High-Frequency Oscillations Recorded on the Scalp of Patients With Epilepsy Using Tripolar Concentric Ring Electrodes

Characteristic analysis of epileptic brain network based on attention mechanism

Constructing an efficient and accurate epilepsy detection system is an urgent research task. In this paper, we developed an EEG-based multi-frequency multilayer brain network (MMBN) and an attentional mechanism based convolutional neural network (AM-CNN) model to study epilepsy detection. Specifically, based on the multi-frequency characteristics of the brain, we first use wavelet packet decomposition and reconstruction methods to divide the original EEG signals into eight frequency bands, and then construct MMBN through correlation analysis between brain regions, where each layer corresponds to a specific frequency band. The time, frequency and channel related information of EEG signals are mapped into the multilayer network topology. On this basis, a multi-branch AM-CNN model is designed, which completely matches the multilayer structure of the proposed brain network. The experimental results on public CHB-MIT datasets show that eight frequency bands divided in this work are all helpful for epilepsy detection, and the fusion of multi-frequency information can effectively decode the epileptic brain state, achieving accurate detection of epilepsy with an average accuracy of 99.75%, sensitivity of 99.43%, and specificity of 99.83%. All of these provide reliable technical solutions for EEG-based neurological disease detection, especially for epilepsy detection.

Workshops of the Eighth International Brain-Computer Interface Meeting: BCIs: The Next Frontier

The Eighth International Brain-Computer Interface (BCI) Meeting was held June 7-9th, 2021 in a virtual format. The conference continued the BCI Meeting series' interactive nature with 21 workshops covering topics in BCI (also called brain-machine interface) research. As in the past, workshops covered the breadth of topics in BCI. Some workshops provided detailed examinations of specific methods, hardware, or processes. Others focused on specific BCI applications or user groups. Several workshops continued consensus building efforts designed to create BCI standards and increase the ease of comparisons between studies and the potential for meta-analysis and large multi-site clinical trials. Ethical and translational considerations were both the primary topic for some workshops or an important secondary consideration for others. The range of BCI applications continues to expand, with more workshops focusing on approaches that can extend beyond the needs of those with physical impairments. This paper summarizes each workshop, provides background information and references for further study, presents an overview of the discussion topics, and describes the conclusion, challenges, or initiatives that resulted from the interactions and discussion at the workshop.

Mobile Electroencephalography for Studying Neural Control of Human Locomotion

Walking or running in real-world environments requires dynamic multisensory processing within the brain. Studying supraspinal neural pathways during human locomotion provides opportunities to better understand complex neural circuity that may become compromised due to aging, neurological disorder, or disease. Knowledge gained from studies examining human electrical brain dynamics during gait can also lay foundations for developing locomotor neurotechnologies for rehabilitation or human performance. Technical barriers have largely prohibited neuroimaging during gait, but the portability and precise temporal resolution of non-invasive electroencephalography (EEG) have expanded human neuromotor research into increasingly dynamic tasks. In this narrative mini-review, we provide a (1) brief introduction and overview of modern neuroimaging technologies and then identify considerations for (2) mobile EEG hardware, (3) and data processing, (4) including technical challenges and possible solutions. Finally, we summarize (5) knowledge gained from human locomotor control studies that have used mobile EEG, and (6) discuss future directions for real-world neuroimaging research.

Identification of clinically relevant biomarkers of epileptogenesis - a strategic roadmap

Onset of many forms of epilepsy occurs after an initial epileptogenic insult or as a result of an identified genetic defect. Given that the precipitating insult is known, these epilepsies are, in principle, amenable to secondary prevention. However, development of preventive treatments is difficult because only a subset of individuals will develop epilepsy and we cannot currently predict which individuals are at the highest risk. Biomarkers that enable identification of these individuals would facilitate clinical trials of potential anti-epileptogenic treatments, but no such prognostic biomarkers currently exist. Several putative molecular, imaging, electroencephalographic and behavioural biomarkers of epileptogenesis have been identified, but clinical translation has been hampered by fragmented and poorly coordinated efforts, issues with inter-model reproducibility, study design and statistical approaches, and difficulties with validation in patients. These challenges demand a strategic roadmap to facilitate the identification, characterization and clinical validation of biomarkers for epileptogenesis. In this Review, we summarize the state of the art with respect to biomarker research in epileptogenesis and propose a five-phase roadmap, adapted from those developed for cancer and Alzheimer disease, that provides a conceptual structure for biomarker research.

Recent advances in the noninvasive detection of high-frequency oscillations in the human brain

In recent decades, a significant body of evidence based on invasive clinical research has showed that high-frequency oscillations (HFOs) are a promising biomarker for localization of the seizure onset zone (SOZ), and therefore, have the potential to improve postsurgical outcomes in patients with epilepsy. Emerging clinical literature has demonstrated that HFOs can be recorded noninvasively using methods such as scalp electroencephalography (EEG) and magnetoencephalography (MEG). Not only are HFOs considered to be a useful biomarker of the SOZ, they also have the potential to gauge disease severity, monitor treatment, and evaluate prognostic outcomes. In this article, we review recent clinical research on noninvasively detected HFOs in the human brain, with a focus on epilepsy. Noninvasively detected scalp HFOs have been investigated in various types of epilepsy. HFOs have also been studied noninvasively in other pathologic brain disorders, such as migraine and autism. Herein, we discuss the challenges reported in noninvasive HFO studies, including the scarcity of MEG and high-density EEG equipment in clinical settings, low signal-to-noise ratio, lack of clinically approved automated detection methods, and the difficulty in differentiating between physiologic and pathologic HFOs. Additional studies on noninvasive recording methods for HFOs are needed, especially prospective multicenter studies. Further research is fundamental, and extensive work is needed before HFOs can routinely be assessed in clinical settings; however, the future appears promising.

Power and Coherence in the EEG of the Rat: Impact of Behavioral States, Cortical Area, Lateralization and Light/Dark Phases

The sleep-wake cycle is constituted by three behavioral states: wakefulness (W), non-REM (NREM) and REM sleep. These states are associated with drastic changes in cognitive capacities, mostly determined by the function of the thalamo-cortical system, whose activity can be examined by means of intra-cranial electroencephalogram (iEEG). With the purpose to study in depth the basal activity of the iEEG in adult rats, we analyzed the spectral power and coherence of the iEEG during W and sleep in the paleocortex (olfactory bulb), and in neocortical areas. We also analyzed the laterality of the signals, as well as the influence of the light and dark phases. We found that the iEEG power and coherence of the whole spectrum were largely affected by behavioral states and highly dependent on the cortical areas recorded. We also determined that there are night/day differences in power and coherence during sleep, but not in W. Finally, we observed that, during REM sleep, intra-hemispheric coherence differs between right and left hemispheres. We conclude that the iEEG dynamics are highly dependent on the cortical area and behavioral states. Moreover, there are light/dark phases disparities in the iEEG during sleep, and intra-hemispheric connectivity differs between both hemispheres during REM sleep.

Evaluation of Respiratory Muscle Activity by Means of Concentric Ring Electrodes

Surface electromyography (sEMG) can be used for the evaluation of respiratory muscle activity. Recording sEMG involves the use of surface electrodes in a bipolar configuration. However, electrocardiographic (ECG) interference and electrode orientation represent considerable drawbacks to bipolar acquisition. As an alternative, concentric ring electrodes (CREs) can be used for sEMG acquisition and offer great potential for the evaluation of respiratory muscle activity due to their enhanced spatial resolution and simple placement protocol, which does not depend on muscle fiber orientation. The aim of this work was to analyze the performance of CREs during respiratory sEMG acquisitions. Respiratory muscle sEMG was applied to the diaphragm and sternocleidomastoid muscles using a bipolar and a CRE configuration. Thirty-two subjects underwent four inspiratory load spontaneous breathing tests which was repeated after interchanging the electrode positions. We calculated parameters such as (1) spectral power and (2) median frequency during inspiration, and power ratios of inspiratory sEMG without ECG in relation to (3) basal sEMG without ECG (R_ins/noise), (4) basal sEMG with ECG (R_ins/cardio) and (5) expiratory sEMG without ECG (R_ins/exp). Spectral power, R_ins/noise and R_ins/cardio increased with the inspiratory load. Significantly higher values (p < 0.05) of R_ins/cardio and significantly higher median frequencies were obtained for CREs. R_ins/noise and R_ins/exp were higher for the bipolar configuration only in diaphragm sEMG recordings, whereas no significant differences were found in the sternocleidomastoid recordings. Our results suggest that the evaluation of respiratory muscle activity by means of sEMG can benefit from the remarkably reduced influence of cardiac activity, the enhanced detection of the shift in frequency content and the axial isotropy of CREs which facilitates its placement.

Workshops of the Seventh International Brain-Computer Interface Meeting: Not Getting Lost in Translation

The Seventh International Brain-Computer Interface (BCI) Meeting was held May 21-25th, 2018 at the Asilomar Conference Grounds, Pacific Grove, California, United States. The interactive nature of this conference was embodied by 25 workshops covering topics in BCI (also called brain-machine interface) research. Workshops covered foundational topics such as hardware development and signal analysis algorithms, new and imaginative topics such as BCI for virtual reality and multi-brain BCIs, and translational topics such as clinical applications and ethical assumptions of BCI development. BCI research is expanding in the diversity of applications and populations for whom those applications are being developed. BCI applications are moving toward clinical readiness as researchers struggle with the practical considerations to make sure that BCI translational efforts will be successful. This paper summarizes each workshop, providing an overview of the topic of discussion, references for additional information, and identifying future issues for research and development that resulted from the interactions and discussion at the workshop.

Source localization of high-frequency activity in tripolar electroencephalography of patients with epilepsy

OBJECTIVE

The objective of the study was to localize sources of interictal high-frequency activity (HFA), from tripolar electroencephalography (tEEG), in patient-specific, realistic head models.

METHODS

Concurrent electroencephalogram (EEG) and tEEG were recorded from nine patients undergoing video-EEG, of which eight had seizures during the recordings and the other had epileptic activity. Patient-specific, realistic boundary element head models were generated from the patient's magnetic resonance images (MRIs). Forward and inverse modeling was performed to localize the HFA to cortical surfaces.

RESULTS

In the present study, performed on nine patients with epilepsy, HFA observed in the tEEG was localized to the surface of subject-specific, realistic, cortical models, and found to occur almost exclusively in the seizure onset zone (SOZ)/irritative zone (IZ).

SIGNIFICANCE

High-frequency oscillations (HFOs) have been studied as precise biomarkers of the SOZ in epilepsy and have resulted in good therapeutic effect in surgical candidates. Knowing where the sources of these highly focal events are located in the brain can help with diagnosis. High-frequency oscillations are not commonly observed in noninvasive EEG recordings, and invasive electrocorticography (ECoG) is usually required to detect them. However, tEEG, i.e., EEG recorded on the scalp with tripolar concentric ring electrodes (TCREs), has been found to detect narrowband HFA from high gamma (approximately 80 Hz) to almost 400 Hz that correlates with SOZ diagnosis. Thus, source localization of HFA in tEEG may help clinicians identify brain regions of the epileptic zone. At the least, the tEEG HFA localization may help determine where to perform intracranial recordings used for precise diagnosis.

Tripolar concentric EEG electrodes reduce noise

OBJECTIVE

To assay EEG signal quality recorded with tripolar concentric ring electrodes (TCREs) compared to regular EEG electrodes.

METHODS

EEG segments were recorded simultaneously by TCREs and regular electrodes, low-pass filtered at 35 Hz (REG35) and 70 Hz (REG70). Clips were rated blindly by nine electroencephalographers for presence or absence of key EEG features, relative to the "gold-standard" of the clinical report.

RESULTS

TCRE showed less EMG artifact (F = 15.4, p < 0.0001). Overall quality rankings were not significantly different. Focal slowing was better detected by TCRE and spikes were better detected by regular electrodes. Seizures (n = 85) were detected by TCRE in 64 cases (75.3%), by REG70 in 75 (88.2%) and REG35 in 69 (81.2%) electrodes. TCRE detected 9 (10.6%) seizures not detected by one of the other 2 methods. In contrast, 14 seizures (16.5%) were not detected by TCRE, but were by REG35 electrodes. Each electrode detected interictal spikes when the other did not.

CONCLUSIONS

TCRE produced similar overall quality and confidence ratings versus regular electrodes, but less muscle artifact. TCRE recordings detected seizures in 7% of instances where regular electrodes did not.

SIGNIFICANCE

The combination of the two types increased detection of epileptiform events compared to either alone.

Solving the general inter-ring distances optimization problem for concentric ring electrodes to improve Laplacian estimation

Background

Superiority of noninvasive tripolar concentric ring electrodes over conventional disc electrodes in accuracy of surface Laplacian estimation has been demonstrated in a range of electrophysiological measurement applications. Recently, a general approach to Laplacian estimation for an (n + 1)-polar electrode with n rings using the (4n + 1)-point method has been proposed and used to introduce novel multipolar and variable inter-ring distances electrode configurations. While only linearly increasing and linearly decreasing inter-ring distances have been considered previously, this paper defines and solves the general inter-ring distances optimization problem for the (4n + 1)-point method.

Results

General inter-ring distances optimization problem is solved for tripolar (n = 2) and quadripolar (n = 3) concentric ring electrode configurations through minimizing the truncation error of Laplacian estimation. For tripolar configuration with middle ring radius αr and outer ring radius r the optimal range of values for α was determined to be 0 < α ≤ 0.22 while for quadripolar configuration with an additional middle ring with radius βr the optimal range of values for α and β was determined by inequalities 0 < α < β < 1 and αβ ≤ 0.21. Finite element method modeling and full factorial analysis of variance were used to confirm statistical significance of Laplacian estimation accuracy improvement due to optimization of inter-ring distances (p < 0.0001).

Conclusions

Obtained results suggest the potential of using optimization of inter-ring distances to improve the accuracy of surface Laplacian estimation via concentric ring electrodes. Identical approach can be applied to solving corresponding inter-ring distances optimization problems for electrode configurations with higher numbers of concentric rings. Solutions of the proposed inter-ring distances optimization problem define the class of the optimized inter-ring distances electrode designs. These designs may result in improved noninvasive sensors for measurement systems that use concentric ring electrodes to acquire electrical signals such as from the brain, intestines, heart or uterus for diagnostic purposes.

A Novel Approach for Real-Time Recognition of Epileptic Seizures Using Minimum Variance Modified Fuzzy Entropy

OBJECTIVE

Validation of epileptic seizures annotations from long-term electroencephalogram (EEG) recordings is a tough and tedious task for the neurological community. It is a well-known fact that computerized qualitative methods thoroughly assess the complex brain dynamics toward seizure detection and proven as one of the acceptable clinical indicators.

METHODS

This research study suggests a novel approach for real-time recognition of epileptic seizure from EEG recordings by a technique referred as minimum variance modified fuzzy entropy (MVMFzEn). Multichannel EEG recordings of 4.36 h of epileptic seizures and 25.74 h of normal EEG were considered. Signal processing techniques such as filters and independent component analysis were appropriated to reduce noise and artifacts. Unlike, the predefined fuzzy membership function, the modified fuzzy entropy utilizes relative energy as a membership function followed by scaling operation to obtain the feature.

RESULTS

Results revealed that MVMFzEn drops abruptly during an epileptic activity and this fact was used to set a threshold. An automated threshold derived from MVMFzEn assesses the classification efficiency of the given data during validation. It was observed from the results that the proposed method yields a classification accuracy of 100% without the use of any classifier.

CONCLUSION

The graphical user interface was designed in MATLAB to automatically label the normal and epileptic segments in the long-term EEG recordings.

SIGNIFICANCE

The ground truth clinical validation using validation specificity and validation sensitivity confirms the suitability of the proposed technique for automated annotation of epileptic seizures in real time.

Textile Concentric Ring Electrodes for ECG Recording Based on Screen-Printing Technology

Among many of the electrode designs used in electrocardiography (ECG), concentric ring electrodes (CREs) are one of the most promising due to their enhanced spatial resolution. Their development has undergone a great push due to their use in recent years; however, they are not yet widely used in clinical practice. CRE implementation in textiles will lead to a low cost, flexible, comfortable, and robust electrode capable of detecting high spatial resolution ECG signals. A textile CRE set has been designed and developed using screen-printing technology. This is a mature technology in the textile industry and, therefore, does not require heavy investments. Inks employed as conductive elements have been silver and a conducting polymer (poly (3,4-ethylenedioxythiophene) polystyrene sulfonate; PEDOT:PSS). Conducting polymers have biocompatibility advantages, they can be used with flexible substrates, and they are available for several printing technologies. CREs implemented with both inks have been compared by analyzing their electric features and their performance in detecting ECG signals. The results reveal that silver CREs present a higher average thickness and slightly lower skin-electrode impedance than PEDOT:PSS CREs. As for ECG recordings with subjects at rest, both CREs allowed the uptake of bipolar concentric ECG signals (BC-ECG) with signal-to-noise ratios similar to that of conventional ECG recordings. Regarding the saturation and alterations of ECGs captured with textile CREs caused by intentional subject movements, silver CREs presented a more stable response (fewer saturations and alterations) than those of PEDOT:PSS. Moreover, BC-ECG signals provided higher spatial resolution compared to conventional ECG. This improved spatial resolution was manifested in the identification of P1 and P2 waves of atrial activity in most of the BC-ECG signals. It can be concluded that textile silver CREs are more suitable than those of PEDOT:PSS for obtaining BC-ECG records. These developed textile electrodes bring the use of CREs closer to the clinical environment.

Analysis of variance to assess statistical significance of Laplacian estimation accuracy improvement due to novel variable inter-ring distances concentric ring electrodes

Concentric ring electrodes have shown promise in non-invasive electrophysiological measurement demonstrating their superiority to conventional disc electrodes, in particular, in accuracy of Laplacian estimation. Recently, we have proposed novel variable inter-ring distances concentric ring electrodes. Analytic and finite element method modeling results for linearly increasing distances electrode configurations suggested they may decrease the truncation error resulting in more accurate Laplacian estimates compared to currently used constant inter-ring distances configurations. This study assesses statistical significance of Laplacian estimation accuracy improvement due to novel variable inter-ring distances concentric ring electrodes. Full factorial design of analysis of variance was used with one categorical and two numerical factors: the inter-ring distances, the electrode diameter, and the number of concentric rings in the electrode. The response variables were the Relative Error and the Maximum Error of Laplacian estimation computed using a finite element method model for each of the combinations of levels of three factors. Effects of the main factors and their interactions on Relative Error and Maximum Error were assessed and the obtained results suggest that all three factors have statistically significant effects in the model confirming the potential of using inter-ring distances as a means of improving accuracy of Laplacian estimation.

Computation of Surface Laplacian for tri-polar ring electrodes on high-density realistic geometry head model

Neural activity inside the human brain generate electrical signals that can be detected on the scalp. Electroencephalograph (EEG) is one of the most widely utilized techniques helping physicians and researchers to diagnose and understand various brain diseases. Due to its nature, EEG signals have very high temporal resolution but poor spatial resolution. To achieve higher spatial resolution, a novel tri-polar concentric ring electrode (TCRE) has been developed to directly measure Surface Laplacian (SL). The objective of the present study is to accurately calculate SL for TCRE based on a realistic geometry head model. A locally dense mesh was proposed to represent the head surface, where the local dense parts were to match the small structural components in TCRE. Other areas without dense mesh were used for the purpose of reducing computational load. We conducted computer simulations to evaluate the performance of the proposed mesh and evaluated possible numerical errors as compared with a low-density model. Finally, with achieved accuracy, we presented the computed forward lead field of SL for TCRE for the first time in a realistic geometry head model and demonstrated that it has better spatial resolution than computed SL from classic EEG recordings.

Proof of concept Laplacian estimate derived for noninvasive tripolar concentric ring electrode with incorporated radius of the central disc and the widths of the concentric rings

Tripolar concentric ring electrodes are showing great promise in a range of applications including braincomputer interface and seizure onset detection due to their superiority to conventional disc electrodes, in particular, in accuracy of surface Laplacian estimation. Recently, we proposed a general approach to estimation of the Laplacian for an (n + 1)-polar electrode with n rings using the (4n + 1)-point method for n ≥ 2 that allows cancellation of all the truncation terms up to the order of 2n. This approach has been used to introduce novel multipolar and variable inter-ring distances concentric ring electrode configurations verified using finite element method. The obtained results suggest their potential to improve Laplacian estimation compared to currently used constant interring distances tripolar concentric ring electrodes. One of the main limitations of the proposed (4n + 1)-point method is that the radius of the central disc and the widths of the concentric rings are not included and therefore cannot be optimized. This study incorporates these two parameters by representing the central disc and both concentric rings as clusters of points with specific radius and widths respectively as opposed to the currently used single point and concentric circles. A proof of concept Laplacian estimate is derived for a tripolar concentric ring electrode with non-negligible radius of the central disc and non-negligible widths of the concentric rings clearly demonstrating how both of these parameters can be incorporated into the (4n + 1)-point method.

Identifying the effects of microsaccades in tripolar EEG signals

Microsaccades are tiny, involuntary eye movements that occur during fixation, and they are necessary to human sight to maintain a sharp image and correct the effects of other fixational movements. Researchers have theorized and studied the effects of microsaccades on electroencephalography (EEG) signals to understand and eliminate the unwanted artifacts from EEG. The tripolar concentric ring electrode (TCRE) sensors are used to acquire TCRE EEG (tEEG). The tEEG detects extremely focal signals from directly below the TCRE sensor. We have noticed a slow wave frequency found in some tEEG recordings. Therefore, we conducted the current work to determine if there was a correlation between the slow wave in the tEEG and the microsaccades. This was done by analyzing the coherence of the frequency spectrums of both tEEG and eye movement in recordings where microsaccades are present. Our preliminary findings show that there is a correlation between the two.

How to record high-frequency oscillations in epilepsy: A practical guideline

OBJECTIVE

Technology for localizing epileptogenic brain regions plays a central role in surgical planning. Recent improvements in acquisition and electrode technology have revealed that high-frequency oscillations (HFOs) within the 80-500 Hz frequency range provide the neurophysiologist with new information about the extent of the epileptogenic tissue in addition to ictal and interictal lower frequency events. Nevertheless, two decades after their discovery there remain questions about HFOs as biomarkers of epileptogenic brain and there use in clinical practice.

METHODS

In this review, we provide practical, technical guidance for epileptologists and clinical researchers on recording, evaluation, and interpretation of ripples, fast ripples, and very high-frequency oscillations.

RESULTS

We emphasize the importance of low noise recording to minimize artifacts. HFO analysis, either visual or with automatic detection methods, of high fidelity recordings can still be challenging because of various artifacts including muscle, movement, and filtering. Magnetoencephalography and intracranial electroencephalography (iEEG) recordings are subject to the same artifacts.

SIGNIFICANCE

High-frequency oscillations are promising new biomarkers in epilepsy. This review provides interested researchers and clinicians with a review of current state of the art of recording and identification and potential challenges to clinical translation.

Analytic assessment of Laplacian estimates via novel variable interring distances concentric ring electrodes

Noninvasive concentric ring electrodes are a promising alternative to conventional disc electrodes. Currently, superiority of tripolar concentric ring electrodes over disc electrodes, in particular, in accuracy of Laplacian estimation has been demonstrated in a range of applications. In our recent work we have shown that accuracy of Laplacian estimation can be improved with multipolar concentric ring electrodes using a general approach to estimation of the Laplacian for an (n + 1)-polar electrode with n rings using the (4n + 1)-point method for n ≥ 2. This paper takes the next step toward further improving the Laplacian estimate by proposing novel variable inter-ring distances concentric ring electrodes. Derived using a modified (4n + 1)-point method, linearly increasing inter-ring distances tripolar (n = 2) and quadripolar (n = 3) electrode configurations are analytically compared to their constant inter-ring distances counterparts using coefficients of the Taylor series truncation terms. Obtained results suggest that increasing inter-ring distances electrode configurations may decrease the truncation error of the Laplacian estimation resulting in more accurate Laplacian estimates compared to respective constant inter-ring distances configurations. For currently used tripolar electrode configuration the truncation error may be decreased more than two-fold while for the quadripolar more than seven-fold decrease is expected.

Finite element method modeling to assess Laplacian estimates via novel variable inter-ring distances concentric ring electrodes

Noninvasive concentric ring electrodes are a promising alternative to conventional disc electrodes. Currently, superiority of tripolar concentric ring electrodes over disc electrodes, in particular, in accuracy of Laplacian estimation has been demonstrated in a range of applications. In our recent work we have shown that accuracy of Laplacian estimation can be improved with multipolar concentric ring electrodes using a general approach to estimation of the Laplacian for an (n + 1)-polar electrode with n rings using the (4n + 1)-point method for n ≥ 2. This paper takes the next step toward further improving the Laplacian estimate by proposing novel variable inter-ring distances concentric ring electrodes. Derived using a modified (4n + 1)-point method, linearly increasing and decreasing inter-ring distances tripolar (n = 2) and quadripolar (n = 3) electrode configurations are compared to their constant inter-ring distances counterparts using finite element method modeling. Obtained results suggest that increasing inter-ring distances electrode configurations may decrease the estimation error resulting in more accurate Laplacian estimates compared to respective constant inter-ring distances configurations. For currently used tripolar electrode configuration the estimation error may be decreased more than two-fold while for the quadripolar configuration more than six-fold decrease is expected.

Improving the Accuracy of Laplacian Estimation with Novel Variable Inter-Ring Distances Concentric Ring Electrodes

Noninvasive concentric ring electrodes are a promising alternative to conventional disc electrodes. Currently, the superiority of tripolar concentric ring electrodes over disc electrodes, in particular, in accuracy of Laplacian estimation, has been demonstrated in a range of applications. In our recent work, we have shown that accuracy of Laplacian estimation can be improved with multipolar concentric ring electrodes using a general approach to estimation of the Laplacian for an (n + 1)-polar electrode with n rings using the (4n + 1)-point method for n ≥ 2. This paper takes the next step toward further improving the Laplacian estimate by proposing novel variable inter-ring distances concentric ring electrodes. Derived using a modified (4n + 1)-point method, linearly increasing and decreasing inter-ring distances tripolar (n = 2) and quadripolar (n = 3) electrode configurations are compared to their constant inter-ring distances counterparts. Finite element method modeling and analytic results are consistent and suggest that increasing inter-ring distances electrode configurations may decrease the truncation error resulting in more accurate Laplacian estimates compared to respective constant inter-ring distances configurations. For currently used tripolar electrode configuration, the truncation error may be decreased more than two-fold, while for the quadripolar configuration more than a six-fold decrease is expected.

Improving the accuracy of Laplacian estimation with novel multipolar concentric ring electrodes

Conventional electroencephalography with disc electrodes has major drawbacks including poor spatial resolution, selectivity and low signal-to-noise ratio that are critically limiting its use. Concentric ring electrodes, consisting of several elements including the central disc and a number of concentric rings, are a promising alternative with potential to improve all of the aforementioned aspects significantly. In our previous work, the tripolar concentric ring electrode was successfully used in a wide range of applications demonstrating its superiority to conventional disc electrode, in particular, in accuracy of Laplacian estimation. This paper takes the next step toward further improving the Laplacian estimation with novel multipolar concentric ring electrodes by completing and validating a general approach to estimation of the Laplacian for an (n + 1)-polar electrode with n rings using the (4n + 1)-point method for n ≥ 2 that allows cancellation of all the truncation terms up to the order of 2n. An explicit formula based on inversion of a square Vandermonde matrix is derived to make computation of multipolar Laplacian more efficient. To confirm the analytic result of the accuracy of Laplacian estimate increasing with the increase of n and to assess the significance of this gain in accuracy for practical applications finite element method model analysis has been performed. Multipolar concentric ring electrode configurations with n ranging from 1 ring (bipolar electrode configuration) to 6 rings (septapolar electrode configuration) were directly compared and obtained results suggest the significance of the increase in Laplacian accuracy caused by increase of n.