Detection of seizure rhythmicity by recurrences

Abstract

Epileptic seizures show a certain degree of rhythmicity, a feature of heuristic and practical interest. In this paper, we introduce a simple model of this type of behavior, and suggest a measure for detecting and quantifying it. To evaluate our method, we develop a set of test segments that incorporate rhythmicity features, and present results from the application of this measure to test segments. We then analyze electrocorticogram segments containing seizures, and present two examples. Finally, we discuss the similarity of our method to techniques for detecting unstable periodic orbits in chaotic time series.

Figure 1

(a) A simulated ECoG segment containing a frequently observed simulated spike-wave-type pattern commonly found in epileptiform ECoG. The repetitive waveform consists of a short spike followed by a longer half-wave, and may occur in unbroken trains or interspersed with arbitrary signal. The latter is the case in this segment, with the nonepileptiform arbitrary signal approximated by random noise. (b) A signal with the same power spectral density (PSD) as the signal depicted in (a), but with randomized phases. While the PSD is the same, the signal no longer shows the same type of rhythmic pattern as depicted in (a). However, time domain analysis methods based on signal recurrences can distinguish between these two signals.

Figure 2

Each group of two panels represents a segment of ECoG approximately 4.17 s in length (top) and the corresponding recurrence plot (below), computed with ϵ=0.03. The top two groups are taken from preseizure activity, while the middle and bottom left groups are taken from seizure activity. The bottom right group depicts postseizure activity.

Figure 3

Recurrence can be defined in terms of occurrences in which a signal passes within ϵ of template points spaced by T_i.

Figure 4

Simulated rhythmic signal segments 1000 points in length are used to test the rhythmicity algorithm. Segments (a)–(h) are repetitions of signal blocks resembling types of activity commonly sees in seizures. These baseline rhythmic segments are modulated in amplitude [segments (i)–(p)], frequency-chirped [segments (q–x)], and varied in temporal spacing [segments (y)–(3)].

Figure 5

For the simulated data segments depicted in Fig. 4, the first return times are depicted, with the major peaks indicated by a circle. Prior to analysis, all segments are normalized to zero mean and unit variance. For all segments, ϵ=0.1, m=3, and τ=5.

Figure 6

Typical rhythmic segments of ECoG from the primary seizure onset channel, taken during a seizure. Segments shown are taken from different time intervals in the seizures of two patients. Corresponding times of first recurrences are shown on the right, next to each ECoG segment. Peaks indicated by circles represent the dominant first return times uncovered in the segment.

Figure 7

Using 4 s sliding windows overlapped by 50%, the values of first return statistics (the mean first recurrence time, its standard deviation, and the percent time spent in recurrence) are plotted against the midpoint of the window, indicated by the dashed line on the ECoG plot in the top panel. Windows for which no recurrences were found do not have statistics computed and for these regions, the second through fourth panels are blank.

Figure 8

As in Fig. 7, but with a seizure from a different patient.