Bifurcations and bursting in the Epileptor.

The Epileptor is a phenomenological model for seizure activity that is used in a personalized large-scale brain modeling framework, the Virtual Epileptic Patient, with the aim of improving surgery outcomes for drug-resistant epileptic patients. Transitions between interictal and ictal states are modeled as bifurcations, enabling the definition of seizure classes in terms of onset/offset bifurcations. This establishes a taxonomy of seizures grounded in their essential underlying dynamics and the Epileptor replicates the activity of the most common class, as observed in patients with focal epilepsy, which is characterized by square-wave bursting properties. The Epileptor also encodes an additional mechanism to account for interictal spikes and spike and wave discharges. Here we use insights from a more generic model for square-wave bursting, based on the Unfolding Theory approach, to guide the bifurcation analysis of the Epileptor and gain a deeper understanding of the model and the role of its parameters. We show how the Epileptor's parameters can be modified to produce activities for other seizures classes of the taxonomy, as observed in patients, so that the large-scale brain models could be further personalized. Some of these classes have already been described in the literature in the Epileptor, others, predicted by the generic model, are new. Finally, we unveil how the interaction with the additional mechanism for spike and wave discharges alters the bifurcation structure of the main burster.

Parameter estimation in a whole-brain network model of epilepsy: Comparison of parallel global optimization solvers.

The Virtual Epileptic Patient (VEP) refers to a computer-based representation of a patient with epilepsy that combines personalized anatomical data with dynamical models of abnormal brain activities. It is capable of generating spatio-temporal seizure patterns that resemble those recorded with invasive methods such as stereoelectro EEG data, allowing for the evaluation of clinical hypotheses before planning surgery. This study highlights the effectiveness of calibrating VEP models using a global optimization approach. The approach utilizes SaCeSS, a cooperative metaheuristic algorithm capable of parallel computation, to yield high-quality solutions without requiring excessive computational time. Through extensive benchmarking on synthetic data, our proposal successfully solved a set of different configurations of VEP models, demonstrating better scalability and superior performance against other parallel solvers. These results were further enhanced using a Bayesian optimization framework for hyperparameter tuning, with significant gains in terms of both accuracy and computational cost. Additionally, we added a scalable uncertainty quantification phase after model calibration, and used it to assess the variability in estimated parameters across different problems. Overall, this study has the potential to improve the estimation of pathological brain areas in drug-resistant epilepsy, thereby to inform the clinical decision-making process.

Incorporating slow NMDA-type receptors with nonlinear voltage-dependent magnesium block in a next generation neural mass model: derivation and dynamics.

We derive a next generation neural mass model of a population of quadratic-integrate-and-fire neurons, with slow adaptation, and conductance-based AMPAR, GABAR and nonlinear NMDAR synapses. We show that the Lorentzian ansatz assumption can be satisfied by introducing a piece-wise polynomial approximation of the nonlinear voltage-dependent magnesium block of NMDAR current. We study the dynamics of the resulting system for two example cases of excitatory cortical neurons and inhibitory striatal neurons. Bifurcation diagrams are presented comparing the different dynamical regimes as compared to the case of linear NMDAR currents, along with sample comparison simulation time series demonstrating different possible oscillatory solutions. The omission of the nonlinearity of NMDAR currents results in a shift in the range (and possible disappearance) of the constant high firing rate regime, along with a modulation in the amplitude and frequency power spectrum of oscillations. Moreover, nonlinear NMDAR action is seen to be state-dependent and can have opposite effects depending on the type of neurons involved and the level of input firing rate received. The presented model can serve as a computationally efficient building block in whole brain network models for investigating the differential modulation of different types of synapses under neuromodulatory influence or receptor specific malfunction.

Inference on the Macroscopic Dynamics of Spiking Neurons.

The process of inference on networks of spiking neurons is essential to decipher the underlying mechanisms of brain computation and function. In this study, we conduct inference on parameters and dynamics of a mean-field approximation, simplifying the interactions of neurons. Estimating parameters of this class of generative model allows one to predict the system's dynamics and responses under changing inputs and, indeed, changing parameters. We first assume a set of known state-space equations and address the problem of inferring the lumped parameters from observed time series. Crucially, we consider this problem in the setting of bistability, random fluctuations in system dynamics, and partial observations, in which some states are hidden. To identify the most efficient estimation or inversion scheme in this particular system identification, we benchmark against state-of-the-art optimization and Bayesian estimation algorithms, highlighting their strengths and weaknesses. Additionally, we explore how well the statistical relationships between parameters are maintained across different scales. We found that deep neural density estimators outperform other algorithms in the inversion scheme, despite potentially resulting in overestimated uncertainty and correlation between parameters. Nevertheless, this issue can be improved by incorporating time-delay embedding. We then eschew the mean-field approximation and employ deep neural ODEs on spiking neurons, illustrating prediction of system dynamics and vector fields from microscopic states. Overall, this study affords an opportunity to predict brain dynamics and responses to various perturbations or pharmacological interventions using deep neural networks.

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.

Brain fingerprint is based on the aperiodic, scale-free, neuronal activity.

Subject differentiation bears the possibility to individualize brain analyses. However, the nature of the processes generating subject-specific features remains unknown. Most of the current literature uses techniques that assume stationarity (e.g., Pearson's correlation), which might fail to capture the non-linear nature of brain activity. We hypothesize that non-linear perturbations (defined as neuronal avalanches in the context of critical dynamics) spread across the brain and carry subject-specific information, contributing the most to differentiability. To test this hypothesis, we compute the avalanche transition matrix (ATM) from source-reconstructed magnetoencephalographic data, as to characterize subject-specific fast dynamics. We perform differentiability analysis based on the ATMs, and compare the performance to that obtained using Pearson's correlation (which assumes stationarity). We demonstrate that selecting the moments and places where neuronal avalanches spread improves differentiation (P < 0.0001, permutation testing), despite the fact that most of the data (i.e., the linear part) are discarded. Our results show that the non-linear part of the brain signals carries most of the subject-specific information, thereby clarifying the nature of the processes that underlie individual differentiation. Borrowing from statistical mechanics, we provide a principled way to link emergent large-scale personalized activations to non-observable, microscopic processes.

The virtual aging brain: Causal inference supports interhemispheric dedifferentiation in healthy aging.

The mechanisms of cognitive decline and its variability during healthy aging are not fully understood, but have been associated with reorganization of white matter tracts and functional brain networks. Here, we built a brain network modeling framework to infer the causal link between structural connectivity and functional architecture and the consequent cognitive decline in aging. By applying in-silico interhemispheric degradation of structural connectivity, we reproduced the process of functional dedifferentiation during aging. Thereby, we found the global modulation of brain dynamics by structural connectivity to increase with age, which was steeper in older adults with poor cognitive performance. We validated our causal hypothesis via a deep-learning Bayesian approach. Our results might be the first mechanistic demonstration of dedifferentiation during aging leading to cognitive decline.

From phenomenological to biophysical models of seizures.

Epilepsy is a complex disease that requires various approaches for its study. This short review discusses the contribution of theoretical and computational models. The review presents theoretical frameworks that underlie the understanding of certain seizure properties and their classification based on their dynamical properties at the onset and offset of seizures. Dynamical system tools are valuable resources in the study of seizures. These tools can provide insights into seizure mechanisms and offer a framework for their classification, by analyzing the complex, dynamic behavior of seizures. Additionally, computational models have high potential for clinical applications, as they can be used to develop more accurate diagnostic and personalized medicine tools. We discuss various modeling approaches that span different scales and levels, while also questioning the neurocentric view, emphasizing the importance of considering glial cells. Finally, we explore the epistemic value provided by this type of approach.

Fading of brain network fingerprint in Parkinson's disease predicts motor clinical impairment.

The clinical connectome fingerprint (CCF) was recently introduced as a way to assess brain dynamics. It is an approach able to recognize individuals, based on the brain network. It showed its applicability providing network features used to predict the cognitive decline in preclinical Alzheimer's disease. In this article, we explore the performance of CCF in 47 Parkinson's disease (PD) patients and 47 healthy controls, under the hypothesis that patients would show reduced identifiability as compared to controls, and that such reduction could be used to predict motor impairment. We used source-reconstructed magnetoencephalography signals to build two functional connectomes for 47 patients with PD and 47 healthy controls. Then, exploiting the two connectomes per individual, we investigated the identifiability characteristics of each subject in each group. We observed reduced identifiability in patients compared to healthy individuals in the beta band. Furthermore, we found that the reduction in identifiability was proportional to the motor impairment, assessed through the Unified Parkinson's Disease Rating Scale, and, interestingly, able to predict it (at the subject level), through a cross-validated regression model. Along with previous evidence, this article shows that CCF captures disrupted dynamics in neurodegenerative diseases and is particularly effective in predicting motor clinical impairment in PD.

Combining sodium MRI, proton MR spectroscopic imaging, and intracerebral EEG in epilepsy.

Whole brain ionic and metabolic imaging has potential as a powerful tool for the characterization of brain diseases. We combined sodium MRI (23 Na MRI) and 1 H-MR Spectroscopic Imaging (1 H-MRSI), assessing changes within epileptogenic networks in comparison with electrophysiologically normal networks as defined by stereotactic EEG (SEEG) recordings analysis. We applied a multi-echo density adapted 3D projection reconstruction pulse sequence at 7 T (23 Na-MRI) and a 3D echo-planar spectroscopic imaging sequence at 3 T (1 H-MRSI) in 19 patients suffering from drug-resistant focal epilepsy who underwent presurgical SEEG. We investigated 23 Na MRI parameters including total sodium concentration (TSC) and the sodium signal fraction associated with the short component of T2 * decay (f), alongside the level of metabolites N-acetyl aspartate (NAA), choline compounds (Cho), and total creatine (tCr). All measures were extracted from spherical regions of interest (ROIs) centered between two adjacent SEEG electrode contacts and z-scored against the same ROI in controls. Group comparison showed a significant increase in f only in the epileptogenic zone (EZ) compared to controls and compared to patients' propagation zone (PZ) and non-involved zone (NIZ). TSC was significantly increased in all patients' regions compared to controls. Conversely, NAA levels were significantly lower in patients compared to controls, and lower in the EZ compared to PZ and NIZ. Multiple regression analyzing the relationship between sodium and metabolites levels revealed significant relations in PZ and in NIZ but not in EZ. Our results are in agreement with the energetic failure hypothesis in epileptic regions associated with widespread tissue reorganization.

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.

Altered spreading of neuronal avalanches in temporal lobe epilepsy relates to cognitive performance: A resting-state hdEEG study.

OBJECTIVE: Large aperiodic bursts of activations named neuronal avalanches have been used to characterize whole-brain activity, as their presence typically relates to optimal dynamics. Epilepsy is characterized by alterations in large-scale brain network dynamics. Here we exploited neuronal avalanches to characterize differences in electroencephalography (EEG) basal activity, free from seizures and/or interictal spikes, between patients with temporal lobe epilepsy (TLE) and matched controls. METHOD: We defined neuronal avalanches as starting when the z-scored source-reconstructed EEG signals crossed a specific threshold in any region and ending when all regions returned to baseline. This technique avoids data manipulation or assumptions of signal stationarity, focusing on the aperiodic, scale-free components of the signals. We computed individual avalanche transition matrices to track the probability of avalanche spreading across any two regions, compared them between patients and controls, and related them to memory performance in patients. RESULTS: We observed a robust topography of significant edges clustering in regions functionally and structurally relevant for the TLE, such as the entorhinal cortex, the inferior parietal and fusiform area, the inferior temporal gyrus, and the anterior cingulate cortex. We detected a significant correlation between the centrality of the entorhinal cortex in the transition matrix and the long-term memory performance (delay recall Rey-Osterrieth Complex Figure Test). SIGNIFICANCE: Our results show that the propagation patterns of large-scale neuronal avalanches are altered in TLE during the resting state, suggesting a potential diagnostic application in epilepsy. Furthermore, the relationship between specific patterns of propagation and memory performance support the neurophysiological relevance of neuronal avalanches.

Personalized whole brain modeling of status epilepticus.

How status epilepticus (SE) is generated and propagates in the brain is not known. As for seizures, a patient-specific approach is necessary, and the analysis should be performed at the whole brain level. Personalized brain models can be used to study seizure genesis and propagation at the whole brain scale in The Virtual Brain (TVB), using the Epileptor mathematical construct. Building on the fact that SE is part of the repertoire of activities that the Epileptor can generate, we present the first attempt to model SE at the whole brain scale in TVB, using data from a patient who experienced SE during presurgical evaluation. Simulations reproduced the patterns found with SEEG recordings. We find that if, as expected, the pattern of SE propagation correlates with the properties of the patient's structural connectome, SE propagation also depends upon the global state of the network, i.e., that SE propagation is an emergent property. We conclude that individual brain virtualization can be used to study SE genesis and propagation. This type of theoretical approach may be used to design novel interventional approaches to stop SE. This paper was presented at the 8th London-Innsbruck Colloquium on Status Epilepticus and Acute Seizures held in September 2022.

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.

Brain simulation as a cloud service: The Virtual Brain on EBRAINS.

The Virtual Brain (TVB) is now available as open-source services on the cloud research platform EBRAINS (ebrains.eu). It offers software for constructing, simulating and analysing brain network models including the TVB simulator; magnetic resonance imaging (MRI) processing pipelines to extract structural and functional brain networks; combined simulation of large-scale brain networks with small-scale spiking networks; automatic conversion of user-specified model equations into fast simulation code; simulation-ready brain models of patients and healthy volunteers; Bayesian parameter optimization in epilepsy patient models; data and software for mouse brain simulation; and extensive educational material. TVB cloud services facilitate reproducible online collaboration and discovery of data assets, models, and software embedded in scalable and secure workflows, a precondition for research on large cohort data sets, better generalizability, and clinical translation.

Computational modeling of seizure spread on a cortical surface.

In the field of computational epilepsy, neural field models helped to understand some large-scale features of seizure dynamics. These insights however remain on general levels, without translation to the clinical settings via personalization of the model with the patient-specific structure. In particular, a link was suggested between epileptic seizures spreading across the cortical surface and the so-called theta-alpha activity (TAA) pattern seen on intracranial electrographic signals, yet this link was not demonstrated on a patient-specific level. Here we present a single patient computational study linking the seizure spreading across the patient-specific cortical surface with a specific instance of the TAA pattern recorded in the patient. Using the realistic geometry of the cortical surface we perform the simulations of seizure dynamics in The Virtual Brain platform, and we show that the simulated electrographic signals qualitatively agree with the recorded signals. Furthermore, the comparison with the simulations performed on surrogate surfaces reveals that the best quantitative fit is obtained for the real surface. The work illustrates how the patient-specific cortical geometry can be utilized in The Virtual Brain for personalized model building, and the importance of such approach.

A unified physiological framework of transitions between seizures, sustained ictal activity and depolarization block at the single neuron level.

The majority of seizures recorded in humans and experimental animal models can be described by a generic phenomenological mathematical model, the Epileptor. In this model, seizure-like events (SLEs) are driven by a slow variable and occur via saddle node (SN) and homoclinic bifurcations at seizure onset and offset, respectively. Here we investigated SLEs at the single cell level using a biophysically relevant neuron model including a slow/fast system of four equations. The two equations for the slow subsystem describe ion concentration variations and the two equations of the fast subsystem delineate the electrophysiological activities of the neuron. Using extracellular K+ as a slow variable, we report that SLEs with SN/homoclinic bifurcations can readily occur at the single cell level when extracellular K+ reaches a critical value. In patients and experimental models, seizures can also evolve into sustained ictal activity (SIA) and depolarization block (DB), activities which are also parts of the dynamic repertoire of the Epileptor. Increasing extracellular concentration of K+ in the model to values found during experimental status epilepticus and DB, we show that SIA and DB can also occur at the single cell level. Thus, seizures, SIA, and DB, which have been first identified as network events, can exist in a unified framework of a biophysical model at the single neuron level and exhibit similar dynamics as observed in the Epileptor.Author Summary: Epilepsy is a neurological disorder characterized by the occurrence of seizures. Seizures have been characterized in patients in experimental models at both macroscopic and microscopic scales using electrophysiological recordings. Experimental works allowed the establishment of a detailed taxonomy of seizures, which can be described by mathematical models. We can distinguish two main types of models. Phenomenological (generic) models have few parameters and variables and permit detailed dynamical studies often capturing a majority of activities observed in experimental conditions. But they also have abstract parameters, making biological interpretation difficult. Biophysical models, on the other hand, use a large number of variables and parameters due to the complexity of the biological systems they represent. Because of the multiplicity of solutions, it is difficult to extract general dynamical rules. In the present work, we integrate both approaches and reduce a detailed biophysical model to sufficiently low-dimensional equations, and thus maintaining the advantages of a generic model. We propose, at the single cell level, a unified framework of different pathological activities that are seizures, depolarization block, and sustained ictal activity.

Virtual epileptic patient brain modeling: Relationships with seizure onset and surgical outcome.

OBJECTIVE: The virtual epileptic patient (VEP) is a large-scale brain modeling method based on virtual brain technology, using stereoelectroencephalography (SEEG), anatomical data (magnetic resonance imaging [MRI] and connectivity), and a computational neuronal model to provide computer simulations of a patient's seizures. VEP has potential interest in the presurgical evaluation of drug-resistant epilepsy by identifying regions most likely to generate seizures. We aimed to assess the performance of the VEP approach in estimating the epileptogenic zone and in predicting surgical outcome. METHODS: VEP modeling was retrospectively applied in a cohort of 53 patients with pharmacoresistant epilepsy and available SEEG, T1-weighted MRI, and diffusion-weighted MRI. Precision recall was used to compare the regions identified as epileptogenic by VEP (EZVEP ) to the epileptogenic zone defined by clinical analysis incorporating the Epileptogenicity Index (EI) method (EZC ). In 28 operated patients, we compared the VEP results and clinical analysis with surgical outcome. RESULTS: VEP showed a precision of 64% and a recall of 44% for EZVEP detection compared to EZC . There was a better concordance of VEP predictions with clinical results, with higher precision (77%) in seizure-free compared to non-seizure-free patients. Although the completeness of resection was significantly correlated with surgical outcome for both EZC and EZVEP , there was a significantly higher number of regions defined as epileptogenic exclusively by VEP that remained nonresected in non-seizure-free patients. SIGNIFICANCE: VEP is the first computational model that estimates the extent and organization of the epileptogenic zone network. It is characterized by good precision in detecting epileptogenic regions as defined by a combination of visual analysis and EI. The potential impact of VEP on improving surgical prognosis remains to be exploited. Analysis of factors limiting the performance of the actual model is crucial for its further development.

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.

Evidence for spreading seizure as a cause of theta-alpha activity electrographic pattern in stereo-EEG seizure recordings.

Intracranial electroencephalography is a standard tool in clinical evaluation of patients with focal epilepsy. Various early electrographic seizure patterns differing in frequency, amplitude, and waveform of the oscillations are observed. The pattern most common in the areas of seizure propagation is the so-called theta-alpha activity (TAA), whose defining features are oscillations in the θ - α range and gradually increasing amplitude. A deeper understanding of the mechanism underlying the generation of the TAA pattern is however lacking. In this work we evaluate the hypothesis that the TAA patterns are caused by seizures spreading across the cortex. To do so, we perform simulations of seizure dynamics on detailed patient-derived cortical surfaces using the spreading seizure model as well as reference models with one or two homogeneous sources. We then detect the occurrences of the TAA patterns both in the simulated stereo-electroencephalographic signals and in the signals of recorded epileptic seizures from a cohort of fifty patients, and we compare the features of the groups of detected TAA patterns to assess the plausibility of the different models. Our results show that spreading seizure hypothesis is qualitatively consistent with the evidence available in the seizure recordings, and it can explain the features of the detected TAA groups best among the examined models.