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.     

Influence of anisotropic conductivity on EEG source reconstruction: investigations in a rabbit model

The aim of our work was to quantify the influence of white matter anisotropic conductivity information on electroencephalography (EEG) source reconstruction. We performed this quantification in a rabbit head using both simulations and source localization based on invasive measurements. In vivo anisotropic (tensorial) conductivity information was obtained from magnetic resonance diffusion tensor imaging and included into a high-resolution finite-element model. When neglecting anisotropy in the simulations, we found a shift in source location of up to 1.3 mm with a mean value of 0.3 mm. The averaged orientational deviation was 10 degree and the mean magnitude error of the dipole was 29%. Source localization of the first cortical components after median and tibial nerve stimulation resulted in anatomically verified dipole positions with no significant anisotropy effect. Our results indicate that the expected average source localization error due to anisotropic white matter conductivity is within the principal accuracy limits of current inverse procedures. However, larger localization errors might occur in certain cases. In contrast, dipole orientation and dipole strength are influenced significantly by the anisotropy. We conclude that the inclusion of tissue anisotropy information improves source estimation procedures.     

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.     

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     

Conventional and reciprocal approaches to the inverse dipole localization problem of electroencephalography

Forward transfer matrices relating dipole source to surface potentials can be determined via conventional or reciprocal approaches. In numerical simulations with a triangulated boundary-element three-concentric-spheres head model, we compare four inverse electroencephalogram (EEG) solutions: those obtained utilizing conventional or reciprocal forward transfer matrices, relating in each case source dipole components to potentials at either triangle centroids or triangle vertices. Single-dipole inverse solutions were obtained using simplex optimization with an additional position constraint limiting solution dipoles to within the brain region. Dipole localization errors are presented in all four cases, for varying dipole eccentricity and two different values of skull conductivity. Both conventional and reciprocal forward transfer matrices yielded inverse dipole solutions of comparable accuracy. Localization errors were low even for highly eccentric source dipoles on account of the nonlinear nature of the single-dipole solution and the position constraint. In the presence of Gaussian noise, both conventional and reciprocal approaches were also found to be equally robust to skull conductivity errors.     

The conductivity of the human skull: results of in vivo and in vitro measurements

The conductivity of the human skull was measured both in vitro and in vivo. The in vitro measurement was performed on a sample of fresh skull placed within a saline environment. For the in vivo measurement a small current was passed through the head by means of two electrodes placed on the scalp. The potential distribution thus generated on the scalp was measured in two subjects for two locations of the current injecting electrodes. Both methods revealed a skull conductivity of about 0.015 [symbol: see text]/m. For the conductivities of the brain, the skull and the scalp a ratio of 1:1/15:1 was found. This is consistent with some of the reports on conductivities found in the literature, but differs considerably from the ratio 1:1/80:1 commonly used in neural source localization. An explanation is provided for this discrepancy, indicating that the correct ratio is 1:1/15:1.     

Estimating brain conductivities and dipole source signals with EEG arrays

Techniques based on electroencephalography (EEG) measure the electric potentials on the scalp and process them to infer the location, distribution, and intensity of underlying neural activity. Accuracy in estimating these parameters is highly sensitive to uncertainty in the conductivities of the head tissues. Furthermore, dissimilarities among individuals are ignored when standarized values are used. In this paper, we apply the maximum-likelihood and maximum a posteriori (MAP) techniques to simultaneously estimate the layer conductivity ratios and source signal using EEG data. We use the classical 4-sphere model to approximate the head geometry, and assume a known dipole source position. The accuracy of our estimates is evaluated by comparing their standard deviations with the Cramér-Rao bound (CRB). The applicability of these techniques is illustrated with numerical examples on simulated EEG data. Our results show that the estimates have low bias and attain the CRB for sufficiently large number of experiments. We also present numerical examples evaluating the sensitivity to imprecise assumptions on the source position and skull thickness. Finally, we propose extensions to the case of unknown source position and present examples for real data.     

EEG dipole localization bounds and MAP algorithms for head modelswith parameter uncertainties

The Cramer-Rao bound for unbiased dipole location estimation is derived under the assumption of a general head model parameterized by deterministic and stochastic parameters. The expression thus characterizes fundamental limits on EEG dipole localization performance due to the effects of both model uncertainty and statistical measurement noise. Expressions are derived for the cases of multivariate Gaussian and gamma distribution priors, and examples are given to illustrate the derived bounds when the radii and conductivities of a four-concentric sphere head model are allowed to be random. The joint MAP estimate of location/model parameters is then examined as a means of achieving robustness to deviations from an ideal head model. Random variations in both the multiple sphere radii and the layer conductivities are shown, via the stochastic Cramer-Rao bounds and Monte Carlo simulation of the MAP estimator, to have the most impact on localization performance in high SNR regions, where finite sample effects are not the limiting factors. This corresponds most often to spatial regions that are close to the scalp electrodes     

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.     

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.     

The Influence of Model Parameters on BEG/MEG Single Dipole Source Estimation

This paper deals with source localization and strength estimation based on EEG and MEG data. It describes an estimation method (inverse procedure) which uses a four-spheres model of the head and a single current dipole. The dependency of the inverse solution on model parameters is investigated. It is found that sphere radii and conductivities influence especially the strength of the EEG equivalent dipole and not its location or direction. The influence on the equivalent dipole of the gradiometer is investigated. In general the MEG produces better location estimates than the EEG whereas the reverse is found for the component estimates. An inverse solution simultaneously based on EEG and MEG data appears slightly better than the average of separate EEG and MEG solutions. Variances of parameter estimators which can be calculated on the basis of a linear approximation of the model, were tested by Monte Carlo simulations.     

Partially Constrained Blind Source Separation for Localization of Unknown Sources Exploiting Non-homogeneity of the Head Tissues

A new brain source localization technique using electroencephalograms (EEGs) is investigated in this paper. The information which describes the location of certain known sources is used as the constraint within the proposed blind source separation (BSS) algorithm and leads to a solution to the ill-posed inverse problem of source localization. Non-homogeneity of the head tissues, on the other hand, is exploited by introducing a realistic model of the mixing system. This model is used to better identify the location of the unknown sources within the brain from projection of the separated independent components on to the scalp. A separate procedure is employed to highlight the rhythmic EEG sources such as Alpha rhythm as the known sources. The performance of the scheme is shown on real EEG measurements and compared with that of “conventional dipole fitting algorithm”.

A Global Sensitivity Analysis of Three- and Four-Layer EEG Conductivity Models

The accuracy of forward models for EEG partly depends on the conductivity values of the head tissues. Yet, the influence of the conductivities on the model output is still not well understood. In this paper, we apply a variance-based sensitivity analysis method to the most common EEG forward models (three or four layers). This method is global because it quantifies the influence of each parameter with all the parameters varying at the same time. With nonlinear models, it helps to understand the interaction between parameters, which is not possible with simple sensitivity analyses (one-at-a-time variations, derivatives, and perturbations). By analyzing the potential topographies at the electrodes, we obtained several results. For a shallow dipole, the EEG topographies are mainly sensitive to the interaction between skull and scalp conductivities. It means that the variability of the EEG topographies is driven mostly by a function of skull and scalp conductivities. Similar results are presented for skull anisotropy and a current injection as performed in electrical impedance tomography. This global sensitivity analysis gives new information about EEG forward models—it identifies the main input parameters that need model refinement—and directions on how to calibrate these models.      

多校准站TDOA/FDOA无源定位方法

针对运动目标到达时差（Time Difference-of-Arrival,TDOA）/到达频差（Frequency Difference-of-Arrival,FDOA）定位中的接收站定位误差问题,提出了基于多校准站的TDOA/FDOA定位方法,有效降低接收站定位误差的影响,并推导了该方法的克拉美罗下限（Cramér-Rao Lower Bound,CRLB）。理论分析表明,采用多校准站法能有效降低CRLB,提高目标定位精度。同时,当校准站自身定位存在误差时,也将影响对接收站的校准和目标的定位精度。通过仿真实验定量分析了采用多校准站法对定位精度的改善程度。     

A finite element model for radiofrequency ablation of themyocardium

A finite element model was developed to simulate the temperature distributions produced by radiofrequency catheter ablation. This model incorporated blood, myocardium and torso tissues. The Laplace equation was solved to determine the steady-state electric field. The heat generation in the tissues was then computed from the power density distribution and the bioheat equation was solved to determine the time-varying temperature distribution, taking into account the convective energy exchange at the blood-myocardium and torso-air interfaces. This model was used to predict the lesion depth and to evaluate the effects of electrode location, changes of the electrical and thermal conductivities, and the electrode radius on the thermally induced damage to the myocardium. Temperature distributions induced by radiofrequency ablation were found to be: i) not very sensitive to the reference electrode location, ii) more sensitive to electrical conductivity changes than to thermal conductivity changes, and iii) larger electrodes allow a current distribution at higher level of power with reducing the chance of impedance rise     

EEG localization accuracy improvements using realistically shapedhead models

A model of the head must be used in making estimates of the locations of electrical sources in the brain using electroencephalograms (EEGs) measured on the scalp. In part, the accuracy of these estimates is dependent on how accurately the model represents the actual head. In most work performed to date, spherical models of the head have been used. This paper presents results in which the estimates of source location are made in realistically shaped head models. Techniques for accurately and conveniently developing realistically shaped head models from CTs, MRIs, X-rays, and/or physical measurements are also presented. Realistically shaped head models are developed for three subjects with electrical sources implanted at known locations in the brain. Localization accuracy is found to be significantly better in the realistically shaped bead models than in spherical models if EEGs with good signal-to-noise ratio are used     

Cylindrical FDTD Analysis of LWD Tools Through Anisotropic Dipping-Layered Earth Media

Electrical logging-while-drilling (LWD) tools are commonly used in oil and gas exploration to estimate the conductivity (resistivity) of adjacent Earth media. In general, Earth media exhibit anisotropic conductivities. This implies that when LWD tools are used for deviated and horizontal drilling, the resulting borehole problem may include dipping-layered media with dipping beds having full 3 times 3 conductivity tensors. To model this problem, we describe a 3-D cylindrical finite-difference time-domain (FDTD) algorithm extended to fully anisotropic conductive media and implemented with cylindrical perfectly matched layers to mimic open-domain problems. The 3-D FDTD algorithm is validated against analytical results in simple formations, showing good agreement, and used to simulate the response of LWD tools through anisotropic dipping beds for various values of anisotropic conductivities and dipping angles     

传感器位置误差情况下基于多维标度分析的时差定位算法

传统时差定位方法一般是在假设传感器位置信息准确已知的前提下进行的.然而在实际情形中,传感器位置信息往往含有随机误差,这些误差会严重影响对目标的定位精度.针对这一问题,提出了一种传感器位置误差情况下的多维标度时差定位算法.首先利用传感器位置和时差构造对称标量积矩阵,然后利用子空间理论建立关于目标位置的伪线性方程,最后通过设计加权矩阵来减少传感器位置误差对目标定位精度的影响.采用一阶小噪声扰动理论求出了目标位置估计的偏差及协方差矩阵,并通过仿真实验验证了该算法的有效性.     

A Comparison of Moving Dipole Inverse Solutions Using EEG''s and MEG''s

Moving dipole inverse solutions provide a very useful method of estimating the location of an electrical source in the brain from EEG's or MEG's measured at the surface of the head. In this method, a dipolar source model is moved about in a model of the head while its amplitude and orientation are also adjusted to obtain the least-squares error fit between the measured EEG's or MEG's and those produced by the dipolar source.     

Effects of local variations in skull and scalp thickness on EEG'sand MEG's

The results of a computer modeling study are reported. They indicate that local variations in skull and scalp thickness have effects on electroencephalograms (EEGs) and magnetoencephalograms (MEGs) which range from a simple intuitive effect to complex effects which depend on such factors as source depth and orientation, the geometry of the variation in skull and scalp thickness, etc. These results also indicate that local variations in skull and scalp thickness cause EEG localization errors which are generally much less than 1 cm and MEG localization errors which are even smaller. These results also indicate that multichannel and single-channel MEG measurements will produce localization errors of approximately the same amplitude when there is a bump on the external surface of the head but that multichannel measurements will produce significantly smaller localization errors than single-channel measurements when a depression is present in that surface