White-matter degradation and dynamical compensation support age-related functional alterations in human brain.

Structural connectivity of the brain at different ages is analyzed using diffusion-weighted magnetic resonance imaging (MRI) data. The largest decrease of streamlines is found in frontal regions and for long inter-hemispheric links. The average length of the tracts also decreases, but the clustering is unaffected. From functional MRI we identify age-related changes of dynamic functional connectivity (dFC) and spatial covariation features of functional connectivity (FC) links captured by metaconnectivity. They indicate more stable dFC, but wider range and variance of MC, whereas static features of FC did not show any significant differences with age. We implement individual connectivity in whole-brain models and test several hypotheses for the mechanisms of operation among underlying neural system. We demonstrate that age-related functional fingerprints are only supported if the model accounts for: (i) compensation of the individual brains for the overall loss of structural connectivity and (ii) decrease of propagation velocity due to the loss of myelination. We also show that with these 2 conditions, it is sufficient to decompose the time-delays as bimodal distribution that only distinguishes between intra- and inter-hemispheric delays, and that the same working point also captures the static FC the best, and produces the largest variability at slow time-scales.

Optimization of ictal aborting stimulation using the dynamotype taxonomy.

Electrical stimulation is an increasingly popular method to terminate epileptic seizures, yet it is not always successful. A potential reason for inconsistent efficacy is that stimuli are applied empirically without considering the underlying dynamical properties of a given seizure. We use a computational model of seizure dynamics to show that different bursting classes have disparate responses to aborting stimulation. This model was previously validated in a large set of human seizures and led to a description of the Taxonomy of Seizure Dynamics and the dynamotype, which is the clinical analog of the bursting class. In the model, the stimulation is realized as an applied input, which successfully aborts the burst when it forces the system from a bursting state to a quiescent state. This transition requires bistability, which is not present in all bursters. We examine how topological and geometric differences in the bistable state affect the probability of termination as the burster progresses from onset to offset. We find that the most significant determining factors are the burster class (dynamotype) and whether the burster has a DC (baseline) shift. Bursters with a baseline shift are far more likely to be terminated due to the necessary structure of their state space. Furthermore, we observe that the probability of termination varies throughout the burster's duration, is often dependent on the phase when it was applied, and is highly correlated to dynamotype. Our model provides a method to predict the optimal method of termination for each dynamotype. These results lead to the prediction that optimization of ictal aborting stimulation should account for seizure dynamotype, the presence of a DC shift, and the timing of the stimulation.

High-resolution virtual brain modeling personalizes deep brain stimulation for treatment-resistant depression: Spatiotemporal response characteristics following stimulation of neural fiber pathways.

Over the past 15 years, deep brain stimulation (DBS) has been actively investigated as a groundbreaking therapy for patients with treatment-resistant depression (TRD); nevertheless, outcomes have varied from patient to patient, with an average response rate of ∼50%. The engagement of specific fiber tracts at the stimulation site has been hypothesized to be an important factor in determining outcomes, however, the resulting individual network effects at the whole-brain scale remain largely unknown. Here we provide a computational framework that can explore each individual's brain response characteristics elicited by selective stimulation of fiber tracts. We use a novel personalized in-silico approach, the Virtual Big Brain, which makes use of high-resolution virtual brain models at a mm-scale and explicitly reconstructs more than 100,000 fiber tracts for each individual. Each fiber tract is active and can be selectively stimulated. Simulation results demonstrate distinct stimulus-induced event-related potentials as a function of stimulation location, parametrized by the contact positions of the electrodes implanted in each patient, even though validation against empirical patient data reveals some limitations (i.e., the need for individual parameter adjustment, and differential accuracy across stimulation locations). This study provides evidence for the capacity of personalized high-resolution virtual brain models to investigate individual network effects in DBS for patients with TRD and opens up novel avenues in the personalized optimization of brain stimulation.

The Human Brain Project-Synergy between neuroscience, computing, informatics, and brain-inspired technologies.

The Human Brain Project (HBP) is a European flagship project with a 10-year horizon aiming to understand the human brain and to translate neuroscience knowledge into medicine and technology. To achieve such aims, the HBP explores the multilevel complexity of the brain in space and time; transfers the acquired knowledge to brain-derived applications in health, computing, and technology; and provides shared and open computing tools and data through the HBP European brain research infrastructure. We discuss how the HBP creates a transdisciplinary community of researchers united by the quest to understand the brain, with fascinating perspectives on societal benefits.

On the influence of prior information evaluated by fully Bayesian criteria in a personalized whole-brain model of epilepsy spread.

Individualized anatomical information has been used as prior knowledge in Bayesian inference paradigms of whole-brain network models. However, the actual sensitivity to such personalized information in priors is still unknown. In this study, we introduce the use of fully Bayesian information criteria and leave-one-out cross-validation technique on the subject-specific information to assess different epileptogenicity hypotheses regarding the location of pathological brain areas based on a priori knowledge from dynamical system properties. The Bayesian Virtual Epileptic Patient (BVEP) model, which relies on the fusion of structural data of individuals, a generative model of epileptiform discharges, and a self-tuning Monte Carlo sampling algorithm, is used to infer the spatial map of epileptogenicity across different brain areas. Our results indicate that measuring the out-of-sample prediction accuracy of the BVEP model with informative priors enables reliable and efficient evaluation of potential hypotheses regarding the degree of epileptogenicity across different brain regions. In contrast, while using uninformative priors, the information criteria are unable to provide strong evidence about the epileptogenicity of brain areas. We also show that the fully Bayesian criteria correctly assess different hypotheses about both structural and functional components of whole-brain models that differ across individuals. The fully Bayesian information-theory based approach used in this study suggests a patient-specific strategy for epileptogenicity hypothesis testing in generative brain network models of epilepsy to improve surgical outcomes.

Data-driven method to infer the seizure propagation patterns in an epileptic brain from intracranial electroencephalography.

Surgical interventions in epileptic patients aimed at the removal of the epileptogenic zone have success rates at only 60-70%. This failure can be partly attributed to the insufficient spatial sampling by the implanted intracranial electrodes during the clinical evaluation, leading to an incomplete picture of spatio-temporal seizure organization in the regions that are not directly observed. Utilizing the partial observations of the seizure spreading through the brain network, complemented by the assumption that the epileptic seizures spread along the structural connections, we infer if and when are the unobserved regions recruited in the seizure. To this end we introduce a data-driven model of seizure recruitment and propagation across a weighted network, which we invert using the Bayesian inference framework. Using a leave-one-out cross-validation scheme on a cohort of 45 patients we demonstrate that the method can improve the predictions of the states of the unobserved regions compared to an empirical estimate that does not use the structural information, yet it is on the same level as the estimate that takes the structure into account. Furthermore, a comparison with the performed surgical resection and the surgery outcome indicates a link between the inferred excitable regions and the actual epileptogenic zone. The results emphasize the importance of the structural connectome in the large-scale spatio-temporal organization of epileptic seizures and introduce a novel way to integrate the patient-specific connectome and intracranial seizure recordings in a whole-brain computational model of seizure spread.

Dynamical Mechanisms of Interictal Resting-State Functional Connectivity in Epilepsy.

Drug-resistant focal epilepsy is a large-scale brain networks disorder characterized by altered spatiotemporal patterns of functional connectivity (FC), even during interictal resting state (RS). Although RS-FC-based metrics can detect these changes, results from RS functional magnetic resonance imaging (RS-fMRI) studies are unclear and difficult to interpret, and the underlying dynamical mechanisms are still largely unknown. To better capture the RS dynamics, we phenomenologically extended the neural mass model of partial seizures, the Epileptor, by including two neuron subpopulations of epileptogenic and nonepileptogenic type, making it capable of producing physiological oscillations in addition to the epileptiform activity. Using the neuroinformatics platform The Virtual Brain, we reconstructed 14 epileptic and 5 healthy human (of either sex) brain network models (BNMs), based on individual anatomical connectivity and clinically defined epileptogenic heatmaps. Through systematic parameter exploration and fitting to neuroimaging data, we demonstrated that epileptic brains during interictal RS are associated with lower global excitability induced by a shift in the working point of the model, indicating that epileptic brains operate closer to a stable equilibrium point than healthy brains. Moreover, we showed that functional networks are unaffected by interictal spikes, corroborating previous experimental findings; additionally, we observed higher excitability in epileptogenic regions, in agreement with the data. We shed light on new dynamical mechanisms responsible for altered RS-FC in epilepsy, involving the following two key factors: (1) a shift of excitability of the whole brain leading to increased stability; and (2) a locally increased excitability in the epileptogenic regions supporting the mixture of hyperconnectivity and hypoconnectivity in these areas.SIGNIFICANCE STATEMENT Advances in functional neuroimaging provide compelling evidence for epilepsy-related brain network alterations, even during the interictal resting state (RS). However, the dynamical mechanisms underlying these changes are still elusive. To identify local and network processes behind the RS-functional connectivity (FC) spatiotemporal patterns, we systematically manipulated the local excitability and the global coupling in the virtual human epileptic patient brain network models (BNMs), complemented by the analysis of the impact of interictal spikes and fitting to the neuroimaging data. Our results suggest that a global shift of the dynamic working point of the brain model, coupled with locally hyperexcitable node dynamics of the epileptogenic networks, provides a mechanistic explanation of the epileptic processes during the interictal RS period. These, in turn, are associated with the changes in FC.

Phase-lags in large scale brain synchronization: Methodological considerations and in-silico analysis.

Architecture of phase relationships among neural oscillations is central for their functional significance but has remained theoretically poorly understood. We use phenomenological model of delay-coupled oscillators with increasing degree of topological complexity to identify underlying principles by which the spatio-temporal structure of the brain governs the phase lags between oscillatory activity at distant regions. Phase relations and their regions of stability are derived and numerically confirmed for two oscillators and for networks with randomly distributed or clustered bimodal delays, as a first approximation for the brain structural connectivity. Besides in-phase, clustered delays can induce anti-phase synchronization for certain frequencies, while the sign of the lags is determined by the natural frequencies and by the inhomogeneous network interactions. For in-phase synchronization faster oscillators always phase lead, while stronger connected nodes lag behind the weaker during frequency depression, which consistently arises for in-silico results. If nodes are in anti-phase regime, then a distance π is added to the in-phase trends. The statistics of the phases is calculated from the phase locking values (PLV), as in many empirical studies, and we scrutinize the method's impact. The choice of surrogates do not affects the mean of the observed phase lags, but higher significance levels that are generated by some surrogates, cause decreased variance and might fail to detect the generally weaker coherence of the interhemispheric links. These links are also affected by the non-stationary and intermittent synchronization, which causes multimodal phase lags that can be misleading if averaged. Taken together, the results describe quantitatively the impact of the spatio-temporal connectivity of the brain to the synchronization patterns between brain regions, and to uncover mechanisms through which the spatio-temporal structure of the brain renders phases to be distributed around 0 and π. TRIAL REGISTRATION: South African Clinical Trials Register: http://www.sanctr.gov.za/SAClinicalbrnbspTrials/tabid/169/Default.aspx, then link to respiratory tract then link to tuberculosis, pulmonary; and TASK Applied Sciences Clinical Trials, AP-TB-201-16 (ALOPEXX): https://task.org.za/clinical-trials/.

Transmission time delays organize the brain network synchronization.

The timing of activity across brain regions can be described by its phases for oscillatory processes, and is of crucial importance for brain functioning. The structure of the brain constrains its dynamics through the delays due to propagation and the strengths of the white matter tracts. We use self-sustained delay-coupled, non-isochronous, nonlinearly damped and chaotic oscillators to study how spatio-temporal organization of the brain governs phase lags between the coherent activity of its regions. In silico results for the brain network model demonstrate a robust switching from in- to anti-phase synchronization by increasing the frequency, with a consistent lagging of the stronger connected regions. Relative phases are well predicted by an earlier analysis of Kuramoto oscillators, confirming the spatial heterogeneity of time delays as a crucial mechanism in shaping the functional brain architecture. Increased frequency and coupling are also shown to distort the oscillators by decreasing their amplitude, and stronger regions have lower, but more synchronized activity. These results indicate specific features in the phase relationships within the brain that need to hold for a wide range of local oscillatory dynamics, given that the time delays of the connectome are proportional to the lengths of the structural pathways. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.

Individual brain structure and modelling predict seizure propagation.

See Lytton (doi:10.1093/awx018) for a scientific commentary on this article.Neural network oscillations are a fundamental mechanism for cognition, perception and consciousness. Consequently, perturbations of network activity play an important role in the pathophysiology of brain disorders. When structural information from non-invasive brain imaging is merged with mathematical modelling, then generative brain network models constitute personalized in silico platforms for the exploration of causal mechanisms of brain function and clinical hypothesis testing. We here demonstrate with the example of drug-resistant epilepsy that patient-specific virtual brain models derived from diffusion magnetic resonance imaging have sufficient predictive power to improve diagnosis and surgery outcome. In partial epilepsy, seizures originate in a local network, the so-called epileptogenic zone, before recruiting other close or distant brain regions. We create personalized large-scale brain networks for 15 patients and simulate the individual seizure propagation patterns. Model validation is performed against the presurgical stereotactic electroencephalography data and the standard-of-care clinical evaluation. We demonstrate that the individual brain models account for the patient seizure propagation patterns, explain the variability in postsurgical success, but do not reliably augment with the use of patient-specific connectivity. Our results show that connectome-based brain network models have the capacity to explain changes in the organization of brain activity as observed in some brain disorders, thus opening up avenues towards discovery of novel clinical interventions.

Anatomic consistencies across epilepsies: a stereotactic-EEG informed high-resolution structural connectivity study.

See Bernasconi (doi:10.1093/brain/awx229) for a scientific commentary on this article. Drug-resistant localization-related epilepsies are now recognized as network diseases. However, the exact relationship between the organization of the epileptogenic network and brain anatomy overall remains incompletely understood. To better understand this relationship, we studied structural connectivity obtained from diffusion weighted imaging in patients with epilepsy using both stereo-electroencephalography (SEEG)-determined epileptic brain regions and whole-brain analysis. High resolution structural connectivity analysis was applied in 15 patients with drug-resistant localization-related epilepsies and 36 healthy control subjects to study structural connectivity changes in epilepsy. Two different methods of structural connectivity analysis were carried out using diffusion weighted imaging, one focusing on the relationship between epileptic regions determined by SEEG investigations and one blinded to epileptic regions looking at whole-brain connectivity. First, we performed zone-based analysis comparing structural connectivity findings in patients and controls within and between SEEG-defined zones of interest. Next, we performed whole-brain structural connectivity analysis in all subjects and compared findings to the same SEEG-defined zones of interest. Finally, structural connectivity findings were correlated against clinical features. Zone-based analysis revealed no significant decreased structural connectivity within nodes of the epilepsy network at the group level, but did demonstrate significant structural connectivity differences between nodes of the epileptogenic network (regions involved in seizures generation and propagation) and the remaining of the brain in patients compared to controls. Whole-brain analyses showed a total of 133 clusters of significantly decreased structural connectivity across all patients. One cluster of significantly increased structural connectivity was identified in a single patient. Clusters of decreased structural connectivity showed topographical preference for both the salience and default mode networks despite clinical heterogeneity within our patient sample. Correlation analysis did not reveal any significant findings regarding either the effect of age at disease onset, disease duration or post-surgical outcome on structural connectivity. Taken together, this work demonstrates that structural connectivity disintegration targets distributed functional networks while sparing the epilepsy network.

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.

Emerging concepts for the dynamical organization of resting-state activity in the brain.

A broad body of experimental work has demonstrated that apparently spontaneous brain activity is not random. At the level of large-scale neural systems, as measured with functional MRI (fMRI), this ongoing activity reflects the organization of a series of highly coherent functional networks. These so-called resting-state networks (RSNs) closely relate to the underlying anatomical connectivity but cannot be understood in those terms alone. Here we review three large-scale neural system models of primate neocortex that emphasize the key contributions of local dynamics, signal transmission delays and noise to the emerging RSNs. We propose that the formation and dissolution of resting-state patterns reflects the exploration of possible functional network configurations around a stable anatomical skeleton.

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.

Identification of optimal structural connectivity using functional connectivity and neural modeling.

The complex network dynamics that arise from the interaction of the brain's structural and functional architectures give rise to mental function. Theoretical models demonstrate that the structure-function relation is maximal when the global network dynamics operate at a critical point of state transition. In the present work, we used a dynamic mean-field neural model to fit empirical structural connectivity (SC) and functional connectivity (FC) data acquired in humans and macaques and developed a new iterative-fitting algorithm to optimize the SC matrix based on the FC matrix. A dramatic improvement of the fitting of the matrices was obtained with the addition of a small number of anatomical links, particularly cross-hemispheric connections, and reweighting of existing connections. We suggest that the notion of a critical working point, where the structure-function interplay is maximal, may provide a new way to link behavior and cognition, and a new perspective to understand recovery of function in clinical conditions.

Functional connectivity dynamics: modeling the switching behavior of the resting state.

Functional connectivity (FC) sheds light on the interactions between different brain regions. Besides basic research, it is clinically relevant for applications in Alzheimer's disease, schizophrenia, presurgical planning, epilepsy, and traumatic brain injury. Simulations of whole-brain mean-field computational models with realistic connectivity determined by tractography studies enable us to reproduce with accuracy aspects of average FC in the resting state. Most computational studies, however, did not address the prominent non-stationarity in resting state FC, which may result in large intra- and inter-subject variability and thus preclude an accurate individual predictability. Here we show that this non-stationarity reveals a rich structure, characterized by rapid transitions switching between a few discrete FC states. We also show that computational models optimized to fit time-averaged FC do not reproduce these spontaneous state transitions and, thus, are not qualitatively superior to simplified linear stochastic models, which account for the effects of structure alone. We then demonstrate that a slight enhancement of the non-linearity of the network nodes is sufficient to broaden the repertoire of possible network behaviors, leading to modes of fluctuations, reminiscent of some of the most frequently observed Resting State Networks. Because of the noise-driven exploration of this repertoire, the dynamics of FC qualitatively change now and display non-stationary switching similar to empirical resting state recordings (Functional Connectivity Dynamics (FCD)). Thus FCD bear promise to serve as a better biomarker of resting state neural activity and of its pathologic alterations.

An automated pipeline for constructing personalized virtual brains from multimodal neuroimaging data.

Large amounts of multimodal neuroimaging data are acquired every year worldwide. In order to extract high-dimensional information for computational neuroscience applications standardized data fusion and efficient reduction into integrative data structures are required. Such self-consistent multimodal data sets can be used for computational brain modeling to constrain models with individual measurable features of the brain, such as done with The Virtual Brain (TVB). TVB is a simulation platform that uses empirical structural and functional data to build full brain models of individual humans. For convenient model construction, we developed a processing pipeline for structural, functional and diffusion-weighted magnetic resonance imaging (MRI) and optionally electroencephalography (EEG) data. The pipeline combines several state-of-the-art neuroinformatics tools to generate subject-specific cortical and subcortical parcellations, surface-tessellations, structural and functional connectomes, lead field matrices, electrical source activity estimates and region-wise aggregated blood oxygen level dependent (BOLD) functional MRI (fMRI) time-series. The output files of the pipeline can be directly uploaded to TVB to create and simulate individualized large-scale network models that incorporate intra- and intercortical interaction on the basis of cortical surface triangulations and white matter tractograpy. We detail the pitfalls of the individual processing streams and discuss ways of validation. With the pipeline we also introduce novel ways of estimating the transmission strengths of fiber tracts in whole-brain structural connectivity (SC) networks and compare the outcomes of different tractography or parcellation approaches. We tested the functionality of the pipeline on 50 multimodal data sets. In order to quantify the robustness of the connectome extraction part of the pipeline we computed several metrics that quantify its rescan reliability and compared them to other tractography approaches. Together with the pipeline we present several principles to guide future efforts to standardize brain model construction. The code of the pipeline and the fully processed data sets are made available to the public via The Virtual Brain website (thevirtualbrain.org) and via github (https://github.com/BrainModes/TVB-empirical-data-pipeline). Furthermore, the pipeline can be directly used with High Performance Computing (HPC) resources on the Neuroscience Gateway Portal (http://www.nsgportal.org) through a convenient web-interface.

Mathematical framework for large-scale brain network modeling in The Virtual Brain.

In this article, we describe the mathematical framework of the computational model at the core of the tool The Virtual Brain (TVB), designed to simulate collective whole brain dynamics by virtualizing brain structure and function, allowing simultaneous outputs of a number of experimental modalities such as electro- and magnetoencephalography (EEG, MEG) and functional Magnetic Resonance Imaging (fMRI). The implementation allows for a systematic exploration and manipulation of every underlying component of a large-scale brain network model (BNM), such as the neural mass model governing the local dynamics or the structural connectivity constraining the space time structure of the network couplings. Here, a consistent notation for the generalized BNM is given, so that in this form the equations represent a direct link between the mathematical description of BNMs and the components of the numerical implementation in TVB. Finally, we made a summary of the forward models implemented for mapping simulated neural activity (EEG, MEG, sterotactic electroencephalogram (sEEG), fMRI), identifying their advantages and limitations.

Effects of task and age on the magnitude and structure of force fluctuations: insights into underlying neuro-behavioral processes.

BACKGROUND: The present study aimed at characterizing the effects of increasing (relative) force level and aging on isometric force control. To achieve this objective and to infer changes in the underlying control mechanisms, measures of information transmission, as well as magnitude and time-frequency structure of behavioral variability were applied to force-time-series. RESULTS: Older adults were found to be weaker, more variable, and less efficient than young participants. As a function of force level, efficiency followed an inverted-U shape in both groups, suggesting a similar organization of the force control system. The time-frequency structure of force output fluctuations was only significantly affected by task conditions. Specifically, a narrower spectral distribution with more long-range correlations and an inverted-U pattern of complexity changes were observed with increasing force level. Although not significant older participants displayed on average a less complex behavior for low and intermediate force levels. The changes in force signal's regularity presented a strong dependence on time-scales, which significantly interacted with age and condition. An inverted-U profile was only observed for the time-scale relevant to the sensorimotor control process. However, in both groups the peak was not aligned with the optimum of efficiency. CONCLUSION: Our results support the view that behavioral variability, in terms of magnitude and structure, has a functional meaning and affords non-invasive markers of the adaptations of the sensorimotor control system to various constraints. The measures of efficiency and variability ought to be considered as complementary since they convey specific information on the organization of control processes. The reported weak age effect on variability and complexity measures suggests that the behavioral expression of the loss of complexity hypothesis is not as straightforward as conventionally admitted. However, group differences did not completely vanish, which suggests that age differences can be more or less apparent depending on task properties and whether difficulty is scaled in relative or absolute terms.

On the nature of seizure dynamics.

Seizures can occur spontaneously and in a recurrent manner, which defines epilepsy; or they can be induced in a normal brain under a variety of conditions in most neuronal networks and species from flies to humans. Such universality raises the possibility that invariant properties exist that characterize seizures under different physiological and pathological conditions. Here, we analysed seizure dynamics mathematically and established a taxonomy of seizures based on first principles. For the predominant seizure class we developed a generic model called Epileptor. As an experimental model system, we used ictal-like discharges induced in vitro in mouse hippocampi. We show that only five state variables linked by integral-differential equations are sufficient to describe the onset, time course and offset of ictal-like discharges as well as their recurrence. Two state variables are responsible for generating rapid discharges (fast time scale), two for spike and wave events (intermediate time scale) and one for the control of time course, including the alternation between 'normal' and ictal periods (slow time scale). We propose that normal and ictal activities coexist: a separatrix acts as a barrier (or seizure threshold) between these states. Seizure onset is reached upon the collision of normal brain trajectories with the separatrix. We show theoretically and experimentally how a system can be pushed toward seizure under a wide variety of conditions. Within our experimental model, the onset and offset of ictal-like discharges are well-defined mathematical events: a saddle-node and homoclinic bifurcation, respectively. These bifurcations necessitate a baseline shift at onset and a logarithmic scaling of interspike intervals at offset. These predictions were not only confirmed in our in vitro experiments, but also for focal seizures recorded in different syndromes, brain regions and species (humans and zebrafish). Finally, we identified several possible biophysical parameters contributing to the five state variables in our model system. We show that these parameters apply to specific experimental conditions and propose that there exists a wide array of possible biophysical mechanisms for seizure genesis, while preserving central invariant properties. Epileptor and the seizure taxonomy will guide future modeling and translational research by identifying universal rules governing the initiation and termination of seizures and predicting the conditions necessary for those transitions.