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Cortical function emerges from the interactions of multi-scale networks that may be studied at a high level using neural mass models (NMM), representing the mean activity of large numbers of neurons. In order to properly reproduce experimental data, these models require the addition of further elements. Here we provide a framework integrating conduction physics that can be used to simulate cortical electrophysiology measurements, particularly those obtained from multi-contact laminar electrodes. This is achieved by endowing NMMs with basic physical properties, such as the average laminar location of the apical and basal dendrites of pyramidal cell populations. We call this framework laminar NMM, or LaNMM for short. We then employ this framework to infer the location of oscillatory generators from laminar-resolved data collected from the prefrontal cortex in the macaque monkey. Based on the literature on columnar connectivity, we define a minimal neural mass model capable of generating amplitude and phase coupled slow (alpha/beta, 4–22 Hz) and fast (gamma, 30–250 Hz) oscillations. The synapse layer locations of the two pyramidal cell populations are treated as optimization parameters, together with two more LaNMM-specific parameters, to compare the models with the multi-contact recordings. We rank the candidate models using an optimization function that evaluates the match between the functional connectivity (FC) of the model and data, where the FC is defined by the covariance between bipolar voltage measurements at different cortical depths. The family of best solutions reproduces the FC of the observed electrophysiology while selecting locations of pyramidal cells and their synapses that result in the generation of fast activity at superficial layers and slow activity across most depths, in line with recent literature proposals.HighlightsWe provide a neural mass modeling formalism that includes a physical layer to simulate electrophysiology measurements.To analyze in-vivo data collected in the macaque monkey during a memory task, we propose a specific model with two coupled main circuits that can generate realistic electrophysiological signals in two important oscillatory regimes—the alpha/beta and the gamma bands.Physical elements in the model shed light on the generation of oscillations in the two regimes and on the relative power distribution of fast and slow oscillatory signals across cortical depth, which we show can be altered by the choice of the reference location or method.The model is contrasted with in-vivo data, with parameters adjusted by matching voltage statistics in the alpha/beta and gamma bands, leading to a solution with slow frequency components generated by synapses spanning most cortical layers and fast oscillations in superficial layers.The resulting formalism provides useful tools and concepts to analyze and model data, with implications for understanding altered oscillatory EEG activity in dementia, Alzheimer’s disease and other disorders with oscillatory features.

ObjectiveStereotactic-EEG (SEEG) and scalp EEG recordings can be modeled using mesoscale neural mass population models (NMM). However, the relationship between those mathematical models and the physics of the measurements is unclear. In addition, it is challenging to represent SEEG data by combining NMMs and volume conductor models due to the intermediate spatial scale represented by these measurements.ApproachWe provide a framework combining the multicompartmental modeling formalism and a detailed geometrical model to simulate the transmembrane currents that appear in layer 3, 5 and 6 pyramidal cells due to a synaptic input. With this approach, it is possible to realistically simulate the current source density (CSD) depth profile inside a cortical patch due to inputs localized into a single cortical layer and the induced voltage measured by two SEEG contacts using a volume conductor model. Based on this approach, we built a framework to connect the activity of a NMM with a volume conductor model and we simulated an example of SEEG signal as a proof of concept.Main resultsCSD depends strongly on the distribution of the synaptic inputs onto the different cortical layers and the equivalent current dipole strengths display substantial differences (of up to a factor of four in magnitude in our example). Thus, the inputs coming from different neural populations do not contribute equally to the electrophysiological recordings. A direct consequence of this is that the raw output of neural mass models is not a good proxy for electrical recordings. We also show that the simplest CSD model that can accurately reproduce SEEG measurements can be constructed from discrete monopolar sources (one per cortical layer).SignificanceOur results highlight the importance of including a physical model in NMMs to represent measurements. We provide a framework connecting microscale neuron models with the neural mass formalism and with physical models of the measurement process that can improve the accuracy of predicted electrophysiological recordings.

Objective. In partial epilepsies, interictal epileptiform discharges (IEDs) are paroxysmal events observed in epileptogenic zone (EZ) and non-epileptogenic zone (NEZ). IEDs’ generation and recurrence are subject to different hypotheses: they appear through glutamatergic and gamma-aminobutyric acidergic (GABAergic) processes; they may trigger seizures or prevent seizure propagation. This paper focuses on a specific class of IEDs, spike-waves (SWs), characterized by a short-duration spike followed by a longer duration wave, both of the same polarity. Signal analysis and neurophysiological mathematical models are used to interpret puzzling IED generation. Approach. Interictal activity was recorded by intracranial stereo-electroencephalography (SEEG) electrodes in five different patients. SEEG experts identified the epileptic and non-epileptic zones in which IEDs were detected. After quantifying spatial and temporal features of the detected IEDs, the most significant features for classifying epileptic and non-epileptic zones were determined. A neurophysiologically-plausible mathematical model was then introduced to simulate the IEDs and understand the underlying differences observed in epileptic and non-epileptic zone IEDs. Main results. Two classes of SWs were identified according to subtle differences in morphology and timing of the spike and wave component. Results showed that type-1 SWs were generated in epileptogenic regions also involved at seizure onset, while type-2 SWs were produced in the propagation or non-involved areas. The modeling study indicated that synaptic kinetics, cortical organization, and network interactions determined the morphology of the simulated SEEG signals. Modeling results suggested that the IED morphologies were linked to the degree of preserved inhibition. Significance. This work contributes to the understanding of different mechanisms generating IEDs in epileptic networks. The combination of signal analysis and computational models provides an efficient framework for exploring IEDs in partial epilepsies and classifying EZ and NEZ.

The brain is a complex, plastic, electrical network where dysfunctions result in neurological disorders. Transcranial electrical stimulation (tES or tCS, as often abbreviated) is a noninvasive neuromodulatory technique with the potential for network-oriented therapy. The creation of multichannel systems has delivered unprecedented control over the electric fields delivered to the human brain, raising several challenges for designing appropriate protocols. These include the proper characterization of physiopathological brain networks in a patient-specific context, a deeper understanding of the effects of stimulation on interconnected neuronal populations—both immediate and plastic—and, based on these, developing strategies for personalized interventions. Although there already exist methods for personalization and optimization based on the electrophysical characteristics of the brain (i.e., head geometry and tissue conductivities) and electrical fields generated by tES, unavoidably, we argue, the next generation of solutions will rely on the creation of hybrid computational models (HBMs) of the brain, i.e., models descriptive of physics and physiology at the appropriate scales. These models, stemming from the description of the brain as a network of neural masses embedded in a realistic physical matrix, can represent measurable electrical brain activity, interactions with electric fields and the effects of drugs. They can be personalized using the neurophysiological (electrophysiology and neuroimaging) data to provide a realistic, effective in silico experimentation framework for each patient. Dynamical HBMs and data can then be used to optimize and follow up treatment over time to accommodate for plastic or other changes, what we call tES 3.0. They can also provide a powerful platform to gain mechanistic insights. In this chapter, we provide an overview of this area with a focus on the treatment of disorders with oscillatory signatures such as epilepsy and Alzheimer’s disease. We provide a brief overview of modeling at the neuron, circuit, neural mass, and hybrid brain modeling. We discuss the inclusion of tES and drug effects in models, and then optimization strategies going beyond traditional excitation/inhibition approaches, working in the space of dynamic network models and the future outlook of data-driven, computationally empowered tES.

Several decades of research suggest that weak electric fields may influence neural processing, including those induced by neuronal activity and proposed as a substrate for a potential new cellular communication system, i.e., ephaptic transmission. Here we aim to model mesoscopic ephaptic activity in the human brain and explore its trajectory during aging by characterizing the electric field generated by cortical dipoles using realistic finite element modeling. Extrapolating from electrophysiological measurements, we first observe that modeled endogenous field magnitudes are comparable to those in measurements of weak but functionally relevant self-generated fields and to those produced by noninvasive transcranial brain stimulation, and therefore possibly able to modulate neuronal activity. Then, to evaluate the role of these fields in the human cortex in large MRI databases, we adapt an interaction approximation that considers the relative orientation of neuron and field to estimate the membrane potential perturbation in pyramidal cells. We use this approximation to define a simplified metric (EMOD1) that weights dipole coupling as a function of distance and relative orientation between emitter and receiver and evaluate it in a sample of 401 realistic human brain models from healthy subjects aged 16–83. Results reveal that ephaptic coupling, in the simplified mesoscopic modeling approach used here, significantly decreases with age, with higher involvement of sensorimotor regions and medial brain structures. This study suggests that by providing the means for fast and direct interaction between neurons, ephaptic modulation may contribute to the complexity of human function for cognition and behavior, and its modification across the lifespan and in response to pathology., Author summary We study the potential role of a less understood type of communication between neurons in the brain. While the principal mechanism for neuron communication is synaptic, active neurons generate electric fields. Whether this is physiologically relevant at the systems level or merely an epiphenomenon is uncertain because these fields are rather weak at the mesoscopic scale (i.e., between single neuron and entire brain scales). We first review converging evidence from in-vitro and in-vivo studies that suggest the former, and then, using realistic finite element modeling, we show that the electric fields generated by transcranial electrical current stimulation are of the same magnitude as endogenous ones in this scale. We then develop a method to estimate the amount of potential ephaptic or electric-field interaction in an individual brain using finite element modeling and show its decrease with age in a large cohort of 401 subjects. Ephaptic interaction may be important for complex processing in biological neural networks, because it travels at very fast speeds and provides a potential communication link across distant neurons in the cortex. Assessing the physiological relevance of this mechanism may be key in understanding some brain disorders and to design improved tES protocols.

Several decades of research suggest that weak electric fields may influence neural processing, including those induced by neuronal activity and recently proposed as substrate for a potential new cellular communication system, i.e., ephaptic transmission. Here we aim to map ephaptic activity in the human brain and explore its trajectory during aging by characterizing the macroscopic electric field generated by cortical dipoles using realistic finite element modeling. We find that modeled endogenous field magnitudes are comparable to those in measurements of weak but functionally relevant endogenous fields and to those generated by noninvasive transcranial brain stimulation, therefore possibly able to modulate neuronal activity. Then, to evaluate the role of self-generated ephaptic fields in the human cortex, we adapt an interaction approximation that considers the relative orientation of neuron and field to derive the membrane potential perturbation in pyramidal cells. Building on this, we define a simplified metric (EMOD1) that weights dipole coupling as a function of distance and relative orientation between emitter and receiver and evaluate it in a sample of 401 realistic human brain models from subjects aged 16-83. Results reveal that ephaptic modulation follows gyrification patterns in the human brain, and significantly decreases with age, with higher involvement of sensorimotor regions and medial brain structures. By providing the means for fast and direct interaction between neurons, ephaptic modulation likely contributes to the complexity of human function for cognition and behavior, and its modification across the lifespan and in response to pathology.

Personalization is rapidly becoming standard practice in medical diagnosis and treatment. This study is part of an ambitious program towards computational personalization of neuromodulatory interventions in neuropsychiatry. We propose to model the individual human brain as a network of neural masses embedded in a realistic physical matrix capable of representing measurable electrical brain activity. We call this ahybrid brain model (HBM)to highlight that it encodes both biophysical and physiological characteristics of an individual brain. Although the framework is general, we provide here a pipeline for the integration of anatomical, structural and functional connectivity data obtained from magnetic resonance imaging (MRI), diffuse tensor imaging (DTIconnectome) and electroencephalography (EEG). We personalize model parameters through a comparison of simulated cortical functional connectivity with functional connectivity profiles derived from cortically-mapped, subject-specific EEG. We show that individual information can be represented in model space through the proper adjustment of two parameters (global coupling strength and conduction velocity), and that the underlying structural information has a strong impact on the functional outcome of the model. These findings provide a proof of concept and open the door for further advances, including the model-driven design of non-invasive brain-stimulation protocols.