Population models are a powerful mathematical tool to study the dynamics of neuronal networks and to simulate the brain at macroscopic scales. We present a mean-field model capable of quantitatively predicting the temporal dynamics of a network of complex spiking neuronal models, from Integrate-and-Fire to Hodgkin–Huxley, thus linking population models to neurons electrophysiology. This opens a perspective on generating biologically realistic mean-field models from electrophysiological recordings.

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.

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.

Current clinical methods often overlook individual variability by relying on population-wide trials, while mechanismbased trials remain underutilized in neuroscience due to the brain's complexity. This situation may change through the use of a Virtual Brain Twin (VBT), which is a personalized digital replica of an individual's brain, integrating structural and functional brain data into advanced computational models and inference algorithms. By bridging the gap between molecular mechanisms, whole-brain dynamics, and imaging data, VBTs enhance the understanding of (patho)physiological mechanisms, advancing insights into both healthy and disordered brain function. Central to VBT is the network modeling that couples mesoscopic representation of neuronal activity through white matter connectivity, enabling the simulation of brain dynamics at a network level. This transformative approach provides interpretable predictive capabilities, supporting clinicians in personalizing treatments and optimizing interventions. This Review outlines the key components of VBT development, covering the conceptual, mathematical, technical, and clinical aspects. We describe the stages of VBT construction-from anatomical coupling and modeling to simulation and Bayesian inference-and demonstrate their applications in resting-state, healthy aging, multiple sclerosis, and epilepsy. Finally, we discuss potential extensions to other neurological disorders, such as Parkinson's disease, and explore future applications in consciousness research and brain-computer interfaces, paving the way for advancements in personalized medicine and brainmachine integration.

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.

Understanding the many facets of the organization of brain dynamics at large scales remains largely unexplored. Here, we construct a brain-wide model based on recent progress in biologically-realistic population models obtained using mean-field techniques. We use The Virtual Brain (TVB) as a simulation platform and incorporate mean-field models of networks of Adaptive Exponential (AdEx) integrate-and-fire neurons. Such models can capture the main intrinsic firing properties of central neurons, such as adaptation, and also include the typical kinetics of postsynaptic conductances. We hypothesize that such features are important to a biologically realistic simulation of brain dynamics. The resulting “TVB-AdEx” model is shown here to generate two fundamental dynamical states, asynchronous-irregular (AI) and Up-Down states, which correspond to the asynchronous and synchronized dynamics of wakefulness and slow-wave sleep, respectively. The synchrony of slow waves appear as an emergent property at large scales, and reproduce the very different patterns of functional connectivity found in slow-waves compared to asynchronous states. Next, we simulated experiments with transcranial magnetic stimulation (TMS) during asynchronous and slow-wave states, and show that, like in experimental data, the effect of the stimulation greatly depends on the activity state. During slow waves, the response is strong but remains local, in contrast with asynchronous states, where the response is weaker but propagates across brain areas. To compare more quantitatively with wake and slow-wave sleep states, we compute the perturbational complexity index and show that it matches the value estimated from TMS experiments. We conclude that the TVB-AdEx model replicates some of the properties of synchrony and responsiveness seen in the human brain, and is a promising tool to study spontaneous and evoked large-scale dynamics in the normal, anesthetized or pathological brain.