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

Directional Sensors for Recording Uterine EMG During Pregnancy

Multichannel uterine electromyography (uEMG) during pregnancy is traditionally performed with electrocardiography (ECG) sensors. Similar signals are often observed in two or more channels, suggesting the ECG sensors report activities originating from the same location on the uterus. To improve signal source localization, we designed a directional sensor or "Area Sensor". Here we compare Area Sensors with ECG sensors for source localization. Subjects were ≥ 38 wks experiencing regular contractions. 6 Area Sensors (n = 8) or 6 to 7 ECG sensors (n = 7) were used to record multichannel uEMG for 60 min. For each sensor type, the similarity of signals observed in pairs of channels during contractions was assessed by quantifying channel crosstalk. Since crosstalk depends on the separation between sensors, analyses were performed within distance groups: A 9-12 cm; B 13-16 cm; C 17-20 cm; D 21-24 cm; E ≥ 25 cm. For ECG sensors, crosstalk was 67.9 ± 14.4% in group A, decreasing to 27.8 ± 17.5% in group E. For Area Sensors, crosstalk was 24.6 ± 18.6% in Group A, decreasing to 12.5 ± 13.8% in group E. Area Sensors showed less crosstalk than ECG sensors in distance groups A, B, C and D, with all p < 0.002. Compared with ECG sensors, Area Sensors are more directional and report uterine activity from a smaller area of the uterine wall. Using 6 Area Sensors separated by at least 17 cm provides acceptably independent multichannel recording. This introduces the possibility of non-invasively evaluating uterine synchronization and the strength of individual uterine contractions in real time.

Identification of atrial fibrillation drivers by means of concentric ring electrodes

BACKGROUND AND OBJECTIVE

The prevalence of atrial fibrillation (AF) has tripled in the last 50 years due to population aging. High-frequency (DFdriver) activated atrial regions lead the activation of the rest of the atria, disrupting the propagation wavefront. Fourier based spectral analysis of body surface potential maps have been proposed for DFdriver identification, although these approaches present serious drawbacks due to their limited spectral resolution for short AF epochs and the blurring effect of the volume conductor. Laplacian signals (BC-ECG) from bipolar concentric ring electrodes (CRE) have been shown to outperform the spatial resolution achieved with conventional unipolar recordings. Our aimed was to determine the best DFdriver estimator in endocardial electrograms and to assess the BC-ECG capacity of CRE to quantify AF activity non-invasively.

METHODS

31 AF episodes were simulated using realistic tridimensional models of the atria electrical activity and torso. Periodogram and autoregressive (AR) spectral estimators were computed and the percentile (P90^th, P95^th and P98^th) to impose on the dominant frequencies (DFs) across whole atria to define the best DFdriver estimator evaluated. The identification of DFdriver on DFs from BC-ECG and unipolar surface signals with conventional disc electrodes was compared.

RESULTS

The best DFdriver estimator was P95^th and AR order 100. BC-ECG signals allowed better detection of AF activity than unipolar signals, with a significantly greater percentage of electrode locations in which DFdriver was identified (p-value 0.0095).

CONCLUSIONS

The use of BC-ECG signals for body surface Laplacian potential mapping with CRE could be helpful for better AF diagnosis, prognosis and ablation procedures than those with conventional disk electrodes.

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.

Finite element method modeling to confirm the results of comprehensive optimization of the tripolar concentric ring electrode based on its finite dimensions model

Concentric ring electrodes are noninvasive and wearable sensors for electrophysiological measurement capable of estimating the surface Laplacian (second spatial derivative of surface potential) at each electrode. Significant progress has been made toward optimization of inter-ring distances (distances between the recording surfaces of the electrode), maximizing the accuracy of the surface Laplacian estimate based on the negligible dimensions model of the electrode. However, novel finite dimensions model offers comprehensive optimization including all of the electrode parameters simultaneously by including the radius of the central disc and the widths of the concentric rings into the model. Recently, such comprehensive optimization problem has been solved analytically for the tripolar electrode configuration. This study, for the first time, introduces a finite dimensions model based finite element method model (as opposed to the negligible dimensions model based one used in the past) to confirm the analytic results. Specifically, finite element method modeling results confirmed that previously proposed linearly increasing inter-ring distances and constant inter-ring distances configurations of tripolar concentric ring electrodes correspond to an almost two-fold and more than three-fold increases in relative and normalized maximum errors of Laplacian estimation when directly compared to the optimal tripolar concentric ring electrode configuration of the same size.Clinical Relevance- This study assesses and confirms the electrode configuration that maximizes the accuracy of the estimated Laplacian recorded via concentric ring electrodes. Therefore, it is potentially useful for designing future concentric ring electrodes for diagnostic purposes such as localization of epileptic foci.

Comprehensive Optimization of the Tripolar Concentric Ring Electrode Based on Its Finite Dimensions Model and Confirmed by Finite Element Method Modeling

The optimization performed in this study is based on the finite dimensions model of the concentric ring electrode as opposed to the negligible dimensions model used in the past. This makes the optimization problem comprehensive, as all of the electrode parameters including, for the first time, the radius of the central disc and individual widths of concentric rings, are optimized simultaneously. The optimization criterion used is maximizing the accuracy of the surface Laplacian estimation, as the ability to estimate the Laplacian at each electrode constitutes primary biomedical significance of concentric ring electrodes. For tripolar concentric ring electrodes, the optimal configuration was compared to previously proposed linearly increasing inter-ring distances and constant inter-ring distances configurations of the same size and based on the same finite dimensions model. The obtained analytic results suggest that previously proposed configurations correspond to almost two-fold and more than three-fold increases in the Laplacian estimation error compared with the optimal configuration proposed in this study, respectively. These analytic results are confirmed using finite element method modeling, which was adapted to the finite dimensions model of the concentric ring electrode for the first time. Moreover, the finite element method modeling results suggest that optimal electrode configuration may also offer improved sensitivity and spatial resolution.

Evaluation of Bipolar, Tripolar, and Quadripolar Laplacian Estimates of Electrocardiogram via Concentric Ring Electrodes

Surface Laplacian estimates via concentric ring electrodes (CREs) have proven to enhance spatial resolution compared to conventional disc electrodes, which is of great importance for P-wave analysis. In this study, Laplacian estimates for traditional bipolar configuration (BC), two tripolar configurations with linearly decreasing and increasing inter-ring distances (TC_LDIRD and TC_LIIRD, respectively), and quadripolar configuration (QC) were obtained from cardiac recordings with pentapolar CREs placed at CMV1 and CMV2 positions. Normalized P-wave amplitude (NAP) was computed to assess the contrast to study atrial activity. Signals were of good quality (20-30 dB). Atrial activity was more emphasized at CMV1 (NAP ≃ 0.19-0.24) compared to CMV2 (NAP ≃ 0.08-0.10). Enhanced spatial resolution of TC_LIIRD and QC resulted in higher NAP values than BC and TC_LDIRD. Comparison with simultaneous standard 12-lead ECG proved that Laplacian estimates at CMV1 outperformed all the limb and chest standard leads in the contrast to study P-waves. Clinical recordings with CRE at this position could allow more detailed observation of atrial activity and facilitate the diagnosis of associated pathologies. Furthermore, such recordings would not require additional electrodes on limbs and could be performed wirelessly, so it should also be suitable for ambulatory monitoring, for example, using cardiac Holter monitors.

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.

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.

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.

Stretchable Dry Electrodes with Concentric Ring Geometry for Enhancing Spatial Resolution in Electrophysiology

The multichannel concentric-ring electrodes are stencil printed on stretchable elastomers modified to improve adhesion to skin and minimize motion artifacts for electrophysiological recordings of electroencephalography, electromyography, and electrocardiography. These dry electrodes with a poly(3,4-ethylenedioxythiophene) polystyrene sulfonate interface layer are optimized to show lower noise level than that of commercial gel disc electrodes. The concentric ring geometry enables Laplacian filtering to pinpoint the bioelectric potential source with spatial resolution determined by the ring distance. This work shows a new fabrication approach to integrate and create designs that enhance spatial resolution for high-quality electrophysiology monitoring devices.