Trujillo-Barreto Nelson J, Aubert-Vázquez Eduardo, Valdés-Sosa Pedro A
Cuban Neuroscience Center, Havana, Cuba.
Neuroimage. 2004 Apr;21(4):1300-19. doi: 10.1016/j.neuroimage.2003.11.008.
In this paper, the Bayesian Theory is used to formulate the Inverse Problem (IP) of the EEG/MEG. This formulation offers a comparison framework for the wide range of inverse methods available and allows us to address the problem of model uncertainty that arises when dealing with different solutions for a single data. In this case, each model is defined by the set of assumptions of the inverse method used, as well as by the functional dependence between the data and the Primary Current Density (PCD) inside the brain. The key point is that the Bayesian Theory not only provides for posterior estimates of the parameters of interest (the PCD) for a given model, but also gives the possibility of finding posterior expected utilities unconditional on the models assumed. In the present work, this is achieved by considering a third level of inference that has been systematically omitted by previous Bayesian formulations of the IP. This level is known as Bayesian model averaging (BMA). The new approach is illustrated in the case of considering different anatomical constraints for solving the IP of the EEG in the frequency domain. This methodology allows us to address two of the main problems that affect linear inverse solutions (LIS): (a) the existence of ghost sources and (b) the tendency to underestimate deep activity. Both simulated and real experimental data are used to demonstrate the capabilities of the BMA approach, and some of the results are compared with the solutions obtained using the popular low-resolution electromagnetic tomography (LORETA) and its anatomically constraint version (cLORETA).
在本文中，贝叶斯理论被用于阐述脑电图/脑磁图的逆问题（IP）。这种阐述为现有的多种逆方法提供了一个比较框架，并使我们能够解决在处理单个数据的不同解决方案时出现的模型不确定性问题。在这种情况下，每个模型由所使用的逆方法的假设集以及数据与脑内初级电流密度（PCD）之间的函数依赖关系定义。关键在于，贝叶斯理论不仅为给定模型提供了感兴趣参数（PCD）的后验估计，还给出了找到不依赖于所假设模型的后验期望效用的可能性。在当前工作中，这是通过考虑一个被先前贝叶斯IP公式系统忽略的第三级推理来实现的。这一级别被称为贝叶斯模型平均（BMA）。在频域中考虑不同解剖约束来解决脑电图逆问题的情况下，对新方法进行了说明。这种方法使我们能够解决影响线性逆解（LIS）的两个主要问题：（a）鬼源的存在和（b）低估深部活动的趋势。模拟和真实实验数据均用于证明BMA方法的能力，并将一些结果与使用流行的低分辨率电磁断层成像（LORETA）及其解剖约束版本（cLORETA）获得的解决方案进行比较。
