OBJECTIVE: Synchronization between distributed rhythms in the brain is commonly assessed by estimating the synchronization strength from simultaneous measurements. This approach, however, does not elucidate the phase dynamics that underlies synchronization. For this, an explicit dynamical model is required. Based on the assumption that the recorded rhythms can be described as weakly coupled oscillators, we propose a method for characterizing their phase-interaction dynamics. METHODS: We propose to model ongoing magnetoencephalographic (MEG) oscillations as weakly coupled oscillators. Based on this model, the phase interactions between simultaneously recorded signals are characterized by estimating the modulation in instantaneous frequency as a function of their phase difference. Furthermore, we mathematically derive the effect of volume conduction on the model and show how indices for strength and direction of coupling can be derived. RESULTS: The methodology is tested using simulations and is applied to ongoing occipital-frontal MEG oscillations of healthy subjects in the alpha and beta bands during rest. The simulations show that the model is robust against the presence of noise, short observation times, and model violations. The application to MEG data shows that the model can reconstruct the observed occipital-frontal phase difference distributions. Furthermore, it suggests that phase locking in the alpha and beta band is established by qualitatively different mechanisms. CONCLUSION: When the recorded rhythms are assumed to be weakly coupled oscillators, a dynamical model for the phase interactions can be fitted to data. The model is able to reconstruct the observed phase difference distribution, and hence, provides a dynamical explanation for observed phase locking.
OBJECTIVE: Synchronization between distributed rhythms in the brain is commonly assessed by estimating the synchronization strength from simultaneous measurements. This approach, however, does not elucidate the phase dynamics that underlies synchronization. For this, an explicit dynamical model is required. Based on the assumption that the recorded rhythms can be described as weakly coupled oscillators, we propose a method for characterizing their phase-interaction dynamics. METHODS: We propose to model ongoing magnetoencephalographic (MEG) oscillations as weakly coupled oscillators. Based on this model, the phase interactions between simultaneously recorded signals are characterized by estimating the modulation in instantaneous frequency as a function of their phase difference. Furthermore, we mathematically derive the effect of volume conduction on the model and show how indices for strength and direction of coupling can be derived. RESULTS: The methodology is tested using simulations and is applied to ongoing occipital-frontal MEG oscillations of healthy subjects in the alpha and beta bands during rest. The simulations show that the model is robust against the presence of noise, short observation times, and model violations. The application to MEG data shows that the model can reconstruct the observed occipital-frontal phase difference distributions. Furthermore, it suggests that phase locking in the alpha and beta band is established by qualitatively different mechanisms. CONCLUSION: When the recorded rhythms are assumed to be weakly coupled oscillators, a dynamical model for the phase interactions can be fitted to data. The model is able to reconstruct the observed phase difference distribution, and hence, provides a dynamical explanation for observed phase locking.
Authors: Michael G Rosenblum; Laura Cimponeriu; Anastasios Bezerianos; Andreas Patzak; Ralf Mrowka Journal: Phys Rev E Stat Nonlin Soft Matter Phys Date: 2002-03-28