Shown are horizontal slices approximately midway along the exposed electrode for animals A, B, and C. Arrows indicate tracts made by insertion of working electrode (WE) and counter-electrode (CE). Sections from animal D were not interpretable, nor could the electrode tracts be identified. The scale bar is 450 μm in length.

Shown are 2 s traces from animal D of depth LFP recording near the stimulation electrode during an applied 15 Hz sinusoidal field. The upper trace is prior to artifact reduction. The lower trace (green) is after removal of an amount of signal proportional to the applied current. Note that some residual artifact remains.

A stimulation electrode is targeted to align along the dorsal-ventral axis of the ventral hippocampus centered within the arc of the CA3. The electrode is exposed over 3 mm of its length from the tip, and in its local field produces a radially expanding current. The field is therefore locally aligned with the main dendrite-soma axis of the CA3 pyramidal cells. Tetanus toxin is focally injected at a point 1.5 mm above the tip of the stimulation electrode and along the same trajectory.

Shown is a 1 s segment of hippocampal depth LFP, after stimulation artifact has been reduced (upper trace) along with the 15 Hz periodic current used to create the polarizing electrical field. Extracted fPSP spike times are marked by red dots, and appear to be synchronized with the stimulation. Trace taken from animal D, stimulated with peak current of about 90 μA, approximately 16 s into this particular seizure.

There are three major steps. 1. Preprocessing: This includes seizure detection and verification, followed by stimulus artifact reduction, and then fPSP spike detection and reduction to point process. 2. Testing for Entrainment: The data is then broken into 4 s windows, within which we estimate the point spectrum and apply the F-test for lines at the drive frequency f_stim. 3. Quantifying entrainment: For each seizure we quantify N_w = number of windows with significant entrainment (p < 0.001). For each channel recorded and each frequency of stimulation applied, we further count N_sz = number of seizures detected and N_ent = number of seizures entrained (i.e., with N_w > 0).

Stimulation was performed by controlling the whole-cell potential, defined as the potential between the two stimulation electrodes in the tissue. For this figure, current was averaged over 5 cycles of stimulation from animal B. The maximum current grows much more slowly than frequency for these electrodes. The measured current output (μA) is plotted against voltage applied (mV) between the stimulation and reference electrode for sinusoidal stimulation at 1, 9 and 15 Hz. The charge storage capacity (CSC, μC) was estimated by computing the cumulative integral of the current waveform over one averaged cycle at each frequency and subtracting the minimum from the maximum value of the result. The peak applied voltage was 800 mV.

(A) Box plot (top left) of estimated residual artifact amplitude from the stimulated seizures of animal D (n = 7), estimated from the difference in root mean square (RMS) signal amplitude in the half minute just prior to seizure onset, compared to unstimulated seizures (n = 44) in the same period. Fraction of seizures P with entrained windows N_w≥ n={1,2,3} marked by ‘□’, ‘x’ and ‘○’ respectively, for unstimulated seizures (n = 44) with artificially added sinusoidal artifact as a function of artifact amplitude. (B) Probabilities of N_w ≥ n from stimulated seizures (closed circles) and from unstimulated seizures (dashes) with added artifact of 0.5 mV or approximately twice the estimated maximum residual artifact amplitude.

Shown are the experimentally observed distributions for the SNR computed from the ratio of first and second moments of the tapered spectral estimates for spike time series from animal D for both unstimulated and 15 Hz stimulated seizures. (a) Probability density function (PDF) and (b) cumulative density function (CDF) for SNR averaged over all frequencies for unstimulated seizures (blue line); averaged over all frequencies except the stimulation frequency (15 Hz) for stimulated seizures (black line); at 15 Hz for stimulated seizures (green line); and for F_2,2(K−1) (red line). The pale blue vertical bar indicates the theoretical 99.9 % confidence level. (c,d) CDFs for individual frequencies averaged over (c) unstimulated and (d) 15 Hz stimulated seizures. Empirical CDFs for all cases are consistent with the assumed null hypothesis distribution except that for the stimulation frequency of stimulated seizures.

A 150 s trace recorded from a bipolar hippocampal depth electrode in the left dorsal CA3 of animal D, starting 30 s before seizure initiation. The bottom traces are two axes of acceleration measured from the animal’s head by DC sensitive MEMS accelerometers. Seizure generalization is typically accompanied by a rearing motion, which is reflected by slow DC changes in acceleration along the accelerometer axis (marked by *). Field postsynaptic potential (fPSP) spikes at different points in seizure evolution are shown at an expanded scale in the upper traces. Large dots mark the dominant positive or negative peak within a moving 100 ms window used to define fPSP spike times. In the top center panel, some negative spikes of relatively small fPSPs are marked because they were the only features that satisfied both the amplitude and gradient constraints for spike detection.

Both seizures were taken from the same animal, D, as recorded from a depth electrode in the same hippocampus as the stimulation. Analysis was done for 150 s starting 30 s prior to seizure onset. The seizure on the left (A–D) was unstimulated, and the one on the right (E–H) was stimulated at 15 Hz. Analysis was done in 4 s non-overlapping windows. Shown are (A, E) spectrograms computed from the spike-time series, (B, F) average spike rate R_s per 4 s window, (C, G) Thomson’s F-statistic normalized by a critical value (p = 0.1 %) at 15 Hz, and (D, H) number of entrained windows N_w for each frequency (0.25 Hz resolution) for the seizures. No obvious persistent spectral lines are observed from the unstimulated seizure, and the observed N_w values are consistent with chance. The stimulated seizure has a significant line at 15 Hz that persists for 4 windows, which is highly unlikely (p ~ 10⁻⁷) from chance. Note that the data from Figure 6 is from the same seizure, starting at time t = 16 s, and marked by the arrow.

Results are shown here for one animal (D) determined by analysis of left dorsal hippocampal EEG ipsilateral to the stimulation site. (Upper) Histogram of N_sz = the total number of seizures stimulated at each frequency f. (Center) Number of N_ent seizures entrained by the stimulation at each frequency f. Seizures were classified as being entrained if the number of 4 s windows N_w with significant spectral lines at the stimulation frequency N_w ≥1. The 99 % confidence limit for the proportion of seizures with N_w≥1 from binomial considerations is marked with an asterisk for each frequency. By this criterion, there were significantly large numbers of seizures entrained at 3, 11, 14, 15 and 20 Hz. (Lower) Box plot representation of the observed distribution of N_w at each stimulation frequency. The boxplot is a standard way of representing the distribution of a sample as a box, with the lower quartile, median and upper quartile (i.e., 25th, 50th and 75th percentile, respectively) of the distribution as the horizontal edges, and whiskers that extend from the edges up to 1.5 times the interquartile distance or up to the most extreme value in the sample, whichever is smaller. If there are values beyond the whiskers, they are called outliers and shown as dots. In some instances, as seen here at 3 and 20 Hz, the quartiles of the distribution may coincide with one another giving an asymmetric box plot; this is especially likely with very small samples of integer values. Note that the probability of any one seizure having N_w≥2 is approximately 0.06 %.