Timothée Proix

Permittivity Coupling across Brain Regions Determines Seizure Recruitment in Partial Epilepsy

Brain regions generating seizures in patients with refractory partial epilepsy are referred to as the epileptogenic zone (EZ). During a seizure, paroxysmal activity is not restricted to the EZ, but may recruit other brain regions and propagate activity through large brain networks, which comprise brain regions that are not necessarily epileptogenic. The identification of the EZ is crucial for candidates for neurosurgery and requires unambiguous criteria that evaluate the degree of epileptogenicity of brain regions. To obtain such criteria and investigate the mechanisms of seizure recruitment and propagation, we develop a mathematical framework of coupled neural populations, which can interact via signaling through a slow permittivity variable. The permittivity variable captures effects evolving on slow timescales, including extracellular ionic concentrations and energy metabolism, with time delays of up to seconds as observed clinically. Our analyses provide a set of indices quantifying the degree of epileptogenicity and predict conditions, under which seizures propagate to nonepileptogenic brain regions, explaining the responses to intracerebral electric stimulation in epileptogenic and nonepileptogenic areas. In conjunction, our results provide guidance in the presurgical evaluation of epileptogenicity based on electrographic signatures in intracerebral electroencephalograms.

The Virtual Epileptic Patient: Individualized whole-brain models of epilepsy spread

ABSTRACT Individual variability has clear effects upon the outcome of therapies and treatment approaches. The customization of healthcare options to the individual patient should accordingly improve treatment results. We propose a novel approach to brain interventions based on personalized brain network models derived from non‐invasive structural data of individual patients. Along the example of a patient with bitemporal epilepsy, we show step by step how to develop a Virtual Epileptic Patient (VEP) brain model and integrate patient‐specific information such as brain connectivity, epileptogenic zone and MRI lesions. Using high‐performance computing, we systematically carry out parameter space explorations, fit and validate the brain model against the patients empirical stereotactic EEG (SEEG) data and demonstrate how to develop novel personalized strategies towards therapy and intervention. HighlightsA novel approach to brain interventions is proposed based on personalized large‐scale brain network models.The approach relies on the fusion of structural data of individual patients and mathematical modeling of brain activations.Personalization is achieved by integrating patient specific brain connectivity, epileptogenic zone and MRI lesions.High‐performance computing enables systematic parameter space explorations, fitting and validation of the brain model.Large‐scale brain models foster the development of personalized strategies towards therapy and intervention.

Individual brain structure and modelling predict seizure propagation

See Lytton (doi:10.1093/awx018) for a scientific commentary on this article. Patients with drug-resistant epilepsy show different seizure propagation patterns and postsurgical outcomes. Proix et al. merge structural information from brain imaging with mathematical modelling to generate personalized brain network models. Validation of the models against presurgical stereotactic EEGs and clinical data shows that they can account for the variability observed.

Whole-brain analytic measures of network communication reveal increased structure-function correlation in right temporal lobe epilepsy.

The in vivo structure-function relationship is key to understanding brain network reorganization due to pathologies. This relationship is likely to be particularly complex in brain network diseases such as temporal lobe epilepsy, in which disturbed large-scale systems are involved in both transient electrical events and long-lasting functional and structural impairments. Herein, we estimated this relationship by analyzing the correlation between structural connectivity and functional connectivity in terms of analytical network communication parameters. As such, we targeted the gradual topological structure-function reorganization caused by the pathology not only at the whole brain scale but also both in core and peripheral regions of the brain. We acquired diffusion (dMRI) and resting-state fMRI (rsfMRI) data in seven right-lateralized TLE (rTLE) patients and fourteen healthy controls and analyzed the structure-function relationship by using analytical network communication metrics derived from the structural connectome. In rTLE patients, we found a widespread hypercorrelated functional network. Network communication analysis revealed greater unspecific branching of the shortest path (search information) in the structural connectome and a higher global correlation between the structural and functional connectivity for the patient group. We also found evidence for a preserved structural rich-club in the patient group. In sum, global augmentation of structure-function correlation might be linked to a smaller functional repertoire in rTLE patients, while sparing the central core of the brain which may represent a pathway that facilitates the spread of seizures.

How do parcellation size and short-range connectivity affect dynamics in large-scale brain network models?

Recent efforts to model human brain activity on the scale of the whole brain rest on connectivity estimates of large-scale networks derived from diffusion magnetic resonance imaging (dMRI). This type of connectivity describes white matter fiber tracts. The number of short-range cortico-cortical white-matter connections is, however, underrepresented in such large-scale brain models. It is still unclear on the one hand, which scale of representation of white matter fibers is optimal to describe brain activity on a large-scale such as recorded with magneto- or electroencephalography (M/EEG) or functional magnetic resonance imaging (fMRI), and on the other hand, to which extent short-range connections that are typically local should be taken into account. In this article we quantified the effect of connectivity upon large-scale brain network dynamics by (i) systematically varying the number of brain regions before computing the connectivity matrix, and by (ii) adding generic short-range connections. We used dMRI data from the Human Connectome Project. We developed a suite of preprocessing modules called SCRIPTS to prepare these imaging data for The Virtual Brain, a neuroinformatics platform for large-scale brain modeling and simulations. We performed simulations under different connectivity conditions and quantified the spatiotemporal dynamics in terms of Shannon Entropy, dwell time and Principal Component Analysis. For the reconstructed connectivity, our results show that the major white matter fiber bundles play an important role in shaping slow dynamics in large-scale brain networks (e.g. in fMRI). Faster dynamics such as gamma oscillations (around 40 Hz) are sensitive to the short-range connectivity if transmission delays are considered.

Heterogeneity of time delays determines synchronization of coupled oscillators.

Network couplings of oscillatory large-scale systems, such as the brain, have a space-time structure composed of connection strengths and signal transmission delays. We provide a theoretical framework, which allows treating the spatial distribution of time delays with regard to synchronization, by decomposing it into patterns and therefore reducing the stability analysis into the tractable problem of a finite set of delay-coupled differential equations. We analyze delay-structured networks of phase oscillators and we find that, depending on the heterogeneity of the delays, the oscillators group in phase-shifted, anti-phase, steady, and non-stationary clusters, and analytically compute their stability boundaries. These results find direct application in the study of brain oscillations.

Modern concepts of seizure modeling.

Seizures are complex phenomena spanning multiple spatial and temporal scales, from ion dynamics to communication between brain regions, from milliseconds (spikes) to days (interseizure intervals). Because of the existence of such multiple scales, the experimental evaluation of the mechanisms underlying the initiation, propagation, and termination of epileptic seizures is a difficult problem. Theoretical models and numerical simulations provide new tools to investigate seizure mechanisms at multiple scales. In this chapter, we review different theoretical approaches and their contributions to our understanding of seizure mechanisms.

Reward-based online learning in non-stationary environments: Adapting a P300-speller with a “backspace” key

We adapt a policy gradient approach to the problem of reward-based online learning of a non-invasive EEG-based “P300”-speller. We first clarify the nature of the P300-speller classification problem and present a general regularized gradient ascent formula. We then show that when the reward is immediate and binary (namely “bad response” or “good response”), each update is expected to improve the classifier accuracy, whether the actual response is correct or not. We also estimate the robustness of the method to occasional mistaken rewards, i.e. show that the learning efficacy may only linearly decrease with the rate of invalid rewards. The effectiveness of our approach is tested in a series of simulations reproducing the conditions of real experiments. We show in a first experiment that a systematic improvement of the spelling rate is obtained for all subjects in the absence of initial calibration. In a second experiment, we consider the case of the online recovery that is expected to follow failed electrodes. Combined with a specific failure detection algorithm, the spelling error information (typically contained in a “backspace” hit) is shown useful for the policy gradient to adapt the P300 classifier to the new situation, provided the feedback is reliable enough (namely having a reliability greater than 70%).

Effects of multimodal distribution of delays in brain network dynamics

Large-scale modeling of the brain is defined by the local oscillatory dynamics that are superimposed on an architecture based on a comprehensive map of neural connections in the brain - connectome [1]. Besides coupling strengths, time-delays due to transmissions via tracts are crucial features of a connectome. They represent a proxy of the spatial structure (the tract lengths) to the temporal dynamics. Thus, the most straightforward approach to model brain dynamics in space and time is to concatenate oscillatory nodes to a connectome-based network. The analysis that we performed on the experimentally derived connectome suggests that the tract lengths - distances between different brain nodes, thus the time delays, follow a multimodal distribution. Here, we investigated the conceptual implementation of multimodal distributions of discrete time delays of network links, and its effects on the mean-field dynamics. Because of the analytical tractability, the Kuramoto oscillator describes the temporal dynamics of each node, and the links between the nodes are symmetric but heterogeneous. Hence, we analyze synchronization in populations of phase oscillators [2], which have the same distribution of natural frequencies and coupling strengths, but their structure is defined solely by their different intra- and inter-population delays. Assuming a same overall distribution of time delays, several cases are investigated: from fully random distribution, to two delays-imposed structures of subpopulations, Figure ​Figure11. Figure 1 Schematic representation of the delay-imposed structure of population of oscillators: with different inter and same intra delays in A; same inter and intra delays in B; and random distribution of the delays, in C. For all scenarios, mean-field dynamics are analytically obtained [3] and numerically confirmed. Moreover, boundaries and stabilities of different low-dimensional solutions are also investigated. These reveal a split of phase dynamics in different clusters, which can be phase shifted, or even non-stationary with different time-varying frequencies of synchronization and order parameters for the clusters. In summary, the large-scale spatial organization of the brain is integrated in a network model. Using this model, we present the effects of the multimodal distribution of time delays and the structure that they impose on the network dynamics such as synchronization. Hence, we stress the role of the spatial organization of the brain that is reflected through the different time-delays between different parts of the brain in the formation of spatiotemporal dynamics.

Using the connectome to predict epileptic seizure propagation in the human brain

Partial seizures in epileptic patients are generated in localized networks, so-called Epileptogenic Zone (EZ), before recruiting other regions, so-called Propagation Zone (PZ) [1]. For drug-resistant patients, surgical resection is sometimes possible. Correctly delineating the extent of the EZ and PZ is critical for a successful surgical resection, in order to remove enough of the epileptogenic tissue to prevent seizures while minimizing the cognitive collateral damages. EZ and PZ extents are evaluated using imaging tools such as M/EEG, MRI, PET and stereotaxic EEG (sEEG). In this modelisation work, we used the large-scale connectome to build a network of neural masses in order to reproduce seizure propagation through the human brain. In particular, we aimed at predicting the propagation of epileptic seizures, i.e. the PZ, using the localization of the EZ. We preprocessed data obtained from 18 different patients with different types of partial epilepsy. Using MRI and diffusion MRI data, we generated patient-specific connectomes along with cortical surfaces, using different parcellation resolutions. Epileptic dynamics of a single region was based on the Epileptor, a neural mass model able to autonomously generate epileptic seizures [2]. The different regions interacted via a permittivity coupling allowing to reproduce seizures propagation such as observed in sEEG [3]. Using a reduced Epileptor model, we performed a stability analysis at the edge of the seizure onset. We confirmed our results with simulations of the network of Epileptors using The Virtual Brain, a neuroinformatics platform to simulate large-scale dynamics [4]. The analytical prediction of seizure spatial extent correctly reproduces seizure simulations. We systematically predicted the spatial spread of the seizure, i.e. the PZ, for each patient, according to the spatial extent and localization of the EZ such as observed with sEEG, using different global connectivity and excitability parameters. An example of an EZ and PZ along with a simulation of the forward calculation on sEEG electrodes are shown in Figure ​Figure1.1. Our results show a good agreement with clinician predictions, surgery results, and sEEG signals. To confirm the determinant role of the connectome in spatial seizure propagation, we performed several surrogate analysis with other neural mass models (e.g. FitzHugh-Nagumo model), connectivity of control subjects and generic connectivities such as shuffled connectivities, random and small-world networks, again evaluated against clinical data. Real connectomes always performed better than generic connectivities. The connectome particular structure of a patient was often but not always better to predict seizure propagation than connectome of controls. Figure 1 A. Example of the EZ (red) and the calculated PZ (yellow) displayed on the patient cortical surface, along with sEEG electrodes (small spheres). B. Corresponding simulated time series. In conclusion, our results show that large-scale white matter tracts play an important role in the propagation of epileptic seizures. Better understanding of their exact role can help to significantly improve the success rate of surgical resections for epileptic patients.