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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.