Causal information quantification of prominent dynamical features of biological neurons

Abstract

Neurons tend to fire a spike when they are near a bifurcation from the resting state to spiking activity. It is a delicate balance between noise, dynamic currents and initial condition that determines the phase diagram of neural activity. Many possible ionic mechanisms can be accounted for as the source of spike generation. Moreover, the biophysics and the dynamics behind it can usually be described through a phase diagram that involves membrane voltage versus the activation variable of the ionic channel. In this paper, we present a novel methodology to characterize the dynamics of this system, which takes into account the fine temporal 'structures' of the complex neuronal signals. This allows us to accurately distinguish the most fundamental properties of neurophysiological neurons that were previously described by Izhikevich considering the phase-space trajectory, using a time causal space: statistical complexity versus Fisher information versus Shannon entropy.

Rhythmic activities of the brain: Quantifying the high complexity of beta and gamma oscillations during visuomotor tasks

“…This provides a distinction between chaotic-deterministic and stochastic dynamics. 2,35,36,38,39,53 Note that neural oscillatory activity patterns are rhythmic neural activities in the brain that can be generated by interactions between neurons. Particularly, beta rhythm changes are associated with the normal motor/sensory function.…”

“…More specifically, we propose an efficient methodology to quantify the degree of complexity within the different oscillations bands of the electrical activity of the brain recorded through the EEG signals while performing a visuomotor or imaginative cognitive task using the BCI2000 system. 21,34 We precisely quantify the different features of oscillatory patterns considering subtle measures accounting for the causal information: Shannon permutation entropy 2,[35][36][37][38][39] and Martín, Plastino, and Rosso (MPR) permutation statistical complexity. 2,[35][36][37][38][39] Importantly, we used the NSB methodology to remove sample size dependent bias from the entropy and complexity estimations 32 that are estimated using the BP methodology.…”

“…21,34 We precisely quantify the different features of oscillatory patterns considering subtle measures accounting for the causal information: Shannon permutation entropy 2,[35][36][37][38][39] and Martín, Plastino, and Rosso (MPR) permutation statistical complexity. 2,[35][36][37][38][39] Importantly, we used the NSB methodology to remove sample size dependent bias from the entropy and complexity estimations 32 that are estimated using the BP methodology. Our approach allows us to classify the "clustering properties"of the EEG frequency bands, quantifying the causality of the signal and inferring the emergent dynamical of the different oscillation patterns of the brain while performing different tasks of visual-motor or imagery characteristics.…”

Bandt-Pompe symbolization dynamics for time series with tied values: A data-driven approach

“…This approach, which employs the Complexity-Entropy plane, has been successfully used in visualization and characterization of different dynamical regimes when the system parameters change, [4][5][6][7][8][9][10][11] optical chaos, [12][13][14][15][16] hydrology, [17][18][19] geophysics, [20][21][22] engineering, [23][24][25][26] biometrics, 27 characterization of pseudo-random number generators, 28,29 biomedical signal analysis (Ref. 30 and references therein [31][32][33][34][35][36][37][38][39][40], and econophysics (Ref. 30 and references therein [41][42][43][44][45][46] ), just to mention a few.…”

Topics on non-equilibrium statistical mechanics and nonlinear physics (II)

“…The phase diagram is determined by a delicate balance between noise, dynamic currents and initial conditions. Montani et al [9] present a novel methodology to characterize the dynamics of this system that takes into account the fine temporal 'structures' of the complex neuronal signals. This allows the authors to accurately distinguish the most fundamental properties of neurophysiological neurons that were previously described by Izhikevich applying nonlinear dynamic theory, and its classification depending on bifurcation and resting state.…”