statistically significant resetting occurs mostly at epileptic seizures than at any random point in the interictal periods.

DISCUSSION AND CONCLUSIONS

Previous studies on prediction of epileptic seizures have revealed the existence of a preictal period where the dynamics of different brain sites become entrained (synchronized). The existence of a preictal period provides us with a time window for intervention to prevent seizure occurrence [9-11]. However, the physiological substrate of the observed entrainment of dynamics has not been established yet. In this study we investigated whether preictal synchronization of epileptic spikes could constitute such a physiological substrate. We observed that synchronization of epileptic spikes occurs in the preictal periods and dynamical desynchronization in the postictal periods. Also, the presence of preictal synchronization hours to minutes prior to the onset of the ictal state indicates a possible predictive value of interictal spikes. Further, these observations suggest that epileptic seizures might have an antagonist effect on spiking, reflecting a physiological mechanism for resetting of the spiking by seizures (e.g., ictal activity may severely deplete critical neurotransmitters and deactivate critical neuroreceptors for generation and propagation of spike activity). The relationship between spikes and seizures depends on the applied spatiotemporal meta-analysis and could partially explain the inconclusive and at times conflicting results in the literature about epileptic seizures and spikes. Therefore, appropriate analysis of the EEG could lead to further elucidation of the mechanisms of ictogenesis and epileptogenesis. Extension of this study to more subjects and into the role of epileptogenic focus in the generation of epileptic spikes and ictogenesis is currently underway.

REFERENCES (4)

[1] J. P. Lieb, S. C. Woods, A. Siccardi, P. H. Crandall, D. O. Walter & B. Leake, "Quantitative analysis of depth spiking in relation to seizure foci in patients with temporal lobe epilepsy," Electroencephalogr. Clin. Neurophysiol., vol. 44, pp.641-663 1978.

[2] H. H. Lange, J. P. Lieb, J. Engel Jr. & P. H. Crandall, "Temporo-spatial patterns of preictal spike activity in human temporal lobe epilepsy," Electroencephalogr. Clin. Neurophysiol., vol. 56, pp. 543-555, 12, 1983.

[3] J. Gotman, "Relationships between interictal spiking and Seizures--Human and Experimental evidence," Canadian Journal of Neurological Sciences, vol. 18, pp. 573-576, 1991.

[4] A. Katz, D. Marks, G. McCarthy and S. Spencer, "Does interictal spiking change prior to seizures?" Electroencephalogr. Clin. Neurophysiol., vol. 79, pp. 153-156, 1991.

[5] B. Krishnan, I. Vlachos, A. Faith, S. Mullane, K. Williams, A. Alexopoulos, & L. Iasemidis. "A Novel spatiotemporal analysis of peri-ictal spiking to probe the relation of spikes and seizures in epilepsy," Annals of Biomedical Engineering, 42(8), 1606-1617, 2014.

[6] L.D. Iasemidis, J.C. Principe & J.C. Sackellares, "Measurement and quantification of spatiotemporal dynamics of human epileptic seizures", In: Nonlinear biomedical signal processing, ed. M. Akay, IEEE Press, vol. II, pp. 294-318, 2000.

[7] L.D. Iasemidis, D. S. Shiau, J. Sackellares, P. Pardalos and A. Prasad, "Dynamical resetting of the human brain at epileptic seizures: application of nonlinear dynamics and global optimization techniques," IEEE Transactions on Biomedical Engineering, vol. 51, pp. 493-506, 2004.

[8] B. Krishnan, A. Faith, I. Vlachos, A. Roth, K. Williams, K. Noe, J. Drazkowski, L. Tapsell, J. Sirven and L. Iasemidis, "Resetting of brain dynamics: epileptic versus psychogenic nonepileptic seizures," Epilepsy & Behavior, vol. 22, pp. S74-S81, 2011.

[9] N. Chakravarthy, K. Tsakalis, S. Sabesan & L.D. Iasemidis, "Homeostasis of brain dynamics in epilepsy: a feedback control systems perspective of seizures," Annals of Biomedical Engineering, vol. 37, pp. 565-585, 2009.

[10] L. Good, S. Sabesan, S. Marsh, K. Tsakalis, D. Treiman & L.D. Iasemidis, "Control of synchronization of brain dynamics leads to control of epileptic seizures in rodents," Int. J. Neural Systems, vol. 19, pp. 173-196, 2009.

[11] L.D. Iasemidis, "Seizure prediction and its applications," Neurosurg. Clin. N. Am., vol. 22, pp. 489-506, 2011.

Balu Krishnan *, Ioannis Vlachos (#), Aaron Faith (^), Stephen Mullane (+), Korwyn Williams (~), Leonidas Iasemidis (#)

Cleveland Clinic Foundation *, Cleveland, OH; Louisiana Tech University (#), Ruston, LA; Phoenix Children's Hospital (~), Phoenix, AZ; Arizona State University (^), Tempe, AZ; Biotronik (+), Lake Oswego, OR.

Table 1: Patient and EEG Data Characteristics Patient ID # of Recording # of Seizures electrodes Duration Sub-clinical Clinical P1 28 143.4 Hrs 10 9 P2 28 322.8 Hrs 7 10 Patient ID Focus (clinical assessment) P1 Right Anterior Mesial Temporal P2 Right Temporal

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Author: | Krishnan, Balu; Vlachos, Ioannis; Faith, Aaron; Mullane, Stephen; Williams, Korwyn; Iasemidis, Leoni |
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Publication: | Journal of the Mississippi Academy of Sciences |

Article Type: | Report |

Date: | Apr 1, 2015 |

Words: | 2067 |

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