Current source density estimation and interpolation based on the spherical harmonic Fourier expansion

Nonparametric Bayesian Regression and Classification on Manifolds, With Applications to 3D Cochlear Shapes

Advanced shape analysis studies such as regression and classification need to be performed on curved manifolds, where often, there is a lack of standard statistical formulations. To overcome these limitations, we introduce a novel machine-learning method on the shape space of curves that avoids direct inference on infinite-dimensional spaces and instead performs Bayesian inference with spherical Gaussian processes decomposition. As an application, we study the shape of the cochlear spiral-shaped cavity within the petrous part of the temporal bone. This problem is particularly challenging due to the relationship between shape and gender, especially in children. Experimental results for both synthetic and real data show improved performance compared to state-of-the-art methods.

Which Reference Should We Use for EEG and ERP practice?

Which reference is appropriate for the scalp ERP and EEG studies? This unsettled problem still inspires unceasing debate. The ideal reference should be the one with zero or constant potential but unfortunately it is well known that no point on the body fulfills this condition. Consequently, more than ten references are used in the present EEG-ERP studies. This diversity seriously undermines the reproducibility and comparability of results across laboratories. A comprehensive review accompanied by a brief communication with rigorous derivations and notable properties (Hu et al. Brain Topogr, 2019. https://doi.org/10.1007/s10548-019-00706-y ) is thus necessary to provide application-oriented principled recommendations. In this paper current popular references are classified into two categories: (1) unipolar references that construct a neutral reference, including both online unipolar references and offline re-references. Examples of unipolar references are the reference electrode standardization technique (REST), average reference (AR), and linked-mastoids/ears reference (LM); (2) non-unipolar references that include the bipolar reference and the Laplacian reference. We show that each reference is derived with a different assumption and serves different aims. We also note from (Hu et al. 2019) that there is a general form for the reference problem, the 'no memory' property of the unipolar references, and a unified estimator for the potentials at infinity termed as the regularized REST (rREST) which has more advantageous statistical evidence than AR. A thorough discussion of the advantages and limitations of references is provided with recommendations in the hope to clarify the role of each reference in the ERP and EEG practice.

The Statistics of EEG Unipolar References: Derivations and Properties

In this brief communication, which complements the EEG reference review (Yao et al. in Brain Topogr, 2019), we provide the mathematical derivations that show: (1) any EEG reference admits the general form of a linear transformation of the ideal multichannel EEG potentials with reference to infinity; (2) the average reference (AR), the reference electrode standardization technique (REST), and its regularized version (rREST) are solving the linear inverse problems that can be derived from both the maximum likelihood estimate (MLE) and the Bayesian theory; however, REST is based on more informative prior/constraint of volume conduction than that of AR; (3) we show for the first time that REST is also a unipolar reference (UR), allowing us to define a general family of URs with unified notations; (4) some notable properties of URs are ‘no memory’, ‘rank deficient by 1’, and ‘orthogonal projector centering’; (5) we also point out here, for the first time, that rREST provides the optimal interpolating function that can be used when the reference channel is missing or the ‘bad’ channels are rejected. The derivations and properties imply that: (a) any two URs can transform to each other and referencing with URs multiple times will not accumulate artifacts; (b) whatever URs the EEG data was previously transformed with, the minimum norm solution to the reference problem will be REST and AR with and without modeling volume conduction, respectively; (c) the MLE and the Bayesian theory show the theoretical optimality of REST. The advantages and limitations of AR and REST are discussed to guide readers for their proper use.

Multi-Scale Neural Sources of EEG: Genuine, Equivalent, and Representative. A Tutorial Review

A biophysical framework needed to interpret electrophysiological data recorded at multiple spatial scales of brain tissue is developed. Micro current sources at membrane surfaces produce local field potentials, electrocorticography, and electroencephalography (EEG). We categorize multi-scale sources as genuine, equivalent, or representative. Genuine sources occur at the micro scale of cell surfaces. Equivalent sources provide identical experimental outcomes over a range of scales and applications. In contrast, each representative source distribution is just one of many possible source distributions that yield similar experimental outcomes. Macro sources ("dipoles") may be defined at the macrocolumn (mm) scale and depend on several features of the micro sources-magnitudes, micro synchrony within columns, and distribution through the cortical depths. These micro source properties are determined by brain dynamics and the columnar structure of cortical tissue. The number of representative sources underlying EEG data depends on the spatial scale of neural tissue under study. EEG inverse solutions (e.g. dipole localization) and high resolution estimates (e.g. Laplacian, dura imaging) have both strengths and limitations that depend on experimental conditions. The proposed theoretical framework informs studies of EEG source localization, source characterization, and low pass filtering. It also facilitates interpretations of brain dynamics and cognition, including measures of synchrony, functional connections between cortical locations, and other aspects of brain complexity.

Effectiveness of music therapy as an aid to neurorestoration of children with severe neurological disorders

This study was a two-armed parallel group design aimed at testing real world effectiveness of a music therapy (MT) intervention for children with severe neurological disorders. The control group received only the standard neurorestoration program and the experimental group received an additional MT "Auditory Attention plus Communication protocol" just before the usual occupational and speech therapy. Multivariate Item Response Theory (MIRT) identified a neuropsychological status-latent variable manifested in all children and which exhibited highly significant changes only in the experimental group. Changes in brain plasticity also occurred in the experimental group, as evidenced using a Mismatch Event Related paradigm which revealed significant post intervention positive responses in the latency range between 308 and 400 ms in frontal regions. LORETA EEG source analysis identified prefrontal and midcingulate regions as differentially activated by the MT in the experimental group. Taken together, our results showing improved attention and communication as well as changes in brain plasticity in children with severe neurological impairments, confirm the importance of MT for the rehabilitation of patients across a wide range of dysfunctions.

Issues and considerations for using the scalp surface Laplacian in EEG/ERP research: A tutorial review

Despite the recognition that the surface Laplacian may counteract adverse effects of volume conduction and recording reference for surface potential data, electrophysiology as a discipline has been reluctant to embrace this approach for data analysis. The reasons for such hesitation are manifold but often involve unfamiliarity with the nature of the underlying transformation, as well as intimidation by a perceived mathematical complexity, and concerns of signal loss, dense electrode array requirements, or susceptibility to noise. We revisit the pitfalls arising from volume conduction and the mandated arbitrary choice of EEG reference, describe the basic principle of the surface Laplacian transform in an intuitive fashion, and exemplify the differences between common reference schemes (nose, linked mastoids, average) and the surface Laplacian for frequently-measured EEG spectra (theta, alpha) and standard event-related potential (ERP) components, such as N1 or P3. We specifically review common reservations against the universal use of the surface Laplacian, which can be effectively addressed by employing spherical spline interpolations with an appropriate selection of the spline flexibility parameter and regularization constant. We argue from a pragmatic perspective that not only are these reservations unfounded but that the continued predominant use of surface potentials poses a considerable impediment on the progress of EEG and ERP research.

Hemifield-dependent N1 and event-related theta/delta oscillations: An unbiased comparison of surface Laplacian and common EEG reference choices

Surface Laplacian methodology has been used to reduce the impact of volume conduction and arbitrary choice of EEG recording reference for the analysis of surface potentials. However, the empirical implications of employing these different transformations to the same EEG data remain obscure. This study directly compared the statistical effects of four commonly-used (nose, linked mastoids, average) or recommended (reference electrode standardization technique [REST]) references and their spherical spline current source density (CSD) transformation for a large data set stemming from a well-understood experimental manipulation. ERPs (72 sites) recorded from 130 individuals during a visual half-field paradigm with highly-controlled emotional stimuli were characterized by mid-parietooccipital N1 (125 ms peak latency) and event-related synchronization (ERS) of theta/delta (160 ms), which were most robust over the contralateral hemisphere. All five data transformations were rescaled to the same covariance and submitted to a single temporal or time-frequency PCA (Varimax) to yield simplified estimates of N1 or theta/delta ERS. Unbiased nonparametric permutation tests revealed that these hemifield-dependent asymmetries were by far most focal and prominent for CSD data, despite all transformations showing maximum effects at mid-parietooccipital sites. Employing smaller subsamples (signal-to-noise) or window-based ERP/ERS amplitudes did not affect these comparisons. Furthermore, correlations between N1 and theta/delta ERS at these sites were strongest for CSD and weakest for nose-referenced data. Contrary to the common notion that the spatial high pass filter properties of a surface Laplacian reduce important contributions of neuronal generators to the EEG signal, the present findings demonstrate that instead volume conduction inherent in surface potentials weakens the representation of neuronal activation patterns at scalp that directly reflect regional brain activity.

The use of current source density as electrophysiological correlates in neuropsychiatric disorders: A review of human studies

The use of current source density (CSD), the Laplacian of the scalp surface voltage, to map the electrical activity of the brain is a powerful method in studies of cognitive and affective phenomena. During the last few decades, mapping of CSD has been successfully applied to characterize several neuropsychiatric conditions such as alcoholism, schizophrenia, depression, anxiety disorders, childhood/developmental disorders, and neurological conditions (i.e., epilepsy and brain lesions) using electrophysiological data from resting state and during cognitive performance. The use of CSD and Laplacian measures has proven effective in elucidating topographic and activation differences between groups: i) patients with a specific diagnosis vs. healthy controls, ii) subjects at high risk for a specific diagnosis vs. low risk or normal controls, and iii) patients with specific symptom(s) vs. patients without these symptom(s). The present review outlines and summarizes the studies that have employed CSD measures in investigating several neuropsychiatric conditions. The advantages and potential of CSD-based methods in clinical and research applications along with some of the limitations inherent in the CSD-based methods are discussed in the review, as well as future directions to expand the implementation of CSD to other potential clinical applications. As CSD methods have proved to be more advantageous than using scalp potential data to understand topographic and source activations, its clinical applications offer promising potential, not only for a better understanding of a range of psychiatric conditions, but also for a variety of focal neurological disorders, including epilepsy and other conditions involving brain lesions and surgical interventions.

QEEG norms for the first year of life

BACKGROUND

QEEG allows a more objective evaluation of cerebral electrical activity as well as the production of topographical maps for easier comprehension. Here we have developed qEEG norms for the first year of life using methods previously published for other age ranges, including for example, regression for Gausssianity before Z transformation. These norms constitute a non-invasive and low cost tool for the functional evaluation of the infant's brain.

RESULTS

Developmental equations were obtained from 101 healthy infants recording at spontaneous quiet sleep stage II. Polynomial regression equations, with age as independent variable, were calculated for full Broad Band Spectral Parameters (BBSP) using the Least Squares technique. Interpolated maps of the BBSP values or their Z transformation were constructed for linked-ear reference, average reference and Laplacian montages. All montages produced similar tendency curves and Z maps of absolute and relative power, and mean frequency at all frequency bands. The norms obtained were validated against an independent group of 50 healthy infants and some pathological cases. 91-98% of cases were well classified as normal across all measures and montages. To exemplify, two pathological cases are presented of which their qEEG maps show resemblance to CT and MRI.

CONCLUSIONS

These qEEG norms are highly useful as an aid to visual interpretation and for the study of pathology further evolution as well as for assessment of infants showing brain risk factors. To our knowledge this is the first normative qEEG study for the initial year of life with such large sample and validation-group.

Cortical Cartography

Architecture is one part science, one part craft, and two parts art.—David Rutten

This article describes the investigation of structural-functional associations in the brain. Using light microscopy in 1909, Brodmann divided the human and primate brains into dozens of areas based on cell types and distributions, which has since been supplemented by a 3-dimensional coordinate system, an xyz system of millimeter distances. A number of electroencephalograph tomographic (volume) solutions exist, and this article explains the Brodmann montage developed by the author using the spherical harmonic expansion solution by Pascual-Marqui. The author describes his approach to training specific Brodmann areas with electroencephalograhic operant conditioning or feedback.

From EEG dependency multichannel matching pursuit to sparse topographic EEG decomposition

In this work, we present a multichannel EEG decomposition model based on an adaptive topographic time-frequency approximation technique. It is an extension of the Matching Pursuit algorithm and called dependency multichannel matching pursuit (DMMP). It takes the physiologically explainable and statistically observable topographic dependencies between the channels into account, namely the spatial smoothness of neighboring electrodes that is implied by the electric leadfield. DMMP decomposes a multichannel signal as a weighted sum of atoms from a given dictionary where the single channels are represented from exactly the same subset of a complete dictionary. The decomposition is illustrated on topographical EEG data during different physiological conditions using a complete Gabor dictionary. Further the extension of the single-channel time-frequency distribution to a multichannel time-frequency distribution is given. This can be used for the visualization of the decomposition structure of multichannel EEG. A clustering procedure applied to the topographies, the vectors of the corresponding contribution of an atom to the signal in each channel produced by DMMP, leads to an extremely sparse topographic decomposition of the EEG.

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.

Preattentive discrimination of across-category and within-category change in consonant–vowel syllable

Event-related potentials to infrequently presented spoken deviant syllables /pi/ and /po/ among repetitive standard [see text] syllables were recorded in Thai study participants who ignored these stimuli while reading books of their choices. The vowel across-category and within-category changes elicited a change-specific mismatch negativity response. The across-category and within-category change discrimination of vowels in consonant-vowel syllable was also assessed using the low-resolution electromagnetic tomography. The results of low-resolution electromagnetic tomography mismatch negativity generator analysis suggest that the within-category change perception of vowels is analyzed as the change in physical features of the stimuli, thus predominantly activating the right temporal cortex. In contrast, the left temporal cortex is predominantly activated in the across-category change perception of vowels, emphasizing the role of the left hemisphere in speech processing already at a preattentive processing level also in consonant-vowel syllables. The results support the hypothesis that a part of the superior temporal gyrus contains neurons specialized for speech perception.

EEG phase synchrony differences across visual perception conditions may depend on recording and analysis methods

OBJECTIVE

(1) To investigate the neural synchrony hypothesis by examining if there was more synchrony for upright than inverted Mooney faces, replicating a previous study; (2) to investigate whether inverted stimuli evoke neural synchrony by comparing them to a new scrambled control condition, less likely to produce face perception.

METHODS

Multichannel EEG was recorded via nose reference while participants viewed upright, inverted, and scrambled Mooney face stimuli. Gamma-range spectral power and inter-electrode phase synchrony were calculated via a wavelet-based method for upright stimuli perceived as faces and inverted/scrambled stimuli perceived as non-faces.

RESULTS

When the frequency of interest was selected from the upright condition exhibiting maximal spectral power responses (as in the previous study) greater phase synchrony was found in the upright than inverted/scrambled conditions. However, substantial synchrony was present in all conditions, suggesting that choosing the frequency of interest from the upright condition only may have been biased. In addition, artifacts related to nose reference contamination by micro-saccades were found to be differentially present across experimental conditions in the raw EEG. When frequency of interest was selected instead from each experimental condition and the data were transformed to a laplacian 'reference free' derivation, the between-condition phase synchrony differences disappeared. Spectral power differences were robust to the change in reference, but not the combined changes in reference and frequency selection criteria.

CONCLUSIONS

Synchrony differences between face/non-face perceptions depend upon frequency selection and recording reference. Optimal selection of these parameters abolishes differential synchrony between conditions.

SIGNIFICANCE

Neural synchrony is present not just for face percepts for upright stimuli, but also for non-face percepts achieved for inverted/scrambled Mooney stimuli.

Quantitative Approximation of the Cortical Surface Potential From EEG and ECoG Measurements

A quantitative approximation of the cortical surface potential from measured scalp surface potential data is developed. The derivation is based on a local Taylor series expansion (TSE) in the surface normal coordinate. Analytical and numerical results for the four shell spherical head model show that the TSE method improves the spatial deblurring of the surface Laplacian method. The inclusion of the biharmonic term, the extension to other geometries, and the application to electrocorticogram measurements are discussed.

A novel spatio-temporal decomposition of the EEG: derivation, validation and clinical application

OBJECTIVE

To obtain clinically useful graphical and numerical data on the distribution of activities in the EEG using a novel type of spatio-temporal decomposition.

METHODS

The EEG is divided into 1/4 s epochs. An approximation to the spatial distribution of the locally dominant activity in each epoch is represented as a point in a spatial component space. Points representing epochs dominated by activity from the same source form a cluster. The centres of these clusters represent the global spatial component of each source. As each spatial component is identified, its corresponding temporal activity is removed from the record, allowing activity from sources with smaller amplitude to become dominant in the reduced record. Successive components are identified in the reduced record. The method was applied to 40 normal EEGs and features were identified, which were common to them all. The method was also applied to 4 separate records with different forms of focal abnormality.

RESULTS

The method successfully separated components from the EEG representing alpha rhythm, eye artefact, electrode artefact and EEG. In 40 normal EEGs the method isolated spatial components that were common to all EEGs, and in 4 abnormal EEGs it achieved a high degree of mutual separation of alpha rhythm, focal spikes, focal theta and focal delta activities.

CONCLUSIONS

The method achieved a high degree of mutual separation of the EEG components and successfully differentiated the artefacts due to eye movement, ECG and electrode faults. The clinical implications are discussed.

A general method for remontaging based on a singular value decomposition algorithm

The authors developed a general mathematic algorithm to convert any montage (referential, bipolar, or Laplacian) to any other by linear transformation. Input and output montages are described by matrices, and singular value decomposition is used to find the linear transformation. An error signal can be calculated from the input data to monitor remontaging validity. This algorithm also identifies output channels that cannot be obtained from the specified input. The authors tested this algorithm using an instrument that retrieves digitally encoded EEG data from videotape and produces signals in referential or bipolar form. They obtained good agreement when they compared referential and Laplacian data derived from bipolar output with the same montages calculated from referential output for the same EEG segment.

Estimation of the EEG power spectrum using MRI T(2) relaxation time in traumatic brain injury

OBJECTIVES

To study the relationship between magnetic resonance imaging (MRI) T(2) relaxation time and the power spectrum of the electroencephalogram (EEG) in long-term follow up of traumatic brain injury.

METHODS

Nineteen channel quantitative electroencephalograms or qEEG, tests of cognitive function and quantitative MRI T(2) relaxation times (qMRI) were measured in 18 mild to severe closed head injured outpatients 2 months to 4.6 years after injury and 11 normal controls. MRI T(2) and the Laplacian of T(2) were then correlated with the power spectrum of the scalp electrical potentials and current source densities of the qEEG.

RESULTS

qEEG and qMRI T(2) were related by a frequency tuning with maxima in the alpha (8-12Hz) and the lower EEG frequencies (0.5-5Hz), which varied as a function of spatial location. The Laplacian of T(2) acted like a spatial-temporal "lens" by increasing the spatial-temporal resolution of correlation between 3-dimensional T(2) and the ear referenced alert but resting spontaneous qEEG.

CONCLUSIONS

The severity of traumatic brain injury can be modeled by a linear transfer function that relates the molecular qMRI to qEEG resonant frequencies.

Topographic time-frequency decomposition of the EEG

Frequency-transformed EEG resting data has been widely used to describe normal and abnormal brain functional states as function of the spectral power in different frequency bands. This has yielded a series of clinically relevant findings. However, by transforming the EEG into the frequency domain, the initially excellent time resolution of time-domain EEG is lost. The topographic time-frequency decomposition is a novel computerized EEG analysis method that combines previously available techniques from time-domain spatial EEG analysis and time-frequency decomposition of single-channel time series. It yields a new, physiologically and statistically plausible topographic time-frequency representation of human multichannel EEG. The original EEG is accounted by the coefficients of a large set of user defined EEG like time-series, which are optimized for maximal spatial smoothness and minimal norm. These coefficients are then reduced to a small number of model scalp field configurations, which vary in intensity as a function of time and frequency. The result is thus a small number of EEG field configurations, each with a corresponding time-frequency (Wigner) plot. The method has several advantages: It does not assume that the data is composed of orthogonal elements, it does not assume stationarity, it produces topographical maps and it allows to include user-defined, specific EEG elements, such as spike and wave patterns. After a formal introduction of the method, several examples are given, which include artificial data and multichannel EEG during different physiological and pathological conditions.

Electroencephalographic coherence analysis in multiple sclerosis: correlation with clinical, neuropsychological, and MRI findings

OBJECTIVE

To explore functional corticocortical connections in multiple sclerosis by means of coherence of the EEG, and to evaluate their correlations with the degree of cognitive impairment and with brain lesion load assessed by MRI.

METHODS

EEG coherence was studied from 28 patients with clinically definite multiple sclerosis. Ten minutes of resting EEG were recorded with 20 scalp electrodes, with binaural reference. FFT power and coherence were calculated in artifact free epochs of 1 second and compared with values from 22 control subjects of comparable age and sex distribution. Patients also underwent MRI (n=27) and neuropsychological examination (n=21).

RESULTS

Compared with controls, patients with multiple sclerosis showed increased theta power in the frontotemporal-central regions (p<0.005). theta Band coherence was decreased between homologous areas (p<0.02). alpha Band coherence was decreased both in the local and long distance connections (p<0.0005). These findings were most striking both in patients with high MRI subcortical lesion load and in patients with cognitive involvement. A significant correlation was found between interhemispheric theta (p=0.02) and alpha (p=0. 017) and anteroposterior alpha (p=0.013) coherence and subcortical MRI lesion load, but not with exclusively periventricular lesion load.

CONCLUSIONS

These findings support the hypothesis that cognitive impairment in multiple sclerosis is mostly dependent on involvement of corticocortical connections related to demyelination and/or axonal loss within the white matter immediately underlying the cortex.

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.

EEG coherence in pathological conditions

Coherence analysis of the electroencephalogram is considered an indicator of functional cortico-cortical connections, which makes it suitable for the neurophysiologic investigation of brain connectivity in normal and pathological conditions. In the clinical environment, coherence analysis has been applied in the study of brain development and in the assessment of diseases potentially involving brain connectivity, such as cortical and subcortical dementia, schizophrenia, and corpus callosum lesions. Whereas coherence decrease, at least for the high-frequency bands, is considered the expression of decreased functional cortico-cortical connections, more work needs to be performed in interpreting coherence increases. A special consideration is also required by technical aspects, such as the recording conditions and the reference used, which may greatly influence the results and need to be accounted for when drawing physiopathological interpretations. At present, whereas coherence analysis resulted successful in differentiating patients groups from the normal population, the specificity of coherence changes in various pathological conditions is questionable at the best. The same limits apply to the diagnostic value of the technique in individual patients.

Psychological and electroencephalographic study in school children with iron deficiency

Two groups were chosen from a randomly selected group of one hundred 6-12 years old primary school children. One group was formed by iron deficient (ID), not anemic children, and a control group (C) by iron replete children. Both groups, matched by age, sex, and sociocultural level, were studied using WISC-R, a computerized test of learning (DEL) and a qEEG. The WISC-R test showed that ID children had significantly lower values in WISC items of information, comprehension and verbal, performance and full scale IQ than C children. On the other hand, the EEG power spectrum showed more theta energy in all leads using Laplacian montage and more delta energy in frontal areas using referential montage in ID than in C children. It was found that beside the well known effect of iron deficiency upon intellectual performance during childhood, the EEG power spectrum of ID children had a slower activity than in iron replete children suggesting a developmental lag and/or a CNS dysfunction.

Three-dimensional tomography of event-related potentials during response inhibition: evidence for phasic frontal lobe activation

OBJECTIVES

Spatial analysis of the evoked brain electrical fields during a cued continuous performance test (CPT) revealed an extremely robust anteriorization of the positivity of a P300 microstate in the NoGo compared to the Go condition (NoGo-anteriorization in a previous study). To allow a neuroanatomical interpretation the NoGo-anteriorization was investigated with a new three-dimensional source tomography method (LORETA) was applied.

METHODS

The CPT contains subsets of stimuli requiring the execution (Go) or the inhibition (NoGo) of a cued motor response which can be considered as mutual control conditions for the event-related potential (ERP) study of inhibitory brain functions 21-channel ERPs were obtained from 10 healthy subjects during a cued CPT, and analyzed with LORETA.

RESULTS

Topographic analyses revealed significantly different scalp distributions between the Go and the NoGo conditions in both P100 and P300 microstates, indicating that already at an early stage different neural assemblies are activated. LORETA disclosed a significant hyperactivity located in the right frontal lobe during the NoGo condition in the P300 microstate.

CONCLUSIONS

The results indicate that right frontal sources are responsible for the NoGo-anteriorization of the scalp P300 which is consistent with animal and human lesion studies of inhibitory brain functions. Furthermore, it demonstrates that frontal activation is confined to a brief microstate and time-locked to phasic inhibitory motor control. This adds important functional and chronometric specificity to findings of frontal activation obtained with PET and Near-Infrared-Spectroscopy studies during the cued CPT, and suggests that these metabolic results are not due to general task demands.

On the realization of an analytic high-resolution EEG

The analytic solution of the harmonic downward continuation of the scalp potential field in an N-shell heterogeneous, but isotropic, spherical volume conductor model has been derived. The objective of this paper was to investigate the realization of a so-called "high-resolution electroencephalogram (EEG)": by enhancing the poor spatial resolution of EEG recordings. To this end, the forward problem for a dipolar source arbitrarily located at the source point Q = Q(rs, phi s, theta s) has been determined in a compact matrix notation. It is possible to transfer the potential field given on the outer surface of a spherically shaped volume conductor to an arbitrary inner surface (e.g., to the cortical surface) under consideration of the electrical and geometrical properties of the model. For the application of the proposed method to real-world problems, the coefficients of the series expansion describing the cortical potential distribution are determined by minimizing the squared curvature of the scalp potential field integrated over the scalp surface. Simulation results for distributed sources show that the proposed method is superior to the surface Laplacian method for interelectrode distances below 2.5 cm.

Generalized background qEEG abnormalities in localized symptomatic epilepsy

Spectral features of EEG background activity were studied in patients with localized symptomatic epilepsy (LSE), with origin in the frontal or temporal lobes. Z-values of high resolution spectra and measures of the parametric (xi alpha) model of the EEG were obtained for all 10/20 System leads and were compared with those obtained in a control group. Comparisons were performed between syndromic variants of LSE and between subgroups of patients with or without paroxysmal activity in their digital EEGs (dEEG). Marked reduction of the energy in the alpha range and a mild increase in the theta range were found in the patients, unrelated to the syndromic variant of the epilepsy. These deviations from normality were widespread on the scalp and were not related to antiepileptic medication. Non-parametric testing showed a positive correlation between the magnitude of the quantitative EEG abnormalities and the amount of paroxysmal activity in the dEEG. Slowing of the mean frequency of alpha components of the spectra, an actual decrease of power in the alpha range and an increase in the theta range explained the results. The most striking finding of this paper is that focal epileptogenesis may have a generalized impact in the frequency composition of EEG.

EEG coherence in Alzheimer's disease

EEG coherence can be used to evaluate the functionality of cortical connections and to get information about the synchronization of the regional cortical activity. We studied EEG coherence in patients affected by clinically probable Alzheimer's disease (AD) in order to quantify the modifications in the cortico-cortical or cortico-subcortical connections. The EEGs were recorded in 10 AD patients (with mild or moderate degrees of dementia) and in 10 normal age-matched subjects, at rest and eye-closed, from 16 electrodes with linked-ears reference. Spectral parameters and coherence were calculated by a multichannel autoregressive model using 50 artifact-free epochs, 1 s duration each. Alpha coherence was significantly decreased in 6 patients, the decrease being more accentuated in the area near the electrode taken into account; a significant delta coherence increase was found in a few patients between frontal and posterior regions. The AD group showed a significant decrease of alpha band coherence, in particular in temporo-parieto-occipital areas, more evident in patients with a more severe cognitive impairment. These abnormalities could reflect two different pathophysiological changes: the alpha coherence decrease could be related to alterations in cortico-cortical connections, whereas the delta coherence increase could be related to the lack of influence of subcortical cholinergic structures on cortical electrical activity.

EEG coherency. I: Statistics, reference electrode, volume conduction, Laplacians, cortical imaging, and interpretation at multiple scales

Several methodological issues which impact experimental design and physiological interpretations in EEG coherence studies are considered, including reference electrode and volume conduction contributions to erroneous coherence estimates. A new measure, 'reduced coherency', is introduced as the difference between measured coherency and the coherency expected from uncorrelated neocortical sources, based on simulations and analytic-statistical studies with a volume conductor model. The concept of reduced coherency is shown to be in semi-quantitative agreement with experimental EEG data. The impact of volume conduction on statistical confidence intervals for coherence estimates is discussed. Conventional reference, average reference, bipolar, Laplacian, and cortical image coherencies are shown to be partly independent measures of neocortical dynamic function at different spatial scales, due to each method's unique spatial filtering of intracranial source activity.

Evolution of cerebral edema and its relationship with power in the theta band

In previous papers we have proposed that in patients with space-occupying lesions, delta power was related with the volume of the lesion and theta power with the volume of the edema. In this report we analyze the evolution of 10 patients with space-occupying lesions in whom we measured the volume of the lesion and of the edema before and after treatment that produced changes in these volumes. EEGs were recorded in the leads of the 10-20 system referenced to linked earlobes. Delta and theta powers were calculated for voltage and current source densities (CSD) and compared with age-norms to compute conventional Z-maps. These maps provide probability statements about the deviation of observed values from the norm. Rank correlations between the change in the volume of the lesion before and after treatment and the change in Z-values before and after treatment were significant only in the delta band. However, rank correlations between the change in the volume of the edema and the change in EEG Z-values were only significant in the theta band. These correlations were higher for CSD than for voltage estimates. We also observed that the site of the lesion and of the edema was better represented by CSD maps than by voltage maps. These results are also in agreement with our previous reports, in which we observed more precise localization of brain lesions by CSD than by voltage estimates.

The effect of reference-electrode choice on the spatial resolution of topographical potential maps in the discrimination of deep cerebral sources

Although scalp potential distributions do not uniquely determine the location and configuration of neural generators, they are important because they provide the necessary conditions that any hypothesized sources must satisfy and suggest a basis for testing alternate source hypotheses. One problem that could confound the correct interpretation of scalp potentials is the choice of reference electrode. Changing the reference may make activity patterns and waveform components appear and disappear (Pascual-Marqui et al. (1988) Int. J. Neurosci., 43: 237-249). The cortical imaging technique (CIT), a method for approximating potential fields on the cortical surface, was used to test the effects of the choice of reference electrode on these fields. Simulated and empirical evoked potential scalp-recorded referential data were mathematically analyzed for the case in which the reference (linked-ears) was arbitrarily assumed to be at zero potential, and the case in which the reference was the 'average' electrode, the arithmetic mean of all of the scalp-recorded voltages in the referential montage. The results for the two references were similar. This is encouraging because potential measurements relative to a point at infinity (zero potential) are never available and the assumption that any actual reference used for a recording is at zero potential is therefore suspect.

Comparison of Z and multivariate statistical brain electromagnetic maps for the localization of brain lesions

Conventional Z maps provide probability statements about the deviation of observed values from the norm. Galán et al. (1994) introduced Simultaneous Significance Probability Scales to detect abnormalities over the whole map, making use of the information provided by the topographic structure of dependencies. They also described multivariate brain electromagnetic (MBE) maps for compact presentation of complex spatio-temporal information. In this paper, using the distance-based localization receiver operating characteristic curves (DL-ROC curves), we compare the localization provided by computed tomography with that provided by Z and MBE maps in 61 patients with brain lesions. Maps were calculated for absolute power and relative power in delta, theta, alpha and beta bands for voltage and current source densities (CSD). In each patient, all maps were compared and the map with the highest value of the area of the DL-ROC curve was considered to be the "best map." Z maps of CSD were the "best maps" in 24 patients. In the voltage montage, we observed that multivariate maps add some information not contained in the Z maps. However, for CSD, Z maps were more accurate than multivariate maps. A very consistent finding was the observation that lesions were better detected by maps analyzing the delta band, while edema was better represented by maps in the theta range.

Interelectrode coherences from nearest-neighbor and spherical harmonic expansion computation of laplacian of scalp potential

Interchannel coherence is a measure of spatial extent of and timing relationships among cerebral electroencephalogram (EEG) generators. Interchannel coherence of referentially recorded potentials includes components due to volume conduction and reference site activity. The laplacian of the potential is reference independent and decreases the contribution of volume conduction. Interchannel coherences of the laplacian should, therefore, be less than those of referentially recorded potentials. However, methods used to compute the laplacian involve forming linear combinations of multiple recorded potentials, which may inflate interchannel coherences. WE compared 3 methods of computing the laplacian: (1) modified Hjorth (4 equidistant neighbors to each electrode), (2) Taylor's series (4 nonequidistant neighbors), and (3) spherical harmonic expansion (SHE). Average interchannel coherence introduced by computing the laplacian was less for nearest-neighbor methods (0.0207 +/- 0.0766) but still acceptable for the SHE method (0.0337 +/- 0.0865). Average interchannel coherence for simulated EEG (random data plus a common 10 Hz signal) was less for laplacian than for referential data because of removal of the common referential signal. Interchannel coherences of background EEG and partial seizure activity were less with the laplacian (any method) than with referential recordings. Laplacians calculated from the SHE do not demonstrate excessively large interchannel coherences, as have been reported for laplacians from spherical splines.

Modeling the electroencephalogram by means of spatial spline smoothing and temporal autoregression

A spatial-temporal model for the description of electroencephalographic (EEG) data is introduced that combines smooth reconstruction in the spatial domain and autoregressive representation in the time domain. Its spatial aspect is formulated in a general framework that covers interpolation, smoothing, and regression. Contrary to the multivariate time series models used for EEG analysis up to date, the introduced model provides a smooth spatial reconstruction of the EEG cross-spectrum, keeping the condition of nonnegative definiteness. As an instance of practical importance, the case in which the spatial reconstruction is based on spherical splines is developed in detail. Illustrative examples are presented that show the flexibility of the model to describe both normal and abnormal EEG data.

High resolution quantitative EEG analysis

High resolution spectral methods are explored as an alternative to broad band spectral parameters (BBSP) in quantitative EEG analysis. In a previous paper (Valdes et al. 1990b) regression equations ("Developmental surfaces") were introduced to characterize the age-frequency distribution of the mean and standard deviation of the log spectral EEG power in a normative sample. These normative surfaces allow the calculation of z transformed spectra for all derivations of the 10/20 system and z maps for each frequency. Clinical material is presented that illustrates how these procedures may pinpoint frequencies of abnormal brain activity and their topographic distribution, avoiding the frequency and spatial "smearing" that may occur using BBSP. The increased diagnostic accuracy of high resolution spectral methods is demonstrated by means of receiver operator characteristic (ROC) curve analysis. Procedures are introduced to avoid type I error inflation due to the use of more variables in this type of procedure.

Brain source imaging of focal and multifocal epileptiform EEG activity

Brain electric source analysis (BESA) of the scalp EEG has been used to identify multiple equivalent current sources in the brain during during interictal spikes and seizure onset. To obviate the need for fitting dipole sources to every EEG segment, a new method has been developed on the basis of multiple fixed dipoles, each designed to emphasize functional imaging of particular cortical areas. "FOCUS" can quickly display EEG in various montages including new "sources montages" which provide a high sensitivity for source currents near each dipole while largely suppressing contributions from other brain areas. By comparing this "source EEG" to routine digital EEG in patients with complex partial epilepsy, we have observed that "FOCUS" can more readily determine whether an epileptiform discharge is consistent with a discrete or multifocal generator, characterize likely cerebral source(s), differentiate between spikes and seizures of mesio-basal versus lateral temporal or frontal origin, and estimate the presence and direction of propagation from source potential timing differences. Improved non-invasive EEG evaluations of partial epilepsy will undoubtedly result from this advance.

Uniqueness of the generators of brain evoked potential maps

This study considers the uniqueness of neuronal generators of human brain evoked potentials measured on the scalp using the physical and mathematical properties of the volume conductor model. The results are applicable to a realistic, nonhomogeneous head shape where the potential map is known on a continuous set of points on the scalp. It is shown that sources which occupy "zero volume" in space such as point dipoles or sources distributed on an open surface or a line are uniquely defined by the potential maps. Finite volume nonoverlapping sources are also uniquely defined by their potential map. However, there are infinitely many different but overlapping sources which can create the same map. Several examples of such sources are provided. It is shown that there is a unique, minimum volume source which can be defined in this case. Results suggest that if a reconstruction of the sources starts from a continuous scalp map (obtained by interpolation of the data between electrode sites), one can obtain unique results concerning the source parameters that are not available in a search for a source whose potential map fits only at a discrete set of points.

Correlation between computed tomography and voltage and current source density spectral EEG parameters in patients with brain lesions

In a group of patients with space-occupying brain lesions, CT measurements were correlated with absolute power (AP) and relative power (RP) of the delta, theta, alpha and beta EEG bands, calculated from the raw EEG potentials (EEGp) and from the Laplacian estimates also called "current source densities" (CSD). Rank correlations were calculated between the number of abnormal values in each band and the following CT measures: volume of the lesion and of the edema, density of the edema, percentage of ventricular collapse and midline shift. Abnormal spectral values are those which are significantly higher than the norm for the same age, in the delta and theta bands, and significantly lower in the alpha and beta bands. Spectral parameters obtained from the CSD showed higher correlations with CT measures than those calculated from the EEGp. In the Laplacian, all CT measures had a significant correlation with delta AP. Theta AP was significantly correlated with the volume and density of the edema, as well as with midline shift. Significant correlations were also observed with delta and alpha RP. However, changes in RP were considered to be a consequence of the increase in delta AP. Canonical correlation analyses between AP and RP calculated from EEGp or CSD and the first 3 CT measures showed that the volume of the lesion was only correlated with delta AP and RP. The volume and density of the edema showed a significant correlation with delta, theta and alpha AP calculated from EEGp and only with theta and alpha AP in the Laplacian. Since the EEGp tends to produce a more extensive and diffuse picture of abnormality, whereas the Laplacian acts as a spatial filter emphasizing local sources over distant sources, we concluded that edema is related not to delta activity, but to the theta and alpha power.

Recognition potential: sensitivity to visual field stimulated

The recognition potential (RP) was distinguished from P3 and eye blink responses by its sensitivity to visual area stimulated. Images were flashed in upper and lower hemifields. Current source density profiles were computed, using 16 midline scalp electrodes. For P3 and eye blink profiles, the hemifield stimulated was not a significant factor. For the recognition potential, upper and lower field stimulation produced radically different profiles. An improved recognition potential signal was obtained by a new mathematical procedure. It used the difference in sensitivity to visual area stimulated to reject P3 and eye blink responses.

Determination of 10-20 system electrode locations using magnetic resonance image scanning with markers

We determined locations of 33 scalp electrodes used for electroencephalographic (EEG) recording by placing markers in the positions determined by the 10-20 system and performing magnetic resonance image (MRI) scanning on volunteer subjects. Small Vaseline-filled capsules glued on the scalp with collodion produced easily delineated regions of increased signal on standard MRI head images. Measurements of each capsule's coordinates in 3 dimensions were made from MRI scans. A spherical surface was fitted through the marker positions, giving an average radius and an origin (center of sphere). The coordinate axes were rotated to ensure that electrode Cz was on the z-axis and that the y-axis was oriented in the posterior-anterior direction. Two spherical (angular) coordinates were determined for each electrode. Spherical electrode coordinates for different subjects differed by less than 20 degrees in all cases. An average and standard deviation of the spherical coordinates were calculated for each electrode. Standard deviations of several degrees were obtained. The average spherical coordinates obtained were close to those expected on the basis of applying the 10-20 system of placement to an ideal sphere. These measurements provide data necessary for various analyses of EEG performed to help localize epileptic foci.

Localization error in biomedical imaging

Measures of false positive (FP) and false negative (FN) localization error are defined to assess the accuracy of diagnostic imaging procedures. These measures involve the weighting of FP and FN pixels in accordance to their distances from the true localization of the lesion and the region detected as abnormal by the classifier. The distance-based localization receiver operating characteristic (DL-ROC) curve is defined to describe the dependence of the FP and FN localization measures on the classifier's decision threshold. A computer system is presented for the analysis of localization experiments according to these concepts. As an illustration, the accuracy of two types of brain electric topographic montage is studied in the localization of brain tumors and sites of stroke.

Functional imaging and localization of electromagnetic brain activity

Functional imaging of electric brain activity requires specific models to transform the signals recorded at the surface of the human head into an image. Two categories of model are available: single-time-point and spatio-temporal methods. The instantaneous methods rely only on the few voltage differences measured at one sampling point. To create a spatial image from this limited information, they require strict assumptions that rarely conform with the underlying physiology. Spatio-temporal models create two kinds of images: first, a spatial image of discrete equivalent multiple dipoles or regional sources, and second, an image of source current waveforms that reflect the temporal dynamics of the brain activity in circumscribed areas. The accuracy of the spatial image is model dependent and limited, but it can be validated from the spatio-temporal data by the "regional source imaging" technique, introduced here. The source waveforms are linear combinations of the scalp waveforms, and thus, specific derivations which image local brain activities at a macroscopic level. Brain source imaging of somatosensory evoked potentials revealed temporally overlapping activities from the brainstem, thalamus and from multiple sources in the region of the contralateral somatosensory projection areas.