Modeling seizures: From single neurons to networks

Cortical stability and chaos during focal seizures: insights from inference-based modeling

Objective.Epilepsy affects millions globally, with a significant subset of patients suffering from drug-resistant focal seizures. Understanding the underlying neurodynamics of seizure initiation and propagation is crucial for advancing treatment and diagnostics. In this study, we present a novel, inference-based approach for analyzing the temporal evolution of cortical stability and chaos during focal epileptic seizures.Approach.Utilizing a multi-region neural mass model, we estimate time-varying synaptic connectivity from intracranial electroencephalography (iEEG) data collected from individuals with drug-resistant focal epilepsy.Main results.Our analysis reveals distinct preictal and ictal phases characterized by shifts in cortical stability, heightened chaos in the ictal phase, and highlight the critical role of inter-regional communication in driving chaotic cortical behaviour. We demonstrate that cortical dynamics are consistently destabilized prior to seizure onset, with a transient reduction in instability at seizure onset, followed by a significant increase throughout the seizure.Significance.This work provides new insights into the mechanisms of seizure generation and offers potential biomarkers for predicting seizure events. Our findings pave the way for innovative therapeutic strategies targeting cortical stability and chaos to manage epilepsy.

Development of a Computational Model For ECT Stimulation Titration

Electroconvulsive Therapy (ECT) is an effective treatment for treatment-resistant depression and other neurological illnesses. Nevertheless, the precise mechanism by which the dosage and stimulation configuration of ECT induce seizures in the brain remains unknown. Our objective is to create a computational model for ECT titration dosing and determine the relationship between seizure threshold, stimulus dosage, and individual head structure. We use a first-order differential equation combined with realistic head structures from magnetic resonance images of 7 participants. The ECT electric potential distribution was simulated for each head model using the COMSOL 6.1 finite element software. Reasonable predictions were achieved using a simple first-order RC electric circuit, successfully forecasting the seizure threshold for 5 out of 7 participants. Nevertheless, it is notable that one participant was titrated for a much longer period, potentially triggering an additional inhibitory mechanism not accounted for. The inclusion of non-linear dynamics further enhances predictions. The study revealed a time constant of approximately 0.5-3 seconds, indicating a non-ionic membrane component underlying seizure initiation. More probable mechanisms might be a transient rise in the permeability of the blood-brain barrier or the buildup of neurotransmitters. In conclusion, seizure threshold during ECT titration can be predicted using a finite element head model coupled with first-order dynamics.

A Mean Field to Capture Asynchronous Irregular Dynamics of Conductance-Based Networks of Adaptive Quadratic Integrate-and-Fire Neuron Models

Mean-field models are a class of models used in computational neuroscience to study the behavior of large populations of neurons. These models are based on the idea of representing the activity of a large number of neurons as the average behavior of mean-field variables. This abstraction allows the study of large-scale neural dynamics in a computationally efficient and mathematically tractable manner. One of these methods, based on a semianalytical approach, has previously been applied to different types of single-neuron models, but never to models based on a quadratic form. In this work, we adapted this method to quadratic integrate-and-fire neuron models with adaptation and conductance-based synaptic interactions. We validated the mean-field model by comparing it to the spiking network model. This mean-field model should be useful to model large-scale activity based on quadratic neurons interacting with conductance-based synapses.

Linking fast and slow: The case for generative models

A pervasive challenge in neuroscience is testing whether neuronal connectivity changes over time due to specific causes, such as stimuli, events, or clinical interventions. Recent hardware innovations and falling data storage costs enable longer, more naturalistic neuronal recordings. The implicit opportunity for understanding the self-organised brain calls for new analysis methods that link temporal scales: from the order of milliseconds over which neuronal dynamics evolve, to the order of minutes, days, or even years over which experimental observations unfold. This review article demonstrates how hierarchical generative models and Bayesian inference help to characterise neuronal activity across different time scales. Crucially, these methods go beyond describing statistical associations among observations and enable inference about underlying mechanisms. We offer an overview of fundamental concepts in state-space modeling and suggest a taxonomy for these methods. Additionally, we introduce key mathematical principles that underscore a separation of temporal scales, such as the slaving principle, and review Bayesian methods that are being used to test hypotheses about the brain with multiscale data. We hope that this review will serve as a useful primer for experimental and computational neuroscientists on the state of the art and current directions of travel in the complex systems modelling literature.

An exploratory computational analysis in mice brain networks of widespread epileptic seizure onset locations along with potential strategies for effective intervention and propagation control

Mean-field models have been developed to replicate key features of epileptic seizure dynamics. However, the precise mechanisms and the role of the brain area responsible for seizure onset and propagation remain incompletely understood. In this study, we employ computational methods within The Virtual Brain framework and the Epileptor model to explore how the location and connectivity of an Epileptogenic Zone (EZ) in a mouse brain are related to focal seizures (seizures that start in one brain area and may or may not remain localized), with a specific focus on the hippocampal region known for its association with epileptic seizures. We then devise computational strategies to confine seizures (prevent widespread propagation), simulating medical-like treatments such as tissue resection and the application of an anti-seizure drugs or neurostimulation to suppress hyperexcitability. Through selectively removing (blocking) specific connections informed by the structural connectome and graph network measurements or by locally reducing outgoing connection weights of EZ areas, we demonstrate that seizures can be kept constrained around the EZ region. We successfully identified the minimal connections necessary to prevent widespread seizures, with a particular focus on minimizing surgical or medical intervention while simultaneously preserving the original structural connectivity and maximizing brain functionality.

The time-evolving epileptic brain network: concepts, definitions, accomplishments, perspectives

Epilepsy is now considered a network disease that affects the brain across multiple levels of spatial and temporal scales. The paradigm shift from an epileptic focus-a discrete cortical area from which seizures originate-to a widespread epileptic network-spanning lobes and hemispheres-considerably advanced our understanding of epilepsy and continues to influence both research and clinical treatment of this multi-faceted high-impact neurological disorder. The epileptic network, however, is not static but evolves in time which requires novel approaches for an in-depth characterization. In this review, we discuss conceptual basics of network theory and critically examine state-of-the-art recording techniques and analysis tools used to assess and characterize a time-evolving human epileptic brain network. We give an account on current shortcomings and highlight potential developments towards an improved clinical management of epilepsy.

Human DNA Mutations and their Impact on Genetic Disorders

DNA is a remarkably precise medium for copying and storing biological information. It serves as a design for cellular machinery that permits cells, organs, and even whole organisms to work. The fidelity of DNA replication results from the action of hundreds of genes involved in proofreading and damage repair. All human cells can acquire genetic changes in their DNA all over life. Genetic mutations are changes to the DNA sequence that happen during cell division when the cells make copies of themselves. Mutations in the DNA can cause genetic illnesses such as cancer, or they could help humans better adapt to their environment over time. The endogenous reactive metabolites, therapeutic medicines, and an excess of environmental mutagens, such as UV rays all continuously damage DNA, compromising its integrity. One or more chromosomal alterations and point mutations at a single site (monogenic mutation) including deletions, duplications, and inversions illustrate such DNA mutations. Genetic conditions can occur when an altered gene is inherited from parents, which increases the risk of developing that particular condition, or some gene alterations can happen randomly. Moreover, symptoms of genetic conditions depend on which gene has a mutation. There are many different diseases and conditions caused by mutations. Some of the most common genetic conditions are Alzheimer's disease, some cancers, cystic fibrosis, Down syndrome, and sickle cell disease. Interestingly, scientists find that DNA mutations are more common than formerly thought. This review outlines the main DNA mutations that occur along the human genome and their influence on human health. The subject of patents pertaining to DNA mutations and genetic disorders has been brought up.

High-Density Exploration of Activity States in a Multi-Area Brain Model

To simulate whole brain dynamics with only a few equations, biophysical, mesoscopic models of local neuron populations can be connected using empirical tractography data. The development of mesoscopic mean-field models of neural populations, in particular, the Adaptive Exponential (AdEx mean-field model), has successfully summarized neuron-scale phenomena leading to the emergence of global brain dynamics associated with conscious (asynchronous and rapid dynamics) and unconscious (synchronized slow-waves, with Up-and-Down state dynamics) brain states, based on biophysical mechanisms operating at cellular scales (e.g. neuromodulatory regulation of spike-frequency adaptation during sleep-wake cycles or anesthetics). Using the Virtual Brain (TVB) environment to connect mean-field AdEx models, we have previously simulated the general properties of brain states, playing on spike-frequency adaptation, but have not yet performed detailed analyses of other parameters possibly also regulating transitions in brain-scale dynamics between different brain states. We performed a dense grid parameter exploration of the TVB-AdEx model, making use of High Performance Computing. We report a remarkable robustness of the effect of adaptation to induce synchronized slow-wave activity. Moreover, the occurrence of slow waves is often paralleled with a closer relation between functional and structural connectivity. We find that hyperpolarization can also generate unconscious-like synchronized Up and Down states, which may be a mechanism underlying the action of anesthetics. We conclude that the TVB-AdEx model reveals large-scale properties identified experimentally in sleep and anesthesia.

From phenomenological to biophysical models of seizures

Epilepsy is a complex disease that requires various approaches for its study. In this short review, we discuss 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. By analyzing the complex, dynamic behavior of seizures, these tools can provide insights into seizure mechanisms and offer a framework for their classification. 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, and emphasize the importance of considering glial cells. Finally, we explore the epistemic value provided by this type of approach.

Active fault tolerant deep brain stimulator for epilepsy using deep neural network

Millions of people around the world are affected by different kinds of epileptic seizures. A deep brain stimulator is now claimed to be one of the most promising tools to control severe epileptic seizures. The present study proposes Hodgkin-Huxley (HH) model-based Active Fault Tolerant Deep Brain Stimulator (AFTDBS) for brain neurons to suppress epileptic seizures against ion channel conductance variations using a Deep Neural Network (DNN). The AFTDBS contains the following three modules: (i) Detection of epileptic seizures using black box classifiers such as Support Vector Machine (SVM) and K-Nearest Neighbor (KNN), (ii) Prediction of ion channels conductance variations using Long Short-Term Memory (LSTM), and (iii) Development of Reconfigurable Deep Brain Stimulator (RDBS) to control epileptic spikes using Proportional Integral (PI) Controller and Model Predictive Controller (MPC). Initially, the synthetic data were collected from the HH model by varying ion channel conductance. Then, the seizure was classified into four groups namely, normal and epileptic due to variations in sodium ion-channel conductance, potassium ion-channel conductance, and both sodium and potassium ion-channel conductance. In the present work, current controlled deep brain stimulators were designed for epileptic suppression. Finally, the closed-loop performances and stability of the proposed control schemes were analyzed. The simulation results demonstrated the efficacy of the proposed DNN-based AFTDBS.

HH model based smart deep brain stimulator to detect, predict and control epilepsy using machine learning algorithm

BACKGROUND

Epilepsy is the most common neurological disorder in the world. To control epilepsy, deep brain stimulation is one of the widely accepted treatment techniques. However, conventional deep brain stimulation technique provides continuous stimulation without optimizing the stimulation parameters, resulting in adverse side effects and unexpected death. Hence, understanding the dynamic behavior of brain neural networks at a cellular level is required for patient-specific epilepsy treatment. Considering the underlying mechanism of a single neuronal shift in the brain neural network, computational model-based techniques have a new face for healthcare, which aims to develop effective medical devices for preclinical investigations.

NEW METHOD

This paper discusses the design of a Smart Deep Brain Stimulator (SDBS) using the Hodgkin-Huxley (HH) conductance-based cellular model of brain neurons to automatically detect, predict and regulate epilepsy against patient-specific conditions. Epileptic activity is simulated as a spike train of action potential due to sodium and potassium channel conductance variations in the single-neuron HH model. The proposed SDBS consists of three components:- i) seizure detection using bagging and boosting-based ensemble machine learning classifiers, ii) channel conductance prediction using Long Short Term Memory-Recurrent Neural Network (LSTM-RNN) based Deep Neural Network (DNN) for updating model parameters of brain neuron, and iii) model-based intelligent control of epileptic seizure with Nonlinear Autoregressive Moving Average-L2 (NARMA-L2) Controller and Nonlinear Model Predictive Controller (NMPC).

RESULTS

For effective treatment, improving the overall accuracy and efficiency of SDBS is essential. For epilepsy detection, the ensemble bagging machine learning algorithm provides better accuracy of 92.7% compared to the ensemble boosting algorithm. LSTM-RNN deep neural network model with four layers predicts the variations in channel conductance with Root Mean Square Error (RMSE) of 0.00568 and 0.009081 for sodium and potassium channel conductance, respectively. From the closed-loop performances of SDBS with an intelligent control scheme, it is observed that SDBS with NMPC provides efficient and accurate stimulation with minimum energy consumption. From a stability point of view, SDBS with NMPC provides better stability than SDBS with NARMA-L2 Controller.

COMPARISON WITH EXISTING METHOD

The proposed SDBS is designed to generate accurate stimulation pulses for epilepsy patients with specific conditions depending on the neuronal activity of a single neuron. Moreover, it will also adapt to the dynamic condition of epilepsy patients. The existing deep brain stimulator continuously provides stimulation pulses without adapting to the patient's conditions.

CONCLUSION

The proposed SDBS could provide patient-specific treatment based on sodium/potassium channel conductance variations of brain neurons. It will help increase the use of deep brain stimulation techniques and reduce sudden death. Furthermore, the proposed technique will be extended to neural network models with larger neuronal populations to improve the practical feasibility.

Dynamical systems in computational psychiatry: A toy-model to apprehend the dynamics of psychiatric symptoms

Introduction

These last years, scientific research focuses on the dynamical aspects of psychiatric disorders and their clinical significance. In this article, we proposed a theoretical framework formalized as a generic mathematical model capturing the heterogeneous individual evolutions of psychiatric symptoms. The first goal of this computational model based on differential equations is to illustrate the nonlinear dynamics of psychiatric symptoms. It offers an original approach to nonlinear dynamics to clinical psychiatrists.

Methods

In this study, we propose a 3+1 dimensions model (x, y, z + f) reproducing the clinical observations encountered in clinical psychiatry with: a variable modeling environmental noise (z) on the patient's internal factors (y) with its temporal specificities (f) and symptomatology (x). This toy-model is able to integrate empirical or simulated data from the influence of perceived environmental over time, their potential importance on the internal and subjective patient-specific elements, and their interaction with the apparent intensity of symptoms.

Results

Constrained by clinical observation of case formulations, the dynamics of psychiatric symptoms is studied through four main psychiatric conditions were modeled: i) a healthy situation, ii) a kind of psychiatric disorder evolving following an outbreak (i.e., schizophrenia spectrum), iii) a kind of psychiatric disorder evolving by kindling and bursts (e.g., bipolar and related disorders); iv) and a kind of psychiatric disorder evolving due to its high susceptibility to the environment (e.g., spersistent complex bereavement disorder). Moreover, we simulate the action of treatments on different psychiatric conditions.

Discussion

We show that the challenges of dynamical systems allow to understand the interactions of psychiatric symptoms with environmental, descriptive, subjective or biological variables. Although this non-linear dynamical model has limitations (e.g., explanatory scope or discriminant validity), simulations provide at least five main interests for clinical psychiatry, such as a visualization of the potential different evolution of psychiatric disorders, formulation of clinical cases, information about attracting states and bifurcations, or the possibility of a nosological refinement of psychiatric models (e.g., staging and symptom network models).

A comprehensive neural simulation of slow-wave sleep and highly responsive wakefulness dynamics

Hallmarks of neural dynamics during healthy human brain states span spatial scales from neuromodulators acting on microscopic ion channels to macroscopic changes in communication between brain regions. Developing a scale-integrated understanding of neural dynamics has therefore remained challenging. Here, we perform the integration across scales using mean-field modeling of Adaptive Exponential (AdEx) neurons, explicitly incorporating intrinsic properties of excitatory and inhibitory neurons. The model was run using The Virtual Brain (TVB) simulator, and is open-access in EBRAINS. We report that when AdEx mean-field neural populations are connected via structural tracts defined by the human connectome, macroscopic dynamics resembling human brain activity emerge. Importantly, the model can qualitatively and quantitatively account for properties of empirically observed spontaneous and stimulus-evoked dynamics in space, time, phase, and frequency domains. Large-scale properties of cortical dynamics are shown to emerge from both microscopic-scale adaptation that control transitions between wake-like to sleep-like activity, and the organization of the human structural connectome; together, they shape the spatial extent of synchrony and phase coherence across brain regions consistent with the propagation of sleep-like spontaneous traveling waves at intermediate scales. Remarkably, the model also reproduces brain-wide, enhanced responsiveness and capacity to encode information particularly during wake-like states, as quantified using the perturbational complexity index. The model was run using The Virtual Brain (TVB) simulator, and is open-access in EBRAINS. This approach not only provides a scale-integrated understanding of brain states and their underlying mechanisms, but also open access tools to investigate brain responsiveness, toward producing a more unified, formal understanding of experimental data from conscious and unconscious states, as well as their associated pathologies.

Mean-field based framework for forward modeling of LFP and MEG signals

The use of mean-field models to describe the activity of large neuronal populations has become a very powerful tool for large-scale or whole brain simulations. However, the calculation of brain signals from mean-field models, such as the electric and magnetic fields, is still under development. Thus, the emergence of new methods for an accurate and efficient calculation of such brain signals is currently of great relevance. In this paper we propose a novel method to calculate the local field potentials (LFP) and magnetic fields from mean-field models. The calculation of LFP is done via a kernel method based on unitary LFP's (the LFP generated by a single axon) that was recently introduced for spiking-networks simulations and that we adapt here for mean-field models. The calculation of the magnetic field is based on current-dipole and volume-conductor models, where the secondary currents (due to the conducting extracellular medium) are estimated using the LFP calculated via the kernel method and the effects of medium-inhomogeneities are incorporated. We provide an example of the application of our method for the calculation of LFP and MEG under slow-waves of neuronal activity generated by a mean-field model of a network of Adaptive-Exponential Integrate-and-Fire (AdEx) neurons. We validate our method via comparison with results obtained from the corresponding spiking neuronal networks. Finally we provide an example of our method for whole brain simulations performed with The Virtual Brain (TVB), a recently developed tool for large scale simulations of the brain. Our method provides an efficient way of calculating electric and magnetic fields from mean-field models. This method exhibits a great potential for its application in large-scale or whole-brain simulations, where calculations via detailed biological models are not feasible.

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.