Quantifying the Nonlinear Interaction in the Nervous System Based on Phase-Locked Amplitude Relationship

Yuan Yang; Jun Yao; Julius P.A. Dewald; Frans C.T. Van Der Helm; Alfred C. Schouten

doi:10.1109/TBME.2020.2967079

Quantifying the Nonlinear Interaction in the Nervous System Based on Phase-Locked Amplitude Relationship

Yuan Yang^*, Jun Yao, Julius P.A. Dewald, Frans C.T. Van Der Helm, Alfred C. Schouten

^*Corresponding author for this work

Physical Therapy and Human Movement Sciences

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Objective: This paper introduces the Cross-frequency Amplitude Transfer Function (CATF), a model-free method for quantifying nonlinear stimulus-response interaction based on phase-locked amplitude relationship. Method: The CATF estimates the amplitude transfer from input frequencies at stimulation signal to their harmonics/intermodulation at the response signal. We first verified the performance of CATF in simulation tests with systems containing a static nonlinear function and a linear dynamic, i.e., Hammerstein and Wiener systems. We then applied the CATF to investigate the second-order nonlinear amplitude transfer in the human proprioceptive system from the periphery to the cortex. Result: The simulation demonstrated that the CATF is a general method, which can well quantify nonlinear stimulus-response amplitude transfer for different orders of nonlinearity in Wiener or Hammerstein system configurations. Applied to the human proprioceptive system, we found a complicated nonlinear system behavior with substantial amplitude transfer from the periphery stimulation to cortical response signals in the alpha band. This complicated system behavior may be associated with the nonlinear behavior of the muscle spindle and the dynamic interaction in the thalamocortical radiation. Conclusion: This paper provides a new tool to identify nonlinear interaction in the nervous system. Significance: The results provide novel insight of nonlinear dynamics in the human proprioceptive system.

Original language	English (US)
Article number	8961110
Pages (from-to)	2638-2645
Number of pages	8
Journal	IEEE Transactions on Biomedical Engineering
Volume	67
Issue number	9
DOIs	https://doi.org/10.1109/TBME.2020.2967079
State	Published - Sep 2020

Funding

Manuscript received August 8, 2019; revised November 12, 2019 and January 3, 2020; accepted January 13, 2020. Date of publication January 16, 2020; date of current version August 20, 2020. This work was supported in part by the Dixon Translational Research Grants Initiative (PI: Yang) at Northwestern Medicine and Northwestern University Clinical and Translational Sciences Institute under Grants UL1TR001422 and NIH/NICHD 1R21HD099710 (PIs: Dewald, Yang), and in part by the European Research Council under the ERC Grant agreement 291339 (PI: van der Helm). (Corresponding author. Yuan Yang.) Y. Yang is with the Department of Physical Therapy and Human Movement Sciences Feinberg School of Medicine, Northwestern University, Chicago, IL 60611 USA (e-mail: [email protected]).

Keywords

Cross-frequency Interaction
EEG
Frequency Domain Analysis
Human Proprioceptive System
Nervous System
Nonlinear System

ASJC Scopus subject areas

Biomedical Engineering

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10.1109/TBME.2020.2967079

Cite this

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title = "Quantifying the Nonlinear Interaction in the Nervous System Based on Phase-Locked Amplitude Relationship",

abstract = "Objective: This paper introduces the Cross-frequency Amplitude Transfer Function (CATF), a model-free method for quantifying nonlinear stimulus-response interaction based on phase-locked amplitude relationship. Method: The CATF estimates the amplitude transfer from input frequencies at stimulation signal to their harmonics/intermodulation at the response signal. We first verified the performance of CATF in simulation tests with systems containing a static nonlinear function and a linear dynamic, i.e., Hammerstein and Wiener systems. We then applied the CATF to investigate the second-order nonlinear amplitude transfer in the human proprioceptive system from the periphery to the cortex. Result: The simulation demonstrated that the CATF is a general method, which can well quantify nonlinear stimulus-response amplitude transfer for different orders of nonlinearity in Wiener or Hammerstein system configurations. Applied to the human proprioceptive system, we found a complicated nonlinear system behavior with substantial amplitude transfer from the periphery stimulation to cortical response signals in the alpha band. This complicated system behavior may be associated with the nonlinear behavior of the muscle spindle and the dynamic interaction in the thalamocortical radiation. Conclusion: This paper provides a new tool to identify nonlinear interaction in the nervous system. Significance: The results provide novel insight of nonlinear dynamics in the human proprioceptive system.",

keywords = "Cross-frequency Interaction, EEG, Frequency Domain Analysis, Human Proprioceptive System, Nervous System, Nonlinear System",

author = "Yuan Yang and Jun Yao and Dewald, {Julius P.A.} and {Van Der Helm}, {Frans C.T.} and Schouten, {Alfred C.}",

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AB - Objective: This paper introduces the Cross-frequency Amplitude Transfer Function (CATF), a model-free method for quantifying nonlinear stimulus-response interaction based on phase-locked amplitude relationship. Method: The CATF estimates the amplitude transfer from input frequencies at stimulation signal to their harmonics/intermodulation at the response signal. We first verified the performance of CATF in simulation tests with systems containing a static nonlinear function and a linear dynamic, i.e., Hammerstein and Wiener systems. We then applied the CATF to investigate the second-order nonlinear amplitude transfer in the human proprioceptive system from the periphery to the cortex. Result: The simulation demonstrated that the CATF is a general method, which can well quantify nonlinear stimulus-response amplitude transfer for different orders of nonlinearity in Wiener or Hammerstein system configurations. Applied to the human proprioceptive system, we found a complicated nonlinear system behavior with substantial amplitude transfer from the periphery stimulation to cortical response signals in the alpha band. This complicated system behavior may be associated with the nonlinear behavior of the muscle spindle and the dynamic interaction in the thalamocortical radiation. Conclusion: This paper provides a new tool to identify nonlinear interaction in the nervous system. Significance: The results provide novel insight of nonlinear dynamics in the human proprioceptive system.

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Quantifying the Nonlinear Interaction in the Nervous System Based on Phase-Locked Amplitude Relationship

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