Research Background and Objectives

With the continuous development of neuroscience, identifying indirectly observed processes related to functional networks has become an important research direction. Researchers attempt to estimate the activity of these functional networks through electrophysiological signals such as EEG and MEG. However, this process often involves solving an inverse problem, i.e., inferring the underlying brain activity from the observed data, which poses significant challenges for research.

In this paper, the authors propose new methods to address this challenge. They point out that traditional methods exhibit significant errors in estimating functional connectivity, mainly due to mismatches in the functional network models. These errors substantially affect the accuracy of functional connectivity, thus limiting our understanding of brain function. To solve this problem, the authors introduce a Hidden Gaussian Graphical Spectral (HiGGS) model based on Bayesian theory to more accurately identify oscillatory networks in the brain.

Research Source

This paper was written by Deirel Paz-Linares et al. from the following research institutions: Clinical Hospital of the Brain Science Institute in Chengdu, Cuban Neuroscience Center, Central University “Marta Abreu” of Las Villas Electrical Engineering Department, among others. It was published in the journal Scientific Reports, volume 13, article number 11466, DOI: 10.1038/s41598-023-38513-y.

Research Process

Research Subjects and Experimental Methods

The research process outlined in this paper includes several steps as follows:

1. Data Collection and Preprocessing: First, the researchers used human EEG and monkey EEG/ECoG records as data sources. During experiments, they simulated the alpha rhythm of EEG and used these data to validate the model accuracy.
2. Solving the Inverse Problem: The core of the research is solving the inverse problem for MEG/EEG. This step involves estimating the underlying brain activity from the observed data, i.e., the local currents within the time domain ( t ). These estimated data are used to identify functional connectivity and reveal oscillatory networks in the brain.
3. Model Introduction: To address errors in the inverse problem, the authors introduced the HiGGS model. This model utilizes Bayesian methods and specifies the brain oscillatory network model through a hidden Gaussian spectral model to reduce estimation errors.
4. Model Validation: The authors validated the HiGGS model’s effectiveness through human EEG alpha rhythm simulations. The results show that the error rate in HiGGS inverse solutions is below 2%, whereas traditional methods have an error rate of up to 20%. Additionally, they validated the model with synchronous EEG/ECoG recordings from monkeys, indicating that the HiGGS method’s accuracy is enhanced by one-third compared to traditional methods.

Experimental Details

During the experiments, the researchers first estimated the underlying brain activity from MEG/EEG data and then used these data to estimate functional connectivity. Specific steps include:

1. Simulation and Real Data Validation:

   • Conducted simulation experiments on human EEG alpha rhythm, measured errors, and performed ROC performance evaluation.
   • Used synchronous EEG/ECoG recordings from monkeys for experimental validation, comparing the accuracy of the HiGGS model with traditional methods.

2. Data Analysis and Algorithm Implementation:

   • Used the Bayesian Maximum A Posteriori (MAP) method to solve the inverse problem.
   • Adopted the Hermitian Graphical Lasso algorithm (hglasso) to estimate the precision matrix and used the Expectation-Maximization (EM) algorithm for multi-step approximate solutions.

Research Results

The main results of this paper include:

1. Error Analysis: In HiGGS inverse solutions, the error rate in human EEG alpha rhythm simulation experiments is less than 2%, whereas traditional methods reach up to 20%. The experimental results of monkey’s synchronous EEG/ECoG recordings also demonstrate smaller errors with the HiGGS method, showing a one-third improvement in accuracy.
2. Functional Connectivity Estimation: Through the HiGGS model, researchers can more accurately estimate the functional connectivity of brain oscillatory networks, reducing estimation errors caused by model mismatches.
3. Algorithm Performance: The stable and scalable nature of the algorithm was validated using the hglasso algorithm for precision matrix estimation combined with the EM algorithm for multi-step approximate solutions.

Research Conclusion

By introducing the HiGGS model, this paper effectively addresses the error issues in the MEG/EEG inverse problem, improving the accuracy of estimating functional connectivity in brain oscillatory networks. This research outcome holds significant scientific and practical value, providing new research methods for neuroscience and strong references for other fields requiring inverse problem solutions.

Specifically, the main contributions of this paper are:

1. Proposing the HiGGS Model: By using Bayesian methods and a hidden Gaussian spectral model, the HiGGS model significantly reduces errors in functional connectivity estimation.
2. Validating the Model’s Effectiveness: The effectiveness of the HiGGS model is proven through simulations and experimental validation, demonstrating superior accuracy and stability.
3. Enhancing Neuroscience Research Precision: More accurate functional connectivity estimation helps better understand the relationship between brain function and behavior, promoting advances in neuroscience research.

Research Highlights

The highlights of this research include:

1. Innovative Methods: The introduction of the HiGGS model and hglasso algorithm provides new ideas and methods for solving inverse problems.
2. Multi-step Validation: Comprehensive validation of the model’s effectiveness and accuracy through human EEG simulations and monkey EEG/ECoG experiments.
3. Broad Application Potential: This research method is not only suitable for the field of brain science but can also be applied to other scientific research areas requiring inverse problem solutions.

Through the aforementioned research, this paper provides an efficient and accurate method for identifying functional networks, with significant scientific and practical value.