EEG/MEG Source Imaging: Methods, Challenges, and Open Issues

We present the four key areas of research—preprocessing, the volume conductor, the forward problem, and the inverse problem—that affect the performance of EEG and MEG source imaging. In each key area we identify prominent approaches and methodologies that have open issues warranting further investigation within the community, challenges associated with certain techniques, and algorithms necessitating clarification of their implications. More than providing definitive answers we aim to identify important open issues in the quest of source localization

Imaging Physiological and Pathological Activity in the Brain using Electric Impedance Tomography

Electric Impedance Tomography (EIT) is a promising medical imaging technique that reconstructs the internal conductivity of an object from boundary measurements. EIT is currently being used to monitor the lung during ventilation clinically. Amongst other suggested uses for imaging it can also be used to image neuronal function. There are different ways on how EIT can image neuronal function and two of these are tested in this thesis. The overall aim of our work was to advance imaging of physiological and pathological neuronal activity using EIT and assess its potential for future clinical use. In Chapter 1, a general introduction into brain imaging techniques and EIT is given. In Chapter 2, the effect of different anaesthetics on the neuronal signal was assessed to prepare for EIT recordings under anaesthesia. In Chapter 3, we assessed the validity of two biophysical models regarding the behaviour of the impedance in response to alterations in the carrier frequency experimentally. This allowed an assessment of the ideal carrier frequency to image physiological neuronal activity. In Chapter 4, the source of the fast neural signal in EIT is discussed further. In Chapter 5, the possibility of imaging physiological neuronal activity throughout the brain is tested and its limitations are discussed. In Chapter 6, the impedance response to epileptiform activity is characterized and the potential use of EIT in imaging epileptic foci in epilepsy patients is discussed. In Chapter 7, imaging of epileptic foci in subcortical structures is tested using two different ways of imaging with EIT

Models and image: reconstruction in electrical impedance tomography of human brain function

Electrical Impedance Tomography (EIT) of brain function has the potential to provide a rapid portable bedside neuroimaging device. Recently, our group published the first ever EIT images of evoked activity recorded with scalp electrodes. While the raw data showed encouraging, reproducible changes of a few per cent, the images were noisy. The poor image quality was due, in part, to the use of a simplified reconstruction algorithm which modelled the head as a homogeneous sphere. The purpose of this work has been to develop new algorithms in which the model incorporates extracerebral layers and realistic geometry, and to assess their effect on image quality. An algorithm was suggested which allowed fair comparison between reconstructions assuming analytical and numerical (Finite Element Method - FEM) models of the head as a homogeneous sphere and as concentric spheres representing the brain, CSF, skull and scalp. Comparison was also made between these and numerical models of the head as a homogeneous, head-shaped volume and as a head-shaped volume with internal compartments of contrasting resistivity. The models were tested on computer simulations, on spherical and head-shaped, saline-filled tanks and on data collected during human evoked response studies. EIT also has the potential to image resistance changes which occur during neuronal depolarization in the cortex and last tens of milliseconds. Also presented in this thesis is an estimate of their magnitude made using a mathematical model, based on cable theory, of resistance changes at DC during depolarization in the cerebral cortex. Published values were used for the electrical properties and geometry of cell processes (Rail, 1975). The study was performed in order to estimate the resultant scalp signal that might be obtained and to assess the ability of EIT to produce images of neuronal depolarization

Tomographic neurofeedback : a new technique for the self-regulation of brain electrical activity

A major limitation of the current neurofeedback paradigm is the limited information provided by a single or a small number of electrodes placed on the scalp. A considerable improvement of the neurofeedback efficacy and specificity could be obtained feeding back brain activity of delimited structures. While traditional EEG information reflects the superposition of the electrical activity of a large number of neurons, by means of inverse solutions such as the Low-Resolution Electromagnetic Tomography (LORETA) spatially delimited brain activity can be evaluated in neocortical tissue. In this Dissertation we implement LORETA neurofeedback, we introduce a new feedback function ( 1 ) sensitive to dynamic change over time, and we clarify several issues related to the learning process observable with neurofeedback. The reported set of three experiments is the first attempt I am aware of to prove learning of brain current density activity. Three individuals were trained to improve brain activation (suppress low Alpha (8-10 Hz) and enhance low Beta (16 -20 Hz) current density) in the anterior cingulate gyros cognitive division (ACcd). Participants took part of six experimental sessions, each lasting approximately 30 minutes. Randomization-Permutation ANCOVA tests were conducted on recordings of the neurofeedback training. In addition a randomized trial was performed at the end of the treatment. During eight two-minutes periods (trials) participants were asked to try to obtain as many rewards as they could ( 4 1 trials) or as few rewards as they could ( 4 0 trials). The order of trials was decided at random. The hypothesis under testing was that participants acquired volitional control over their brain activity so to be able to obtain more rewards during the plus condition as compared to the minus condition. We found evidence of volitional control for two subjects (p=0.043 and p=O.l) and no evidence of volitional control for one of them (p=0.27 1). The combination of the three p-values provided an overall probability value for this experiment of 0.012 with the additive method and 0.035 with the multiplicative method. These results strongly support the hypothesis of volitional control across the experimental group. Trends of the Beta/ Alpha power ratio in the ACcd were in the expected direction for all the three subjects, however the combined p-values did not reach significance. With as few as six training sessions, typically insufficient to produce any form of learning with scalp neurofeedback, the experiment showed overall signs of volitional control of the electrical activity of the ACcd. Possible applications of the technique are important and include the treatment of epileptic foci, the treatment of specific brain regions damaged as a consequence of traumatic brain injury, and in general of any specific cortical electrical activity

Review on solving the forward problem in EEG source analysis

Background. The aim of electroencephalogram (EEG) source localization is to find the brain areas responsible for EEG waves of interest. It consists of solving forward and inverse problems. The forward problem is solved by starting from a given electrical source and calculating the potentials at the electrodes. These evaluations are necessary to solve the inverse problem which is defined as finding brain sources which are responsible for the measured potentials at the EEG electrodes. Methods. While other reviews give an extensive summary of the both forward and inverse problem, this review article focuses on different aspects of solving the forward problem and it is intended for newcomers in this research field. Results. It starts with focusing on the generators of the EEG: the post-synaptic potentials in the apical dendrites of pyramidal neurons. These cells generate an extracellular current which can be modeled by Poisson's differential equation, and Neumann and Dirichlet boundary conditions. The compartments in which these currents flow can be anisotropic (e.g. skull and white matter). In a three-shell spherical head model an analytical expression exists to solve the forward problem. During the last two decades researchers have tried to solve Poisson's equation in a realistically shaped head model obtained from 3D medical images, which requires numerical methods. The following methods are compared with each other: the boundary element method (BEM), the finite element method (FEM) and the finite difference method (FDM). In the last two methods anisotropic conducting compartments can conveniently be introduced. Then the focus will be set on the use of reciprocity in EEG source localization. It is introduced to speed up the forward calculations which are here performed for each electrode position rather than for each dipole position. Solving Poisson's equation utilizing FEM and FDM corresponds to solving a large sparse linear system. Iterative methods are required to solve these sparse linear systems. The following iterative methods are discussed: successive over-relaxation, conjugate gradients method and algebraic multigrid method. Conclusion. Solving the forward problem has been well documented in the past decades. In the past simplified spherical head models are used, whereas nowadays a combination of imaging modalities are used to accurately describe the geometry of the head model. Efforts have been done on realistically describing the shape of the head model, as well as the heterogenity of the tissue types and realistically determining the conductivity. However, the determination and validation of the in vivo conductivity values is still an important topic in this field. In addition, more studies have to be done on the influence of all the parameters of the head model and of the numerical techniques on the solution of the forward problem.peer-reviewe

Imaging physiological brain activity and epilepsy with Electrical Impedance Tomography

Electrical Impedance Tomography (EIT) allows reconstructing conductivity changes into images. EIT detects fast impedance changes occurring over milliseconds, due to ion channel opening, and slow impedance changes, appearing in seconds, due to cell swelling/increased blood flow. The purpose of this work was to examine the feasibility of using EIT for imaging a gyrencephalic brain with implanted depth electrodes during seizures. Chapter 1 summarises the principles of EIT. In Chapter 2, it is investigated whether recent technical improvements could enable EIT to image slow impedance changes upon visual stimulation non-invasively. This was unsuccessful so the remaining studies were undertaken on intracranial recordings. Chapter 3 presents a computer modelling study using data from patients, for whom the detection of simulated seizure-onset perturbations for both, fast and slow impedance changes, were improved with EIT compared to stereotactic electroencephalography (SEEG) detection or EEG inverse-source modelling. Chapter 4 describes the development of a portable EIT system that could be used on patients. The system does not require averaging and post-hoc signal processing to remove switching artefacts, which was the case previously. Chapter 5 describes the use of the optimised method in chemically-induced focal epilepsy in anaesthetised pigs implanted with depth electrodes. This shows for the first time EIT was capable of producing reproducible images of the onset and spread of seizure-related slow impedance changes in real-time. Chapter 6 presents a study on imaging ictal/interictal-related fast impedance changes. The feasibility of reconstructing ictal-related impedance changes is demonstrated for one pig and interictal-related impedance changes were recorded for the first time in humans. Chapter 7 summarises all work and future directions. Overall, this work suggests EIT in combination with SEEG has a potential to improve the diagnostic yield in epilepsy and demonstrates EIT can be performed safely and ethically creating a foundation for further clinical trials

A 3D Finite-Difference BiCG Iterative Solver with the Fourier-Jacobi Preconditioner for the Anisotropic EIT/EEG Forward Problem

The Electrical Impedance Tomography (EIT) and electroencephalography (EEG) forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the performance of several new promising numerical techniques, which seem to be more suitable for solving these problems. The proposed numerical schemes combine the fictitious domain approach together with the finite-difference method and the optimally preconditioned Conjugate Gradient- (CG-) type iterative method for treatment of the discrete model. The numerical scheme includes the standard operations of summation and multiplication of sparse matrices and vector, as well as FFT, making it easy to implement and eligible for the effective parallel implementation. Some typical use cases for the EIT/EEG problems are considered demonstrating high efficiency of the proposed numerical technique

Anatomical atlas of the upper part of the human head for electroencephalography and bioimpedance applications

Objective. The objective of this work is to develop a 4D (3D+T) statistical anatomical atlas of the electrical properties of the upper part of the human head for cerebral electrophysiology and bioimpedance applications. Approach. The atlas was constructed based on 3D magnetic resonance images (MRI) of 107 human individuals and comprises the electrical properties of the main internal structures and can be adjusted for specific electrical frequencies. T1w+T2w MRI images were used to segment the main structures of the head while angiography MRI was used to segment the main arteries. The proposed atlas also comprises a time-varying model of arterial brain circulation, based on the solution of the Navier-Stokes equation in the main arteries and their vascular territories. Main results. High-resolution, multi-frequency and time-varying anatomical atlases of resistivity, conductivity and relative permittivity were created and evaluated using a forward problem solver for EIT. The atlas was successfully used to simulate electrical impedance tomography measurements indicating the necessity of signal-to-noise between 100 and 125 dB to identify vascular changes due to the cardiac cycle, corroborating previous studies. The source code of the atlas and solver are freely available to download. Significance. Volume conductor problems in cerebral electrophysiology and bioimpedance do not have analytical solutions for nontrivial geometries and require a 3D model of the head and its electrical properties for solving the associated PDEs numerically. Ideally, the model should be made with patient-specific information. In clinical practice, this is not always the case and an average head model is often used. Also, the electrical properties of the tissues might not be completely known due to natural variability. Anatomical atlases are important tools for in silico studies on cerebral circulation and electrophysiology that require statistically consistent data, e.g. machine learning, sensitivity analyses, and as a benchmark to test inverse problem solvers.Peer reviewe