Paul S. Lewis

Multiple dipole modeling and localization from spatio-temporal MEG data

The authors present general descriptive models for spatiotemporal MEG (magnetoencephalogram) data and show the separability of the linear moment parameters and nonlinear location parameters in the MEG problem. A forward model with current dipoles in a spherically symmetric conductor is used as an example: however, other more advanced MEG models, as well as many EEG (electroencephalogram) models, can also be formulated in a similar linear algebra framework. A subspace methodology and computational approach to solving the conventional least-squares problem is presented. A new scanning approach, equivalent to the statistical MUSIC method, is also developed. This subspace method scans three-dimensional space with a one-dipole model, making it computationally feasible to scan the complete head volume.<<ETX>>

Error bounds for EEG and MEG dipole source localization

General formulas are presented for computing a lower bound on localization and moment error for electroencephalographic (EEG) or magnetoencephalographic (MEG) current source dipole models with arbitrary sensor array geometry. Specific EEG and MEG formulas are presented for multiple dipoles in a head model with 4 spherical shells. Localization error bounds are presented for both EEG and MEG for several different sensor configurations. Graphical error contours are presented for 127 sensors covering the upper hemisphere, for both 37 sensors and 127 sensors covering a smaller region, and for the standard 10-20 EEG sensor arrangement. Both 1- and 2-dipole cases were examined for all possible dipole orientations and locations within a head quadrant. The results show a strong dependence on absolute dipole location and orientation. The results also show that fusion of the EEG and MEG measurements into a combined model reduces the lower bound. A Monte Carlo simulation was performed to check the tightness of the bounds for a selected case. The simple head model, the low power noise and the few strong dipoles were all selected in this study as optimistic conditions to establish possibly fundamental resolution limits for any localization effort. Results, under these favorable assumptions, show comparable resolutions between the EEG and the MEG models, but accuracy for a single dipole, in either case, appears limited to several millimeters for a single time slice. The lower bounds increase markedly with just 2 dipoles. Observations are given to support the need for full spatiotemporal modeling to improve these lower bounds. All of the simulation results presented can easily be scaled to other instances of noise power and dipole intensity.

Adaptive filters for monitoring localized brain activity from surface potential time series

The problem of processing electroencephalographic (EEG) data to monitor the time series of the components of a current dipole source vector at a given location in the head is addressed. This is the spatial filtering problem for vector sources in a lossy, three-dimensional, zero delay medium. Dipolar and distributed sources at other than the desired location are cancelled or attenuated with an adaptive linearly constrained minimum variance (LCMV) beamformer. Actual EEG data acquired from a human subject serve as the interference in a case where the desired source is simulated and superimposed on the actual data. It is shown that the LCMV beamformer extracts the desired dipole time series while effectively canceling the subjects interference.<<ETX>>

Monte Carlo analysis of localization errors in magnetoencephalography

In magnetoencephalography (MEG), the magnetic fields created by electrical activity in the brain are measured on the surface of the skull. To determine the location of the activity, the measured field is fit to a parameterized source generator model by minimizing chi-square. In the case of a current dipole model, the parameters computed by the fitting procedure are the location and orientation of the dipole. For current dipoles and other nonlinear source models, the fit is performed by an iterative least squares procedure such as the Levenberg-Marquardt algorithm (Press 1986). Once the fit has been computed, analysis of the resulting value of chi-square can determine whether the assumed source model is adequate to account for the measurements. If the source model is adequate, then the effect of measurement error on the fitted model parameters must be analyzed.

Anatomical constraints for neuromagnetic source models

The localization of neural electromagnetic sources from measurements at the head surface requires the solution of an inverse problem; that is, the determination of the number, location, spatial configuration, strength, and time-course of the neuronal currents that give rise to the magnetic field or potential distribution. In most general form, the neuromagnetic and electrical inverse problems are ill-posed and have no unique solution; however, approximate solutions are possible if assumptions are made regarding the shape and conductivity of the head and the number and configuration of neuronal currents responsible for the surface distributions. To help resolve ambiguities and to reduce the number and range of free parameters required to model complex neuromagnetic sources, the authors are investigating strategies to constrain the locations of allowable sources, based on a knowledge of individual anatomy. The key assumption, justified by both physiological evidence and theoretical considerations, is that the dominant neuromagnetic sources which contribute to surface field distributions reside within the cortex. It is demonstrated that anatomically constrained source modeling strategies can produce significant improvements in source localization; however, the conclusion is that additional improvements in model fitting or source reconstruction procedures are required.

A magnetic shielded room designed for magnetoencephalography

A magnetic shielded room has been constructed for magnetoencephalographic (MEG) measurements. The room was designed to match the noise levels of superconducting quantum interference device coupled second‐order gradiometers while minimizing the overall cost of the facility. The room measures 2.6×2.6×2.6 m3 internally and consists of a single high‐permeability alloy shell with an outer shell of ultrapure aluminum. The dc shielding factor at the center of the room is 200, and the ac shielding factor at 10 Hz is 2000. This is the frequency which has the maximum amplitude in a Fourier analysis of MEG results. The room is designed to operate without a door closure.

Multiple dipole modeling of spatiotemporal MEG data

Abstract not available.

An optimal systolic array for the algebraic path problem

A systolic array design for the algebraic path problem (APP) is presented that is both simpler and more efficient than previously proposed configurations. This array uses N/sup 2/ orthogonally connected processing elements and requires 2N I/O connections. Total computation time is 5N-2, which is the minimum time possible in a systolic implementation. The data pipelining rate is one, so no pipeline interleave is required. For multiple problem instances a block pipeline rate of N can be achieved, which is optimal for an array of N/sup 2/ processing elements. >

A direct current superconducting quantum interference device gradiometer with a digital signal processor controlled flux-locked loop and comparison with a conventional analog feedback scheme

A double‐washer dc superconducting quantum interference device(SQUID)gradiometer with a flux‐locked loop (FLL) based on a digital signal processor (DSP) has been developed for biomagnetic applications. All of the analog electronics in the conventional FLL are replaced and implemented by the DSP except for the low‐noise field‐effect transistor preamplifier at the front end of the signal recovery components. The DSP performs the signal demodulation by synchronously sampling the recovered signals and applying the appropriate full wave rectification. The signals are then integrated, filtered, and applied to the output. At 4.2 K, the white flux noise of the gradiometer measured in a DSP FLL mode is about 4μΦ0/√Hz and the noise at 1 Hz is 13 μΦ0/√Hz. The corresponding noise levels in the gradiometer operated by the conventional FLL are 1.8 and 3μΦ0/√Hz. The poorer system performance in the DSP FLL compared to the analog FLL is mainly caused by the ambient field noise and interference signals picked up through the connecting cables. Additional noise is also added to the overall noise floor by the instruments employed in the DSP system in the present prototype setup. Further improvement in the noise characteristics and the dynamic behavior of the DSP SQUIDgradiometer is expected when a better configuration of DSP with the associated I/O devices is implemented. Additional improvements of the DSP programs are expected by incorporating higher‐order integration, adaptive control, and noise reduction schemes.

Error bounds for MEG and EEG source localization

Localization error bounds are presented for both electroencephalograms (EEGs) and magnetoencephalograms (MEGs) as graphical error contours for a 37-sensor arrangement. Both one and two dipole cases were examined for all possible dipole orientations and locations within a head quadrant. The results show a strong dependence on absolute dipole location and orientation. The results also show that fusion of the EEG and MEG measurements into a combined model reduces the lower bound. A Monte Carlo simulation was performed to check the tightness of the bounds for a selected case. The simple head model, the white and relatively low power noise, and the few relatively strong dipoles were all selected in this study as optimistic conditions to establish possibly fundamental resolution limits for any localization effort.<<ETX>>