Equivalent dipole source imaging of brain electric activity by means of parametric projection filter

High-Resolution Cortical Dipole Imaging Using Spatial Inverse Filter Based on Filtering Property

Cortical dipole imaging has been developed to visualize brain electrical activity in high spatial resolution. It is necessary to solve an inverse problem to estimate the cortical dipole distribution from the scalp potentials. In the present study, the accuracy of cortical dipole imaging was improved by focusing on filtering property of the spatial inverse filter. We proposed an inverse filter that optimizes filtering property using a sigmoid function. The ability of the proposed method was compared with the traditional inverse techniques, such as Tikhonov regularization, truncated singular value decomposition (TSVD), and truncated total least squares (TTLS), in a computer simulation. The proposed method was applied to human experimental data of visual evoked potentials. As a result, the estimation accuracy was improved and the localized dipole distribution was obtained with less noise.

Localized cortical dipole imaging using a small number of electrodes based on independent component analysis

The spatial resolution of scalp potential mapping is limited because of low conductivity of a skull. Cortical dipole layer imaging has been proposed as a method to visualize brain electrical activity with high spatial resolution. According to this method, about 100 electrodes were required to measure whole brain electrical activity. In the present study, we investigated simplified cortical dipole imaging with a small number of electrodes. The density of electrodes and the spatial resolution are in a trade-off relation. Thus, the number of electrodes was reduced by limiting the visualization region of interest, without lowering the density of electrodes. Moreover, independent component analysis was applied to the multiple signal sources to extract an attention signal from the other signals and noise. In simulation, even if the number of electrodes was reduced to 25, the obtained results were almost equivalent to the case with whole brain electrodes. The proposed method was applied to human experimental data of movement-related potential. We confirmed that the proposed method provided high resolution cortical dipole imaging with localized distribution.

Reconstruction of magnetic source images using the Wiener filter and a multichannel magnetic imaging system

A system for imaging magnetic surfaces using a magnetoresistive sensor array is developed. The experimental setup is composed of a linear array of 12 sensors uniformly spaced, with sensitivity of 150 pT*Hz(-1/2) at 1 Hz, and it is able to scan an area of (16 × 18) cm(2) from a separation of 0.8 cm of the sources with a resolution of 0.3 cm. Moreover, the point spread function of the multi-sensor system is also studied, in order to characterize its transference function and to improve the quality in the restoration of images. Furthermore, the images are generated by mapping the response of the sensors due to the presence of phantoms constructed of iron oxide, which are magnetized by a pulse of 80 mT. The magnetized phantoms are linearly scanned through the sensor array and the remanent magnetic field is acquired and displayed in gray levels using a PC. The images of the magnetic sources are reconstructed using two-dimensional generalized parametric Wiener filtering. Our results exhibit a very good capability to determine the spatial distribution of magnetic field sources, which produce magnetic fields of low intensity.

Objective evaluation of somatic sensation for mechanical stimuli by means of cortical dipole layer imaging

In clinical situations, the objective evaluation of somatic sensations is expected without a patient's subjective opinions to reduce social problems such as those related to lawsuits for nerve injuries and malingering. In this study, the somatosensory evoked potential (SEP) using the mechanical stimulations of the tactile sensation was measured and analyzed in spatiotemporal domains. The spatial resolution of SEP maps was improved by application of cortical dipole layer imaging. The experimentally obtained results suggest that the spatiotemporal distributions of the SEPs reflect the differences for positions, strengths, and patterns of somatosensory stimulations.

High-resolution cortical dipole layer imaging based on noise covariance matrix

We have investigated the suitable spatial filters for inverse estimation of cortical dipole imaging from the scalp electroencephalogram. The effects of incorporating statistical information of noise into inverse procedures were examined by computer simulations and experimental studies. The parametric projection filter (PPF) was applied to an inhomogeneous three-sphere volume conductor head model. The noise covariance matrix was estimated by applying independent component analysis (ICA) to the scalp potentials. Moreover, the sampling method of the noise information was examined for calculating the noise covariance matrix. The simulation results suggest that the spatial resolution was improved while the effect of noise was suppressed by including the separated noise at the time instant of imaging and by adjusting the number of samples according to the signal to noise ratio.

Estimation of signal and noise covariance using ICA for high-resolution cortical dipole imaging

Suitable spatial filters were explored for inverse estimation of cortical dipole imaging from a scalp electroencephalogram. Computer simulations were used to examine the effects of incorporating statistical information of signal and noise into inverse procedures. Actually, the parametric projection filter (PPF) and parametric Wiener filter (PWF) were applied to an inhomogeneous three-sphere head model. The signal and noise covariance matrices were estimated by applying independent component analysis (ICA) to the scalp potentials. The simulation results described herein suggest that the PPF using differential noise between EEG and separated signal were equivalent to those obtained using the method with actual noise. Moreover, the PWF using separated signals has better performance than traditional inverse techniques.

Estimation of cortical dipole sources by equivalent dipole layer imaging and independent component analysis

We explored suitable estimation method for equivalent dipole sources in the brain. In a previous study, we solved an inverse problem that estimated an equivalent dipole-layer distribution from the scalp electroencephalogram by a spatio-temporal inverse filters constructed with parametric projection filter. In the present study, we estimated equivalent dipole sources from dipole layer distributions. Moreover, to identify the number, position, and moment of equivalent dipole sources, we separated each dipole layer distribution using independent component analysis (ICA). The performance of the proposed estimation method was evaluated by computer simulation and human experimental studies in an inhomogeneous three-concentric sphere head model. The present simulation results indicated that the equivalent dipole sources was accurately estimated by ICA and dipole imaging. We also applied the proposed method to human visual evoked potential.

Cortical potential imaging of movement-related potentials using parametric Wiener filter in realistic-shaped head model

Suitable spatial filters were explored for inverse estimation of cortical potential imaging from the scalp electroencephalogram. The effects of incorporating signal and noise covariance into inverse procedures were examined by computer simulations and experimental study. The parametric Wiener filter (PWF) was applied to an inhomogeneous three-sphere head model under various signal and noise conditions. We also examined estimation methods for the signal covariance in PWF. The present simulation results suggest that the PWF with modified matrix transformation method has better performance. The proposed methods were applied to self-paced movement-related potentials In order to identify the anatomic substrate locations of neural generators in realistic head model. The proposed methods demonstrated that the contralateral premotor cortex was preponderantly activated In relation to movement performance.

Evaluation and validity of a LORETA normative EEG database

To evaluate the reliability and validity of a Z-score normative EEG database for Low Resolution Electromagnetic Tomography (LORETA), EEG digital samples (2 second intervals sampled 128 Hz, 1 to 2 minutes eyes closed) were acquired from 106 normal subjects, and the cross-spectrum was computed and multiplied by the Key Institute's LORETA 2,394 gray matter pixel T Matrix. After a log10 transform or a Box-Cox transform the mean and standard deviation of the *.lor files were computed for each of the 2394 gray matter pixels, from 1 to 30 Hz, for each of the subjects. Tests of Gaussianity were computed in order to best approximate a normal distribution for each frequency and gray matter pixel. The relative sensitivity of a Z-score database was computed by measuring the approximation to a Gaussian distribution. The validity of the LORETA normative database was evaluated by the degree to which confirmed brain pathologies were localized using the LORETA normative database. Log10 and Box-Cox transforms approximated Gaussian distribution in the range of 95.64% to 99.75% accuracy. The percentage of normative Z-score values at 2 standard deviations ranged from 1.21% to 3.54%, and the percentage of Z-scores at 3 standard deviations ranged from 0% to 0.83%. Left temporal lobe epilepsy, right sensory motor hematoma and a right hemisphere stroke exhibited maximum Z-score deviations in the same locations as the pathologies. We conclude: (1) Adequate approximation to a Gaussian distribution can be achieved using LORETA by using a log10 transform or a Box-Cox transform and parametric statistics, (2) a Z-Score normative database is valid with adequate sensitivity when using LORETA, and (3) the Z-score LORETA normative database also consistently localized known pathologies to the expected Brodmann areas as an hypothesis test based on the surface EEG before computing LORETA.

Electrical localization of neural activity in the dorsal horn of the spinal cord: a modeling study

Intraspinal microstimulation is a means of eliciting coordinated motor responses for restoration of function. However, detailed maps of the neuroanatomy of the human spinal cord are lacking, and it is not clear where electrodes should be implanted. We developed an electrical approach to localize active neurons in the spinal cord using potentials recorded from the surface of the spinal cord. We evaluated this localization method using an analytical model of the spinal cord and two previously developed inverse algorithms (standardized low resolution brain electromagnetic tomography (sLORETA) and a locally optimal source (LOS) method). The results support electrical source localization as a feasible imaging approach for localizing (within 300 microm) active neurons in the spinal cord. The LOS method could localize the source when 16 recording electrodes were placed on the dorsolateral aspect of the cord and the noise level was 2%. When recording electrodes were positioned around the entire circumference of the spinal cord, either localization method could localize the source, even at 15% noise. Finally, localization error was not sensitive to inaccuracies in the expected electrode positions or the electrical parameters of the forward model, but was sensitive to a geometrical modification of the forward model in one case.

Parametric vs. non-parametric statistics of low resolution electromagnetic tomography (LORETA)

This study compared the relative statistical sensitivity of non-parametric and parametric statistics of 3-dimensional current sources as estimated by the EEG inverse solution Low Resolution Electromagnetic Tomography (LORETA). One would expect approximately 5% false positives (classification of a normal as abnormal) at the P < .025 level of probability (two tailed test) and approximately 1% false positives at the P < .005 level. EEG digital samples (2 second intervals sampled 128 Hz, 1 to 2 minutes eyes closed) from 43 normal adult subjects were imported into the Key Institute's LORETA program. We then used the Key Institute's cross-spectrum and the Key Institute's LORETA output files (*.lor) as the 2,394 gray matter pixel representation of 3-dimensional currents at different frequencies. The mean and standard deviation *.lor files were computed for each of the 2,394 gray matter pixels for each of the 43 subjects. Tests of Gaussianity and different transforms were computed in order to best approximate a normal distribution for each frequency and gray matter pixel. The relative sensitivity of parametric vs. non-parametric statistics were compared using a "leave-one-out" cross validation method in which individual normal subjects were withdrawn and then statistically classified as being either normal or abnormal based on the remaining subjects. Log10 transforms approximated Gaussian distribution in the range of 95% to 99% accuracy. Parametric Z score tests at P < .05 cross-validation demonstrated an average misclassification rate of approximately 4.25%, and range over the 2,394 gray matter pixels was 27.66% to 0.11%. At P < .01 parametric Z score cross-validation false positives were 0.26% and ranged from 6.65% to 0% false positives. The non-parametric Key Institute's t-max statistic at P < .05 had an average misclassification error rate of 7.64% and ranged from 43.37% to 0.04% false positives. The nonparametric t-max at P < .01 had an average misclassification rate of 6.67% and ranged from 41.34% to 0% false positives of the 2,394 gray matter pixels for any cross-validated normal subject. In conclusion, adequate approximation to Gaussian distribution and high cross-validation can be achieved by the Key Institute's LORETA programs by using a log10 transform and parametric statistics, and parametric normative comparisons had lower false positive rates than the non-parametric tests.

Spatio-temporal cortical source imaging of brain electrical activity by means of time-varying parametric projection filter

In the present study, we explore suitable spatio-temporal filters for inverse estimation of an equivalent dipole-layer distribution from the scalp electroencephalogram (EEG) for imaging of brain electric sources. We propose a time-varying parametric projection filter (tPPF) for the spatio-temporal EEG analysis. The performance of this tPPF algorithm was evaluated by computer simulation studies. An inhomogeneous three-concentric-spheres model was used in the present simulation study to represent the head volume conductor. An equivalent dipole layer was used to represent equivalently brain electric sources and estimated from the scalp potentials. The tPPF filter was tested to remove time-varying noise such as instantaneous artifacts caused by eyes-blink. The present simulation results indicate that the proposed time-variant tPPF method provides enhanced performance in rejecting time-varying noise, as compared with the time-invariant parametric projection filter.