Lag synchrony measures dynamical processes underlying progression of seizure states

Benjamin H. Singer, Miron Derchansky, Peter L. Carlen, and Michał Żochowski

Phys. Rev. E 73, 021910 – Published 17 February 2006

Abstract

We investigate the dynamics of bursting behavior in an intact hippocampal preparation using causal entropy, an adaptive measure of lag synchrony. This analysis, together with a heuristic model of coupled bursting networks, separates experimentally observed bursting dynamics into two dynamical regimes, when bursting is driven by (1) the intranetwork dynamics of a single region, or (2) internetwork feedback between spatially disjoint neural populations. Our results suggest that the abrupt transition between these two states heralds the gradual desynchronization of bursting activity. These results illustrate how superficially homogeneous behavior across loosely coupled networks may harbor hidden, but robust, dynamical processes.

Received 10 November 2005

DOI:https://doi.org/10.1103/PhysRevE.73.021910

Authors & Affiliations

Benjamin H. Singer, Miron Derchansky, Peter L. Carlen, and Michał Żochowski

Neuroscience Program, Department of Physics and Biophysics Research Division, University of Michigan, Ann Arbor, Michigan 48109, USA
Division of Cellular and Molecular Biology, Toronto Western Research Institute, Ontario, Toronto, Canada M5T 2S8

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 73, Iss. 2 — February 2006

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Schematic of the explanted mouse hippocampus showing the approximate placement of electrodes. (b) Representative local field potential recording of a single SLE from four positions in the hippocampus.Reuse & Permissions
Figure 2
(a) General schema for calculating interburst intervals $(Δ B)$ from two electrodes. (b) Expanded view of two consecutive bursts recorded from two adjacent electrodes in the hippocampus, demonstrating the calculation of $Δ B$ from the data. (c) Upper panel: Representative record of $Δ B_{1, 2}^{t}$ and $Δ B_{2, 1}^{t}$ over the course of a single SLE. Lower panel: Record of ${\hat{C}}_{1, 2} - {\hat{C}}_{2, 1}$ (arb. units) calculated from the $Δ B$ time series above.Reuse & Permissions
Figure 3
Two-dimensional plot of ${\hat{C}}_{j, i} + {\hat{C}}_{i, j}$ vs ${\hat{C}}_{j, i} - {\hat{C}}_{i, j}$ (arb. units) for a representative SLE (black). Values of ${\hat{C}}_{i, j}$ are paired with their nearest temporal neighbors in ${\hat{C}}_{j, i}$ . Thresholds for $\hat{C}$ sum and difference are set based on the distributions obtained from surrogate data sets (gray). Thresholds are set at the 95th percentile of ${\hat{C}}_{j, i} + {\hat{C}}_{i, j}$ (horizontal line), and the 2.5th and 97.5th percentiles of ${\hat{C}}_{j, i} - {\hat{C}}_{i, j}$ (vertical lines). The intersections of these thresholds form six sectors. In sector I, activity in $i$ significantly leads activity in $j$ , while in sector III, activity in $j$ significantly leads activity in $i$ . Events in other sectors are not significant.Reuse & Permissions
Figure 4
(a) Raster plots for a representative SLE showing times of events pairs among adjacent electrodes $(i, j) ∊ {(1, 2), (2, 3), (3, 4)}$ with significant $\hat{C}$ sum and difference values; gray, septal electrode leads temporal; black, temporal electrode leads septal. Electrode 1 is most septal, while electrode 4 is in the most temporal position. The overall pattern of leading begins as $septal \to temporal$ (area $a$ ) and then enters an epoch of directional switching (area $b$ ). (b) Relative lengths of $septal \to temporal$ phase (area $a$ ) and postswitching phase (area $b$ ) in 15 SLEs recorded from six hippocampi. Bars are aligned to the first directional switch. Mean(standard deviation) duration of $a = 23.1$ $(13.9) s$ , $b = 73.3$ $(78.3) s$ .Reuse & Permissions
Figure 5
(a) Total synaptic activity from each network (arb. units). In the first phase of the model seizure, activity in $N 1$ leads activity in $N 2$ (black bar). In the second phase, switching occurs and activity in $N 2$ leads activity in $N 1$ (gray bar). Step function denotes the period $(t ∊ [1, 6])$ when $Γ_{cut, N 1} = 0$ . $Γ_{cut, N 2} = 0.34$ throughout. (b) Average expectivity (arb. units) as a function of the difference in bursting thresholds in $N 1$ and $N 2$ . $Γ_{cut, N 1} = 0.05$ , while $Γ_{cut, N 2}$ varies in [0.05, 0.29]. (c) Expectivity distinguishes three separate dynamical regimes, all of which display lag synchrony. Regime $a$ : Bursting thresholds of $N 1$ and $N 2$ are unequal, $N 1$ drives $N 2$ , and expectivity is positive ( $Γ_{cut, N 1} = 0.05$ , $Γ_{cut, N 2} = 0.29$ ). Regime $b$ : Bursting thresholds of $N 1$ and $N 2$ are equal, $N 1$ and $N 2$ undergo sustained bursting with lead switching, and expectivity is zero ( $Γ_{cut, N 1} = 0.05$ , $Γ_{cut, N 2} = 0.05$ ). Regime $c$ : Bursting thresholds of $N 1$ and $N 2$ are equal, $N 1$ and $N 2$ display diminishing bursting with lead switching, and expectivity is negative ( $Γ_{cut, N 1} = 0.34$ , $Γ_{cut, N 2} = 0.34$ ).Reuse & Permissions
Figure 6
(a) Illustration of time normalization procedure. (b) Average of expectivity (arb. units) among ten model seizures. Left of dashed vertical line: $Γ_{cut} = 0.0$ . Time from bursting onset to directional switching is normalized to [0, 0.5], and time from switching to end of bursting is normalized to [0.5, 1.0]. Vertical line: onset of switching. (c) Average $(black) \pm SEM$ (gray) of expectivity (arb. units) among 45 electrode pairs [15 SLEs, $(i, j) ∊ {(1, 2), (2, 3), (3, 4)}$ ]. Time from SLE onset to switching is normalized to [0, 0.5], and time from switching to SLE end is normalized to [0.5, 1.0]. Vertical line: onset of switching.Reuse & Permissions

Physical Review E

covering statistical, nonlinear, biological, and soft matter physics