Identification of Interictal Epileptogenic Networks from Dense-EEG

Supplementary Material for

Identification of interictal epileptogenic networks

from dense-EEG

Mahmoud Hassan1,2, Isabelle Merlet1,2, Ahmad Mheich1,2,4, Aya Kabbara1,2,4,

Arnaud Biraben1,2,3, Anca Nica3 and Fabrice Wendling1,2

1 INSERM, U1099, Rennes, F-35000, France

2 Université de Rennes 1, LTSI, F-35000, France

3 Neurology dpt, CHU, Rennes, France

4AZM center-EDST, Lebanese University, Tripoli, Lebanon Similarity Index (SI):

The similarity index (SI) is based on estimating the minimum cost-based changes

(substitution, insertion, deletion) of nodes that are necessary to maps a networkto network, and it is based also on calculating the weight difference between edges in and (Mheich et al., 2015a). The algorithm is based on four main steps:

Step 1: Node substitution

To start, the common nodes between and that have the same spatial location are detected. For the rest of nodes, we define a spatial neighborhood (disk with radius ). The idea is to shift the spatial location of a neighbor node include in to the spatial location of include in if is located into (the spatial neighborhood of). In the case where there are two nodes of graph are located in, the nearest node to will be shifted. The cost of shifting is equal to the Euclidian distance between the two shifted nodes (and). The node distance () is updated by adding a value equal to the Euclidian distance between and .

Step 2: Node Insertion

In this step, when no nodes exist in the defined spatial neighborhood for each nodes of, the notion of insertion is used to insert a new node in have the position of node. The cost of insertion must be higher than the cost of substitution, in our case the cost of insertion is equal to. The node distance () is then updated.

Step 3: Node deletion

At the end of the step 2, all the nodes that are included in must also be included in . The remained nodes of are deleted. The cost of deletion for one node is equal to the radius . The node distance between and is then updated.

Step 4 Edge distance

In this step, the distance between the edges () for andat the initial state is computed. It consists of calculating the weight difference between two edges of two different graphs. In binary graph we consider that the weight of an edge equals 1 if it exists and 0 if it does not exist. We use the equation (2) to calculate the edge distance between two edges of and , the score where 1 means that an edge exists just in one graph and does not exist in the other, while 0 means an edge exists for both graphs between the same nodes. The total is then calculated by equation (3).

Finally, the distance between andis calculated by combining the nodes distance (from step 3) and the edges distance () from step 4

We convert the distance into similarity measure via the formula. The similarity score where

0 means that andare totally dissimilar, while 1 means that andare identical.

Mheich, A., Hassan, M., Gripon, V., Khalil, M., Berrou, C., Dufor, O., Wendling, F., 2015a. A novel algorithm for measuring graph similarity: Application to brain networks. Neural Engineering (NER), 2015 7th International IEEE/EMBS Conference on. IEEE, pp. 1068-1071.