RESUMO
Cross-frequency coupling (CFC) refers to the nonlinear interaction between oscillations in different frequency bands, and it is a rather ubiquitous phenomenon that has been observed in a variety of physical and biophysical systems. In particular, the coupling between the phase of slow oscillations and the amplitude of fast oscillations, referred as phase-amplitude coupling (PAC), has been intensively explored in the brain activity recorded from animals and humans. However, the interpretation of these CFC patterns remains challenging since harmonic spectral correlations characterizing nonsinusoidal oscillatory dynamics can act as a confounding factor. Specialized signal processing techniques are proposed to address the complex interplay between spectral harmonicity and different types of CFC, not restricted only to PAC. For this, we provide an in-depth characterization of the time locked index (TLI) as a tool aimed to efficiently quantify the harmonic content of noisy time series. It is shown that the proposed TLI measure is more robust and outperforms traditional phase coherence metrics (e.g., phase locking value, pairwise phase consistency) in several aspects. We found that a nonlinear oscillator under the effect of additive noise can produce spurious CFC with low spectral harmonic content. On the other hand, two coupled oscillatory dynamics with independent fundamental frequencies can produce true CFC with high spectral harmonic content via a rectification mechanism or other post-interaction nonlinear processing mechanisms. These results reveal a complex interplay between CFC and harmonicity emerging in the dynamics of biologically plausible neural network models and more generic nonlinear and parametric oscillators. We show that, contrary to what is usually assumed in the literature, the high harmonic content observed in nonsinusoidal oscillatory dynamics is neither a sufficient nor necessary condition to interpret the associated CFC patterns as epiphenomenal. There is mounting evidence suggesting that the combination of multimodal recordings, specialized signal processing techniques, and theoretical modeling is becoming a required step to completely understand CFC patterns observed in oscillatory rich dynamics of physical and biophysical systems.
Assuntos
Modelos Neurológicos , Rede Nervosa/fisiologia , Dinâmica não Linear , Rede Nervosa/citologiaRESUMO
Phase-amplitude cross frequency coupling (PAC) is a rather ubiquitous phenomenon that has been observed in a variety of physical domains; however, the mechanisms underlying the emergence of PAC and its functional significance in the context of neural processes are open issues under debate. In this work we analytically demonstrate that PAC phenomenon naturally emerges in mean-field models of biologically plausible networks, as a signature of specific bifurcation structures. The proposed analysis, based on bifurcation theory, allows the identification of the mechanisms underlying oscillatory dynamics that are essentially different in the context of PAC. Specifically, we found that two PAC classes can coexist in the complex dynamics of the analyzed networks: 1) harmonic PAC which is an epiphenomenon of the nonsinusoidal waveform shape characterized by the linear superposition of harmonically related spectral components, and 2) nonharmonic PAC associated with "true" coupled oscillatory dynamics with independent frequencies elicited by a secondary Hopf bifurcation and mechanisms involving periodic excitation/inhibition (PEI) of a network population. Importantly, these two PAC types have been experimentally observed in a variety of neural architectures confounding traditional parametric and nonparametric PAC metrics, like those based on linear filtering or the waveform shape analysis, due to the fact that these methods operate on a single one-dimensional projection of an intrinsically multidimensional system dynamics. We exploit the proposed tools to study the functional significance of the PAC phenomenon in the context of Parkinson's disease (PD). Our results show that pathological slow oscillations (e.g. ß band) and nonharmonic PAC patterns emerge from dissimilar underlying mechanisms (bifurcations) and are associated to the competition of different BG-thalamocortical loops. Thus, this study provides theoretical arguments that demonstrate that nonharmonic PAC is not an epiphenomenon related to the pathological ß band oscillations, thus supporting the experimental evidence about the relevance of PAC as a potential biomarker of PD.
Assuntos
Ondas Encefálicas/fisiologia , Modelos Neurológicos , Redes Neurais de Computação , Doença de Parkinson/fisiopatologia , HumanosRESUMO
Deep brain stimulation (DBS) has become a widely used technique for treating advanced stages of neurological and psychiatric illness. In the case of motor disorders related to basal ganglia (BG) dysfunction, several mechanisms of action for the DBS therapy have been identified which might be involved simultaneously or in sequence. However, the identification of a common key mechanism underlying the clinical relevant DBS configurations has remained elusive due to the inherent complexity related to the interaction between the electrical stimulation and the neural tissue, and the intricate circuital structure of the BG-thalamocortical network. In this work, it is shown that the clinically relevant range for both, the frequency and intensity of the electrical stimulation pattern, is an emergent property of the BG anatomy at the system-level that can be addressed using mean-field descriptive models of the BG network. Moreover, it is shown that the activity resetting mechanism elicited by electrical stimulation provides a natural explanation to the ineffectiveness of irregular (i.e., aperiodic) stimulation patterns, which has been commonly observed in previously reported pathophysiology models of Parkinson's disease. Using analytical and numerical techniques, these results have been reproduced in both cases: 1) a reduced mean-field model that can be thought as an elementary building block capable to capture the underlying fundamentals of the relevant loops constituting the BG-thalamocortical network, and 2) a detailed model constituted by the direct and hyperdirect loops including one-dimensional spatial structure of the BG nuclei. We found that the optimal ranges for the essential parameters of the stimulation patterns can be understood without taking into account biophysical details of the relevant structures.