Electrode modelling for applications of functional electrical stimulation

Abstract

Non-invasive Functional Electrical Stimulation (FES) is the technique of safely applying current via skin surface electrodes to artificially activate nerve fibres to restore impaired body function, such as muscle contraction. The challenge is effective nerve stimulation with minimal tissue trauma. In this thesis, the experimental setup of FES was mathematically modelled to optimise the electrode design. To this end, the Laplace equation with appropriate boundary conditions was solved analytically using the complete electrode model to determine the spatial electric potential distribution in a layered lower half-space of piecewise constant conductivity. A weakly singular Fredholm integral equation of the second kind was obtained for the single layer model while the novel approach using Hankel transforms for multilayered tissues yielded a coupled system of such integral equations with kernels consisting of products of Bessel functions. The equations were solved numerically, and the models implemented in MATLAB. The simulations carried out focused on increasing activation at the nerve depth while minimising the peaks of current density at the edges of the electrodes. An unconventional concentric ring electrode configuration was compared to the traditional two disk one currently used for FES. The FES experimental setup was also tested in vitro on agar phantoms. MATLAB modelling using COMSOL software was used to validate the measurements recorded. The challenge was to model the contact impedance by an electrical equivalent circuit using a constant current source. The MATLAB models were also validated in COMSOL. Finally, skin surface FES applied to the posterior tibial nerve at the ankle for bladder control was modelled using tissue and bone structure data from MRI scanning and converted to a COMSOL model of nerve activation. Numerical simulations revealed that the novel concentric ring electrode configuration proposed for FES applications gives a better performance than the traditional ones currently in use. Furthermore, the design of skin surface electrodes can be optimised for specific medical applications, but nerve activation is highly impacted by the fat tissue layer.