Eccentric spheres models of the head

Equations are derived for electric potentials (electroencephalograms) and magnetic fields (magnetoencephalograms) produced by dipolar sources in three eccentric spheres models of the head. In these models, I) the thickness of the layer representing the skull varies around the model, II) the thickness of the scalp layer varies, and III) the electrical conductivity of an eccentric spherical "bubble" in the brain region varies. Using these equations, it was found that variations in these features of the models have at most only small effects on the general spatial patterns of the electric potentials and the radial component of the magnetic fields. However, some significant effects on the amplitudes were found. The effects of the variations in the skull and scalp layer thicknesses on the field amplitudes were found to be significantly smaller than on the potential amplitudes. The effects on the field amplitudes of the variations in the bubble conductivity were found to be only somewhat smaller than on the potential amplitudes. It was also found that the effects of variations in these features of the models on source localization accuracy were significantly smaller for inverse solutions using fields than for solutions using potentials.     

The need for correct realistic geometry in the inverse EEG problem

For accurate electroencephalogram-based localization of mesial temporal and frontal sources correct modeling of skull shape and thickness is required. In a simulation study in which results for matched sets of computed tomography and magnetic resonance (MR) images are compared, it is found that errors arising from skull models based on smooth and inflated segmented MR images of the cortex are of the order of 1 cm. These errors are comparable to those found when overestimating or underestimating skull conductivity by a factor of two.     

Influence of head tissue conductivity in forward and inverse magnetoencephalographic simulations using realistic head models

The influence of head tissue conductivity on magnetoencephalography (MEG) was investigated by comparing the normal component of the magnetic field calculated at 61 detectors and the localization accuracy of realistic head finite element method (FEM) models using dipolar sources and containing altered scalp, skull, cerebrospinal fluid, gray, and white matter conductivities to the results obtained using a FEM realistic head model with the same dipolar sources but containing published baseline conductivity values. In the models containing altered conductivity values, the tissue conductivity values were varied, one at a time, between 10% and 200% of their baseline values, and then varied simultaneously. Although changes in conductivity values for a single tissue layer often altered the calculated magnetic field and source localization accuracy only slightly, varying multiple conductivity layers simultaneously caused significant discrepancies in calculated results. The conductivity of scalp, and to a lesser extent that of white and gray matter, appears especially influential in determining the magnetic field. Comparing the results obtained from models containing the baseline conductivity values to the results obtained using other published conductivity values suggests that inaccuracies can occur depending upon which tissue conductivity values are employed. We show the importance of accurate head tissue conductivities for MEG source localization in human brain, especially for deep dipole sources or when an accuracy greater than 1.4 cm is needed.     

In vivo measurement of the brain and skull resistivities using an EIT-based method and the combined analysis of SEF/SEP data

Results of "in vivo" measurements of the skull and brain resistivities are presented for six subjects. Results are obtained using two different methods, based on spherical head models. The first method uses the principles of electrical impedance tomography (EIT) to estimate the equivalent electrical resistivities of brain (rhobrain), skull (rhoskull) and skin (rhoskin) according to. The second one estimates the same parameters through a combined analysis of the evoked somatosensory cortical response, recorded simultaneously using magnetoencephalography (MEG) and electroencephalography (EEG). The EIT results, obtained with the same relative skull thickness (0.05) for all subjects, show a wide variation of the ratio rhoskull/rhobrain among subjects (average = 72, SD = 48%). However, the rhoskull/rhobrain ratios of the individual subjects are well reproduced by combined analysis of somatosensory evoked fields (SEF) and somatosensory evoked potentials (SEP). These preliminary results suggest that the rhoskull/rhobrain variations over subjects cannot be disregarded in the EEG inverse problem (IP) when a spherical model is used. The agreement between EIT and SEF/SEP points to the fact that whatever the source of variability, the proposed EIT-based method 相似文献   

Location of Sources of Evoked Scalp Potentials: Corrections for Skull and Scalp Thicknesses

The problem of locating the position of the source of evoked potentials from measurements on the surface of the scalp has been examined. It is shown that the position of the source in a head modeled by a sphere surrounded by two concentric shells of differing conductivities representing the skull and the scalp can be inferred from source localization calculations made on a homogeneous model.     

Effects of head shape on EEGs and MEGs

This paper presents results of computer modeling studies of the effects of head shape on electroencephalograms (EEG's) and magnetoencephalograms (MEG's) and on the localization of electrical sources in the brain using these measurements. The effects of general, nonspherical head shape on EEG's and MEG's are determined by comparisons of EEG and MEG maps from nonspherical head models with corresponding maps from a spherical head model. The effects on source localization accuracy are determined by calculating moving dipole inverse solutions in a spherical head model using EEG's and MEG's from the nonspherical models and comparing the solutions with the known sources. It was found that nonspherical head shape can produce significant changes in the maps produced by some sources in the cortical region of the brain. However, it was also found that such deviations of the head from sphericity produce localization errors of less than approximately 1 cm. No significant differences in the effects of such deviations on EEG's and MEG's were found. Finally, it was found that most such deviations do not cause a dipolar source which is perpendicular to the surface of the head model to produce a significant magnetic field; such a source produces zero magnetic field in a sphere.     

Effects of Measurement Errors and Noise on MEG Moving Dipole Inverse Solutions

Magnetoencephalograms (MEG's) are increasingly being used with the moving dipole method to localize electrical sources in the brain. In this method, also known as the dipole location method, a dipolar source is moved about in a model of the head while its amplitude and orientation are also adjusted to obtain a solution dipole which gives the least squares error fit between the measured MEG's and those produced by the dipolar source. The accuracy of this solution is affected by various measurement errors such as errors in the size of the measurement grid, size of the head model, etc., and by noise in the measured MEG's. This study uses computer modeling methods to investigate the effects of these factors on the localization accuracy of sources in the cortical region of the brain for several different ways of making MEG measurements using single channel and/or multichannel detectors.     

Transformation of multichannel magnetocardiographic signals tostandard grid form

Multichannel magnetocardiographic (MCG) recordings with fixed sensor arrays are not directly comparable with single-channel measurements carried out at standard grid locations. In addition, comparison of data obtained with different types of magnetometers is difficult. The authors present a method for transforming multichannel measurements to the standard-grid format. The minimum-norm estimate (MNE) of the source current distribution in the body is calculated, and the desired field components in standard grid points are then computed from the MNE. The authors measured three subjects with both a 24-channel and a single-channel instrument. The signals extrapolated from the multichannel measurements corresponded quite well to the single-channel data registered at the standard grid locations, especially in those grid points that were covered by the 24-channel device. The signal-amplitude-weighted correlations between the extrapolated and directly measured signals were 0.73-0.87. In simulations with ideal measurement geometry but with a realistic amount of random noise in the signals, the authors obtained a 0.99 correlation. It was also found that the method is relatively tolerant to errors in the location and orientation of the multichannel magnetometer. For example, a simulated 20-mm displacement in the location of the sensor array caused only a 3% decrease in the correlation, and when it was rotated and tilted by 10°, the correlation decreased by 5%. The basic advantage of the authors' extrapolation method is its physiologic nature: the method is based on the mathematical modeling of the source current distribution, rather than on direct constraints applied to the magnetic field     

Correlation between skull thickness asymmetry and scalp potentialestimated by a numerical model of the head

The contribution of asymmetric skull thickness to the scalp potential amplitude was investigated numerically. The model consisted of four conductive layers representing the scalp, the skull, the cerebrospinal fluid, and the cortex with a current dipole in the occipital region. The potential created by the dipole was calculated assuming quasistatic formulation and linear media. The governing equation was discretized by the finite volume method to ensure the conservation of fluxes even in regions with abrupt changes of the conductivity. The large set of the algebraic equations for the electric potential was solved iteratively by the successive overrelaxation method. The model confirmed previous experimental studies suggesting that the potential amplitude is 60% smaller on the side with the thicker bone if the asymmetry of the skull thickness exceeds 40%. The model developed suggests that skull thickness asymmetry can create nonnegligible asymmetries in the potential measured on the scalp above homotopic points of the two hemispheres     

Localization of a dipolar source in a skull phantom: realisticversus spherical model

The dependence of the neuromagnetic source localization accuracy on the volume conductor model was studied by the analysis of measured magnetic fields generated by tangentially oriented dipoles in a realistically shaped skull phantom. When using a homogeneous sphere model in the localization procedure, the errors were found to increase from about 3 mm to about 9 mm when the distance between the dipoles and the inner surface of the skull increased from 1 cm to 3 cm, whereas when using a true, realistic model in the inverse procedure the localization errors were only about 2-3 mm, independent of dipole depth. To account for the realistic geometry of the inner surface of the skull, the Boundary Element Method, based on a surface discretization in terms of about 300 triangles, proved to be sufficient. In addition to these analyses of experimental data, simulations were carried out to study the localization errors in the case of the spherical approximation for a dipole orientation changing from tangential to radial. For the latter orientation, errors of up to a few centimeters were found     

Comparison of two multisheet transmission windows formillimeter-wave radiometers

The design and performance of a triple-sheet Mylar window and a Teflon-and-foam window are studied theoretically and experimentally to determine which window produces the smaller brightness temperature variations and, therefore, leads to better accuracy of radiometers operating at frequencies of 20-90 GHz. Theoretical brightness temperatures due to emission and reflection by the windows are calculated and compared; experimental measurements obtained by using the clear atmosphere as a radiation source are also compared. Both theory and experiment indicate that the Teflon-and-foam window produces smaller brightness temperature variations at these operating frequencies. Effects of the windows on integrated water vapor and liquid measurements are also examined; errors are significant for the triple-sheet Mylar window but are negligible for the Teflon-and-foam window. It is observed that use of the Teflon-and-foam design results in acceptably small errors in radiometric measurements of water vapor and cloud liquid     

Sensitivity distributions of EEG and MEG measurements

It is generally believed that because the skull has low conductivity to electric current but is transparent to magnetic fields, the measurement sensitivity of the magnetoencephalography (MEG) in the brain region should be more concentrated than that of the electroencephalography (EEG). It is also believed that the information recorded by these techniques is very different. If this were indeed the case, it might be possible to justify the cost of MEG instrumentation which is at least 25 times higher than that of EEG instrumentation. The localization of measurement sensitivity using these techniques was evaluated quantitatively in an inhomogeneous spherical head model using a new concept called half-sensitivity volume (HSV). It is shown that the planar gradiometer has a far smaller HSV than the axial gradiometer. However, using the EEG it is possible to achieve even smaller HSVs than with whole-head planar gradiometer MEG devices. The micro-superconducting quantum interference device (SQUID) MEG device does have HSVs comparable to those of the EEG. The sensitivity distribution of planar gradiometers, however, closely resembles that of dipolar EEG leads and, therefore, the MEG and EEG record the electric activity of the brain in a very similar way     

Single-channel blind estimation of arterial input function and tissue impulse response in DCE-MRI

Multipass dynamic MRI and pharmacokinetic modeling are used to estimate perfusion parameters of leaky capillaries. Curve fitting and nonblind deconvolution are the established methods to derive the perfusion estimates from the observed arterial input function (AIF) and tissue tracer concentration function. These nonblind methods are sensitive to errors in the AIF, measured in some nearby artery or estimated by multichannel blind deconvolution. Here, a single-channel blind deconvolution algorithm is presented, which only uses a single tissue tracer concentration function to estimate the corresponding AIF and tissue impulse response function. That way, many errors affecting these functions are reduced. The validity of the algorithm is supported by simulations and tests on real data from mouse. The corresponding nonblind and multichannel methods are also presented.     

Biomagnetic source detection by maximum entropy and graphical models

This article presents a new approach for detecting active sources in the cortex from magnetic field measurements on the scalp in magnetoencephalography (MEG). The solution of this ill-posed inverse problem is addressed within the framework of maximum entropy on the mean (MEM) principle introduced by Clarke and Janday. The main ingredient of this regularization technique is a reference probability measure on the random variables of interest. These variables are the intensity of current sources distributed on the cortical surface for which this measure encompasses all available prior information that could help to regularize the inverse problem. This measure introduces hidden Markov random variables associated with the activation state of predefined cortical regions. MEM approach is applied within this particular probabilistic framework and simulations show that the present methodology leads to a practical detection of cerebral activity from MEG data.     

GPS: primary tool for time transfer

The Global Positioning System (GPS) is not only a navigation system, it is also a time-transfer system. As a time-transfer system it provides stability very close to one part in ten to the fourteenth over one day (1 ns/day). After a brief introduction to timekeeping terms, this paper reviews the role of GPS in time distribution and clock synchronization. The GPS coarse acquisition (C/A)-code single-frequency single-channel (one satellite) common-view (CV) time transfer is then discussed. Special consideration is given to progress in GPS C/A-code CV time and frequency transfer through the use of “all-in-view” multichannel receivers. This technique increases the number of daily observations by a factor of ten relative to conventional single-channel receivers and results in an improvement in time and frequency transfer stability by a factor of about three. Other important improvements discussed are the use of GPS carrier phase measurements and temperature-stabilized antennas. The latter reduce the daily and seasonal delay variations of GPS time-receiving equipment. The use of GLONASS as a complementary tool to GPS time transfer is also be reported. These improvements indicate that GPS, as a time-transfer system, should provide the capability to reach a stability of one part in ten to the sixteenth over one day (10 ps/day)     

Effect of conductivity uncertainties and modeling errors on EEGsource localization using a 2-D model

This paper presents a sensitivity study electroencephalography-based source localization due errors in the head-tissue conductivities and to errors in modeling the conductivity variation inside the brain and scalp. The study is conducted using a two-dimensional (2-D) finite element model obtained from a magnetic resonance imaging (MRI) scan of a head cross section. The effect of uncertainty in the following tissues is studied: white matter, gray matter, cerebrospinal fluid (CSF), skull, and fat. The distribution of source location errors, assuming a single-dipole source model, is examined in detail for different dipole locations over the entire brain region. We also present a detailed analysis of the effect of conductivity on source localization for a four-layer cylinder model and a four-layer sphere model. These two simple models provide insight into how the effect of conductivity on boundary potential translates into source location errors; and also how errors in a 2-D model compare to errors in a three-dimensional model. Results presented in this paper clearly point to the following conclusion: unless the conductivities of the head tissues and the distribution of these tissues throughout the head are modeled accurately, the goal of achieving localization accuracy to within a few millimeters is unattainable     

Combined MEG and EEG source imaging by minimization of mutual information

Though very frequently assumed, the necessity to operate a joint processing of simultaneous magnetoencephalography (MEG) and electroencephalography (EEG) recordings for functional brain imaging has never been clearly demonstrated. However, the very last generation of MEG instruments allows the simultaneous recording of brain magnetic fields and electrical potentials on the scalp. But the general fear regarding the fusion between MEG and EEG data is that the drawbacks from one modality will systematically spoil the performances of the other one without any consequent improvement. This is the case for instance for the estimation of deeper or radial sources with MEG. In this paper, we propose a method for a cooperative processing of MEG and EEG in a distributed source model. First, the evaluation of the respective performances of each modality for the estimation of every dipole in the source pattern is made using a conditional entropy criterion. Then, the algorithm operates a preprocessing of the MEG and EEG gain matrices which minimizes the mutual information between these two transfer functions, by a selective weighting of the MEG and EEG lead fields. This new combined EEG/MEG modality brings major improvements to the localization of active sources, together with reduced sensitivity to perturbations on data.     

Spatiotemporal forward solution of the EEG and MEG using network modeling

Dynamic systems have proven to be well suited to describe a broad spectrum of human coordination behavior such synchronization with auditory stimuli. Simultaneous measurements of the spatiotemporal dynamics of electroencephalographic (EEG) and magnetoencephalographic (MEG) data reveals that the dynamics of the brain signals is highly ordered and also accessible by dynamic systems theory. However, models of EEG and MEG dynamics have typically been formulated only in terms of phenomenological modeling such as fixed-current dipoles or spatial EEG and MEG patterns. In this paper, it is our goal to connect three levels of organization, that is the level of coordination behavior, the level of patterns observed in the EEG and MEG and the level of neuronal network dynamics. To do so, we develop a methodological framework, which defines the spatiotemporal dynamics of neural ensembles, the neural field, on a sphere in three dimensions. Using magnetic resonance imaging we map the neural field dynamics from the sphere onto the folded cortical surface of a hemisphere. The neural field represents the current flow perpendicular to the cortex and, thus, allows for the calculation of the electric potentials on the surface of the skull and the magnetic fields outside the skull to be measured by EEG and MEG, respectively. For demonstration of the dynamics, we present the propagation of activation at a single cortical site resulting from a transient input. Finally, a mapping between finger movement profile and EEG/MEG patterns is obtained using Volterra integrals.     

Spatio-temporal EEG source localization using a three-dimensional subspace FINE approach in a realistic geometry inhomogeneous head model

The subspace source localization approach, i.e., first principle vectors (FINE), is able to enhance the spatial resolvability and localization accuracy for closely-spaced neural sources from EEG and MEG measurements. Computer simulations were conducted to evaluate the performance of the FINE algorithm in an inhomogeneous realistic geometry head model under a variety of conditions. The source localization abilities of FINE were examined at different cortical regions and at different depths. The present computer simulation results indicate that FINE has enhanced source localization capability, as compared with MUSIC and RAP-MUSIC, when sources are closely spaced, highly noise-contaminated, or inter-correlated. The source localization accuracy of FINE is better, for closely-spaced sources, than MUSIC at various noise levels, i.e., signal-to-noise ratio (SNR) from 6 dB to 16 dB, and RAP-MUSIC at relatively low noise levels, i.e., 6 dB to 12 dB. The FINE approach has been further applied to localize brain sources of motor potentials, obtained during the finger tapping tasks in a human subject. The experimental results suggest that the detailed neural activity distribution could be revealed by FINE. The present study suggests that FINE provides enhanced performance in localizing multiple closely spaced, and inter-correlated sources under low SNR, and may become an important alternative to brain source localization from EEG or MEG.     

Method to reduce blur distortion from EEG's using a realistic headmodel

A mathematical procedure, called deblurring, was developed to reduce spatial blur distortion of scalp-recorded brain potentials due to transmission through the skull and other tissues. Deblurring estimates potentials at the superficial cerebral cortical surface from EEGs recorded at the scalp using a finite-element model of each subject's scalp, skull, and cortical surface constructed from their magnetic resonance images (MRIs). Simulations indicate that deblurring is numerically stable, and a comparison of deblurred data with a direct cortical recording from a neurosurgery patient suggests that the procedure is valid. Application of deblurring to somatosensory evoked potential data recorded at 124 scalp sites suggests that the method greatly improves spatial detail and merits further development