Estimating regional brain activity from evoked potential fields on the scalp

Cortical potential imaging of somatosensory evoked potential induced by mechanical stimulation

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 or 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 cortical potential mapping projected onto the realistic-shaped model was estimated to improve the spatial resolution of the SEP maps 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.

Cortical potential imaging of somatosensory evoked potentials by means of the boundary element method in pediatric epilepsy patients

The aim of the present study was to assess the feasibility of identifying the primary hand sensory area and central sulcus in pediatric patients using the cortical potential imaging (CPI) method from the scalp recorded somatosensory evoked potentials (SEPs). The CPI method was used to reconstruct the cortical potential distribution from the scalp potentials with the boundary element (3-layer: scalp, skull and brain) head model based on MR images of individual subjects. The cortical potentials estimated from the pre-operative scalp SEPs of four pediatric patients, were compared with the post-op subdural SEP recordings made in the same subjects. Estimated and directly recorded cortical SEP maps showed comparable spatial patterns on the cortical surface in four patients (spatial correlation coefficient >0.7 in the SEP spikes). For two of four patients, the estimated waveforms correlated significantly to the waveforms obtained by direct cortical recordings. The present results demonstrated the feasibility of the cortical potential imaging approach in noninvasive imaging spatial distribution and temporal waveforms of cortical potentials for pediatric patients. These also suggest that the CPI method may provide a promising means of estimating the cortical potential and noninvasive localizing the central sulcus to aid surgical planning for pediatric patients.

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.

Development and evaluation of the sparse decomposition method with mixed over-complete dictionary for evoked potential estimation

A new method is developed to decompose a physiological signal into a summation of transient and oscillatory components, referred to as mixed over-complete dictionary based sparse component decomposition algorithm (MOSCA). Based on the characteristics of the transient evoked potential (EP) and the background noise, the mixed dictionary is constructed with an over-complete wavelet dictionary and an over-complete discrete cosine (DC) function dictionary, and the signal is separated by learning in this mixed dictionary with a matching pursuit (MP) algorithm. MOSCA is designed specifically for the separation of a desired transient EP from the existing spontaneous EEG or other background noise. The method was evaluated with several simulation tests in which EPs or simulated EPs were deeply masked in different strong noise backgrounds, and the recovered signal is similar to the original assumed EP with a high and stable correlation coefficient (CC). The method was then applied to estimate event related potential (ERP) in the classical oddball experiment, and the results confirmed that the trial number for a reliable ERP estimation might be greatly reduced by MOSCA.

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.

Resistor mesh model of a spherical head: Part 2: A review of applications to cortical mapping

A resistor mesh model (RMM) has been validated with reference to the analytical model by consideration of a set of four dipoles close to the cortex. The application of the RMM to scalp potential interpolation was detailed in Part 1. Using the RMM and the same four dipoles, the different methods of cortical mapping were compared and have shown the potentiality of this RMM for obtaining current and potential cortical distributions. The lead-field matrices are well-adapted tools, but the use of a square matrix of high dimension does not permit the inverse solution to be improved in the presence of noise, as a regularisation technique is necessary with noisy data. With the RMM, the transfer matrix and the cortical imaging technique proved to be easy to implement. Further development of the RMM will include application to more realistic head models with more accurate conductivities.

A study on the reference electrode standardization technique for a realistic head model

One oldest technical problem in EEG practice is the effect of an active reference on EEG recording, and it is especially important for identifying the temporal information of EEG recordings. To solve this problem, a reference electrode standardization technique (REST) has been proposed for a concentric three-sphere head model. REST, based on an equivalent distributed source model, reconstructs the potential with a reference at infinity from the potential with a scalp point reference or with the average reference. In this paper, investigated was the REST for a realistic head model. The results of simulation studies show that the potential reconstruction for the realistic head model is more sensitive to noise than that for the concentric three-sphere head model, so a regularized inverse by truncated singular value decomposition was introduced. The results confirm that REST is still an efficient method even for a realistic head model especially for the most important superficial cortex region.

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.

High-resolution EEG: cortical potential imaging of interictal spikes

BACKGROUND

It is of clinical importance to localize pathologic brain tissue in epilepsy. Noninvasive localization of cortical areas associated with interictal epileptiform spikes may provide important information to facilitate presurgical planning for intractable epilepsy patients.

METHODS

A cortical potential imaging (CPI) technique was used to deconvolve the smeared scalp potentials into the cortical potentials. A 3-spheres inhomogeneous head model was used to approximately represent the head volume conductor. Five pediatric epilepsy patients were studied. The estimated cortical potential distributions of interictal spikes were compared with the subsequent surgical resections of these same patients.

RESULTS

The areas of negativity in the reconstructed cortical potentials of interictal spikes in 5 patients were consistent with the areas of surgical resections for these patients.

CONCLUSIONS

The CPI technique may become a useful alternative for noninvasive mapping of cortical regions displaying epileptiform activity from scalp electroencephalogram recordings.

Electrical activity in visual cortex associated with combined auditory and visual stimulation in temporal sequences known to be associated with a visual illusion

When a subject views a visual stimulus paired with a brief click, a second click occurring approximately 80 ms later produces the hallucination of a second visual stimulus. We have used combinations of visual and sound stimuli to evoke cortical activity and have recorded the associated event-related potentials. We have recorded EPs in a conventional manner, and have calculated from multichannel recordings the Laplacian derivations to determine if the currents were generated in primary visual cortex. Clicks alone do not cause significant activity in V1, but if paired with pattern stimulation, modify the evoked potential. The timing of this extra activity almost certainly excludes "feed back" activation from higher centres, and can most simply be explained if sound-activated thalamo-cortical input can rapidly produce extra activity in 'primed' visual cortex. This finding has general implications for cortical function, for the generation of the hallucination and for 'blindsight'.

Boundary element method-based cortical potential imaging of somatosensory evoked potentials using subjects' magnetic resonance images

A boundary element method-based cortical potential imaging technique has been developed to directly link the scalp potentials with the cortical potentials with the aid of magnetic resonance images of the subjects. First, computer simulations were conducted to evaluate the new approach in a concentric three-sphere inhomogeneous head model. Second, the corresponding cortical potentials were estimated from the patients' preoperative scalp somatosensory evoked potentials (SEPs) based on the boundary element models constructed from subjects' magnetic resonance images and compared to the postoperative direct cortical potential recordings in the same patients. Simulation results demonstrated that the cortical potentials can be estimated from the scalp potentials using different scalp electrode configurations and are robust against measurement noise. The cortical imaging analysis of the preoperative scalp SEPs recorded from patients using the present approach showed high consistency in spatial pattern with the postoperative direct cortical potential recordings. Quantitative comparison between the estimated and the directly recorded subdural grid potentials resulted in reasonably high correlation coefficients in cases studied. Amplitude difference between the estimated and the recorded potentials was also observed as indexed by the relative error, and the possible underlying reasons are discussed. The present numerical and experimental results validate the boundary element method-based cortical potential imaging approach and demonstrate the feasibility of the new approach in noninvasive high-resolution imaging of brain electric activities from scalp potential measurement and magnetic resonance images.

High-resolution EEG: on the cortical equivalent dipole layer imaging

BACKGROUND

Brain electrical activity is a spatio-temporally distributed process. Cortical imaging techniques have been developed to reconstruct cortical activity from the scalp electroencephalographic or magnetoencephalographic measurements. Several cortical imaging approaches, such as the epicortical potentials and a dipole layer accounting for the cortical activity, have been used to represent brain electrical activity.

METHODS

A closed cortical dipole layer source model is used to equivalently represent brain electrical activity. The relationship between the primary brain electrical sources and the cortical equivalent dipole layer is derived from the theory of electromagnetics. Computer simulation studies were conducted using a 3-concentric-sphere head model to validate the proposed theory. The cortical equivalent dipole layer imaging approach was tested in both computer simulation and human visual evoked potential (VEP) experiments.

RESULTS

The strength of the cortical equivalent dipole layer is shown to be proportional to the electrical potential over the same surface generated by primary electrical sources, had the outer medium been replaced by air. The proposed theory was validated by computer simulation in a discrete system. Simulation and VEP experimental studies suggest the feasibility of applying the cortical equivalent dipole layer imaging approach for brain imaging.

CONCLUSIONS

The cortical equivalent dipole layer model can equivalently represent the primary brain electrical sources throughout the entire brain surrounded by the dipole layer. The strength of the cortical equivalent dipole layer due to primary sources can be directly calculated according to the theory developed in the present study.

Source potential mapping: a new modality to image neural electric activities

A new neural electric imaging modality-source potential mapping (SPM)-is presented here, which images the neural sources by the potential produced by the sources in a homogeneous infinite conducting medium. Compared with the extant cortical surface potential mapping (CPM). SPM is a more direct reflection of the sources and is a simpler physical model, thus assuring easy understanding. The simulations show that SPM has a slightly higher spatial resolution than CPM and the calculation of SPM is more economical than that of CPM.

A study of equivalent source techniques for high-resolution EEG imaging

High-resolution EEG imaging has been an important topic in recent EEG research, and much work has been done on the two equivalent source imaging techniques: the equivalent distributed dipole-layer source imaging technique (EST) and the equivalent multipole source imaging technique (SAT). In this paper we first develop a forward density formula for a spherical equivalent distributed dipole layer of an arbitrary dipole in a three-concentric-sphere head model. It is clarified using the derived forward formula that the equivalent dipole-layer source and equivalent multipole source are interrelated in theory. Finally, simulation comparisons are conducted, the results of which suggest that EST has a higher spatial resolution than SAT when both of them are implemented by a truncated singular value decomposition algorithm. This is due to the different singularities of the inversion equations involved in the two techniques. An empirical VEP data study also shows that EST is better than SAT in providing higher spatial resolution EEG imaging.

A cortical potential imaging analysis of the P300 and novelty P3 components

The P300 and Novelty P3 are positive components of the event related brain potential (ERP) with a latency of at least 300 ms, which are manifestations of brain activity evoked by deviant events. Spencer et al. [1999, 2001] demonstrated that these are two distinct components, both of which may be elicited, with different amplitudes, by both rare and novel events. However, the locations of the intracranial sources of the components remain unknown. We describe the application of cortical potential imaging (CPI) analysis to the data described by Spencer et al. [1999]. The ERPs were recorded from 15 healthy subjects presented with auditory oddball sequences. Cortical potential maps (CPMs) were reconstructed from the scalp potential maps (SPMs) corresponding to the P300 and Novelty P3 components by deblurring the smoothing effect of the head volume conductor. The reconstructed CPMs, derived from the SPMs by means of the CPI, showed localized areas of activity distributed in both the frontal and parietal lobes; the parietal region was active throughout the period of the late positivities. The reconstructed CPMs associated with novel events showed prominent activity at the frontal lobe (Novelty P3) followed by progressively pronounced parietal lobe activity (P300), and these two components can be well separated by the CPMs. These analyses show how the CPI can be used to relate the scalp electrical recordings to the underlying brain activity.

High-resolution EEG mappings: a spherical harmonic spectra theory and simulation results

Shown first is the equivalence between the multiple expansion (ME) of the brain electrical generator and the spherical harmonic spectra (SHS) of the potential generated by the electrical generator in an infinite volume conductor. Based on the equivalence, the SHS and the spatial filters which connect the SHS with the ME are deduced, in a concentric 3 sphere conductor and for the 5 EEG source mappings. They are cortical potential mapping (CPM), scalp Laplacian mapping (LM), pseudo-cortical potential mapping (PCPM), equivalent dipole layer mapping (EDM) and equivalent charge layer mapping (ECM). The theoretical simulation study of the spatial filters and mappings indicate that all 5 mappings provide higher resolution imaging maps of brain electrical activity than the scalp potential map. In the inverse problem, a spherical spline fit algorithm is provided to reconstruct the SHS of the scalp recording potential, and then the SHS and maps of the 5 mappings are reconstructed by utilizing the spatial filters and the SHS of the scalp potential. The results indicate that the correlativity order between a reconstructed map and the actual cortical potential map is CPM > or = EDM > PCPM > LM > ECM. An empirical VEP data study shows that any one of the 5 mappings also provides higher spatial resolution than the scalp potential map.

Estimating cortical potentials from scalp EEG's in a realistically shaped inhomogeneous head model by means of the boundary element method

Cortical potentials are estimated from scalp potentials using a realistically shaped inhomogeneous head model, by means of the boundary element method (BEM). A new adaptive algorithm has been developed to achieve high accuracy to link directly the cortical potentials to the scalp potentials in a realistically shaped inhomogeneous head model including the thin low-conductivity skull layer. Computer simulations using a concentric three-spheres head model have tested this approach. The present study demonstrates that the cortical potentials can be directly estimated from the scalp potentials using the BEM in a realistically shaped inhomogeneous head model.

A computer simulation study of cortical imaging from scalp potentials

In this paper, computer simulation studies were conducted to test the feasibility of imaging brain electrical activity from the scalp electroencephalograms. The inhomogeneous three-concentric-sphere head model was used to represent the head volume conductor. Closed spherical dipole layers, consisting of several thousand uniformly distributed dipoles, were used to reconstruct the cortical potential maps corresponding to neuronal sources located inside the brain. Simulation results indicate that the present procedure can image both cortical and deep sources, and for the cortical sources, a spatial resolution as high as 1.2 cm can be achieved.

Estimating cortical activity from VEPS with the shrinking ellipsoid inverse

An iterative inverse method using Tikhonov regularization (the shrinking ellipsoid method) previously tested in a model system is used to invert the sequence of bioelectric scalp fields evoked by the onset of a checkerboard pattern in either the right or left lower hemifield. The shrinking ellipsoid method is modified from its original description to accommodate simultaneously inverting a sequence of thirteen VEP scalp fields measured from 65 to 125 ms after stimulus onset. This allows the evoked cortical activity to be tracked in 5-ms intervals without distortion due to occasional VEP scalp fields in the sequence that have too low a signal-to-noise ratio to be reliably inverted in isolation. A new method is described to identify the surface of the cortex from MRI data. This is required to implement the shrinking ellipsoid inverse. Results from two subjects studied in detail are presented. The earliest cortical activity occurs either in area MT (the middle temporal area) or simultaneously in MT and striate cortex (V1). However when it does occur in both areas, the activity in V1 is relatively weak and quickly subsides. Seventy-five ms after stimulus onset activity is seen mainly near MT corresponding to a region identified from PET studies as one that subserves motion processing. Activity moves to V1 by 90-100 ms after stimulus onset. Near 120 ms after stimulus onset, cortical activity returns to the region near MT. Virtually all activity identified in this time epoch occurs in the cortical hemisphere contralateral to the location of the stimulus in the visual field.

High resolution EEG: a new model-dependent spatial deblurring method using a realistically-shaped MR-constructed subject's head model

This paper presents a new model-dependent method for the spatial deblurring of scalp-recorded EEG potentials based on boundary-element and cortical imaging techniques. This model-dependent spatial deblurring (MDSD) method used MR images for the reconstruction of the subject's head model, and a layer of 364 radially-oriented equivalent current dipoles as a source model. The validation of the MDSD method was performed on simulated potential distributions generated from equivalent dipoles oriented radially, obliquely, and tangentially to the head surface. Furthermore, this method was used to localize neocortical sources of human movement-related and somatosensory-evoked potentials. It was shown that the new MDSD method improved markedly the spatial resolution of the simulated surface potentials and scalp-recorded event-related potentials. The spatial information content of the scalp-recorded EEG potentials increased progressively by increasing the spatial sampling from 28 to 128 channels. These results indicate that the new method could be satisfactorily used for high resolution EEG studies.

A modified boundary element method for the estimation of potential fields on the scalp

A modified boundary element method (BEM) for the calculation of potential fields on the scalp is proposed and tested in a three-shell model. The method greatly reduces the computational burden with only a small cost in accuracy. The resistivity of the skull is taken as infinite and the potential field on the inner skull surface is calculated using the standard BEM method for a one-surface system. Then the potential at any single selected point on the scalp is calculated directly from Green's theorem. The method does not give an accurate estimate of the magnitude of the potential on the scalp, but it does preserve correct relative magnitudes over all source locations in the head.

The Duffing oscillator: a model for the dynamics of the neuronal groups comprising the transient evoked potential

Thirty years ago Zeeman conjectured that the dynamics of the EEG might be modeled by the "equation of motion" of a Duffing oscillator, a pendulum with a nonlinear, cubic, restoring force. In this study the idea is extended to the evoked potential (EP). A transient sensory EP reflects activity from several neuronal groups, pools of neurons that fire in synchrony, with voltage-time curves that overlap appreciably. When the dynamics of each neuronal group is modeled by a Duffing oscillator, multi-electrode transient VEPs are well predicted. Predictions based on Duffing oscillator dynamics are substantially better than those based on the assumption that each neuronal group follows a simpler exponentially damped sinusoid or a function that simulates a post-synaptic potential. The component voltage-time curves are reasonably consistent over 7 subjects, suggesting sequential activation of neuronal groups with delays of several tens of milliseconds between them. The scalp topographies of the components suggest their origins in the occipital cortex.

Continuous current source inversion of evoked potential fields in a spherical model head

This study explores the efficacy of a physiological constraint on cortical current generators in promoting a robust solution for the inverse problem in evoked potentials. It is proposed that the current sources responsible for the evoked potential be modeled as a set of dipoles oriented orthogonal to the surface of the cortex. Rather than using a minimum norm approach, the solution space is searched for a vector that minimizes the error of the predicted evoked potential scalp field.

Human brain responses to different image contrasts

Human brain activity was evoked by a dynamic random-dot display in which a square-wave grating appeared and disappeared at regular intervals. Grating visibility was determined by one of four different contrasts: texture, stereo disparity, luminance, or color. Scalp fields measured with 31 electrodes were used to estimate epicortical potential fields. The estimation procedure required detailed anatomical data for each subject. These were obtained from magnetic resonance images. A three-dimensional digitizer and a stereotactic headgear were used to accurately merge the frame of reference of the magnetic resonance image with that of the evoked potential. Epicortical potential fields provided a better indicator of where brain activity is evoked than did scalp fields. These procedures also corrected for anatomical variations between scalp and brain from subject to subject. In two right-handed female subjects, evoked activity was observed in the left posterior parietal and the right occipital, parieto-occipital and posterior temporal cortices. Evoked activity was observed in the left parietal cortex for luminance processing, in the right parietal cortex for texture processing and in the right temporal cortex for color processing, which was selective for the particular contrast.

Functional brain imaging: dipole localization and Laplacian methods

The performance of two methods, used to localize brain activity from evoked potential fields measured on the scalp, was assessed in a tank model of the human head. This physical model contained a human skull encased in a polymer simulating the resistivity and geometry of brain and scalp. The dipole localization method mislocalized the positions of known dipole sources by several centimeters. The mislocalization was systematic. The dipoles were localized too deeply in the head. The Laplacian method yielded a field resembling the brain surface field (epicortical potential field) provided that the iso-potential contours of the scalp field closed within the measurement range. Clipping resulted in a serious mislocalization of the position of the peak of the epicortical potential field.

Inferring regional brain activity from evoked potential fields on the scalp

A new method is described to calculate epicortical potential fields from scalp fields based on linear algebra. It requires detailed anatomical information, for each subject, obtained from MR images. The calculation is validated in a physical model of the human head and applied to human subjects. The results suggest that the method yields reliable epicortical fields that help to localize evoked cortical activity in humans.