Ephaptic entrainment in hybrid neuronal model

Abstract

In recent decades, there has been a growing interest in the impact of electric fields generated in the brain. Transmembrane ionic currents originate electric fields in the extracellular space and are capable of affecting nearby neurons, a phenomenon called ephaptic neuronal communication. In the present work, the Quadratic Integrated-and-Fire model (QIF-E) underwent an adjustment/improvement to include the ephaptic entrainment behavior between neurons and electric fields. Indeed, the aim of our study is to validate the QIF-E model, which is a model to estimate the influence of electric fields on neurons. For this purpose, we evaluated whether the main properties observed in an experiment by Anastassiou et al. (Nat Neurosci 14:217–223, 2011), which analyzed the effect of an electric field on cortical pyramidal neurons, are reproduced with the QIF-E model. In this way, the analysis tools are employed according to the neuronal activity regime: (i) for the subthreshold regime, the circular statistic is used to describe the phase differences between the input stimulus signal (electrode) and the modeled membrane response; (ii) in the suprathreshold regime, the Population Vector and the Spike Field Coherence are used to estimate phase preferences and the entrainment intensity between the input stimulus and Action Potentials. The results observed are (i) in the subthreshold regime the values of the phase differences change with distinct frequencies of the input stimulus; (ii) in the supra-threshold regime the preferential phase of Action Potentials changes for different frequencies. In addition, we explore other parameters of the model, such as noise and membrane characteristic-time, in order to understand different types of neurons and extracellular environment related to ephaptic communication. Such results are consistent with results observed in empirical experiments based on ephaptic phenomenon. In addition, the QIF-E model allows further studies on the physiological importance of ephaptic communication in the brain, and its simplicity may open a door to simulate the ephaptic response in neuronal networks and assess the impact of ephaptic communication in such scenarios.

Electrophysiological damage to the neuronal membrane alters ephaptic communication

“…Changes in the phospholipid and cholesteric content in the neuronal membrane may be associated with increased noise in the ephaptic communication. As already indicated in a previous study 38 , the increase in background noise does not change the phase or the frequency of the ephaptic communication, but it can change the intensity of the ephaptic entrainment 38 , which is linked to an increasing of the SFC error bars.…”

“…Assuming, at first, that the degenerative process will be equally probably in the phospholipids structure (capacitance) and in the ion channels (resistance). We adopted equal absolute values for the both damage in the simulations, i.e., b = h. The SFC presents high intensities for low frequency values ( f < 10Hz) due to the characteristics of ephaptic communication, since the neural tissue works as a low-pass filter, as indicated in empirically 4,46,47 and theoretically 38 studies. In figure 3(b) and (c), the intensity of the oscillation preference (peak value) remains high and within the range β band (13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30) with losses between 2% and 10% (b = h = 0.02 to 0.1).…”

“…According to Cunha et al 38 , the ephaptic communication can be simulated with the QIF-E hybrid model, datum by the equation:…”

“…In this way, the SFC provide for what external stimulus frequency (LFP) their preferences of entrainment to neuronal spikes. Through this procedure, empirical study 42 and neuronal modeling 38 estimated the ephaptic communication intensity.…”

“…Regarding the importance of applying mathematical models for neuronal studies [33][34][35][36][37] , the present work aims to investigate the hypothesis that given a level of impairment of the neuronal membrane produces a change in ephaptic entrainment. For this purpose, the QIF-E (Quadratic Integrate-and-Fire Ephaptic) 36,38 hybrid model is adopted, which uses the electrophysiological properties of capacitance and electrical resistance of the membrane for the simulation. In this study, two damage parameters related to plasmolemma electrophysiology are thought for the modified QIF-E model: (i) The parameter h, associated with damage to the characteristics of the lipid bilayer; and (ii) The b parameter, related to dysfunction of ion channel opening.…”