Academic News Report on Multidimensional Cross-Frequency Coupling Analysis in EEG/MEG Data

In recent years, with the advancement of neuroscience and medical imaging technology, researchers’ exploration of brain functional connectivity has become increasingly in-depth. This report will introduce a scientific research paper on multi-dimensional cross-frequency coupling analysis, namely “A Bicoherence Approach to Analyze Multi-Dimensional Cross-Frequency Coupling in EEG/MEG Data”. This paper was written by Alessio Basti and others, and was published in the 2024 issue of the “Scientific Reports” journal. It mainly discusses the application and significance of Multi-Dimensional Antisymmetric Cross-Bicoherence (MACB) in Electroencephalogram (EEG) and Magnetoelectroencephalogram (MEG) data.

Research Background

In functional imaging studies of the human brain, detecting the statistical dependency between different brainregions’ time series is crucial for understanding how the brain works. Traditional methods are often one-dimensional (1D) analyses, even though they aid basic research, they often fall short when dealing with complex multi-variate data. Studies have found that phase coupling between different or the same frequencies of brainwaves can reveal more information about brain functional connectivity. The detection of same-frequency and cross-frequency phase coupling can provide theoretical support for neurofunctional integration. However, most current methods can only capture linear dependencies and struggle to fully reflect the complex functional connections of the brain.

Against this background, Alessio Basti and his team have proposed a statistical method based on bicoherence analysis, namely antisymmetric cross-bicoherence (ACB), and extended it to the multi-dimensional space to form Multi-Dimensional Antisymmetric Cross-Bicoherence (MACB).

Source of Research

The authors of this paper include Alessio Basti, Guido Nolte, Roberto Guidotti, Risto J. Ilmoniemi, Gian Luca Romani, Vittorio Pizzella, and Laura Marzetti who come from the interdisciplinary field of brain imaging and clinical science of “G. d’Annunzio” University, the medical center of the University of Hamburg-Eppendorf, the School of Technology of Aalto University and the University of Helsinki. The paper was published in “Scientific Reports” in 2024.

Research Workflow

The overall workflow of this study can be divided into several main parts: derivation of theoretical formulas, design and generation of experimental data, algorithm validation, and performance evaluation. The specific steps are as follows:

Derivation of Theoretical Formulas

The study first proposed the mathematical formula of Multi-Dimensional Antisymmetric Cross-Bicoherence (MACB). Set two frequencies, f1, and f2, and three scalar time-series x, y, and z, they studied their Cross-Bicoherence form. Cross-Bicoherence is often used to mine the non-linear interaction between two time series, and phase coupling can reflect the phase dependency properties of the time series. In order to eliminate the influence of amplitude on Cross-Bicoherence, a relative metric, the Cross-Bicoherence, is usually introduced. This paper further introduces Antisymmetric Cross-Bicoherence (ACB) to eliminate the disguised coupling brought by instantaneous correlated noise.

Design and Generation of Experimental Data

The study designed three synthetic experiments to validate the rationality and superiority of MACB. The experimental data were generated by Matlab, simulating real neuroscience scenarios. In the first experiment, the study investigated the performance of MACB under different levels of noise. In the second experiment, by adjusting the data dimension, the effect of the data space dimension from different brain regions on the results was simulated. In the third experiment, by changing the length of the time series, the performance of MACB under different data lengths was detected.

Algorithm Validation

Through a series of mathematical derivations, the study proved the robustness and consistency of the MACB method under several linear transformations. Through theoretical derivation, it was confirmed that the value of MACB is between 0 and 1, and the exponential bias decreases with the square root of the number of data segments in the Gaussian data case.

Performance Evaluation

1. Impact of Noise Level: By comparing the MACB and ACB results under different noise levels, the study validated that MACB can still accurately detect phase coupling in high noise environments. This robustness shows the potential of MACB in practical applications, especially when dealing with complex EEG data.

2. Impact of Data Dimensions: When the dimension is higher, the performance of MACB is significantly better than ACB, which indicates that more information loss in traditional one-dimensional methods can be compensated for by multi-dimensional analysis. The experimental results show that MACB can more accurately capture the real coupling information of the brain region in the high-dimensional data space.

3. Impact of Time Series Length: The experiment shows that as the time series length decreases, the advantages of MACB become more apparent. In the scenario of short-time data analysis (such as real-time EEG analysis), MACB can achieve more efficient detection performance.

Conclusion and Significance

Overall, the research shows that MACB not only performs well under low signal to noise ratio conditions but also shows its unique advantages when dealing with high-dimensional and short time-series data. This will provide new tools and methods for future functional brain imaging research. Furthermore, because MACB has invariance under different data transformations, it is more suitable for practical applications in the field of neuroscience.

Highlights of Research

1. Superior Robustness: MACB can still accurately detect signal coupling in high noise environments, proving its potential in practical applications.
2. Multidimensional Analytical Capability: MACB compensates for the information loss of one-dimensional methods by handling high-dimensional data spaces, which helps to more accurately reflect the complex functional connections of the brain.
3. Superior Performance with Short-Time Data: In short-time data analysis, MACB shows efficient detection performance, suitable for real-time EEG data analysis.

Additional Information

Future research can further apply MACB to actual measurement data, such as MEG/EEG data in the Human Connectome Project, to further verify the application prospects of this method in actual data. This may lead to a deeper understanding of the research on brain functional connectivity.

Detailed theoretical derivations, experimental results, and data of the study can be obtained by contacting the corresponding author Alessio Basti.