Biomedical subjects

Arye Nehorai

Publications and source records attributed to Arye Nehorai.

7 recordsLinked to original sources

PubMed2005

Ellipsoidal head model for fetal magnetoencephalography: forward and inverse solutions.

Fetal magnetoencephalography (fMEG) is a non-invasive technique where measurements of the magnetic field outside the maternal abdomen are used to infer the source location and signals of the fetus' neural activity. There are a number of aspects related to fMEG modelling that must be addressed, such as the conductor volume, fetal position and orientation, gestation period, etc. We propose a solution to the forward problem of fMEG based on an ellipsoidal head geometry. This model has the advantage of highlighting special characteristics of the field that are inherent to the anisotropy of the human head, such as the spread and orientation of the field in relationship with the localization and position of the fetal head. Our forward solution is presented in the form of a kernel matrix that facilitates the solution of the inverse problem through decoupling of the dipole localization parameters from the source signals. Then, we use this model and the maximum likelihood technique to solve the inverse problem assuming the availability of measurements from multiple trials. The applicability and performance of our methods are illustrated through numerical examples based on a real 151-channel SQUID fMEG measurement system (SARA). SARA is an MEG system especially designed for fetal assessment and is currently used for heart and brain studies. Finally, since our model requires knowledge of the best-fitting ellipsoid's centre location and semiaxes lengths, we propose a method for estimating these parameters through a least-squares fit on anatomical information obtained from three-dimensional ultrasound images.

Algorithms↗

PubMed2005

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.

Algorithms↗

PubMed2005

Model selection in spatio-temporal electromagnetic source analysis.

Several methods [model selection procedures (MSPs)] to determine the number of sources in electroencephalogram (EEG) and magnetoencphalogram (MEG) data have previously been investigated in an instantaneous analysis. In this paper, these MSPs are extended to a spatio-temporal analysis if possible. It is seen that the residual variance (RV) tends to overestimate the number of sources. The Akaike information criterion (AIC) and the Wald test on amplitudes (WA) and the Wald test on locations (WL) have the highest probabilities of selecting the correct number of sources. The WA has the advantage that it offers the opportunity to test which source is active at which time sample.

Algorithms↗

PubMed2005

Distinguishing between moving and stationary sources using EEG/MEG measurements with an application to epilepsy.

Performances of electroencephalography (EEG) and magnetoencephalography (MEG) source estimation methods depend on the validity of the assumed model. In many cases, the model structure is related to physical information. We discuss a number of statistical selection methods to distinguish between two possible models using least-squares estimation and assuming a spherical head model. The first model has a single moving source whereas the second has two stationary sources; these may result in similar EEG/MEG measurements. The need to decide between such models occurs for example in Jacksonian seizures (e.g., epilepsy) or in intralobular activities, where a model with either two stationary dipole sources or a single moving dipole source may be possible. We also show that all of the selection methods discussed choose the correct model with probability one when the number of trials goes to infinity. Finally we present numerical examples and compare the performances of the methods by varying parameters such as the signal-to-noise ratio, source depth, and separation of sources, and also apply the methods to real MEG data for epilepsy.

Algorithms↗

PubMed2005

Line-source modeling and estimation with magnetoencephalography.

We propose a number of source models that are spatially distributed on a line for magnetoencephalography (MEG) using both a spherical head with radial sensors for more efficient computation and a realistic head model for more accurate results. We develop these models with increasing degrees of freedom, derive forward solutions, maximum-likelihood (ML) estimates, and Cramér-Rao bound (CRB) expressions for the unknown source parameters. A model selection method is applied to select the most appropriate model. We also present numerical examples to compare the performances and computational costs of the different models, to determine the regions where better estimates are possible and when it is possible to distinguish between line and focal sources. We demonstrate the usefulness of the proposed line-source models over the previously available focal source model in certain distributed source cases. Finally, we apply our methods to real MEG data, the N2O response after electric stimulation of the median nerve known to be an extended source.

Algorithms↗

PubMed2005

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.

Animals↗

PubMed2004

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.

Brain↗