The Smartphone Brain Scanner: A Portable Real-Time Neuroimaging System

Combining low cost wireless EEG sensors with smartphones offers novel opportunities for mobile brain imaging in an everyday context. We present a framework for building multi-platform, portable EEG applications with real-time 3D source reconstruction. The system - Smartphone Brain Scanner - combines an off-the-shelf neuroheadset or EEG cap with a smartphone or tablet, and as such represents the first fully mobile system for real-time 3D EEG imaging. We discuss the benefits and challenges of a fully portable system, including technical limitations as well as real-time reconstruction of 3D images of brain activity. We present examples of the brain activity captured in a simple experiment involving imagined finger tapping, showing that the acquired signal in a relevant brain region is similar to that obtained with standard EEG lab equipment. Although the quality of the signal in a mobile solution using a off-the-shelf consumer neuroheadset is lower compared to that obtained using high density standard EEG equipment, we propose that mobile application development may offset the disadvantages and provide completely new opportunities for neuroimaging in natural settings

The analytical subtraction approach for solving the forward problem in EEG

Objective: The subtraction approach is known for being a theoretically-rigorous and accurate technique for solving the forward problem in electroencephalography by means of the finite element method. One key aspect of this approach consists of computing integrals of singular kernels over the discretised domain, usually referred to as potential integrals. Several techniques have been proposed for dealing with such integrals, all of them approximating the results at the expense of reducing the accuracy of the solution. In this paper, we derive analytic formulas for the potential integrals, reducing approximation errors to a minimum. Approach: Based on volume coordinates and Gauss theorems, we obtained parametric expressions for all the element matrices needed in the formulation assuming first order basis functions defined on a tetrahedral mesh. This included solving potential integrals over triangles and tetrahedra, for which we found compact and efficient formulas. Main results: Comparison with numerical quadrature schemes allowed to test the advantages of the methodology proposed, which were found of great relevance for highly-eccentric sources, as those found in the somatosensory and visual cortices. Moreover, the availability of compact formulas allowed an efficient implementation of the technique, which resulted in similar computational cost than the simplest numerical scheme. Significance: The analytical subtraction approach is the optimal subtraction-based methodology with regard to accuracy. The computational cost is similar to that obtained with the lowest order numerical integration scheme, making it a competitive option in the field. The technique is highly relevant for improving electromagnetic source imaging results utilising individualised head models and anisotropic electric conductivity fields without imposing impractical mesh requirements

A method for rapid production of subject specific finite element meshes for electrical impedance tomography of the human head

Finite element (FE) methods are widely used in electrical impedance tomography (EIT) to enable rapid image reconstruction of different tissues based on their electrical conductivity. For EIT of brain function, anatomically-accurate (head-shaped) FE meshes have been shown to improve the quality of the reconstructed images. Unfortunately, given the lack of a computational protocol to generate patient-specific meshes suitable for EIT, production of such meshes is currently ad hoc and therefore very time consuming. Here we describe a robust protocol for rapid generation of patient-specific FE meshes from MRI or CT scan data. Most of the mesh generation process is automated and uses freely available user-friendly software. Other necessary custom scripts are provided as supplementary online data and are fully documented. The patient scan data is segmented into four surfaces: brain, cerebrospinal fluid, skull and scalp. The segmented surfaces are then triangulated and used to generate a global mesh of tetrahedral elements. The resulting meshes exhibit high quality when tested with different criteria and were validated in computational simulations. The proposed protocol provides a rapid and practicable method for generation of patient-specific FE meshes of the human head that are suitable for EIT. This method could eventually be extended to other body regions and might confer benefits with other imaging techniques such as optical tomography or EEG inverse source imaging

Splitting method for elliptic equations with line sources

In this paper, we study the mathematical structure and numerical approximation of elliptic problems posed in a (3D) domain $\Omega$ when the right-hand side is a (1D) line source $\Lambda$. The analysis and approximation of such problems is known to be non-standard as the line source causes the solution to be singular. Our main result is a splitting theorem for the solution; we show that the solution admits a split into an explicit, low regularity term capturing the singularity, and a high-regularity correction term $w$ being the solution of a suitable elliptic equation. The splitting theorem states the mathematical structure of the solution; in particular, we find that the solution has anisotropic regularity. More precisely, the solution fails to belong to $H^1$ in the neighbourhood of $\Lambda$, but exhibits piecewise $H^2$-regularity parallel to $\Lambda$. The splitting theorem can further be used to formulate a numerical method in which the solution is approximated via its correction function $w$. This approach has several benefits. Firstly, it recasts the problem as a 3D elliptic problem with a 3D right-hand side belonging to $L^2$, a problem for which the discretizations and solvers are readily available. Secondly, it makes the numerical approximation independent of the discretization of $\Lambda$; thirdly, it improves the approximation properties of the numerical method. We consider here the Galerkin finite element method, and show that the singularity subtraction then recovers optimal convergence rates on uniform meshes, i.e., without needing to refine the mesh around each line segment. The numerical method presented in this paper is therefore well-suited for applications involving a large number of line segments. We illustrate this by treating a dataset (consisting of $\sim 3000$ line segments) describing the vascular system of the brain

Recent advances in modeling and analysis of bioelectric and biomagnetic sources

Determining the centers of electrical activity in the human body and the connectivity between different centers of activity in the brain is an active area of research. To understand brain function and the nature of cardiovascular diseases requires sophisticated methods applicable to non-invasively measured bioelectric and biomagnetic data. As it is difficult to solve for all unknown parameters at once, several strains of data analysis have been developed, each trying to solve a different part of the problem and each requiring a different set of assumptions. Current trends and results from major topics of electro- and magnetoencephalographic data analysis are presented here together with the aim of stimulating research into the unification of the different approaches. The following topics are discussed: source reconstruction using detailed finite element modeling to locate sources deep in cthe brain; connectivity analysis for the quantification of strength and direction of information flow between activity centers, preferably incorporating an inverse solution; the conflict between the statistical independence assumption of sources and a possible connectivity; the verification and validation of results derived from non-invasively measured data through animal studies and phantom measurements. This list already indicates the benefits of a unified view