Chow–Liu trees are sufficient predictive models for reproducing key features of functional networks of periictal EEG time-series

Abstract

Seizure freedom in patients suffering from pharmacoresistant epilepsies is still not achieved in 20 − 30% of all cases. Hence, current therapies need to be improved, based on a more complete understanding of ictogenesis. In this respect, the analysis of functional networks derived from intracranial electroencephalographic (iEEG) data has recently become a standard tool. Functional networks however are purely descriptive models and thus are conceptually unable to predict fundamental features of iEEG time-series, e.g. in the context of therapeutical brain stimulation.In this paper we present some first steps towards overcoming the limitations of functional network analysis, by showing that its results are implied by a simple predictive model of time-sliced iEEG time-series. More specifically, we learn distinct Graphical models (so called Chow-Liu(CL) trees) as models for the spatial dependencies between iEEG signals. Bayesian inference is then applied to the CL trees, allowing for an analytic derivation/prediction of functional networks, based on thresholding of the absolute value Pearson correlation coefficient(CC) matrix. Using various measures, the thus obtained networks are then compared to those which were derived in the classical way from the empirical CC-matrix. In the high threshold limit we find (a) an excellent agreement between the two networks and (b) key features of periictal networks as they have previously been reported in the literature.Apart from functional networks, both matrices are also compared element-wise, showing that the CL approach leads to a sparse representation, by setting small correlations to values close to zero while preserving the larger ones.Overall, this paper shows the validity of CL-trees as simple, spatially predictive models for periictal iEEG data. Moreover, we suggest straightforward generalizations of the CL-approach for modeling also the temporal features of iEEG signals.

Ictal time-irreversible intracranial EEG signals as markers of the epileptogenic zone

“…Finally, time-irreversible iEEG signals may aid recent efforts to build Bayesian statistical based generative models of multi-channel iEEG (Dauwels et al, 2011, Steimer et al, 2015.…”

Predictive modeling of EEG time series for evaluating surgery targets in epilepsy patients

“…Furthermore, the multivariate autoregressive model used by [Varotto et al, 2012] is restricted to linear interactions between the channels and its model complexity cannot be chosen independently from the sampling rate, as the number of parameters the model uses is proportional to D 2 S, where D is the number of channels and S the sampling rate. Note also that the approach is a spatio-temporal generalization of the mere spatial probabilistic model we have examined before (a single Chow-Liu tree) and for which we have shown how to derive functional brain networks from it [Steimer et al, 2015]. This illustrates again the advantages given by a distributional clustering approach that models only the temporal evolution of dynamical regimes (which are allowed to change for each window), while being oblivious to the dynamics that constitute a regime.…”

“…For the sake of simplicity and restriction of computational load, we have used for each patient the same settings of (meta)parameters during the clustering procedure. Likewise one may also consider a more refined class M of probabilistic models from which cluster centroids are chosen, although the adequacy of Chow-Liu trees-which were considered in this study-for modeling epileptiform iEEG time series has been shown recently [Steimer et al, 2015]. It is well-known however that parameters such as K and b affect the generalization capability of some clustering model [Buhmann and Held, 2000;Still and Bialek, 2004].…”

“…Detailed information about the recoding setup, periictal time series and patients-including the patients sex, age, etiology etc.-can be obtained from our previous study [Steimer et al, 2015], the seizure database of which entails 11 of the 12 patients considered here. While after surgery the class I patients were completely free from seizures and auras, there is no unambiguous separation between class III and IV in the Engel classification system, which is why both were lumped into the same class III/IV.…”

“…In this article, we pursue a radically different approach, the foundations of which have been laid by our previous study [Steimer et al, 2015]. The idea is to derive probabilistic clustering models for multivariate, peri-ictal iEEG time series, which-after some learning procedure-permit predictions about the ictal (seizure) state under controlled modulation.…”