Centro Atómico Bariloche and Instituto Balseiro, Comisión Nacional de Energía Atómica (CNEA), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Universidad Nacional de Cuyo (UNCUYO), Av. E. Bustillo 9500, R8402AGP, San Carlos de Bariloche, Río Negro, Argentina.
Centro Atómico Bariloche and Instituto Balseiro, Comisión Nacional de Energía Atómica (CNEA), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Universidad Nacional de Cuyo (UNCUYO), Av. E. Bustillo 9500, R8402AGP, San Carlos de Bariloche, Río Negro, Argentina.
Neuroimage. 2019 Nov 15;202:116031. doi: 10.1016/j.neuroimage.2019.116031. Epub 2019 Jul 19.
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. β 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 β band oscillations, thus supporting the experimental evidence about the relevance of PAC as a potential biomarker of PD.
相位-幅度交叉频率耦合（PAC）是一种普遍存在的现象，已在各种物理领域中观察到；然而，PAC 出现的机制及其在神经过程中的功能意义仍是争论的悬而未决的问题。在这项工作中，我们从理论上证明了 PAC 现象自然出现在具有生物学合理性的网络的平均场模型中，这是特定分岔结构的特征。所提出的基于分岔理论的分析允许识别振荡动力学的潜在机制，这些机制在 PAC 的背景下本质上是不同的。具体而言，我们发现两种 PAC 类可以共存于所分析网络的复杂动力学中：1）谐波 PAC，这是由与正弦波形形状无关的非正弦波形状引起的，其特征是谐波相关的频谱分量的线性叠加，2）非谐波 PAC，与由二次 Hopf 分岔引起的“真实”耦合振荡动力学相关，以及涉及网络群体周期性兴奋/抑制（PEI）的机制。重要的是，由于这些方法作用于固有多维系统动力学的单个一维投影，因此这两种 PAC 类型已在各种神经结构中得到实验观察，这使得传统的参数和非参数 PAC 度量（如基于线性滤波或波形形状分析的度量）变得混乱。我们利用所提出的工具来研究 PAC 现象在帕金森病（PD）背景下的功能意义。我们的结果表明，病理性慢波（例如β波段）和非谐波 PAC 模式源自不同的潜在机制（分岔），并与不同 BG-丘脑-皮质回路的竞争相关。因此，这项研究提供了理论依据，证明了非谐波 PAC 不是与病理性β波段振荡相关的附带现象，从而支持了关于 PAC 作为 PD 潜在生物标志物的重要性的实验证据。
