PB 11 Phase-coupling optimization (PCO) – a new algorithm for the analysis and localization of phase-coupling in multivariate data. Issue 10 (October 2017) - Waterstraat, G.; Curio, G.; Nikulin, V.
Abstract : Introduction: Phase-coupling between neuronal oscillations in the brain has been hypothesized as a mechanism for interactions between brain areas; moreover, phases of neuronal oscillations were found related to performance in memory and perception tasks. However, in multivariate data, such as multi-channel EEG or MEG, the analysis of phase-coupling remains challenging. Sensor-space analysis is suboptimal regarding the signal-to-noise ratio (SNR) and might fail to localize the sources of phase-coupling appropriately. Here, we introduce phase-coupling optimization (PCO), an algorithm seeking spatial filters that maximize the coupling of oscillatory phases to an independent variable (e.g., detected vs. undetected events in a perception task). The resulting spatial filters/patterns can then be used for inverse source modeling. Methods: Due to its simplicity, the "mean vector length" measure was chosen to quantify the degree of phase-coupling and is being maximized using the quasi-Newton Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm. To avoid local minima, the optimization is restarted several times from low-discrepancy pseudo-random initial starting points. As regularization, spatio-spectral decomposition (SSD) reduces the search-space while maximizing the SNR in the selected frequency band. The performance of the algorithm was verified using realistic forward-model EEG simulations. Results: Simulations demonstrated that PCO, together with SSD as pre-processing, can reliably localize the sources of phase-coupling in multi-channel EEG and characterize the coupling relation down to a SNR of −10 dB (i.e., a power ratio of 0.1) using 500 simulated task repetitions. Additionally, PCO is superior to a multiple regression approach and by a large margin outperforms sensor-space analysis based on a current source density estimation. Discussion: The analysis of phase-coupling in sensor space is suboptimal due to the SNR of the signal and might even lead to erroneous source localization. Techniques such as beamforming on the other hand, require a well-founded a priori assumption on the spatial origin of phase-coupling and complex inverse problem solvers. PCO seeks the optimal spatial projection for the analysis of phase-coupling and demonstrated its reliability even for very low SNR. Hence, we regard it as a promising tool for the analysis of neuronal oscillations. Significance: PCO increases the sensitivity and reliability of phase-coupling analyses. The obtained spatial patterns can be used for inverse source modeling.