The Validation of a Portable Functional NIRS System for Assessing Mental Workload.

Portable functional near-infrared spectroscopy (fNIRS) systems have the potential to image the brain in naturalistic settings. Experimental studies are essential to validate such fNIRS systems. Working memory (WM) is a short-term active memory that is associated with the temporary storage and manipulation of information. The prefrontal cortex (PFC) brain area is involved in the processing of WM. We assessed the PFC brain during n-back WM tasks in a group of 25 college students using our laboratory-developed portable fNIRS system, WearLight. We designed an experimental protocol with 32 n-back WM task blocks with four different pseudo-randomized task difficulty levels. The hemodynamic response of the brain was computed from the experimental data and the evaluated brain responses due to these tasks. We observed the incremental mean hemodynamic activation induced by the increasing WM load. The left-PFC area was more activated in the WM task compared to the right-PFC. The task performance was seen to be related to the hemodynamic responses. The experimental results proved the functioning of the WearLight system in cognitive load imaging. Since the portable fNIRS system was wearable and operated wirelessly, it was possible to measure the cognitive load in the naturalistic environment, which could also lead to the development of a user-friendly brain-computer interface system.

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.

Anti-IL-6 neutralizing antibody modulates blood-brain barrier function in the ovine fetus.

Impaired blood-brain barrier function represents an important component of hypoxic-ischemic brain injury in the perinatal period. Proinflammatory cytokines could contribute to ischemia-related blood-brain barrier dysfunction. IL-6 increases vascular endothelial cell monolayer permeability in vitro. However, contributions of IL-6 to blood-brain barrier abnormalities have not been examined in the immature brain in vivo. We generated pharmacologic quantities of ovine-specific neutralizing anti-IL-6 mAbs and systemically infused mAbs into fetal sheep at 126 days of gestation after exposure to brain ischemia. Anti-IL-6 mAbs were measured by ELISA in fetal plasma, cerebral cortex, and cerebrospinal fluid, blood-brain barrier permeability was quantified using the blood-to-brain transfer constant in brain regions, and IL-6, tight junction proteins, and plasmalemma vesicle protein (PLVAP) were detected by Western immunoblot. Anti-IL-6 mAb infusions resulted in increases in mAb (P < 0.05) in plasma, brain parenchyma, and cerebrospinal fluid and decreases in brain IL-6 protein. Twenty-four hours after ischemia, anti-IL-6 mAb infusions attenuated ischemia-related increases in blood-brain barrier permeability and modulated tight junction and PLVAP protein expression in fetal brain. We conclude that inhibiting the effects of IL-6 protein with systemic infusions of neutralizing antibodies attenuates ischemia-related increases in blood-brain barrier permeability by inhibiting IL-6 and modulates tight junction proteins after ischemia.

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.

Neutralizing anti-interleukin-1ß antibodies modulate fetal blood-brain barrier function after ischemia.

We have previously shown that increases in blood-brain barrier permeability represent an important component of ischemia-reperfusion related brain injury in the fetus. Pro-inflammatory cytokines could contribute to these abnormalities in blood-brain barrier function. We have generated pharmacological quantities of mouse anti-ovine interleukin-1ß monoclonal antibody and shown that this antibody has very high sensitivity and specificity for interleukin-1ß protein. This antibody also neutralizes the effects of interleukin-1ß protein in vitro. In the current study, we hypothesized that the neutralizing anti-interleukin-1ß monoclonal antibody attenuates ischemia-reperfusion related fetal blood-brain barrier dysfunction. Instrumented ovine fetuses at 127 days of gestation were studied after 30 min of carotid occlusion and 24h of reperfusion. Groups were sham operated placebo-control- (n=5), ischemia-placebo- (n=6), ischemia-anti-IL-1ß antibody- (n=7), and sham-control antibody- (n=2) treated animals. Systemic infusions of placebo (0.154M NaCl) or anti-interleukin-1ß monoclonal antibody (5.1±0.6 mg/kg) were given intravenously to the same sham or ischemic group of fetuses at 15 min and 4h after ischemia. Concentrations of interleukin-1ß protein and anti-interleukin-1ß monoclonal antibody were measured by ELISA in fetal plasma, cerebrospinal fluid, and parietal cerebral cortex. Blood-brain barrier permeability was quantified using the blood-to-brain transfer constant (Ki) with α-aminoisobutyric acid in multiple brain regions. Interleukin-1ß protein was also measured in parietal cerebral cortices and tight junction proteins in multiple brain regions by Western immunoblot. Cerebral cortical interleukin-1ß protein increased (P<0.001) after ischemia-reperfusion. After anti-interleukin-1ß monoclonal antibody infusions, plasma anti-interleukin-1ß monoclonal antibody was elevated (P<0.001), brain anti-interleukin-1ß monoclonal antibody levels were higher (P<0.03), and interleukin-1ß protein concentrations (P<0.03) and protein expressions (P<0.001) were lower in the monoclonal antibody-treated group than in placebo-treated-ischemia-reperfusion group. Monoclonal antibody infusions attenuated ischemia-reperfusion-related increases in Ki across the brain regions (P<0.04), and Ki showed an inverse linear correlation (r= -0.65, P<0.02) with anti-interleukin-1ß monoclonal antibody concentrations in the parietal cortex, but had little effect on tight junction protein expression. We conclude that systemic anti-interleukin-1ß monoclonal antibody infusions after ischemia result in brain anti-interleukin-1ß antibody uptake, and attenuate ischemia-reperfusion-related interleukin-1ß protein up-regulation and increases in blood-brain barrier permeability across brain regions in the fetus. The pro-inflammatory cytokine, interleukin-1ß, contributes to impaired blood-brain barrier function after ischemia in the fetus.

Language Mapping using tEEG and EEG Data with Convolutional Neural Networks.

Tripolar electroencephalography (tEEG) has been found to have significantly better signal-to-noise ratio, spatial resolution, mutual information, and high-frequencies compared to EEG. This paper analyzes the tEEG signals acquired simultaneously with the EEG signals and compares their ability to map language to left and right hemispheres using convolutional neural networks (CNNs). The results show that while the time-domain features of tEEG and EEG signals lead to comparable functional mapping, the frequency domain features are significantly different. The left and right hemisphere classification performances using tEEG are equivalent in time and frequency domains. However, frequency domain classification for EEG results in less accuracy. Clinical Relevance- This technique could quickly, and noninvasively, guide clinicians about language dominance when preparing for resective surgery.

A Proposed Brain-, Spine-, and Mental- Health Screening Methodology (NEUROSCREEN) for Healthcare Systems: Position of the Society for Brain Mapping and Therapeutics.

The COVID-19 pandemic has accelerated neurological, mental health disorders, and neurocognitive issues. However, there is a lack of inexpensive and efficient brain evaluation and screening systems. As a result, a considerable fraction of patients with neurocognitive or psychobehavioral predicaments either do not get timely diagnosed or fail to receive personalized treatment plans. This is especially true in the elderly populations, wherein only 16% of seniors say they receive regular cognitive evaluations. Therefore, there is a great need for development of an optimized clinical brain screening workflow methodology like what is already in existence for prostate and breast exams. Such a methodology should be designed to facilitate objective early detection and cost-effective treatment of such disorders. In this paper we have reviewed the existing clinical protocols, recent technological advances and suggested reliable clinical workflows for brain screening. Such protocols range from questionnaires and smartphone apps to multi-modality brain mapping and advanced imaging where applicable. To that end, the Society for Brain Mapping and Therapeutics (SBMT) proposes the Brain, Spine and Mental Health Screening (NEUROSCREEN) as a multi-faceted approach. Beside other assessment tools, NEUROSCREEN employs smartphone guided cognitive assessments and quantitative electroencephalography (qEEG) as well as potential genetic testing for cognitive decline risk as inexpensive and effective screening tools to facilitate objective diagnosis, monitor disease progression, and guide personalized treatment interventions. Operationalizing NEUROSCREEN is expected to result in reduced healthcare costs and improving quality of life at national and later, global scales.

Possible therapeutic effects of transcutaneous electrical stimulation via concentric ring electrodes.

Even with the latest advancements in antiepileptic drugs (AEDs) there are still many persons whose seizures are not controlled. There are also side effects reported associated with the AEDs. Electrical stimulation of the brain has shown promise toward controlling seizures. However, most brain stimulation techniques involve invasive procedures to implant electrodes and electronic stimulators. There are no conclusive descriptions of where to place the implanted electrodes to control seizures. Noninvasive electrical stimulation does not require the risks of implantation, and the electrodes can be moved easily as needed to determine where they may be the most effective in reducing seizure activity. Herein we review the progress of our group in the development of noninvasive electrical stimulation via concentric ring electrodes to control seizures in rats induced by penicillin G, pilocarpine, and pentylenetetrazole (PTZ).

Electrode-Electrolyte Interface Modeling and Impedance Characterizing of Tripolar Concentric Ring Electrode.

Electrodes are used to convert ionic currents to electrical currents in biological systems. Modeling the electrode-electrolyte interface and characterizing the impedance of the interface could help to optimize the performance of the electrode interface to achieve higher signal to noise ratios. Previous work has yielded accurate models for single-element biomedical electrodes. This paper introduces a model for a tripolar concentric ring electrode (TCRE) derived from impedance measurements using electrochemical impedance spectroscopy with a Ten20 electrode impedance matching paste. It is shown that the model serves well to predict the performance of the electrode-electrolyte interface for TCREs as well as standard cup electrodes. In this paper, we also discuss the comparison between the TCRE and the standard cup electrode regarding their impedance characterization and demonstrate the benefit of using TCREs in biomedical applications. We have also conducted auditory evoked potential experiments using both TCRE and standard cup electrodes. The results show that electroencephalography (EEG) recorded from tripolar concentric ring electrodes is beneficial, acquiring the auditory brainstem response with less stimuli with respect to recoding EEG using standard cup electrodes.

WearLight: Toward a Wearable, Configurable Functional NIR Spectroscopy System for Noninvasive Neuroimaging.

Functional near-infrared spectroscopy (fNIRS) has emerged as an effective brain monitoring technique to measure the hemodynamic response of the cortical surface. Its wide popularity and adoption in recent time attribute to its portability, ease of use, and flexibility in multimodal studies involving electroencephalography. While fNIRS is still emerging on various fronts including hardware, software, algorithm, and applications, it still requires overcoming several scientific challenges associated with brain monitoring in naturalistic environments where the human participants are allowed to move and required to perform various tasks stimulating brain behaviors. In response to these challenges and demands, we have developed a wearable fNIRS system, WearLight that was built upon an Internet-of-Things embedded architecture for onboard intelligence, configurability, and data transmission. In addition, we have pursued detailed research and comparative analysis on the design of the optodes encapsulating an near-infrared light source and a detector into 3-D printed material. We performed rigorous experimental studies on human participants to test reliability, signal-to-noise ratio, and configurability. Most importantly, we observed that WearLight has a capacity to measure hemodynamic responses in various setups including arterial occlusion on the forearm and frontal lobe brain activity during breathing exercises in a naturalistic environment. Our promising experimental results provide an evidence of preliminary clinical validation of WearLight. This encourages us to move toward intensive studies involving brain monitoring.

Transcranial focal electrical stimulation via concentric ring electrodes in freely moving cats: Antiepileptogenic and postictal effects.

Transcranial focal electrical stimulation (TFS) via tripolar concentric ring electrodes (TCRE), tripolar TFS, is proposed to treat pharmacoresistant epilepsy. We determined the effect of tripolar TFS on electrical amygdaloid kindling (AK) in freely moving cats. Fifteen cats were bilaterally implanted with electrodes in the amygdala (AM) and prefrontal cortex and assigned to three groups: the control group, which only received AK; the tripolar TFS before AK group, in which TCREs were placed over the vertex and tripolar TFS (300 Hz, 200 µs biphasic equal charge, square pulses) was delivered for 40 min just prior to AK; and the tripolar TFS after AK group, in which the TCREs were placed over the temporal bone ipsilateral to the kindled AM, while tripolar TFS was administered for 2 min just after AK onset for 40 days, and, thereafter, only AK was applied. AK was applied daily until all animals reached kindling stage VI. A three concentric spheres finite element cat head model was developed to analyze the electric fields caused by tripolar TFS. Tripolar TFS after AK inhibited kindling development. Animals with tripolar TFS after AK remained at the focal seizure stages for 20 days after tripolar TFS cessation and required 80.0 ±â€¯15.42 AK stimulations to reach stage VI, significantly higher than TFS before AK, and control (P < .001). Tripolar TFS before AK did not show signs of protection against epileptogenesis. The finite modeling of tripolar TFS showed that the electric field is >0.3 mV/mm at depths less than approximately 12.6 mm in the cat brain, which should be strong enough to alter brain activity. In conclusion, tripolar TFS applied via a TCRE over the ipsilateral temporal area significantly delayed AK. This taken together with other reports of tripolar TFS aborting seizures in acute seizure models suggests that tripolar TFS is a promising new modality that should be considered for further testing.

Application of tripolar concentric electrodes and prefeature selection algorithm for brain-computer interface.

For persons with severe disabilities, a brain-computer interface (BCI) may be a viable means of communication. Lapalacian electroencephalogram (EEG) has been shown to improve classification in EEG recognition. In this work, the effectiveness of signals from tripolar concentric electrodes and disc electrodes were compared for use as a BCI. Two sets of left/right hand motor imagery EEG signals were acquired. An autoregressive (AR) model was developed for feature extraction with a Mahalanobis distance based linear classifier for classification. An exhaust selection algorithm was employed to analyze three factors before feature extraction. The factors analyzed were 1) length of data in each trial to be used, 2) start position of data, and 3) the order of the AR model. The results showed that tripolar concentric electrodes generated significantly higher classification accuracy than disc electrodes.

Improvement of spatial selectivity and decrease of mutual information of tri-polar concentric ring electrodes.

Electroencephalography (EEG) signals are spatio-temporal in nature. EEG has very good temporal resolution but typically does not possess high spatial resolution. The surface Laplacian enhances the spatial resolution and selectivity of the surface electrical activity recording. Concentric ring electrodes have been shown to estimate the surface Laplacian directly with significantly better spatial resolution than conventional electrodes. For this report movement-related potentials (MRP) signals were analyzed. The signals were recorded using tri-polar ring electrodes in the original configuration as well as in bipolar and unipolar configurations achieved by excluding or shorting recording surfaces of the tri-polar version, respectively. The electrodes were placed in an array scheme of 35, encompassing the area between Fz-Cz-Pz-P3-T5-T3-F7-F3 centered on C3. Data were measured in five steps sequentially using only seven electrodes at a time, displaced after each step and aligned during evaluation later. Subjects were cued to press a micro-switch. The signal-to-noise ratio (SNR), spatial selectivity, and mutual information (MI) of the MRP signals recorded with the different electrode systems were compared. The MRP signals recorded with the tri-polar concentric ring electrode system have significantly higher SNR than from bipolar concentric ring electrode and conventional disc electrode emulations. The tri-polar electrodes have also shown significantly higher spatial selectivity as well as significantly less mutual information between locations than the other two electrode configurations tested. These characteristics should make tri-polar concentric electrodes beneficial for EEG applications.

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.

Impedance spectroscopy of tripolar concentric ring electrodes with Ten20 and TD246 pastes.

Electrodes are used to transform ionic currents to electrical currents in biological systems. Modeling the electrode-electrolyte interface could help to optimize the performance of the electrode interface to achieve higher signal to noise ratios. There are previous reports of accurate models for single-element biomedical electrodes. In this paper, we measured the impedance on both tripolar concentric ring electrodes and standard cup electrodes by electrochemical impedance spectroscopy (EIS) using both Ten20 and TD246 electrode paste. Furthermore, we applied the model to prove that the model can predict the performance of the electrode-electrolyte interface for tripolar concentric ring electrodes (TCRE) that are used to record brain signals.

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.

Tri-polar concentric ring electrode development for laplacian electroencephalography.

Brain activity generates electrical potentials that are spatio-temporal in nature. Electroencephalography (EEG) is the least costly and most widely used noninvasive technique for diagnosing many brain problems. It has high temporal resolution, but lacks high spatial resolution. In an attempt to increase the spatial selectivity, researchers introduced a bipolar electrode configuration utilizing a five-point finite difference method (FPM) and others applied a quasi-bipolar (tri-polar with two elements shorted) concentric electrode configuration. To further increase the spatial resolution, the authors report on a tri-polar concentric electrode configuration for approximating the analytical Laplacian based on a nine-point finite difference method (NPM). For direct comparison, the FPM, quasi-bipolar method (a hybrid NPM), and NPM were calculated over a 400 x 400 mesh with 1/400 spacing using a computer model. A closed-form analytical computer model was also developed to evaluate and compare the properties of concentric bipolar, quasi-bipolar, and tri-polar electrode configurations, and the results were verified with tank experiments. The tri-polar configuration and the NPM were found to have significantly improved accuracy in Laplacian estimation and localization. Movement-related potential (MRP) signals were recorded from the left prefrontal lobes on the scalp of human subjects while they performed fast repetitive movements. Disc, bipolar, quasi-bipolar, and tri-polar electrodes were used. MRP signals were plotted for all four electrode configurations. The signal-to-noise ratio and spatial selectivity of the MRP signals acquired with the tri-polar electrode configuration were significantly better than the other configurations.

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.