A Generalized Coherence Framework for Detecting and Characterizing Nonlinear Interactions in the Nervous System

Abstract

-Objective: This paper introduces a generalized coherence framework for detecting and characterizing nonlinear interactions in the nervous system, namely cross-spectral coherence (CSC). CSC can detect different types of nonlinear interactions including harmonic and intermodulation coupling as present in static nonlinearities and also subharmonic coupling, which only occurs with dynamic nonlinearities. Methods: We verified the performance of CSC in model simulations with both static and dynamic nonlinear systems. We applied CSC to investigate nonlinear stimulus-response interactions in the human proprioceptive system. A periodic movement perturbation was imposed to the wrist when the subjects performed an isotonic wrist flexion. CSC analysis was performed between the perturbation and brain responses (EEG). Results: Both the simulation and the application demonstrated that CSC successfully detected different types of nonlinear interactions. High-order nonlinearities were revealed in the proprioceptive system, shown in harmonic and intermodulation coupling between the perturbation and EEG for all subjects. Subharmonic coupling was found in some subjects but not all. Conclusion: This work provides a general tool to detect and characterize nonlinear nature and dynamics of the nervous system. The application of CSC on the experimental dataset indicates a complex nonlinear dynamics in the proprioceptive system. Significance: This novel framework 1) unveils the nonlinear neural dynamics in a more complete way than the existing coherence measures, and 2) is more suitable for estimating the input-output relation regarding both phase and amplitude compared to phase synchrony measures (which only consider phase coupling). Subharmonic coupling is reported in human proprioceptive system for the first time.

Nonlinear Coupling between Cortical Oscillations and Muscle Activity during Isotonic Wrist Flexion

“…Harmonic coupling with integer multiples of the stimulation frequencies has been widely reported in the both tactile and proprioceptive studies (Snyder, 1992; Tobimatsu et al, 1999; Jamali and Ross, 2013; Ross et al, 2013; Yang et al, 2016a,b). Recently, Langdon et al (2011) reported non-integer coupling with the ratio 2:3 of brain response to fingertip stimulation.…”

“…The n:m coherence is a generalized coherence measure incorporating both phase and amplitude relationship (Yang et al, 2015, 2016a). A recent study found that EEG oscillations, originating from the primary sensorimotor areas, can transmit not only the phase but also amplitude dynamics through the spinal motoneurons down to the periphery (Bayraktaroglu et al, 2013).…”

“…The n:m coherence is a generalized coherence measure for quantifying cross-frequency coupling between two frequency components (Yang et al, 2015, 2016a). Set X be the Fourier Transform of one IC of EEG, Y be EMG (non-rectified or rectified), n:m coherence ( nmC ) between them is computed as…”

“…More details on the calculations of n:m coherence can be found in a previous study (Yang et al, 2016a). The n:m coherence values in the frequency pairs involving power-line frequency (50 Hz) and its harmonics (100, 150 and 200 Hz) are set to zeros to eliminate the contamination of power-line artifact on n:m coherence.…”

“…Moreover, the clinical relevance of nonlinear coupling has also been demonstrated (Sanger et al, 2002; He et al, 2016). In this work, we use a recently developed method, i.e., n:m coherence (Yang et al, 2015, 2016a), to assess nonlinear, as well as linear, corticomuscular coupling during an isotonic wrist flexion. The n:m coherence is a straightforward extension of the linear coherence used in the corticomuscular coherence (Mima and Hallett, 1999) based on high-order statistics (Nikias and Mendel, 1993) for investigating both nonlinear and linear correlation between signals.…”