Localizing Seizure-Onset Zones in Presurgical Evaluation of Drug-Resistant Epilepsy by Electroencephalography/fMRI: Effectiveness of Alternative Thresholding Strategies

Simultaneous EEG/fMRI is an effective noninvasive tool for identifying and localizing the SOZ in patients with focal epilepsy. In this study, we evaluated different thresholding strategies in EEG/fMRI for the assessment of hemodynamic responses to IEDs in the SOZ of drug-resistant epilepsy.

Low rank subspace clustering (LRSC)

We consider the problem of fitting a union of subspaces to a collection of data points drawn from one or more subspaces and corrupted by noise and/or gross errors. We pose this problem as a non-convex optimization problem, where the goal is to decompose the corrupted data matrix as the sum of a clean and self-expressive dictionary plus a matrix of noise and/or gross errors. By self-expressive we mean a dictionary whose atoms can be expressed as linear combinations of themselves with low-rank coefficients. In the case of noisy data, our key contribution is to show that this non-convex matrix decomposition problem can be solved in closed form from the SVD of the noisy data matrix. The solution involves a novel polynomial thresholding operator on the singular values of the data matrix, which requires minimal shrinkage. For one subspace, a particular case of our framework leads to classical PCA, which requires no shrinkage. For multiple subspaces, the low-rank coefficients obtained by our framework can be used to construct a data affinity matrix from which the clustering of the data according to the subspaces can be obtained by spectral clustering. In the case of data corrupted by gross errors, we solve the problem using an alternating minimization approach, which combines our polynomial thresholding operator with the more traditional shrinkage-thresholding operator. Experiments on motion segmentation and face clustering show that our framework performs on par with state-of-the-art techniques at a reduced computational cost.

The structural substrate of brain function: analysis of brain structural networks based on diffusion-weighted imaging

The brain is a complex neural network with a hierarchical organization and the mapping of its elements and connections is an important step towards the understanding of its function. Recent developments in diffusion-weighted imaging have provided the opportunity to reconstruct the whole-brain structural network in-vivo at a large scale level and to study the brain structural substrate in a framework that is close to the current understanding of brain function. However, methods to construct the connectome are still under development and they should be carefully evaluated. To this end, the first two studies included in my thesis aimed at improving the analytical tools specific to the methodology of brain structural networks. The first of these papers assessed the repeatability of the most common global and local network metrics used in literature to characterize the connectome, while in the second paper the validity of further metrics based on the concept of communicability was evaluated. Communicability is a broader measure of connectivity which accounts also for parallel and indirect connections. These additional paths may be important for reorganizational mechanisms in the presence of lesions as well as to enhance integration in the network. These studies showed good to excellent repeatability of global network metrics when the same methodological pipeline was applied, but more variability was detected when considering local network metrics or when using different thresholding strategies. In addition, communicability metrics have been found to add some insight into the integration properties of the network by detecting subsets of nodes that were highly interconnected or vulnerable to lesions. The other two studies used methods based on diffusion-weighted imaging to obtain knowledge concerning the relationship between functional and structural connectivity and about the etiology of schizophrenia. The third study integrated functional oscillations measured using electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) as well as diffusion-weighted imaging data. The multimodal approach that was applied revealed a positive relationship between individual fluctuations of the EEG alpha-frequency and diffusion properties of specific connections of two resting-state networks. Finally, in the fourth study diffusion-weighted imaging was used to probe for a relationship between the underlying white matter tissue structure and season of birth in schizophrenia patients. The results are in line with the neurodevelopmental hypothesis of early pathological mechanisms as the origin of schizophrenia. The different analytical approaches selected in these studies also provide arguments for discussion of the current limitations in the analysis of brain structural networks. To sum up, the first studies presented in this thesis illustrated the potential of brain structural network analysis to provide useful information on features of brain functional segregation and integration using reliable network metrics. In the other two studies alternative approaches were presented. The common discussion of the four studies enabled us to highlight the benefits and possibilities for the analysis of the connectome as well as some current limitations.

Multi-Environment Model Estimation for Motility Analysis of Caernorhabditis elegans

The nematode Caenorhabditis elegans is a well-known model organism used to investigate fundamental questions in biology. Motility assays of this small roundworm are designed to study the relationships between genes and behavior. Commonly, motility analysis is used to classify nematode movements and characterize them quantitatively. Over the past years, C. elegans' motility has been studied across a wide range of environments, including crawling on substrates, swimming in fluids, and locomoting through microfluidic substrates. However, each environment often requires customized image processing tools relying on heuristic parameter tuning. In the present study, we propose a novel Multi-Environment Model Estimation (MEME) framework for automated image segmentation that is versatile across various environments. The MEME platform is constructed around the concept of Mixture of Gaussian (MOG) models, where statistical models for both the background environment and the nematode appearance are explicitly learned and used to accurately segment a target nematode. Our method is designed to simplify the burden often imposed on users; here, only a single image which includes a nematode in its environment must be provided for model learning. In addition, our platform enables the extraction of nematode ‘skeletons’ for straightforward motility quantification. We test our algorithm on various locomotive environments and compare performances with an intensity-based thresholding method. Overall, MEME outperforms the threshold-based approach for the overwhelming majority of cases examined. Ultimately, MEME provides researchers with an attractive platform for C. elegans' segmentation and ‘skeletonizing’ across a wide range of motility assays.

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

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.

A New Approach for Automatic Removal of Movement Artifacts in Near-Infrared Spectroscopy Time Series by Means of Acceleration Data

Abstract: Near-infrared spectroscopy (NIRS) enables the non-invasive measurement of changes in hemodynamics and oxygenation in tissue. Changes in light-coupling due to movement of the subject can cause movement artifacts (MAs) in the recorded signals. Several methods have been developed so far that facilitate the detection and reduction of MAs in the data. However, due to fixed parameter values (e.g., global threshold) none of these methods are perfectly suitable for long-term (i.e., hours) recordings or were not time-effective when applied to large datasets. We aimed to overcome these limitations by automation, i.e., data adaptive thresholding specifically designed for long-term measurements, and by introducing a stable long-term signal reconstruction. Our new technique (“acceleration-based movement artifact reduction algorithm”, AMARA) is based on combining two methods: the “movement artifact reduction algorithm” (MARA, Scholkmann et al. Phys. Meas. 2010, 31, 649–662), and the “accelerometer-based motion artifact removal” (ABAMAR, Virtanen et al. J. Biomed. Opt. 2011, 16, 087005). We describe AMARA in detail and report about successful validation of the algorithm using empirical NIRS data, measured over the prefrontal cortex in adolescents during sleep. In addition, we compared the performance of AMARA to that of MARA and ABAMAR based on validation data.