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Clusella P, Köksal-Ersöz E, Garcia-Ojalvo J, Ruffini G. Comparison between an exact and a heuristic neural mass model with second-order synapses. BIOLOGICAL CYBERNETICS 2023; 117:5-19. [PMID: 36454267 PMCID: PMC10160168 DOI: 10.1007/s00422-022-00952-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2022] [Accepted: 10/23/2022] [Indexed: 05/05/2023]
Abstract
Neural mass models (NMMs) are designed to reproduce the collective dynamics of neuronal populations. A common framework for NMMs assumes heuristically that the output firing rate of a neural population can be described by a static nonlinear transfer function (NMM1). However, a recent exact mean-field theory for quadratic integrate-and-fire (QIF) neurons challenges this view by showing that the mean firing rate is not a static function of the neuronal state but follows two coupled nonlinear differential equations (NMM2). Here we analyze and compare these two descriptions in the presence of second-order synaptic dynamics. First, we derive the mathematical equivalence between the two models in the infinitely slow synapse limit, i.e., we show that NMM1 is an approximation of NMM2 in this regime. Next, we evaluate the applicability of this limit in the context of realistic physiological parameter values by analyzing the dynamics of models with inhibitory or excitatory synapses. We show that NMM1 fails to reproduce important dynamical features of the exact model, such as the self-sustained oscillations of an inhibitory interneuron QIF network. Furthermore, in the exact model but not in the limit one, stimulation of a pyramidal cell population induces resonant oscillatory activity whose peak frequency and amplitude increase with the self-coupling gain and the external excitatory input. This may play a role in the enhanced response of densely connected networks to weak uniform inputs, such as the electric fields produced by noninvasive brain stimulation.
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Affiliation(s)
- Pau Clusella
- Department of Medicine and Life Sciences, Universitat Pompeu Fabra, Barcelona Biomedical Research Park, 08003, Barcelona, Spain.
| | - Elif Köksal-Ersöz
- LTSI - UMR 1099, INSERM, Univ Rennes, Campus Beaulieu, 35000, Rennes, France
| | - Jordi Garcia-Ojalvo
- Department of Medicine and Life Sciences, Universitat Pompeu Fabra, Barcelona Biomedical Research Park, 08003, Barcelona, Spain
| | - Giulio Ruffini
- Brain Modeling Department, Neuroelectrics, Av. Tibidabo, 47b, 08035, Barcelona, Spain.
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Köksal Ersöz E, Lazazzera R, Yochum M, Merlet I, Makhalova J, Mercadal B, Sanchez-Todo R, Ruffini G, Bartolomei F, Benquet P, Wendling F. Signal processing and computational modeling for interpretation of SEEG-recorded interictal epileptiform discharges in epileptogenic and non-epileptogenic zones. J Neural Eng 2022; 19. [PMID: 36067727 DOI: 10.1088/1741-2552/ac8fb4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2022] [Accepted: 09/06/2022] [Indexed: 11/12/2022]
Abstract
OBJECTIVE In partial epilepsies, interictal epileptiform discharges (IEDs) are paroxysmal events observed in epileptogenic and non-epileptogenic zones. IEDs' generation and recurrence are subject to different hypotheses: they appear through glutamatergic and 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 epileptogenic and non-epileptogenic zones.
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Affiliation(s)
- Elif Köksal Ersöz
- INSERM, LTSI - UMR 1099, Universite de Rennes 1, Campus de Beaulieu, Rennes, Bretagne, 35042 , FRANCE
| | - Remo Lazazzera
- INSERM, LTSI - UMR 1099, Universite de Rennes 1, Campus de Beaulieu, Rennes, Bretagne, 35042 , FRANCE
| | - Maxime Yochum
- INSERM, LTSI - UMR 1099, Universite de Rennes 1, Campus de Beaulieu, Rennes, Bretagne, 35042 , FRANCE
| | - Isabelle Merlet
- INSERM, LTSI - UMR 1099, Universite de Rennes 1, Campus de Beaulieu, Rennes, Bretagne, 35042 , FRANCE
| | - Julia Makhalova
- Neurophysiologie clinique, Service d'Epileptologie et de Rythmologie Cerebrale, Assistance Publique Hopitaux de Marseille, Hôpital de la Timone, Marseille, Provence-Alpes-Côte d'Azu, 13354, FRANCE
| | - Borja Mercadal
- Neuroelectrics Barcelona SL, Av. Tibidabo, 47b, Barcelona, 08035, SPAIN
| | - Roser Sanchez-Todo
- Neuroelectrics Barcelona SL, Avda Tibidabo, 47 bis, Barcelona, Catalunya, 08035, SPAIN
| | - Giulio Ruffini
- Neuroelectrics Barcelona SL, Av. Tibidabo, 47b, Barcelona, Catalunya, 08035, SPAIN
| | - Fabrice Bartolomei
- Neurophysiologie clinique, Service d'Epileptologie et de Rythmologie Cerebrale, Assistance Publique Hopitaux de Marseille, Hôpital de la Timone, Marseille, Provence-Alpes-Côte d'Azu, 13354, FRANCE
| | - Pascal Benquet
- INSERM, LTSI - UMR 1099, Universite de Rennes 1, Campus de Beaulieu, Rennes, Bretagne, 35042 , FRANCE
| | - Fabrice Wendling
- INSERM, LTSI - UMR 1099, Universite de Rennes 1, Campus Beaulieu, Rennes, Bretagne, 35042, FRANCE
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