Epileptic seizures from abnormal networks: why some seizures defy predictability

Abstract

Seizure prediction has proven to be difficult in clinically realistic environments. Is it possible that fluctuations in cortical firing could influence the onset of seizures in an ictal zone? To test this, we have now used neural network simulations in a computational model of cortex having a total of 65,536 neurons with intercellular wiring patterned after histological data. A spatially distributed Poisson driven background input representing the activity of neighboring cortex affected 1% of the neurons. Gamma distributions were fit to the interbursting phase intervals, a non-parametric test for randomness was applied, and a dynamical systems analysis was performed to search for period-1 orbits in the intervals. The non-parametric analysis suggests that intervals are being drawn at random from their underlying joint distribution and the dynamical systems analysis is consistent with a nondeterministic dynamical interpretation of the generation of bursting phases. These results imply that in a region of cortex with abnormal connectivity analogous to a seizure focus, it is possible to initiate seizure activity with fluctuations of input from the surrounding cortical regions. These findings suggest one possibility for ictal generation from abnormal focal epileptic networks. This mechanism additionally could help explain the difficulty in predicting partial seizures in some patients.

Figure 1

(A) Representative connectivity of the excitatory cellular component in a given modeled minicolumn, wiring after (Douglas & Martin, 2004). (B) Three dimensional arrangement of the 16 X 16 array of minicolumns in space. (C) Representative snapshots of evolving activity over 0.02 seconds in the layer II/III pyramidal cell component. Each pixel represents one cell, color coded proportionally to the number of action potentials fired in bins of 1/100 of a second.

Figure 2

Network activity produced by sequential increases in the mean frequency of the applied background activity (background synaptic input provided to a fixed 1% set of the modeled cells, summed layer II/III pyramidal cell action potentials in 10 msec bins.) The model exhibits a transition from episodic bursting to a very regular bursting behavior driven by the background input.

Figure 3

(A) Network activity induced by varying the random connectivity pattern between cell classes (different connectivity seeds, $N_{\mathit{\text{seed}}}^{\mathit{\text{conn}}}$, for the random number generator). Numbers of action potentials in layer II/III pyramidal cell component, 10 msec time bins. (B) Network activity induced by varying the random time sequence of background synaptic input, $N_{\mathit{\text{seed}}}^{\mathit{\text{time}}}$. In these experiments, all cellular connections remain fixed, and the identity of the cells undergoing background synaptic input remain fixed.

Figure 3

(A) Network activity induced by varying the random connectivity pattern between cell classes (different connectivity seeds, $N_{\mathit{\text{seed}}}^{\mathit{\text{conn}}}$, for the random number generator). Numbers of action potentials in layer II/III pyramidal cell component, 10 msec time bins. (B) Network activity induced by varying the random time sequence of background synaptic input, $N_{\mathit{\text{seed}}}^{\mathit{\text{time}}}$. In these experiments, all cellular connections remain fixed, and the identity of the cells undergoing background synaptic input remain fixed.

Figure 4

Changing the absolute connectivity in the layer II/III pyramidal cell component (Number of layer II/III pyramidal cells contacted by a given layer II/III pyramidal cell, N_2/3:2/3) in the model produces alterations in the network bursting behavior. At very low absolute connectivity (N_2/3:2/3=110) network bursting is brief and isolated, while at higher levels of absolute connectivity periods of constant bursting can be observed.

Figure 5

Statistical analysis of the interbursting phase intervals. (A, D), Interval histograms are fit with gamma distributions revealing shape parameters α >1 in the case of Continuous Run 1 (A) and Continuous Run 4 (D). (B, E), Two dimensional delay embedding of sequential intervals (Spearman correlation coefficients are not significantly different from zero) for Continuous Runs 1 and 4 respectively. (C, F), Testing the significance of potential period-1 orbits detected through a dynamical analysis of the sequence of points displayed in B and E respectively. The y-axis represents the fraction of surrogate (shuffled, see Materials and Methods) sequences with a maximal deviation from the mean surrogate result of greater than W (So et al., 1996, So et al., 1997) (10⁴ random matrices and 10² surrogates were used). The horizontal dotted (red) line displays the maximal deviation for the simulation data. Since there exists a significant fraction of surrogates with deviation greater than that for the simulation data (for both C – 20% and F – 10%), neither plot displays convincing evidence of the existence of a period-1 orbit.