Magnetoencephalography with diversely oriented and multicomponentsensors

To locate endocranial current sources, a magnetoencephalography (MEG) system usually measures the magnetic field at many points around the skull with an array of radial sensors. Despite the success of using radial components of the field, the authors show that using nonradial components may potentially also be beneficial. They demonstrate some benefits of using diversely oriented and multicomponent sensors to measure the nonradial components. A framework is provided for analyzing the accuracy of a system that estimates the location and direction of a current dipole inside a spherical skull. The framework is then used to determine the effect on accuracy of varying the orientations of sensors in an array and, as a consequence, it is found that the radial orientations commonly used in practice are suboptimal for locating dipoles near the array's center. A diversely oriented array that improves performance is presented. The authors show how a single multicomponent sensor can locate a dipole, and derive a simple algorithm for locating a dipole near the sensor     

On identifiability and information-regularity in parametrized normal distributions

We describe methods to establish identifiability and information-regularity of parameters in normal distributions. Parameters are considered identifiable when they are determined uniquely by the probability distribution and they are information-regular when their Fisher information matrix is full rank. In normal distributions, information-regularity implies local identifiability, but the converse is not always true. Using the theory of holomorphic mappings, we show when the converse is true, allowing information-regularity to be established without having to explicitly compute the information matrix. Some examples are given.This work was supported by the Air Force Office of Scientific Research under Grant no. F49620-93-1-0096, the National Science Foundation under Grant no. MIP-9122753, and the Office of Naval Research under Grant no. N00014-91-J-1298.     

MEG forward problem formulation using equivalent surface current densities

We present a formulation for the magnetoencephalography (MEG) forward problem with a layered head model. Traditionally the magnetic field is computed based on the electric potential on the interfaces between the layers. We propose to express the effect of the volumetric currents in terms of an equivalent surface current density on each interface, and obtain the magnetic field based on them. The boundary elements method is used to compute the equivalent current density and the magnetic field for a realistic head geometry. We present numerical results showing that the MEG forward problem is solved correctly with this formulation, and compare it with the performance of the traditional formulation. We conclude that the traditional formulation generally performs better, but still the new formulation is useful in certain situations.     

A meshless method for solving the EEG forward problem

We present a numerical method to solve the quasistatic Maxwell equations and compute the electroencephalography (EEG) forward problem solution. More generally, we develop a computationally efficient method to obtain the electric potential distribution generated by a source of electric activity inside a three-dimensional body of arbitrary shape and layers of different electric conductivities. The method needs only a set of nodes on the surface and inside the head, but not a mesh connecting the nodes. This represents an advantage over traditional methods like boundary elements or finite elements since the generation of the mesh is typically computationally intensive. The performance of the proposed method is compared with the boundary element method (BEM) by numerically solving some EEG forward problems examples. For a large number of nodes and the same precision, our method has lower computational load than BEM due to a faster convergence rate and to the sparsity of the linear system to be solved.     

Circular Acoustic Vector-Sensor Array for Mode Beamforming

Undersea warfare relies heavily on acoustic means to detect a submerged vessel. The frequency of the acoustic signal radiated by the vessel is typically very low, thus requires a large array aperture to achieve acceptable angular resolution. In this paper, we present a novel approach for low-frequency direction-of-arrival (DOA) estimation using miniature circular vector-sensor array mounted on the perimeter of a cylinder. Under this approach, we conduct beamforming using decomposition in the acoustic mode domain rather than frequency domain, to avoid the long wavelength constraints. We first introduce a multi-layer acoustic gradient scattering model to provide a guideline and performance predication tool for the mode beamformer design and algorithm. We optimize the array gain and frequency response with this model. We further develop the adaptive DOA estimation algorithm based on this model. We formulate the Capon spectra of the mode beamformer which is independent of the frequency band after the mode decomposition. Numerical simulations are conducted to quantify the performance and evaluate the theoretical results developed in this study.     

Effect of Head Shape Variations Among Individuals on the EEG/MEG Forward and Inverse Problems

We study the effect of the head shape variations on the EEG/magnetoencephalography (MEG) forward and inverse problems. We build a random head model such that each sample represents the head shape of a different individual and solve the forward problem assuming this random head model, using a polynomial chaos expansion. The random solution of the forward problem is then used to quantify the effect of the geometry when the inverse problem is solved with a standard head model. The results derived with this approach are valid for a continuous family of head models, rather than just for a set of cases. The random model consists of three random surfaces that define layers of different electric conductivity, and we built an example based on a set of 30 deterministic models from adults. Our results show that for a dipolar source model, the effect of the head shape variations on the EEG/MEG inverse problem due to the random head model is slightly larger than the effect of the electronic noise present in the sensors. The variations in the EEG inverse problem solutions are due to the variations in the shape of the volume conductor, while the variations in the MEG inverse problem solutions, larger than the EEG ones, are caused mainly by the variations of the absolute position of the sources in a coordinate system based on anatomical landmarks, in which the magnetometers have a fixed position.     

Array response kernels for EEG and MEG in multilayer ellipsoidal geometry

We present forward modeling solutions in the form of array response kernels for electroencephalography (EEG) and magnetoencephalography (MEG), assuming that a multilayer ellipsoidal geometry approximates the anatomy of the head and a dipole current models the source. The use of an ellipsoidal geometry is useful in cases for which incorporating the anisotropy of the head is important but a better model cannot be defined. The structure of our forward solutions facilitates the analysis of the inverse problem by factoring the lead field into a product of the current dipole source and a kernel containing the information corresponding to the head geometry and location of the source and sensors. This factorization allows the inverse problem to be approached as an explicit function of just the location parameters, which reduces the complexity of the estimation solution search. Our forward solutions have the potential of facilitating the solution of the inverse problem, as they provide algebraic representations suitable for numerical implementation. The applicability of our models is illustrated with numerical examples on real EEG/MEG data of N20 responses. Our results show that the residual data after modeling the N20 response using a dipole for the source and an ellipsoidal geometry for the head is in average lower than the residual remaining when a spherical geometry is used for the same estimated dipole.     

Statistical design of position-encoded microsphere arrays

We propose a microsphere array device with microspheres having controllable positions for error-free target identification. We conduct a statistical design analysis to select the optimal distance between the microspheres as well as the optimal temperature. Our design simplifies the imaging and ensures a desired statistical performance for a given sensor cost. Specifically, we compute the posterior Cramér-Rao bound on the errors in estimating the unknown target concentrations. We use this performance bound to compute the optimal design variables. We discuss both uniform and sparse concentration levels of targets, and replace the unknown imaging parameters with their maximum likelihood estimates. We illustrate our design concept using numerical examples. The proposed microarray has high sensitivity, efficient packing, and guaranteed imaging performance. It simplifies the imaging analysis significantly by identifying targets based on the known positions of the microspheres. Potential applications include molecular recognition, specificity of targeting molecules, protein-protein dimerization, high throughput screening assays for enzyme inhibitors, drug discovery, and gene sequencing.     

EEG/MEC error bounds for a static dipole source with a realistichead model

We derive Cramer-Rao bounds (CRBs) on the errors of estimating the parameters (location and moment) of a static current dipole source using data from electro-encephalography (EEG), magneto-encephalography (MEG), or the combined EEG/MEG modality. We use a realistic head model based on knowledge of surfaces separating tissues of different conductivities obtained from magnetic resonance (MR) or computer tomography (CT) imaging systems. The electric potentials and magnetic field components at the respective sensors are functions of the source parameters through integral equations. These potentials and field are formulated for solving them by the boundary or the finite element method (BEM or FEM) with a weighted residuals technique. We present a unified framework for the measurements computed by these methods that enables the derivation of the bounds. The resulting bounds may be used, for instance, to choose the best configuration of the sensors for a given patient and region of expected source location. Numerical results are used to demonstrate an application for showing expected accuracies in estimating the source parameters as a function of its position in the brain, based on real EEG/MEG system and MR or CT images