Reconstruction of electric fields and source distributions in EEG brain imaging

In this thesis, three different approaches are developed for the estimation of focal brain activity using EEG measurements. The proposed approaches have been tested and found feasible using simulated data. First, we develop a robust solver for the recovery of focal dipole sources. The solver uses a weighted dipole strength penalty term (also called weighted L1,2 norm) as prior information in order to ensure that the sources are sparse and focal, and that both the source orientation and depth bias are reduced. The solver is based on the truncated Newton interior point method combined with a logarithmic barrier method for the approximation of the penalty term. In addition, we use a Bayesian framework to derive the depth weights in the prior that are used to reduce the tendency of the solver to favor superficial sources. In the second approach, vector field tomography (VFT) is used for the estimation of underlying electric fields inside the brain from external EEG measurements. The electric field is reconstructed using a set of line integrals. This is the first time that VFT has been used for the recovery of fields when the dipole source lies inside the domain of reconstruction. The benefit of this approach is that we do not need a mathematical model for the sources. The test cases indicated that the approach can accurately localize the source activity. In the last part of the thesis, we show that, by using the Bayesian approximation error approach (AEA), precise knowledge of the tissue conductivities and head geometry are not always needed. We deliberately use a coarse head model and we take the typical variations in the head geometry and tissue conductivities into account statistically in the inverse model. We demonstrate that the AEA results are comparable to those obtained with an accurate head model.Open Acces

Electrocardiographic Imaging of Sinus Rhythm in Pig Hearts Using Bayesian Maximum A Posteriori Estimation

Background: Electrocardiographic imaging (ECGI) has potential to guide physicians to plan treatment strategies. Previously, Bayesian maximum a posteriori (MAP) estimation has been successfully applied to solve this inverse problem for paced data. In this study, we evaluate its effectiveness using experimental data in reconstructing sinus rhythm. Methods: Four datasets from Langendorff-perfused pig hearts, suspended in a human-shaped torso-tank, were used. Each experiment included 3-5 simultaneous electrogram (EGM) and body surface potential (BSP) recordings of 10 beats, in baseline and under dofetilide and pinacidil perfusion. Bayesian MAP estimation and Tikhonov regularization were used to solve the inverse problem. Prior models in MAP were generated using beats from the same recording but excluding the test beat. Pearson's correlation was used to evaluate EGM reconstructions, activation time (AT) maps, and gradient of ATs. Results: In almost all quantitative evaluations and qualitative comparisons of AT maps and epicardial breakthrough sites, MAP outperformed substantially better than Tikhonov regularization. Conclusion: These preliminary results showed that with a "good" prior model, MAP improves over Tikhonov regularization in terms of preventing misdiagnosis of conduction abnormalities associated with arrhythmogenic substrates and identifying epicardial breakthrough sites

Multimodal Integration: fMRI, MRI, EEG, MEG

This chapter provides a comprehensive survey of the motivations, assumptions and pitfalls associated with combining signals such as fMRI with EEG or MEG. Our initial focus in the chapter concerns mathematical approaches for solving the localization problem in EEG and MEG. Next we document the most recent and promising ways in which these signals can be combined with fMRI. Specically, we look at correlative analysis, decomposition techniques, equivalent dipole tting, distributed sources modeling, beamforming, and Bayesian methods. Due to difculties in assessing ground truth of a combined signal in any realistic experiment difculty further confounded by lack of accurate biophysical models of BOLD signal we are cautious to be optimistic about multimodal integration. Nonetheless, as we highlight and explore the technical and methodological difculties of fusing heterogeneous signals, it seems likely that correct fusion of multimodal data will allow previously inaccessible spatiotemporal structures to be visualized and formalized and thus eventually become a useful tool in brain imaging research

-Norm Regularization in Volumetric Imaging of Cardiac Current Sources

Advances in computer vision have substantially improved our ability to analyze the structure and mechanics of the heart. In comparison, our ability to observe and analyze cardiac electrical activities is much limited. The progress to computationally reconstruct cardiac current sources from noninvasive voltage data sensed on the body surface has been hindered by the ill-posedness and the lack of a unique solution of the reconstruction problem. Common L2- and L1-norm regularizations tend to produce a solution that is either too diffused or too scattered to reflect the complex spatial structure of current source distribution in the heart. In this work, we propose a general regularization with Lp-norm () constraint to bridge the gap and balance between an overly smeared and overly focal solution in cardiac source reconstruction. In a set of phantom experiments, we demonstrate the superiority of the proposed Lp-norm method over its L1 and L2 counterparts in imaging cardiac current sources with increasing extents. Through computer-simulated and real-data experiments, we further demonstrate the feasibility of the proposed method in imaging the complex structure of excitation wavefront, as well as current sources distributed along the postinfarction scar border. This ability to preserve the spatial structure of source distribution is important for revealing the potential disruption to the normal heart excitation