Emergence of spatially heterogeneous burst suppression in a neural field model of electrocortical activity

Abstract

Burst suppression in the electroencephalogram (EEG) is a well-described phenomenon that occurs during deep anesthesia, as well as in a variety of congenital and acquired brain insults. Classically it is thought of as spatially synchronous, quasi-periodic bursts of high amplitude EEG separated by low amplitude activity. However, its characterization as a "global brain state" has been challenged by recent results obtained with intracranial electrocortigraphy. Not only does it appear that burst suppression activity is highly asynchronous across cortex, but also that it may occur in isolated regions of circumscribed spatial extent. Here we outline a realistic neural field model for burst suppression by adding a slow process of synaptic resource depletion and recovery, which is able to reproduce qualitatively the empirically observed features during general anesthesia at the whole cortex level. Simulations reveal heterogeneous bursting over the model cortex and complex spatiotemporal dynamics during simulated anesthetic action, and provide forward predictions of neuroimaging signals for subsequent empirical comparisons and more detailed characterization. Because burst suppression corresponds to a dynamical end-point of brain activity, theoretically accounting for its spatiotemporal emergence will vitally contribute to efforts aimed at clarifying whether a common physiological trajectory is induced by the actions of general anesthetic agents. We have taken a first step in this direction by showing that a neural field model can qualitatively match recent experimental data that indicate spatial differentiation of burst suppression activity across cortex.

Keywords: EEG; anesthesia; burst suppression; neural field model; neuronal hyperexcitability.

Figure 1

Topology of the Liley model (Liley et al., ; Bojak and Liley, 2005). Its two distinct neural populations (E = excitatory, I = inhibitory) are shown for two separate positions on the cortical sheet. Each one can be considered as representing a single macrocolumn. All synaptic connections that occur in the model are shown by red (excitatory) and blue (inhibitory) disks, respectively. Extracortical inputs to the cortical populations are shown by green fibers. Symbols illustrate the various inputs to the excitatory population in the left macrocolumn and to the inhibitory population in the right macrocolumn, respectively, according to Equations (3, 4).

Figure 2

(A) Imposed concentration of isoflurane (red curve), and the h_e response (blue curve) at the cortical location indicated by black arrows in the snapshot panels below. Different plateaus of concentration are labeled “C,” “D,” “E,” and “F.” Arrows point to the central times of the corresponding time series shown below. (B) PSDs of h_e averaged over the entire grid and normed to unit area for plateaus “C” (blue), “D” (green), “E” (red), and “F” (cyan). The motion of the alpha peak to lower frequencies persists qualitatively into the burst suppression phase “E” at much increased power. (C1) Snapshot of the h_e activity of the cortical surface at 0 MAC isoflurane. The size of h_e is indicated by both height and color, cf. the color bar. A black arrow shows the position from which the corresponding time series were recorded. (C2) Time series of h_e (blue) and Γ_ee (green) over the 10 s of the “C” plateau. Regular alpha rhythms in h_e and slow Γ_ee oscillations around the standard value Γ⁰_ee can be seen. (D1) Snapshot at 0.5 MAC. (D2) Time series of the “D” plateau. The oscillations of h_e have larger amplitude at a lower average. The slow Γ_ee oscillations now occur at an elevated level. (E1) Snapshot at 1 MAC. Burst suppression patterns have emerged and move across the cortical surface. (E2) Time series of the “E” plateau. Burst suppression is apparent both in h_e and Γ_ee, with a rapid drop in Γ_ee caused by the strongest h_e oscillations. An animation of this simulation is provided as Movie 1 in the Supplementary Material.

Figure 3

(A) Snapshot of the h_e activity of the cortical surface at simulation time 54.94 s under the influence of 1 MAC isoflurane. Black arrows with labels “a,” “b,” and “c” point to the cortical locations of the time series shown in the other panel. Note the toroidal boundaries, e.g., the circular burst front that appears cut off around (x,y) = (44.8, 0) cm continues at x = (44.8, 51.2) cm. (B) Time series of h_e (blue) and Γ_ee (green) taken from the three different positions marked as “a,” “b,” and “c” in the other panel. It is obvious that bursts are not generally synchronized in time at the different positions. Spatiotemporal correlations from propagating “burst waves” can occur, but are removed at larger distances by the interference from other emergent patterns. An animation of this simulation is provided as Movie 1 in the Supplementary Material.

Figure 4

(A) Snapshot of the h_e activity of the cortical surface at simulation time 16.78 s under the influence of 0.25 mM isoflurane, where in a circular patch (center (x, y) = (20.0, 20.0) cm, radius 9.6 cm) the inhibitory synaptic depletion factor f_i has been increased from 0.175 to 1.25, leading to an increase of Γ^r_ie,ii there by a factor 1.91. The size of h_e is indicated by both height and color, cf. the color bar. One can see that the circular patch does not participate in the burst suppression pattern. Black arrows with labels “B,” “C,” and “D” point to the cortical locations used in the other panels. (B) Six seconds long time series of h_e (blue), h_i (green), Γ_ee/Γ⁰_ee (red), and Γ_ie/Γ⁰_ie (cyan) around the time of the snapshot from a point outside of the circular patch. Burst suppression is clearly visible in all variables. (C) Time series from just inside the circular patch. There is no local burst suppression, but some of the outside burst activity spills in. (D) Time series taken from the center of the circular patch. There is neither local burst suppression nor spill-in. Animations of this simulation are provided as Movie 2 in the Supplementary Material.

Figure 5

Time series of the mean excitatory soma membrane potential h_e (blue), the excitatory post-synaptic peak amplitude Γ_ee (green) and the average excitatory firing rate normed to the maximum attainable rate S_e(h_e)/S^max_e (red). Note that both Γ_ee and S_e(h_e)/S^max_e map by value to the black ordinate on the right, though with different units. The time series shown here is part of the times series labeled “a” in Figure 3B. One sees that the strongly non-linear relationship between h_e and S_e in the anesthetic regime transforms the “symmetric” h_e oscillation that would be visible in local field potentials and the EEG during the burst phase into strong “spikes” in the firing rate S_e, and consequently to a “jagged” appearance of the synaptic depletion of Γ_ee.

Figure 6

(A) Snapshot of the h_e activity of cortex at simulation time 9.54 s at 0.25 mM isoflurane with λ_ek = λ₁ = 2.7 cm. A black arrow shows the cortical location at which the corresponding time was recorded. An animation is provided as Movie 3 in the Supplementary Material (B) Snapshot at simulation time 5.79 s with λ_ek = λ₂ = 2.4 cm, the standard value. An animation is provided as Movie 4 in the Supplementary Material. The characteristic size of the burst patterns is reduced. (C) Snapshot at simulation time 11.70 s with λ_ek = λ₃ = 2.1 cm. An animation is provided as Movie 5 in the Supplementary Material. The characteristic size of the burst patterns is reduced even further. (D) Time series of h_e (blue) and Γ_ee (green) taken from these three simulations, marked as “λ₁,” “λ₂,” and “λ₃.” We see that inter-burst interval remains roughly the same.