Fast Approximation of EEG Forward Problem and Application to Tissue Conductivity Estimation

Bioelectric source analysis in the human brain from scalp electroencephalography (EEG) signals is sensitive to the conductivity of the different head tissues. Conductivity values are subject dependent, so non-invasive methods for conductivity estimation are necessary to fine tune the EEG models. To do so, the EEG forward problem solution (so-called lead field matrix) must be computed for a large number of conductivity configurations. Computing one lead field requires a matrix inversion which is computationally intensive for realistic head models. Thus, the required time for computing a large number of lead fields can become impractical. In this work, we propose to approximate the lead field matrix for a set of conductivity configurations, using the exact solution only for a small set of basis points in the conductivity space. Our approach accelerates the computing time, while controlling the approximation error. Our method is tested for brain and skull conductivity estimation , with simulated and measured EEG data, corresponding to evoked somato-sensory potentials. This test demonstrates that the used approximation does not introduce any bias and runs significantly faster than if exact lead field were to be computed.Comment: Copyright (c) 2019 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected]

Numerical modeling in electro- and magnetoencephalography

This Thesis concerns the application of two numerical methods, Boundary Element Method (BEM) and Finite Element Method (FEM) to forward problem solution of bioelectromagnetic source localization in the brain. The aim is to improve the accuracy of the forward problem solution in estimating the electrical activity of the human brain from electric and magnetic field measurements outside the head. Electro- and magnetoencephalography (EEG, MEG) are the most important tools enabling us to gather knowledge about the human brain non-invasively. This task is alternatively named brain mapping. An important step in brain mapping is determining from where the brain signals originate. Using appropriate mathematical models, a localization of the sources of measured signals can be performed. A general motivation of this work was the fact that source localization accuracy can be improved by solving the forward problem with higher accuracy. In BEM studies, accurate representation of model geometry using higher order elements improves the solution of the forward problem. In FEM, complex conductivity information can be incorporated into numerical model. Using Whitney-type finite elements instead of using singular sources such as point dipoles, primary and volume currents are represented as continuous sources. With comparison to analytical solutions available in simple geometries such as sphere, the studied numerical methods show improvements in the forward problem solution of bioelectromagnetic source imaging.reviewe

On the Volume Conduction Model Validation with Stereo EEG Data

Volume conduction can be defined as the transmission of electric potential and magnetic field generated by a primary current source of brain activation in the surrounding medium, i.e., the human head. Volume conduction simulations are based on sophisticated models whose construction represents a current challenge within the neuroscientific community. Volume conduction models are used in various applications such as electroencephalography (EEG) or magnetoencephalography (MEG) source reconstruction, or in the optimization of the electrode placement in a transcranial electrical stimulation session. Clinical applications based on volume conduction models are, for example, the localization of the epileptogenic zone, i.e., the brain area responsible for the generation of seizures, in the presurgical assessment of focal drug-resistant epilepsy patients, and the antidepressant effects given by transcranial electrical stimulation. Increasing the accuracy of volume conduction simulations is therefore crucial. To the best of our knowledge, the accuracy of volume conduction models have never been validated directly with actual measurements in human patients. The main goal of this thesis is to describe a first attempt to validate volume conduction modeling using electric stimulation stereo-encephalografic (sEEG) data. This work therefore is focused on the research, investigation and test of tools and methods which can be used to describe the accuracy of volume conduction models used in both clinical and basic research. Given a dataset of one pharmaco-resistant epilepsy patient, composed by the anatomical T1 weighted magnetic resonance image (MRI), the electrophysiological signal recorded during electric brain stimulation sessions with sEEG technique and sEEG contact positions extracted by post-implantation CT image, the analysis conducted in this work can be split into three main steps. First, we built volume conduction head models and we simulated the electric potentials during the electric brain stimulations. In this step, we solved the so-called (s)EEG forward problem by means of the finite element method in its classical formulation, and we considered three different conductivity profile to assign to the computational domain, individually extracted by the T1-w MRI. Moreover we computed the solution in meshes with two different resolution, i.e., 1 mm and 2 mm, with three different ways to model the source term, i.e., the partial integration approach, the subtraction approach and Venant\u2019s approach. Second, we extracted the responses to the electric brain stimulations from the actual sEEG measurements. Particular emphasis in this step was given to the optimal referencing systems of sEEG electrodes. Third, we compared the simulated and measured potentials for each of the three volume conduction head models, both in a single shaft and global comparison. The comparison results in overall high relative differences, with only slight modulations given by the distance from the stimulation site, the underlying volume conduction head model used and the compartment where the dipolar source is located. Simulation results show that the computation of sEEG forward problem solution is feasible with the same scheme adopted for scalp EEG in the duneuro software (http:// duneuro.org/), and it is stable for different mesh resolutions and source models also for intracranial electrodes, i.e., for electrodes close to the source positions. From this first validation attempt, we can conclude that the distance contact-source modulates the relative error between measured and simulated potential; for the contacts in the white matter compartment we observed the most accurate results, and the results relative to the three and four compartment results were more accurate than the ones relative to the five compartment results. While we achieved topographical errors within 10% for most of the shafts, the amplitude of simulated and measured potentials notably differs