Evaluation of Respiratory Muscle Activity by Means of Concentric Ring Electrodes

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.

Assessment of the Non-linear Response of the fSampEn on Simulated EMG Signals

Fixed sample entropy (fSampEn) is a promising technique for the analysis of respiratory electromyographic (EMG) signals. Its use has shown outperformance of amplitude-based estimators such as the root mean square (RMS) in the evaluation of respiratory EMG signals with cardiac noise and a high correlation with respiratory signals, allowing changes in respiratory muscle activity to be tracked. However, the relationship between the fSampEn response to a given muscle activation has not been investigated. The aim of this study was to analyze the nature of the fSampEn measurements that are produced as the EMG activity increases linearly. Simulated EMG signals were generated and increased linearly. The effect of the parameters r and the size of the moving window N of the fSampEn were evaluated and compared with those obtained using the RMS. The RMS showed a linear trend throughout the study. A non-linear, sigmoidal-like behavior was found when analyzing the EMG signals using the fSampEn. The lower the values of r, the higher the non-linearity observed in the fSampEn results. Greater moving windows reduced the variation produced by too small values of r.Clinical Relevance- Understanding the inherent non-linear relationship produced when using the fSampEn in EMG recordings will contribute to the improvement of the respiratory muscle activation assessment at different levels of respiratory effort in patients with respiratory conditions, particularly during the inspiratory phase.

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.