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Complex interplay between spectral harmonicity and different types of cross-frequency couplings in nonlinear oscillators and biologically plausible neural network models
Physical Review E ( IF 2.2 ) Pub Date : 2020-12-01 , DOI: 10.1103/physreve.102.062401 Damián Dellavale 1 , Osvaldo Matías Velarde 1 , Germán Mato 1 , Eugenio Urdapilleta 1
Physical Review E ( IF 2.2 ) Pub Date : 2020-12-01 , DOI: 10.1103/physreve.102.062401 Damián Dellavale 1 , Osvaldo Matías Velarde 1 , Germán Mato 1 , Eugenio Urdapilleta 1
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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.
中文翻译：
非线性振荡器和生物学上合理的神经网络模型中频谱谐波与不同类型的跨频耦合之间的复杂相互作用
跨频耦合（CFC）是指不同频段振荡之间的非线性相互作用，是在各种物理和生物物理系统中观察到的相当普遍的现象。特别是，慢振荡相位与快振荡振幅之间的耦合，称为相位振幅耦合（PAC），已在动物和人类记录的大脑活动中得到深入探索。然而，对这些 CFC 模式的解释仍然具有挑战性，因为表征非正弦振荡动力学的谐波谱相关性可能会成为混杂因素。专门的信号处理技术被提出来解决频谱谐波和不同类型的 CFC 之间复杂的相互作用，而不仅限于 PAC。为此，我们提供了时间锁定指数（TLI）的深入表征，作为旨在有效量化噪声时间序列的谐波含量的工具。结果表明，所提出的 TLI 测量更加稳健，并且在多个方面优于传统的相位相干性度量（例如锁相值、成对相位一致性）。我们发现非线性振荡器在加性噪声的影响下会产生具有低频谱谐波含量的寄生 CFC。另一方面，具有独立基频的两个耦合振荡动力学可以通过整流机制或其他相互作用后非线性处理机制产生具有高频谱谐波含量的真正的CFC。这些结果揭示了 CFC 与生物学上合理的神经网络模型和更通用的非线性和参数振荡器的动力学中出现的谐波之间复杂的相互作用。 我们表明，与文献中通常假设的相反，在非正弦振荡动力学中观察到的高谐波含量既不是将相关 CFC 模式解释为副现象的充分条件也不是必要条件。越来越多的证据表明，多模态记录、专门的信号处理技术和理论建模的结合正在成为完全理解在物理和生物物理系统的振荡丰富动力学中观察到的 CFC 模式的必要步骤。
更新日期：2020-12-01
中文翻译：
非线性振荡器和生物学上合理的神经网络模型中频谱谐波与不同类型的跨频耦合之间的复杂相互作用
跨频耦合（CFC）是指不同频段振荡之间的非线性相互作用，是在各种物理和生物物理系统中观察到的相当普遍的现象。特别是，慢振荡相位与快振荡振幅之间的耦合，称为相位振幅耦合（PAC），已在动物和人类记录的大脑活动中得到深入探索。然而，对这些 CFC 模式的解释仍然具有挑战性，因为表征非正弦振荡动力学的谐波谱相关性可能会成为混杂因素。专门的信号处理技术被提出来解决频谱谐波和不同类型的 CFC 之间复杂的相互作用，而不仅限于 PAC。为此，我们提供了时间锁定指数（TLI）的深入表征，作为旨在有效量化噪声时间序列的谐波含量的工具。结果表明，所提出的 TLI 测量更加稳健，并且在多个方面优于传统的相位相干性度量（例如锁相值、成对相位一致性）。我们发现非线性振荡器在加性噪声的影响下会产生具有低频谱谐波含量的寄生 CFC。另一方面，具有独立基频的两个耦合振荡动力学可以通过整流机制或其他相互作用后非线性处理机制产生具有高频谱谐波含量的真正的CFC。这些结果揭示了 CFC 与生物学上合理的神经网络模型和更通用的非线性和参数振荡器的动力学中出现的谐波之间复杂的相互作用。 我们表明，与文献中通常假设的相反，在非正弦振荡动力学中观察到的高谐波含量既不是将相关 CFC 模式解释为副现象的充分条件也不是必要条件。越来越多的证据表明，多模态记录、专门的信号处理技术和理论建模的结合正在成为完全理解在物理和生物物理系统的振荡丰富动力学中观察到的 CFC 模式的必要步骤。
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