Bhavya Vasudeva1, Runfeng Tian2, Dee H Wu3, Shirley A James4, Hazem H Refai5, Lei Ding2,6, Fei He7, Yuan Yang2,5,6,7,8,9. 1. Indian Statistical Institute, Kolkata, West Bengal 700108, India. 2. Stephenson School of Biomedical Engineering, The University of Oklahoma, Norman, Oklahoma 73019, USA. 3. Department of Radiological Sciences, The University of Oklahoma Health Sciences Center, Oklahoma City, Oklahoma 73104, USA. 4. Department of Rehabilitation Sciences, College of Allied Health, The University of Oklahoma Health Sciences Center, Oklahoma City, Oklahoma 73117, USA. 5. Department of Electrical and Computer Engineering, The University of Oklahoma, Tulsa, Oklahoma-74135, USA. 6. Institute for Biomedical Engineering, Science, and Technology, Carson Engineering Center, The University of Oklahoma, Norman, Oklahoma 73019, USA. 7. Centre for Computational Science and Mathematical Modelling, Coventry University, Coventry CV1 2JH, UK. 8. Department of Physical Therapy and Human Movement Sciences, Feinberg School of Medicine, Northwestern University, Chicago, Illinois-60611, USA. 9. Laureate Institute for Brain Research, 6655 S Yale Ave, Tulsa, OK 74136, USA.
Abstract
BACKGROUND: Many physical, biological and neural systems behave as coupled oscillators, with characteristic phase coupling across different frequencies. Methods such as n : m phase locking value (where two coupling frequencies are linked as: mf 1 = nf 2) and bi-phase locking value have previously been proposed to quantify phase coupling between two resonant frequencies (e.g. f, 2f/3) and across three frequencies (e.g. f 1, f 2, f 1 + f 2), respectively. However, the existing phase coupling metrics have their limitations and limited applications. They cannot be used to detect or quantify phase coupling across multiple frequencies (e.g. f 1, f 2, f 3, f 4, f 1 + f 2 + f 3 - f 4), or coupling that involves non-integer multiples of the frequencies (e.g. f 1, f 2, 2f 1/3 + f 2/3). NEW METHODS: To address the gap, this paper proposes a generalized approach, named multi-phase locking value (M-PLV), for the quantification of various types of instantaneous multi-frequency phase coupling. Different from most instantaneous phase coupling metrics that measure the simultaneous phase coupling, the proposed M-PLV method also allows the detection of delayed phase coupling and the associated time lag between coupled oscillators. RESULTS: The M-PLV has been tested on cases where synthetic coupled signals are generated using white Gaussian signals, and a system comprised of multiple coupled Rössler oscillators, as well as a human subject dataset. Results indicate that the M-PLV can provide a reliable estimation of the time window and frequency combination where the phase coupling is significant, as well as a precise determination of time lag in the case of delayed coupling. This method has the potential to become a powerful new tool for exploring phase coupling in complex nonlinear dynamic systems.
BACKGROUND: Many physical, biological and neural systems behave as coupled oscillators, with characteristic phase coupling across different frequencies. Methods such as n : m phase locking value (where two coupling frequencies are linked as: mf 1 = nf 2) and bi-phase locking value have previously been proposed to quantify phase coupling between two resonant frequencies (e.g. f, 2f/3) and across three frequencies (e.g. f 1, f 2, f 1 + f 2), respectively. However, the existing phase coupling metrics have their limitations and limited applications. They cannot be used to detect or quantify phase coupling across multiple frequencies (e.g. f 1, f 2, f 3, f 4, f 1 + f 2 + f 3 - f 4), or coupling that involves non-integer multiples of the frequencies (e.g. f 1, f 2, 2f 1/3 + f 2/3). NEW METHODS: To address the gap, this paper proposes a generalized approach, named multi-phase locking value (M-PLV), for the quantification of various types of instantaneous multi-frequency phase coupling. Different from most instantaneous phase coupling metrics that measure the simultaneous phase coupling, the proposed M-PLV method also allows the detection of delayed phase coupling and the associated time lag between coupled oscillators. RESULTS: The M-PLV has been tested on cases where synthetic coupled signals are generated using white Gaussian signals, and a system comprised of multiple coupled Rössler oscillators, as well as a human subject dataset. Results indicate that the M-PLV can provide a reliable estimation of the time window and frequency combination where the phase coupling is significant, as well as a precise determination of time lag in the case of delayed coupling. This method has the potential to become a powerful new tool for exploring phase coupling in complex nonlinear dynamic systems.
Entities:
Keywords:
cross-frequency coupling; nonlinear system; phase coupling; signal processing; time delay
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