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.

Virtual brain twins: from basic neuroscience to clinical use.

Virtual brain twins are personalized, generative and adaptive brain models based on data from an individual's brain for scientific and clinical use. After a description of the key elements of virtual brain twins, we present the standard model for personalized whole-brain network models. The personalization is accomplished using a subject's brain imaging data by three means: (1) assemble cortical and subcortical areas in the subject-specific brain space; (2) directly map connectivity into the brain models, which can be generalized to other parameters; and (3) estimate relevant parameters through model inversion, typically using probabilistic machine learning. We present the use of personalized whole-brain network models in healthy ageing and five clinical diseases: epilepsy, Alzheimer's disease, multiple sclerosis, Parkinson's disease and psychiatric disorders. Specifically, we introduce spatial masks for relevant parameters and demonstrate their use based on the physiological and pathophysiological hypotheses. Finally, we pinpoint the key challenges and future directions.

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.

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 Model for the Propagation of Seizure Activity in Normal Brain Tissue.

Epilepsies are characterized by paroxysmal electrophysiological events and seizures, which can propagate across the brain. One of the main unsolved questions in epilepsy is how epileptic activity can invade normal tissue and thus propagate across the brain. To investigate this question, we consider three computational models at the neural network scale to study the underlying dynamics of seizure propagation, understand which specific features play a role, and relate them to clinical or experimental observations. We consider both the internal connectivity structure between neurons and the input properties in our characterization. We show that a paroxysmal input is sometimes controlled by the network while in other instances, it can lead the network activity to itself produce paroxysmal activity, and thus will further propagate to efferent networks. We further show how the details of the network architecture are essential to determine this switch to a seizure-like regime. We investigated the nature of the instability involved and in particular found a central role for the inhibitory connectivity. We propose a probabilistic approach to the propagative/non-propagative scenarios, which may serve as a guide to control the seizure by using appropriate stimuli.

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.

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.

Modeling seizures: From single neurons to networks.

Dynamical system tools offer a complementary approach to detailed biophysical seizure modeling, with a high potential for clinical applications. This review describes the theoretical framework that provides a basis for theorizing certain properties of seizures and for their classification according to their dynamical properties at onset and offset. We describe various modeling approaches spanning different scales, from single neurons to large-scale networks. This narrative review provides an accessible overview of this field, including non-exhaustive examples of key recent works.

Visual cortical prosthesis: an electrical perspective.

The electrical stimulation of the visual cortices has the potential to restore vision to blind individuals. Until now, the results of visual cortical prosthetics have been limited as no prosthesis has restored a full working vision but the field has shown a renewed interest these last years, thanks to wireless and technological advances. However, several scientific and technical challenges are still open to achieve the therapeutic benefit expected by these new devices. One of the main challenges is the electrical stimulation of the brain itself. In this review, we analyse the results in electrode-based visual cortical prosthetics from the electrical point of view. We first describe what is known about the electrode-tissue interface and safety of electrical stimulation. Then we focus on the psychophysics of prosthetic vision and the state-of-the-art on the interplay between the electrical stimulation of the visual cortex and the phosphene perception. Lastly, we discuss the challenges and perspectives of visual cortex electrical stimulation and electrode array design to develop the new generation implantable cortical visual prostheses.

Conductance-Based Adaptive Exponential Integrate-and-Fire Model.

The intrinsic electrophysiological properties of single neurons can be described by a broad spectrum of models, from realistic Hodgkin-Huxley-type models with numerous detailed mechanisms to the phenomenological models. The adaptive exponential integrate-and-fire (AdEx) model has emerged as a convenient middle-ground model. With a low computational cost but keeping biophysical interpretation of the parameters, it has been extensively used for simulations of large neural networks. However, because of its current-based adaptation, it can generate unrealistic behaviors. We show the limitations of the AdEx model, and to avoid them, we introduce the conductance-based adaptive exponential integrate-and-fire model (CAdEx). We give an analysis of the dynamics of the CAdEx model and show the variety of firing patterns it can produce. We propose the CAdEx model as a richer alternative to perform network simulations with simplified models reproducing neuronal intrinsic properties.

Realistic spiking neural network: Non-synaptic mechanisms improve convergence in cell assembly.

Learning in neural networks inspired by brain tissue has been studied for machine learning applications. However, existing works primarily focused on the concept of synaptic weight modulation, and other aspects of neuronal interactions, such as non-synaptic mechanisms, have been neglected. Non-synaptic interaction mechanisms have been shown to play significant roles in the brain, and four classes of these mechanisms can be highlighted: (i) electrotonic coupling; (ii) ephaptic interactions; (iii) electric field effects; and iv) extracellular ionic fluctuations. In this work, we proposed simple rules for learning inspired by recent findings in machine learning adapted to a realistic spiking neural network. We show that the inclusion of non-synaptic interaction mechanisms improves cell assembly convergence. By including extracellular ionic fluctuation represented by the extracellular electrodiffusion in the network, we showed the importance of these mechanisms to improve cell assembly convergence. Additionally, we observed a variety of electrophysiological patterns of neuronal activity, particularly bursting and synchronism when the convergence is improved.

Gold Nanoparticles for X-ray Microtomography of Neurons.

Commonly used methods to visualize the biological structure of brain tissues at subcellular resolution are confocal microscopy and two-photon microscopy. Both require slicing the sample into sections of a few tens of micrometers. The recent developments in X-ray microtomography enable three-dimensional imaging at sub-micrometer and isotropic resolution with larger biological samples. In this work, we developed and compared original microtomography methods and staining protocols to improve the contrast for in vitro mouse neuron imaging. Using Golgi's method to stain neurons randomly, we imaged the whole set of mouse brain structures. For specific and nonrandom neuron labeling, we conjugated 20 nm gold nanoparticles to antibodies used in the immunohistochemistry (IHC) method, using anti-NeuN to label specifically neuronal nuclei. We applied an original subtraction dual-energy method for microtomography in the vicinity of the Au L-III absorption edge and compared image reconstructions to confocal microscopy images acquired on the same samples. The results show the possibility to characterize the 3D entire brain structure of mice. They demonstrated a high contrast and neuron detection improvement by applying the dual-energy method coupled to IHC staining.