Relating Cortical Atrophy in Temporal Lobe Epilepsy with Graph Diffusion-Based Network Models

Abstract

Mesial temporal lobe epilepsy (TLE) is characterized by stereotyped origination and spread pattern of epileptogenic activity, which is reflected in stereotyped topographic distribution of neuronal atrophy on magnetic resonance imaging (MRI). Both epileptogenic activity and atrophy spread appear to follow white matter connections. We model the networked spread of activity and atrophy in TLE from first principles via two simple first order network diffusion models. Atrophy distribution is modeled as a simple consequence of the propagation of epileptogenic activity in one model, and as a progressive degenerative process in the other. We show that the network models closely reproduce the regional volumetric gray matter atrophy distribution of two epilepsy cohorts: 29 TLE subjects with medial temporal sclerosis (TLE-MTS), and 50 TLE subjects with normal appearance on MRI (TLE-no). Statistical validation at the group level suggests high correlation with measured atrophy (R = 0.586 for TLE-MTS, R = 0.283 for TLE-no). We conclude that atrophy spread model out-performs the hyperactivity spread model. These results pave the way for future clinical application of the proposed model on individual patients, including estimating future spread of atrophy, identification of seizure onset zones and surgical planning.

Fig 1

(a) TLE-MTS atrophy distribution. As expected, the hippocampus has the highest atrophy, consistent with TLE-MTS. (b) Pearson correlation R between Φ₁ and measured atrophy vs. the number of eigen-modes used. Peak R is reached when eigen-modes u _2–68 are used. (c) Atrophy distribution estimated using Model 1 using eigen-modes u ₂ − u ₆₈. Model 2: (d) Correlation R obtained when each node is seeded (model Φ₂). The highest R is obtained when the hippocampus is seeded. (e) R vs. graph diffusion depth. Hippocampus seeding leads to the highest R is obtained at t = 5.56, followed by amygdala and the hypothalamus. (f) Estimated TLE-MTS atrophy obtained from Model 2 when the hippocampus is seeded.

Fig 2. Model 1: Atrophy distribution via exitotoxicity.

(a) Eigen-mode u ₅ captures the essentials of estimating network diffusion from the Laplacian’s eigen-modes for TLE-MTS when the ipsilateral hippocampus is seeded. (b) Eigen-mode u ₂ recovers features of the TLE-no when the temporal lobe is bilaterally seeded. (c) Plot of R vs the eigen-mode index for TLE-MTS when each eigen-mode u _i is correlated with the group atrophy. (d) Plot of R vs. the eigen-mode index for the TLE-no when eigen-modes u _i are each correlated with the group atrophy.

Fig 3

TLE-no case, Model 1: (a) Cortical/subcortical atrophy obtained from t-statistics of epileptic and healthy groups’ volumetrics. (b) R vs. the number of eigen-modes Eq (10) used for neuronal atrophy estimation. (c) Atrophy distribution estimated using Model 1 and eigen-modes u ₂ − u ₂₇. Model 2: (d) Correlation R of group atrophy and Φ₂ obtained when each node is seeded. (e) R vs. graph diffusion depth t. Left paracentral gives the maximum R, followed by the left post central and the left frontal pole. (f) Neuronal atrophy estimate obtained from Model 2 when the paracentral lobe is seeded.

Fig 4. Scatter plots for each model and epilepsy type of the measured neuronal atrophy vs. the neuronal atrophy as estimated by the two models.

Empirical vs. estimated neuronal atrophy for the case of TLE-MTS; Model 1 (a), and Model 2 (b); and measured vs. estimated neuronal atrophy for the case of TLE-no; Model 1 (c), and Model 2 (d). For both types of epilepsy, Model 2 outperforms Model 1.

Fig 5. Histograms of R resulting from 1,000 instances of random permutations of the neuronal atrophy for each type of epilepsy and for both models.

From the histograms, the estimated neuronal atrophy is likely to be specific to the atrophies obtained from both epilepsy groups, more so in the case of Model 2 where high R is obtained for both types of epilepsy. Histograms of R resulting from random permutation of neuronal atrophy, (a) TLE-MTS Model 1, (b) TLE-MTS, Model 2. Histogram of R resulting from TLE-no neuronal atrophy random permutation, (c) Model 1, and (d) Model 2.