Performance of prewhitening beamforming in MEG dual experimental conditions.

This paper presents an analysis on the performance of the prewhitening beamformer when applied to magnetoencephalography (MEG) experiments involving dual (task and control) conditions. We first analyze the method's robustness to two types of violations of the prerequisites for the prewhitening method that may arise in real-life two-condition experiments. In one type of violation, some sources exist only in the control condition but not in the task condition. In the other type of violation, some signal sources exist both in the control and the task conditions, and that they change intensity between the two conditions. Our analysis shows that the prewhitening method is very robust to these nonideal conditions. In this paper, we also present a theoretical analysis showing that the prewhitening method is considerably insensitive to overestimation of the signal-subspace dimensionality. Therefore, the prewhitening beamformer does not require accurate estimation of the signal subspace dimension. Results of our theoretical analyses are validated in numerical experiments and in experiments using a real MEG data set obtained during self-paced hand movements.

Transient activation of inferior prefrontal cortex during cognitive set shifting.

The Wisconsin Card Sorting Test, which probes the ability to shift attention from one category of stimulus attributes to another (shifting cognitive sets), is the most common paradigm used to detect human frontal lobe pathology. However, the exact relationship of this card test to prefrontal function and the precise anatomical localization of the cognitive shifts involved are controversial. By isolating shift-related signals using the temporal resolution of functional magnetic resonance imaging, we reproducibly found transient activation of the posterior part of the bilateral inferior frontal sulci. This activation was larger as the number of dimensions (relevant stimulus attributes that had to be recognized) were increased. These results suggest that the inferior frontal areas play an essential role in the flexible shifting of cognitive sets.

Serial activation of distinct cytoarchitectonic areas of the human S1 cortex after posterior tibial nerve stimulation.

MEG recordings visualized non-invasively a dynamic anterior-posterior activation in the pyramidal cell population of the human primary somatosensory cortex (S1) after posterior tibial nerve stimulation. Somatosensory evoked fields (SEFs) were recorded over the foot area in response to right posterior tibial nerve stimulation at the ankle in six normal subjects. A newly developed MEG vector beamformer technique applied to the SEFs revealed two distinct sources in the mesial wall of the left hemisphere around the primary P37m response typically separated by 1.3 cm. The first source was located in area 3b and oriented toward the contralateral hemisphere. The second source was assumed to be in an area near the marginal sulcus and the source orientation was directed posteriorly. The first source began to be active during the initial slope of the P37m. The second source was active after the P37m peak and the signal intensities of the first and second sources were equal at a mean latency of 2.6 ms after the peak of P37m. Then the first source became inactive and the second source was dominant after about 5 ms post-P37m peak. These findings suggest that a single peaked posterior tibial nerve P37m consists of partially overlapping two subcomponents generated in area 3b and an area near the marginal sulcus.

Dynamic activation of distinct cytoarchitectonic areas of the human SI cortex after median nerve stimulation.

MEG recordings visualized non-invasively a serial mediolateral activation of the human somatosensory 3b area followed by a stationary activation of area 1 after median nerve stimulation. Somatosensory evoked fields (SEFs) were recorded over the hand area contralateral to the right median nerve stimulation at the wrist in six normal subjects. A newly developed MEG vector beamformer technique applied to the SEFs revealed two distinct sources (areas 3b and 1) in the primary somatosensory cortex (SI) during the primary N20m-P22m response in all subjects. The first source was located in area 3b, which started to move sequentially toward mediolateral direction 0.7 ms prior to the peak of N20m and ended its movement 1.4 ms after the peak with a total distance of 11.2 mm. We speculate that the movement reflects a sequential mediolateral activation of the pyramidal cells in area 3b, which is mediated by horizontal connections running parallel to the cortical surface. The second source in area 1, located 5.6 mm medial and 4.2 mm posterior to the first source, was active 1.0 ms after the N20m peak. Then, the first source became inactive and the second source was dominant. In sharp contrast with the first source, the second source was stationary. The different behavior of these two components (moving vs stationary) indicates independent parallel inputs to area 3b and area 1 from the thalamus.

Neural source estimation from a time-frequency component of somatic evoked high-frequency magnetic oscillations to posterior tibial nerve stimulation.

OBJECTIVE: High frequency oscillations (HFOs) evoked by posterior tibial nerve stimulation were recorded using magnetoencephalography (MEG). Time-frequency domain multiple signal classification (TF-MUSIC) algorithm was applied, and the usefulness of this method was demonstrated. METHODS: Ten normal subjects were studied. To localize sources for the HFOs of those somatosensory evoked fields, we applied two kinds of methods: the single moving dipole (SMD) method and the TF-MUSIC method. The SMD method was applied after digitally band-pass filtering the somatosensory response with a bandwidth of 500-800 Hz. To estimate the locations of sources with the TF-MUSIC algorithm, we first set the target region on the spectrogram of the somatosensory responses. Then, the procedure described in Section 2.2 was applied with this target region. RESULTS: A clear, isolated region was detected in 6 out of 10 subjects using a time-frequency spectrogram. The averaged distance of the dipole sources between the HFOs and the underlying P37m using the TF-MUSIC algorithm was smaller than using the SMD method. CONCLUSIONS: The TF-MUSIC algorithm is suitable for extracting a target response whose spectrum changes significantly during the observation.

Image restoration from nonuniform static field influence in modified echo-planar imaging.

Experimental results of images restored from the influence of nonuniform static fields in modified echo-planar imaging are presented. The same restoration technique is used as that proposed for Fourier imaging. Experimental results show that both density variation and geometrical distortion can almost completely be eliminated in the restored image. Image restoration can relax the stringent requirement on the amplitude of the time-modulated gradient needed in modified echo-planar imaging.

Steady-state magnetizations in rapid NMR imaging using small flip angles and short repetition intervals.

The steady-state magnetizations in three versions of rapid NMR imaging using small flip angles and short repetition intervals are studied. It is shown that in the original version, the estimation using (1 - E(1)) sin alpha/(1 - E(1) cos alpha) contains errors that depend on the increment of the phase rotation angle arising from the phase encoding process. The modified version of rapid imaging, where the phase rotation due to the phase encoding process is compensated for in each time interval, can have sensitivity superior to the original version where the phase rotation is not compensated for. Here, flip angles larger than the Ernst angle must be used. In the third version, the steady-state magnetization is obtained by a rapid imaging sequence in which the phase rotations arising not only from the application of the phase encoding gradient but also from the applications of other gradients are compensated for. Analysis of this version showed a remarkable increase in sensitivity although it required the use of an extremely uniform field. It is estimated that this increase reaches 80 percent with a repetition interval of 10 ms, although a field uniformity less than 1 muT is necessary.

NMR imaging for magnets with large nonuniformities.

Nuclear magnet resonance (NMR) imaging in the presence of large static field nonuniformity is presented. The method involves three steps: field mapping, imaging by a conventional method, and image restoration from nonuniform field influence. Two-dimensional experiments are performed to demonstrate effectiveness of this method, as well as to clarify practical problems in employing the method. Experimental results show that, with this method, images free from distortion can be obtained using a magnet with an order of magnitude greater nonuniformity than magnets commonly used for whole-body imaging.

Reconstructing current distributions from biomagnetic measurements under large external noise disturbances.

External noise fields cause spatially coherent noise in the biomagnetic data measured by a multichannel magnetometer. The authors propose a method of incorporating this spatial coherence into current-density reconstruction. This method can reconstruct current distributions from biomagnetic measurements affected by external noise fields. Computer simulations demonstrate its effectiveness.

Details of simulated annealing algorithm to estimate parameters of multiple current dipoles using biomagnetic data.

The details of the simulated annealing algorithm proposed to estimate the parameters of multiple current dipoles using biomagnetic data are described. The effects of the choices of such numerical conditions as the amount of estimate transitions, the equilibrium criterion, and the temperature decrement on the algorithm's performance are discussed. Incorrect results from the computer simulation obtained with inappropriate choices of such conditions are presented. The verification of a near-optimum convergence by reheating and reannealing is demonstrated. A modification of this algorithm is proposed for implementation by parallel computer, and the validity of this parallel algorithm is demonstrated by computer simulation.

Time-frequency MEG-MUSIC algorithm.

We propose a method that incorporates the time-frequency characteristics of neural sources into magnetoencephalographic (MEG) source estimation. The method is based on the multiple-signal-classification (MUSIC) algorithm and it calculates a time--frequency matrix in which diagonal and off-diagonal terms are the auto and crosstime--frequency distributions of multichannel MEG recordings, respectively. The method averages this time-frequency matrix over the time--frequency region of interest. The locations of neural sources are then estimated by checking the orthogonality between the noise subspace of this averaged matrix and the sensor lead field. Accordingly, the method allows us to estimate the locations of neural sources from each time--frequency component. A computer simulation was performed to test the validity of the proposed method, and the results demonstrate its effectiveness.

Image restoration from non-uniform magnetic field influence for direct Fourier NMR imaging.

A new technique is proposed for NMR image restoration from the influence of main magnetic field non-uniformities. This technique is applicable to direct Fourier NMR imaging. The mathematical basis and details of this technique are fully described. Modification to include image restoration from non-linear field gradient influence is also presented. Computer simulation demonstrates the effectiveness of this technique for both Fourier zeugmatography and spin-warp imaging.

Reduction of brain noise influence in evoked neuromagnetic source localization using noise spatial correlation.

In magnetoencephalographic measurements, magnetic fields caused by spontaneous brain activities not related to the neural activities under study are often referred to as brain noise. This is because the accuracy in neural source localization is considerably degraded by such spontaneous neuromagnetic fields. This paper reports the experimental results of applying the previously proposed noise covariance method to reducing the degradation caused by brain noise and to improving the accuracy in localizing auditory-evoked neural sources. Firstly we present the results of our experiments using measured brain noise and computer-generated signal fields. These results confirm that the covariance method can, in principle, improve the accuracy of evoked neural source localization. Next, the method was applied to source localization for actual neuromagnetic fields evoked by speech sounds. The results obtained strongly suggest that the method is effective in processing actual evoked neuromagnetic data.

Reconstruction of two-dimensional current distribution from tangential MCG measurement.

We describe a two-dimensional reconstruction method for tangential magnetocardiograms (MCGs). This method is based on two-dimensional Fourier analysis, and we used a new type of window function for tangential MCG to solve the problem of the small number of measurement points. By using this method, cardiac activity can be estimated as a two-dimensional current distribution. To determine the effectiveness of this method, we measured tangential MCGs of normal subjects, and compared the estimated current distribution with the actual cardiac muscle activity. Using this method, we were able to clearly show cardiac activity.

Relationship between dipole parameter estimation errors and measurement conditions in magnetoencephalography.

The relationship between dipole parameter estimation errors and measurement conditions in magnetoencephalography is determined by computer simulation. The model uses a single current dipole in a spherical homogeneous medium. Dipole parameters are estimated using a moving dipole procedure. Signal-to-noise ratio (SNR) is defined as the square-root of the ratio of the average signal power to the average noise power over all measurement points. At SNR > 20, accurate estimation can be carried out independently of dipole depth and coil size. At SNR < 20, dipole depth influences estimation error. When the dipole is located near the center of the sphere, the measurement region should include both extrema of the magnetic field to minimize estimation error. However, when the dipole is not so deep, the position of the measurement region does not influence estimation error. When SNR < 4, estimation error increases as coil size increases. Coil size minimizing estimation error is determined by the ratio of environmental magnetic field noise to electrical noise. For a constant size of measurement region, increasing the number of measurement points decreases estimation error to a certain level. This error level depends on SNR. The number of measurement points required to minimize estimation error also depends on SNR.

Average-intensity reconstruction and Wiener reconstruction of bioelectric current distribution based on its estimated covariance matrix.

This paper proposes two methods for reconstructing current distributions from biomagnetic measurements. Both of these methods are based on estimating the source-current covariance matrix from the measured-data covariance matrix. One method is the reconstruction of average current intensity distributions. This method first estimates the source-current covariance matrix and, using its diagonal terms, it reconstructs current intensity distributions averaged over a certain time. Although the method does not reconstruct the orientation of each current element at each time instant, it can retrieve information regarding the current time-averaged intensity at each voxel location using extremely low SNR data. The second method is Wiener reconstruction using the estimated source-current covariance matrix. Unlike the first method, this Wiener reconstruction can provide a current distribution with its orientation at each time instant. Computer simulation shows that the Wiener method is less affected by the choice of the regularization parameter, resulting in a method that is more effective than the conventional minimum-norm method when the SNR of the measurement is low.

Generalized Wiener estimation of three-dimensional current distribution from biomagnetic measurements.

This paper proposes a method for estimating three-dimensional (3-D) biocurrent distribution from spatio-temporal biomagnetic data. This method is based on the principle of generalized Wiener estimation, and it is formulated based on the assumption that current sources are uncorrelated. Computer simulation demonstrates that the proposed method can reconstruct a 3-D current distribution where the conventional least-squares minimum-norm method fails. The influence of noise is also simulated, and the results indicate that a signal-to-noise ratio of more than 20 for the uncorrelated sensor noise is needed to implement the proposed method. The calculated point spread function shows that the proposed method has very high spatial resolution compared to the conventional minimum norm method. The results of computer simulation of the distributed current sources are also presented, including cases where current sources are correlated. These results suggest that no serious errors arise if the source correlation is weak.

Maximum-likelihood estimation of current-dipole parameters for data obtained using multichannel magnetometer.

A method is proposed to reduce the influence of external noise magnetic field on the accuracy of estimating current dipole parameters. It utilizes the spatial correlation of external noises, and is applied to data measured using a multichannel magnetometer. Computer simulation clearly demonstrates the effectiveness of the proposed method.

Multiple current dipole estimation using simulated annealing.

A method for estimating electrical current distribution in the human brain using a multiple current dipole model is presented. A cost function for estimating multiple dipoles is proposed and a simulated annealing algorithm is used to obtain an acceptable solution. Computer simulation is used to evaluate the effectiveness of this method.

MEG spatio-temporal analysis using a covariance matrix calculated from nonaveraged multiple-epoch data.

We propose a magnetoencephalographic (MEG) spatio-temporal analysis in which the measurement-covariance matrix is calculated using nonaveraged multiple epoch data. The proposed analysis has two advantages. First, a very narrow time window can be used for the source estimation. Second, accurate localization is possible even when the source activation has a time jitter. Experiments using auditory evoked MEG data clearly demonstrate these advantages.