Cross-Frequency Coupling and Intelligent Neuromodulation

Abstract

Cross-frequency coupling (CFC) reflects (nonlinear) interactions between signals of different frequencies. Evidence from both patient and healthy participant studies suggests that CFC plays an essential role in neuronal computation, interregional interaction, and disease pathophysiology. The present review discusses methodological advances and challenges in the computation of CFC with particular emphasis on potential solutions to spurious coupling, inferring intrinsic rhythms in a targeted frequency band, and causal interferences. We specifically focus on the literature exploring CFC in the context of cognition/memory tasks, sleep, and neurological disorders, such as Alzheimer's disease, epilepsy, and Parkinson's disease. Furthermore, we highlight the implication of CFC in the context and for the optimization of invasive and noninvasive neuromodulation and rehabilitation. Mainly, CFC could support advancing the understanding of the neurophysiology of cognition and motor control, serve as a biomarker for disease symptoms, and leverage the optimization of therapeutic interventions, e.g., closed-loop brain stimulation. Despite the evident advantages of CFC as an investigative and translational tool in neuroscience, further methodological improvements are required to facilitate practical and correct use in cyborg and bionic systems in the field.

Fig. 1.

Concepts of phase–amplitude coupling (PAC) and amplitude–amplitude coupling (AAC). (A) High-frequency oscillation (13 Hz). (B) Low-frequency oscillation (2.5 Hz). (C) Low-frequency oscillation with varying amplitude modulations. (D) Phase of a 2.5-Hz oscillation. (E) Envelope of x_a(t) oscillation. (F) Oscillatory coupling formations of PAC with 2.5-Hz phase shown in (D) modulating 13-Hz amplitude shown in (A). (G) Oscillatory coupling formations of AAC with 2.5-Hz amplitude shown in (C) modulating 13-Hz amplitude shown in (A).

Fig. 2.

Demonstrating methodology of CFC between 6-Hz phase and 65-Hz amplitude modulations. The left panels show the 5 steps to calculate CFC. The middle panels summarize the indicators of each step to guarantee a reliable CFC. The right panels present schematic diagrams of each step. Firstly, a raw signal with a 65-Hz amplitude modulated by a 6-Hz phase is illustrated. Secondly, all phase-given S_p and amplitude-given S_A IMFs are calculated, wherein all IMFs are extracted by IMF-based decompositions. Next, the instantaneous phases φ_p and envelopes A_a of the corresponding IMF are obtained by HT with MI serving as a measure of coupling strength. After that, surrogate data are created to access the significance of MI. Lastly, a cross-frequency comodulogram is adopted to display coupling strength across multiple frequencies. The white block denotes the desired coupling between the 6-Hz phase and 65-Hz amplitude, while the blue block represents a spurious coupling.

Fig. 3.

PAC associating various brain rhythms and varying by physiological states. (A) CAP consists of A and B phases, in which A contains 3 subtypes including A₁, A₂, and A₃. (B) PAC comodulograms differ by phase-A subtypes, of which A₁ shows stronger α/low β-amplitude-related PACs. (C) Significant differences (P < 0.0001) of δ-α/low β PACs among phase-A subtypes in all sleep stages except S4 were shown. (D) The distribution of phase difference between δ phase and α/low β amplitude is displayed in the polar histogram chart. Subtype A₃ showed a relatively disperse distribution compared to the 2 other subtypes.

Fig. 4.

An example of applying CFC with multiple neuromodulations to rehabilitation interventions for individuals with Parkinson's disease. (A) A 3-dimensional gait signal and gait-related EEG of a PD patient with motor impairment. (B) After signal decomposition, excessive β power emerged in basal ganglia. (C) Excessive PAC between Lβ/Hβ and HFO in the STN was observed in a patient with PD, as shown in the left panel, which was suppressed by stimulation (middle panel), with a subsequent rebound after the stimulation was removed (right panel). (D) Neuromodulations, such as DBS, TMS, and sensory stimulation. (E) The varying PAC with stimulation provides feedback to the neuromodulation paradigm. (F) PAC results reflect the interregional interaction/communication in the brain.