Optimal design of electrodes for functional electrical stimulation applications to single layer isotropic tissues

Abstract

Purpose The purpose of this paper is to investigate the design of skin surface electrodes for functional electrical stimulation using an isotropic single layered model of the skin and underlying tissue. A concentric ring electrode geometry was analysed and compared with a conventional configuration, specifically to localise and maximise the activation at depth and minimise the peak current density at the skin surface. Design/methodology/approach The mathematical formulation determines the spatial electric potential distribution in the tissue, using the solution to the Laplace equation in the lower half space subject to boundary conditions given by the complete electrode model and appropriate asymptotic decay. Hence, it is shown that the electric potential satisfies a weakly singular Fredholm integral equation of the second kind which is then solved numerically in MATLAB for a novel concentric ring electrode configuration and the conventional two disk side-by-side electrode configuration. Findings In both models, the electrode geometry can be optimised to obtain a higher activation and lower maximum current density. The concentric ring electrode configuration, however, provides improved performance over the traditional two disk side-by-side electrode configuration. Research limitations/implications In this study, only a single layer of medium was investigated. A comparison with multilayer tissue models and in vivo validation of numerical simulations are required. Originality/value The developed mathematical approaches and simulations revealed the parameters that influence nerve activation and facilitated the theoretical comparison of the two electrode configurations. The concentric ring configuration potentially may have significant clinical advantages.

Continuous Electrode Models and Application of Exact Schemes in Modeling of Electrical Impedance Measurements

“…Based on Figure 1, the measurement method is modeled using the following statements defined in Equation (2). The application of these constraints, and the substitution of Equation (10), simplifies the corresponding system of linear equations in Equation ( 6) in the following, easily applicable, form:…”

“…It is also remarkable that the difference between the electrodes placed on the input and the output is also highlighted. on the interval [10,11] functions are calculated using Equations ( 26), ( 25) and ( 27)), respectively. The next step in solving the case study using the CEM is to calculate the potentials based on Theorem 1 and on the derived system of the linear equation in Equation (12).…”

“…Figure 6 shows the function κ ⋆ (jω, x) at only one frequency, 0.1 Hz, due to the high dynamics of the frequency dependence. el,1 (jω, x) on the interval [0, 1], the κ m (jω, x) on the interval [1,10], and the κ ⋆ el,2 (jω, x) on the interval [10,11] functions are calculated using Equations ( 29), ( 25) and ( 30)), respectively.…”

“…are illustrated in Figure 7. (jω,x) on the interval [1,10], and the 1 κ ⋆ el,2 (jω,x) on the interval [10,11] functions are calculated using Equations ( 29), ( 25) and ( 30)), respectively.…”

“…The role of the electrode is also essential from another point of view, since electrodes are made of a conductive material and, due to the presence of galvanic connections, they significantly influence the electric field in the material [9]. Incorrect recognition and modeling of the electrodes (and the interaction between electrode and material) significantly reduces the reliability of the EI measurement since the resulting distortions and artifacts are propagated into the result generation, causing errors [10,11]. The state-of-the-art electrode modeling technique is the Complete Electrode Model (CEM), which is the basis for various EIT imaging algorithms [12][13][14].…”