Electric potential produced by a dipole in a homogeneous conducting sphere

Gut Microbiome Redox Sensors With Ultrasonic Wake-Up and Galvanic Coupling Wireless Links

Tools to measure in vivo redox activity of the gut microbiome and its influence on host health are lacking. In this paper, we present the design of new in vivo gut oxidation-reduction potential (ORP) sensors for rodents, to study host-microbe and microbe-environment interactions throughout the gut. These are the first in vivo sensors to combine ultrasonic wake-up and galvanic coupling telemetry, allowing for sensor miniaturization, experiment flexibility, and robust wireless measurements in live rodents. A novel study of in situ ORP along the intestine reveals biogeographical redox features that the ORP sensors can uniquely access in future gut microbiome studies.

Wearable Measurement of ECG Signals Based on Smart Clothing

Smart clothing that can measure electrocardiogram (ECG) signals and monitor the health status of people meets the needs of our increasingly aging society. However, the conventional measurement of ECG signals is complicated and its electrodes can cause irritation to the skin, which makes the conventional measurement method unsuitable for applications in smart clothing. In this paper, a novel wearable measurement of ECG signals is proposed. There are only three ECG textile electrodes knitted into the fabric of smart clothing. The acquired ECG signals can be transmitted to a smartphone via Bluetooth, and they can also be sent out to a PC terminal by a smartphone via WiFi or Internet. To get more significant ECG signals, the ECG differential signal between two electrodes is calculated based on a spherical volume conductor model, and the best positions on the surface of a human body for two textile electrodes to measure ECG signals are simulated by using the body-surface potential mapping (BSPM) data. The results show that position 12 in the lower right and position 11 in the upper left of the human body are the best for the two electrodes to measure ECG signals, and the presented wearable measurement can obtain good performance when one person is under the conditions of sleeping and jogging.

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.

Effect of EEG Referencing Methods on Auditory Mismatch Negativity

Auditory event-related potentials (ERPs) have consistently been used in the investigation of auditory and cognitive processing in the research and clinical laboratories. There is currently no consensus on the choice of appropriate reference for auditory ERPs. The most commonly used references in auditory ERP research are the mathematically linked-mastoids (LM) and average referencing (AVG). Since LM and AVG referencing procedures do not solve the issue of electrically-neutral reference, Reference Electrode Standardization Technique (REST) was developed to create a neutral reference for EEG recordings. The aim of the current research is to compare the influence of the reference on amplitude and latency of auditory mismatch negativity (MMN) as a function of magnitude of frequency deviance across three commonly used electrode montages (16, 32, and 64-channel) using REST, LM, and AVG reference procedures. The current study was designed to determine if the three reference methods capture the variation in amplitude and latency of MMN with the deviance magnitude. We recorded MMN from 12 normal hearing young adults in an auditory oddball paradigm with 1,000 Hz pure tone as standard and 1,030, 1,100, and 1,200 Hz as small, medium and large frequency deviants, respectively. The EEG data recorded to these sounds was re-referenced using REST, LM, and AVG methods across 16-, 32-, and 64-channel EEG electrode montages. Results revealed that while the latency of MMN decreased with increment in frequency of deviant sounds, no effect of frequency deviance was present for amplitude of MMN. There was no effect of referencing procedure on the experimental effect tested. The amplitude of MMN was largest when the ERP was computed using LM referencing and the REST referencing produced the largest amplitude of MMN for 64-channel montage. There was no effect of electrode-montage on AVG referencing induced ERPs. Contrary to our predictions, the results suggest that the auditory MMN elicited as a function of increments in frequency deviance does not depend on the choice of referencing procedure. The results also suggest that auditory ERPs generated using REST referencing is contingent on the electrode arrays more than the AVG referencing.

Multi-channel algorithms for epileptic high-frequency oscillation detection

Short-lasting rhythmic activity in intracranial electroencephalogram (iEEG) in the frequency range of 80 to 500 Hz is regarded to be a promising biomarker of epileptogenicity. This activity is referred to as high-frequency oscillation (HFO), and its detection from iEEG is considered the first step to several applications. In this study, several multi-channel algorithms for HFO detection are proposed. With the proposed multi-channel statistics and threshold determination scheme, the algorithms allow HFO detection to be performed without breaking the iEEG channel structure and the detection threshold to be determined automatically. Experimental simulation results illustrate the advantage of the proposed algorithms over existing single-channel-based approaches.

SEEG dipole source localization based on an empirical Bayesian approach taking into account forward model uncertainties

Electromagnetic brain source localization consists in the inversion of a forward model based on a limited number of potential measurements. A wide range of methods has been developed to regularize this severely ill-posed problem and to reduce the solution space, imposing spatial smoothness, anatomical constraint or sparsity of the activated source map. This last criteria, based on physiological assumptions stating that in some particular events (e.g., epileptic spikes, evoked potential) few focal area of the brain are simultaneously actives, has gained more and more interest. Bayesian approaches have the ability to provide sparse solutions under adequate parametrization, and bring a convenient framework for the introduction of priors in the form of probabilistic density functions. However the quality of the forward model is rarely questioned while this parameter has undoubtedly a great influence on the solution. Its construction suffers from numerous approximation and uncertainties, even when using realistic numerical models. In addition, it often encodes a coarse sampling of the continuous solution space due to the computational burden its inversion implies. In this work we propose an empirical Bayesian approach to take into account the uncertainties of the forward model by allowing constrained variations around a prior physical model, in the particular context of SEEG measurements. We demonstrate on simulations that the method enhance the accuracy of the source time-course estimation as well as the sparsity of the resulting source map. Results on real signals prove the applicability of the method in real contexts.

Is the Surface Potential Integral of a Dipole in a Volume Conductor Always Zero? A Cloud Over the Average Reference of EEG and ERP

Currently, average reference is one of the most widely adopted references in EEG and ERP studies. The theoretical assumption is the surface potential integral of a volume conductor being zero, thus the average of scalp potential recordings might be an approximation of the theoretically desired zero reference. However, such a zero integral assumption has been proved only for a spherical surface. In this short communication, three counter-examples are given to show that the potential integral over the surface of a dipole in a volume conductor may not be zero. It depends on the shape of the conductor and the orientation of the dipole. This fact on one side means that average reference is not a theoretical 'gold standard' reference, and on the other side reminds us that the practical accuracy of average reference is not only determined by the well-known electrode array density and its coverage but also intrinsically by the head shape. It means that reference selection still is a fundamental problem to be fixed in various EEG and ERP studies.

Incorporating priors for EEG source imaging and connectivity analysis

Electroencephalography source imaging (ESI) is a useful technique to localize the generators from a given scalp electric measurement and to investigate the temporal dynamics of the large-scale neural circuits. By introducing reasonable priors from other modalities, ESI reveals the most probable sources and communication structures at every moment in time. Here, we review the available priors from such techniques as magnetic resonance imaging (MRI), functional MRI (fMRI), and positron emission tomography (PET). The modality's specific contribution is analyzed from the perspective of source reconstruction. For spatial priors, EEG-correlated fMRI, temporally coherent networks (TCNs) and resting-state fMRI are systematically introduced in the ESI. Moreover, the fiber tracking (diffusion tensor imaging, DTI) and neuro-stimulation techniques (transcranial magnetic stimulation, TMS) are also introduced as the potential priors, which can help to draw inferences about the neuroelectric connectivity in the source space. We conclude that combining EEG source imaging with other complementary modalities is a promising approach toward the study of brain networks in cognitive and clinical neurosciences.

Combining bayesian source imaging with equivalent dipole approach to solve the intracranial EEG source localization problem

The brain source localization problem has been extensively studied in the past years, yielding a large panel of methodologies, each bringing their own strengths and weaknesses. Combining several of these approaches might help in enhancing their respective performance. Our study is carried out in the particular context of intracranial recordings, with the objective to explain the measurements based on a reduced number of dipolar activities. We take benefit of the sparse nature of the Bayesian approaches to separate the noise from the source space, and to distinguish between several source contributions on the electrodes. This first step provides accurate estimates of the dipole projections, which can be used as an entry to an equivalent current dipole fitting procedure. We demonstrate on simulations that the localization results are significantly enhanced by this post-processing step when up to five dipoles are activated simultaneously.

Monitoring brain damage using bioimpedance technique in a 3D numerical model of the head

Disturbance in the blood supply to the brain causes a stroke or cerebrovascular accident. This can be due to ischemia caused by blockage (thrombosis, arterial embolism) or a hemorrhage. In this study, the feasibility of basic electrical impedance technique for monitoring such damage was analyzed using a computerized model. Simulations were conducted on a realistic 3D numerical model of the head. Tissues were assumed to act as linear isotropic volume conductors, and the quasi-static approximation was applied. Electrical potentials were calculated by solving Poisson's equation, using the finite volume method and the successive over relaxation method. Left-right asymmetry was calculated for several conductivities and volumes of the damaged region. The results were compared with the left-right asymmetry in a head model with normal brain. A negative asymmetry was revealed for blockage (i.e. the potential amplitude over the ischemic hemisphere was greater than that over the intact hemisphere). In case of hemorrhage, a positive asymmetry was found. Furthermore, correlation was found between the location of the damaged region and the electrodes with significant asymmetry. The 3D numerical simulations revealed that the electrical conductivity and the size of the damaged tissue have an effect on the left-right asymmetry of the surface potential.

Evaluating dipolar source localization feasibility from intracerebral SEEG recordings

Stereo-electroencephalography (SEEG) is considered as the golden standard for exploring targeted structures during pre-surgical evaluation in drug-resistant partial epilepsy. The depth electrodes, inserted in the brain, consist of several collinear measuring contacts (sensors). Clinical routine analysis of SEEG signals is performed on bipolar montage, providing a focal view of the explored structures, thus eliminating activities of distant sources that propagate through the brain volume. We propose in this paper to exploit the common reference SEEG signals. In this case, the volume propagation information is preserved and electrical source localization (ESL) approaches can be proposed. Current ESL approaches used to localize and estimate the activity of the neural generators are mainly based on surface EEG/MEG signals, but very few studies exist on real SEEG recordings, and the case of equivalent current dipole source localization has not been explored yet in this context. In this study, we investigate the influence of volume conduction model, spatial configuration of SEEG sensors and level of noise on the ESL accuracy, using a realistic simulation setup. Localizations on real SEEG signals recorded during intracerebral electrical stimulations (ICS, known sources) as well as on epileptic interictal spikes are carried out. Our results show that, under certain conditions, a straightforward approach based on an equivalent current dipole model for the source and on simple analytical volume conduction models yields sufficiently precise solutions (below 10mm) of the localization problem. Thus, electrical source imaging using SEEG signals is a promising tool for distant brain source investigation and might be used as a complement to routine visual interpretations.

Partial information transmission can be found in music attributes

Previous studies have proved that partial information transmission can be found between intensity and pitch. In our last study, it was demonstrated that the timbre attribute can be transmitted as partial information between timbre and intensity. We manipulated the two attributes of stimulus, namely, timbre (piano vs. violin) and pitch (high vs. low), to find out whether they also have partial information transmission. We used the two-choice ‘go/no-go’ paradigm, which included more ‘go’ trials of timbre. Our result showed that lateralized readiness potentials were elicited in ‘no-go’ trials, which meant that the timbre attribute had been transmitted to the response preparation stage before the intensity attribute was processed in the stimuli identification stage. This result supports the asynchronous discrete coding model in information processing. Therefore, we suggest that partial information transmission can be found in music attributes including timbre, intensity, and pitch.

Influence of the stereo-EEG sensors setup and of the averaging on the dipole localization problem

While scalp EEG/MEG source imaging have been extensively studied in the last two decades, the case of source localization from invasive measurements has resulted in few works to date. Yet there is a lot to gain from stereo-electroencephalographic (SEEG) recordings, providing high signal to noise ratio measurements of the explored brain structures. The SEEG setup consists in multi-contact electrodes inserted in the brain volume, each containing a dozen of collinear measuring contacts. This particular setup raises the question of the conditioning of the inverse problem. In recent works, we have evaluated the feasibility to localize a single dominant equivalent dipole facing different sensors and noise configurations. We deepen here the analysis by evaluating the influence of the chosen subset of sensors and of the number of averaged time samples on the accuracy of the localization. We conduct experiments on simulated data as well as on real epileptic spikes, illustrating the trade off to be made between these two factors.

A review of EEG and MEG for brainnetome research

The majority of brain activities are performed by functionally integrating separate regions of the brain. Therefore, the synchronous operation of the brain's multiple regions or neuronal assemblies can be represented as a network with nodes that are interconnected by links. Because of the complexity of brain interactions and their varying effects at different levels of complexity, one of the corresponding authors of this paper recently proposed the brainnetome as a new -ome to explore and integrate the brain network at different scales. Because electroencephalography (EEG) and magnetoencephalography (MEG) are noninvasive and have outstanding temporal resolution and because they are the primary clinical techniques used to capture the dynamics of neuronal connections, they lend themselves to the analysis of the neural networks comprising the brainnetome. Because of EEG/MEG's applicability to brainnetome analyses, the aim of this review is to identify the procedures that can be used to form a network using EEG/MEG data in sensor or source space and to promote EEG/MEG network analysis for either neuroscience or clinical applications. To accomplish this aim, we show the relationship of the brainnetome to brain networks at the macroscale and provide a systematic review of network construction using EEG and MEG. Some potential applications of the EEG/MEG brainnetome are to use newly developed methods to associate the properties of a brainnetome with indices of cognition or disease conditions. Associations based on EEG/MEG brainnetome analysis may improve the comprehension of the functioning of the brain in neuroscience research or the recognition of abnormal patterns in neurological disease.

Local temporal correlation common spatial patterns for single trial EEG classification during motor imagery

Common spatial pattern (CSP) is one of the most popular and effective feature extraction methods for motor imagery-based brain-computer interface (BCI), but the inherent drawback of CSP is that the estimation of the covariance matrices is sensitive to noise. In this work, local temporal correlation (LTC) information was introduced to further improve the covariance matrices estimation (LTCCSP). Compared to the Euclidean distance used in a previous CSP variant named local temporal CSP (LTCSP), the correlation may be a more reasonable metric to measure the similarity of activated spatial patterns existing in motor imagery period. Numerical comparisons among CSP, LTCSP, and LTCCSP were quantitatively conducted on the simulated datasets by adding outliers to Dataset IVa of BCI Competition III and Dataset IIa of BCI Competition IV, respectively. Results showed that LTCCSP achieves the highest average classification accuracies in all the outliers occurrence frequencies. The application of the three methods to the EEG dataset recorded in our laboratory also demonstrated that LTCCSP achieves the highest average accuracy. The above results consistently indicate that LTCCSP would be a promising method for practical motor imagery BCI application.

Why do we need to use a zero reference? Reference influences on the ERPs of audiovisual effects

Using ERPs in the audiovisual stimulus, the current study is the first to investigate the influence of the reference on experimental effects (between two conditions). Three references, the average reference (AR), the mean mastoid (MM), and a new infinity zero reference (IR), were comparatively investigated via ERPs, statistical parametric scalp mappings (SPSM), and LORETA. Specifically, for the N1 (170-190 ms), the SPSM results showed an anterior distribution for MM, a posterior distribution for IR, and both anterior and posterior distributions for AR. However, the circumstantial evidence provided by LORETA is consistent with SPSM of IR. These results indicated that the newly developed IR could provide increased accuracy; thus, we recommend IR for future ERP studies.

Attentional orienting and response inhibition: insights from spatial-temporal neuroimaging

Attentional orienting and response inhibition have largely been studied separately. Each has yielded important findings, but controversy remains concerning whether they share any neurocognitive processes. These conflicting findings may originate from two issues: (1) at the cognitive level, attentional orienting and response inhibition are typically studied in isolation; and (2) at the technological level, a single neuroimaging method is typically used to study these processes. This article reviews recent achievements in both spatial and temporal neuroimaging, emphasizing the relationship between attentional orienting and response inhibition. We suggest that coordinated engagement, both top-down and bottom-up, serves as a common neural mechanism underlying these two cognitive processes. In addition, the right ventrolateral prefrontal cortex may play a major role in their harmonious operation.

Scale-free brain-wave music from simultaneously EEG and fMRI recordings

In the past years, a few methods have been developed to translate human EEG to music. In 2009, PloS One 4 e5915, we developed a method to generate scale-free brainwave music where the amplitude of EEG was translated to music pitch according to the power law followed by both of them, the period of an EEG waveform is translated directly to the duration of a note, and the logarithm of the average power change of EEG is translated to music intensity according to the Fechner's law. In this work, we proposed to adopt simultaneously-recorded fMRI signal to control the intensity of the EEG music, thus an EEG-fMRI music is generated by combining two different and simultaneous brain signals. And most importantly, this approach further realized power law for music intensity as fMRI signal follows it. Thus the EEG-fMRI music makes a step ahead in reflecting the physiological process of the scale-free brain.

Integration of consonant and pitch processing as revealed by the absence of additivity in mismatch negativity

Consonants, unlike vowels, are thought to be speech specific and therefore no interactions would be expected between consonants and pitch, a basic element for musical tones. The present study used an electrophysiological approach to investigate whether, contrary to this view, there is integrative processing of consonants and pitch by measuring additivity of changes in the mismatch negativity (MMN) of evoked potentials. The MMN is elicited by discriminable variations occurring in a sequence of repetitive, homogeneous sounds. In the experiment, event-related potentials (ERPs) were recorded while participants heard frequently sung consonant-vowel syllables and rare stimuli deviating in either consonant identity only, pitch only, or in both dimensions. Every type of deviation elicited a reliable MMN. As expected, the two single-deviant MMNs had similar amplitudes, but that of the double-deviant MMN was also not significantly different from them. This absence of additivity in the double-deviant MMN suggests that consonant and pitch variations are processed, at least at a pre-attentive level, in an integrated rather than independent way. Domain-specificity of consonants may depend on higher-level processes in the hierarchy of speech perception.

Bioimpedance technique for monitoring cerebral artery stenosis in a 3D numerical model of the head

Insufficient blood supply to the brain causes a transient ischemic attack (TIA) or a stroke. One of the causes to insufficient blood supply is cerebral artery stenosis. In this study, the feasibility of bioimpedance for monitoring such stenosis was analyzed. Simulations were conducted on a realistic numerical model of the head, focusing on the left middle cerebral artery (LMCA). Tissues were assumed to act as linear isotropic volume conductors, and the quasi-static approximation was applied. Electrical potentials were calculated by solving Poisson's equation, using the finite volume method (FVM) and the successive over relaxation (SOR) method. The best sensitivity found was 0.471 μV/% stenosis, using this electrode configuration: one injector near the left eye and the other injector near the right ear, one measurement position near the left eye and the other one in the right ear, keeping a distance of at least 2.5 cm between measurement and injection positions. The maximal sensitivity achieved in the numerical model under the applied assumptions supports the feasibility of bioimpedance technique for monitoring cerebral artery stenosis. However, according to sensitivity [1/m(4)] maps, calculated for the preferable electrode configurations, the measurements' specificity to the stenosis degree might be inadequate and should be further studied.

Multimodal functional network connectivity: an EEG-fMRI fusion in network space

EEG and fMRI recordings measure the functional activity of multiple coherent networks distributed in the cerebral cortex. Identifying network interaction from the complementary neuroelectric and hemodynamic signals may help to explain the complex relationships between different brain regions. In this paper, multimodal functional network connectivity (mFNC) is proposed for the fusion of EEG and fMRI in network space. First, functional networks (FNs) are extracted using spatial independent component analysis (ICA) in each modality separately. Then the interactions among FNs in each modality are explored by Granger causality analysis (GCA). Finally, fMRI FNs are matched to EEG FNs in the spatial domain using network-based source imaging (NESOI). Investigations of both synthetic and real data demonstrate that mFNC has the potential to reveal the underlying neural networks of each modality separately and in their combination. With mFNC, comprehensive relationships among FNs might be unveiled for the deep exploration of neural activities and metabolic responses in a specific task or neurological state.

Physical modeling of pulse artefact sources in simultaneous EEG/fMRI

The collection of electroencephalography (EEG) data during simultaneous functional magnetic resonance imaging (fMRI) is impeded by large artefacts in the EEG recordings, with the pulse artefact (PA) being particularly challenging because of its persistence even after application of artefact correction algorithms. Despite several possible causes of the PA having been hypothesized, few studies have rigorously quantified the contributions from the different putative sources. This article presents analytic expressions and simulations describing two possible sources of the PA corresponding to different movements in the strong static field of the MR scanner: cardiac-pulse-driven head rotation and blood-flow-induced Hall voltages. Models of head rotation about a left-right axis and flow in a deep artery running in the anterior-posterior direction reproduced properties of the PA including the left/right spatial variation of polarity. Of these two sources, head rotation was shown to be the most likely source of the PA with simulated magnitudes of >200 muV being generated at 3 T, similar to the in vivo PA magnitudes, for an angular velocity of just 0.5 degrees /s. Smaller artefact voltages of less than 10 muV were calculated for flow in a model artery with physical characteristics similar to the internal carotid artery. A deeper physical understanding of the PA is a key step in working toward production of higher fidelity EEG/fMRI data: analytic expressions for the artefact voltages can guide a redesign of the wiring layout on EEG caps to minimize intrinsic artefact pickup, while simulated artefact maps could be incorporated into selective filters.

A Matlab library for solving quasi-static volume conduction problems using the boundary element method

The boundary element method (BEM) is commonly used in the modeling of bioelectromagnetic phenomena. The Matlab language is increasingly popular among students and researchers, but there is no free, easy-to-use Matlab library for boundary element computations. We present a hands-on, freely available Matlab BEM source code for solving bioelectromagnetic volume conduction problems and any (quasi-)static potential problems that obey the Laplace equation. The basic principle of the BEM is presented and discretization of the surface integral equation for electric potential is worked through in detail. Contents and design of the library are described, and results of example computations in spherical volume conductors are validated against analytical solutions. Three application examples are also presented. Further information, source code for application examples, and information on obtaining the library are available in the WWW-page of the library: (http://biomed.tkk.fi/BEM).

Representation of bioelectric current sources using Whitney elements in the finite element method

Bioelectric current sources of magneto- and electroencephalograms (MEG, EEG) are usually modelled with discrete delta-function type current dipoles, despite the fact that the currents in the brain are naturally continuous throughout the neuronal tissue. In this study, we represent bioelectric current sources in terms of Whitney-type elements in the finite element method (FEM) using a tetrahedral mesh. The aim is to study how well the Whitney elements can reproduce the potential and magnetic field patterns generated by a point current dipole in a homogeneous conducting sphere. The electric potential is solved for a unit sphere model with isotropic conductivity and magnetic fields are calculated for points located on a cap outside the sphere. The computed potential and magnetic field are compared with analytical solutions for a current dipole. Relative difference measures between the FEM and analytical solutions are less than 1%, suggesting that Whitney elements as bioelectric current sources are able to produce the same potential and magnetic field patterns as the point dipole sources.

The magnetic field inside special conducting geometries due to internal current

In view of recent attempts to directly and noninvasively detect the neuromagnetic field, we derive an analytic formula for the magnetic field inside a homogeneous conducting sphere due to a point current dipole. It has a similar structure to a well-known formula for the field outside any spherically symmetric conductivity profile. For a radial dipole, the field on the inside has a very simple expression. A symmetry argument is given as to why the field of a radial dipole vanishes outside a spherical conductor. Illustrative plots of the magnetic field are presented for a radial and a tangential dipole; the slope of the tangential component of the magnetic field is discontinuous at the surface of the sphere. A spherical conductor having three concentric regions is discussed; and we also derive an analytic formula for the magnetic field inside a homogeneous infinite half space.

Equivalent physical models and formulation of equivalent source layer in high-resolution EEG imaging

In high-resolution EEG imaging, both equivalent dipole layer (EDL) and equivalent charge layer (ECL) assumed to be located just above the cortical surface have been proposed as high-resolution imaging modalities or as intermediate steps to estimate the epicortical potential. Presented here are the equivalent physical models of these two equivalent source layers (ESL) which show that the strength of EDL is proportional to the surface potential of the layer when the outside of the layer is filled with an insulator, and that the strength of ECL is the normal current of the layer when the outside is filled with a perfect conductor. Based on these equivalent physical models, closed solutions of ECL and EDL corresponding to a dipole enclosed by a spherical layer are given. These results provide the theoretical basis of ESL applications in high-resolution EEG mapping.

MRI detection of weak magnetic fields due to an extended current dipole in a conducting sphere: a model for direct detection of neuronal currents in the brain

To investigate the feasibility of direct MR detection of neuronal activity in the brain, neuronal current flow was modeled as an extended current dipole located in a conducting sphere. The spatially varying magnetic field induced within the sphere by such a dipole was calculated, including its form close to and within the current source. The predicted field variation was experimentally verified by measurements of the variation in phase of the MR signal in a sphere containing a model dipole. The effects of the calculated magnetic field distributions on the phase and magnitude of the signal in MR images were explored. The minimum detectable dipole strength under normal experimental conditions was calculated to be about 4.5 nAm, which is similar in magnitude to dipole strengths from evoked neuronal activity, and is an order of magnitude smaller than dipole strengths expected from spontaneous activity. This minimum detectable dipole strength increases with increasing spatial extent of the primary current distribution. In the experimental work, the effects of a field of [1.1 +/- 0.5] x 10(-10) T strength were detected, corresponding to the maximum net field caused by a dipole of 6.3 nAm strength with a spatial extent of 3 x 3 x 2 mm(3).

Dipole models for the EEG and MEG

The current dipole is a widely used source model in forward and inverse electroencephalography and magnetoencephalography applications. Analytic solutions to the governing field equations have been developed for several approximations of the human head using ideal dipoles as the source model. Numeric approaches such as the finite-element and finite-difference methods have become popular because they allow the use of anatomically realistic head models and the increased computational power that they require has become readily available. Although numeric methods can represent more realistic domains, the sources in such models are an approximation of the ideal dipole. In this paper, we examine several methods for representing dipole sources in finite-element models and compare the resulting surface potentials and external magnetic field with those obtained from analytic solutions using ideal dipoles.

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 method to standardize a reference of scalp EEG recordings to a point at infinity

The effect of an active reference in EEG recording is one of the oldest technical problems in EEG practice. In this paper, a method is proposed to approximately standardize the reference of scalp EEG recordings to a point at infinity. This method is based on the fact that the use of scalp potentials to determine the neural electrical activities or their equivalent sources does not depend on the reference, so we may approximately reconstruct the equivalent sources from scalp EEG recordings with a scalp point or average reference. Then the potentials referenced at infinity are approximately reconstructed from the equivalent sources. As a point at infinity is far from all the possible neural sources, this method may be considered as a reference electrode standardization technique (REST). The simulation studies performed with assumed neural sources included effects of electrode number, volume conductor model and noise on the performance of REST, and the significance of REST in EEG temporal analysis. The results showed that REST is potentially very effective for the most important superficial cortical region and the standardization could be especially important in recovering the temporal information of EEG recordings.

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.