Long-term effects of temporal lobe epilepsy on local neural networks: a graph theoretical analysis of corticography recordings.

Three network types.Three network types based on the model of Watts and Strogatz, 1998. In an ordered network the points are connected to their nearest neighbours (left) but there are no long-distance connections. In a random network (right), there is no local clustering. In a small-world network (middle), some local connections are rewired to long distance connections, resulting in high clustering combined with a short path length.

Intra-cranial corticography recording.Picture of a grid, placed directly on the cortex for intra-cranial recording.

Visualisation of the functional connectivity pattern over the temporal lobe.A grid of 4x5 electrodes is placed directly on the temporal lobe and the registered area is schematically documented. 5 Epochs of representative ECoG recordings are selected per patient. The PLI values are calculated based on these recordings, resulting in a matrix with synchronization values for all possible electrode combinations. The figure shows a mean PLI value for each grid electrode based on this synchronization matrix, representing the average synchronization with the other channels.

Correlation between epilepsy duration and functional connectivity.The Phase Lag Index (PLI) value is given as a function of epilepsy duration of each patient, showing a decreased PLI with longer epilepsy duration.

Correlation between epilepsy duration and network characteristics.The clustering coefficient C and average shortest path length L were calculated for each patient and compared to 1000 random networks, resulting in a ratio C/Cs and L/Ls. Network characteristics were plotted into a graph as a function of epilepsy duration, showing a decrease of C/Cs (5A) and no change of L/Ls (5B), resulting in a decrease of the small world index S (5C). The shown results represent the network characteristics for an average number of connections k = 3.

Network representation on the ECoG grid.Network representation of patient 13 for an average number of connections k = 3. The characteristics of this network are: C/Cs = 2.12, L/Ls = 1.07 and S = 1.98. Note that some edges are printed bold. These edges represent connections between three so-called ‘hub’ vertices (vertices with a relative high number of connections), which increase the small world properties of the network in two ways. Firstly, the edges mark a local cluster, which increases the network characteristic C/Cs. Secondly, this particular cluster also increases the global integration of the network as almost all connected vertices in the network can be reached through these hubs, resulting in a lower L/Ls.