Paz-Linares Deirel, Gonzalez-Moreira Eduardo, Areces-Gonzalez Ariosky, Wang Ying, Li Min, Vega-Hernandez Mayrim, Wang Qing, Bosch-Bayard Jorge, Bringas-Vega Maria L, Martinez-Montes Eduardo, Valdes-Sosa Mitchel J, Valdes-Sosa Pedro A
MOE Key Lab for Neuroinformation, The Clinical Hospital of Chengdu Brain Science Institute, University of Electronic Science and Technology of China, Chengdu, China.
Neuroinformatics Department, Cuban Neuroscience Center, Havana, Cuba.
Front Neurosci. 2023 Mar 15;17:978527. doi: 10.3389/fnins.2023.978527. eCollection 2023.
Oscillatory processes at all spatial scales and on all frequencies underpin brain function. Electrophysiological Source Imaging (ESI) is the data-driven brain imaging modality that provides the inverse solutions to the source processes of the EEG, MEG, or ECoG data. This study aimed to carry out an ESI of the source cross-spectrum while controlling common distortions of the estimates. As with all ESI-related problems under realistic settings, the main obstacle we faced is a severely ill-conditioned and high-dimensional inverse problem. Therefore, we opted for Bayesian inverse solutions that posited probabilities on the source process. Indeed, rigorously specifying both the likelihoods and probabilities of the problem leads to the proper Bayesian inverse problem of cross-spectral matrices. These inverse solutions are our formal definition for cross-spectral ESI (cESI), which requires of the source cross-spectrum to counter the severe ill-condition and high-dimensionality of matrices. However, inverse solutions for this problem were NP-hard to tackle or approximated within iterations with bad-conditioned matrices in the standard ESI setup. We introduce cESI with a probability upon the source cross-spectrum to avoid these problems. cESI inverse solutions are low-dimensional ones for the set of random vector instances and not random matrices. We achieved cESI inverse solutions through the variational approximations our Spectral Structured Sparse Bayesian Learning (ssSBL) algorithm https://github.com/CCC-members/Spectral-Structured-Sparse-Bayesian-Learning. We compared low-density EEG (10-20 system) ssSBL inverse solutions with reference cESIs for two experiments: (a) high-density MEG that were used to simulate EEG and (b) high-density macaque ECoG that were recorded simultaneously with EEG. The ssSBL resulted in two orders of magnitude with less distortion than the state-of-the-art ESI methods. Our cESI toolbox, including the ssSBL method, is available at https://github.com/CCC-members/BC-VARETA_Toolbox.
所有空间尺度和频率下的振荡过程是脑功能的基础。电生理源成像（ESI）是一种数据驱动的脑成像方式，它能为脑电图（EEG）、脑磁图（MEG）或皮层脑电图（ECoG）数据的源过程提供逆解。本研究旨在进行源互谱的电生理源成像，同时控制估计中的常见失真。与现实环境下所有与电生理源成像相关的问题一样，我们面临的主要障碍是一个严重病态且高维的逆问题。因此，我们选择了贝叶斯逆解，它为源过程设定概率。实际上，严格指定问题的似然性和概率会导致互谱矩阵的恰当贝叶斯逆问题。这些逆解是我们对互谱电生理源成像（cESI）的正式定义，它需要源互谱来应对矩阵的严重病态和高维性。然而，在标准电生理源成像设置中，这个问题的逆解在处理病态矩阵时是NP难的，或者只能在迭代中近似求解。我们引入了一种基于源互谱概率的cESI来避免这些问题。cESI逆解对于随机向量实例集来说是低维的，而不是随机矩阵。我们通过变分近似，利用我们的谱结构稀疏贝叶斯学习（ssSBL）算法（https://github.com/CCC-members/Spectral-Structured-Sparse-Bayesian-Learning）实现了cESI逆解。我们针对两个实验，将低密度脑电图（10 - 20系统）的ssSBL逆解与参考cESI进行了比较：（a）用于模拟脑电图的高密度脑磁图，以及（b）与脑电图同时记录的高密度猕猴皮层脑电图。与最先进的电生理源成像方法相比，ssSBL产生的失真小两个数量级。我们的cESI工具箱，包括ssSBL方法，可在https://github.com/CCC-members/BC-VARETA_Toolbox获取。
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