Arbitrary Electrode Geometries Research Articles

Choosing the right electrode representation for modeling real bioelectronic interfaces: a comprehensive guide

Objective.Producing realistic numerical models of neurostimulation electrodes in contact with the electrolyte and tissue, for use in time-domain finite element method simulations while maintaining a reasonable computational burden remains a challenge. We aim to provide a straightforward experimental-theoretical hybrid approach for common electrode materials (Ti, TiN, ITO, Au, Pt, IrOx) that are relevant to the research field of bioelectronics, along with all the information necessary to replicate our approach in arbitrary geometry for real-life experimental applications.Approach.We used electrochemical impedance spectroscopy (EIS) to extract the electrode parameters in the AC regime under different DC biases. The pulsed electrode response was obtained by fast amperometry (FA) to optimize and verify the previously obtained electrode parameters in a COMSOL Multiphysics model. For optimization of the electrode parameters a constant phase element (CPE) needed to be implemented in time-domain.Main results.We find that the parameters obtained by EIS can be used to accurately simulate pulsed response only close to the electrode open circuit potential, while at other potentials we give corrections to the obtained parameters, based on FA measurements. We also find that for many electrodes (Au, TiN, Pt, and IrOx), it is important to implement a distributed CPE rather than an ideal capacitor for estimating the electrode double-layer capacitance. We outline and provide examples for the novel time-domain implementation of the CPE for finite element method simulations in COMSOL Multiphysics.Significance.An overview of electrode parameters for some common electrode materials can be a valuable and useful tool in numerical bioelectronics models. A provided FEM implementation model can be readily adapted to arbitrary electrode geometries and used for various applications. Finally, the presented methodology for parametrization of electrode materials can be used for any materials of interest which were not covered by this work.

Prediction of partial discharge and breakdown voltages in CF4 for arbitrary electrode geometries

In literature a model was described for the simulation of the breakdown behaviour of SF6. As input parameters, results from swarm experiments—the critical field strength and the effective ionization coefficient—and thermodynamic properties are sufficient. Recently it was shown that it is possible to transfer this model to another strongly attaching gas. In this contribution the model is applied to tetrafluoromethane (CF4), which has a smaller critical field strength and is less attaching than SF6. Furthermore, the breakdown field strengths of alternating and lightning impulse voltages of different field configurations—from homogeneous to inhomogeneous fields—are predicted for CF4. A comparison to experimental results from the literature shows good agreement. Thus, the model is applicable not only to predict partial discharges and breakdown voltages in strongly attaching gases but also to gases less attaching than SF6.

Optical manipulation of charged microparticles in polar fluids

In this study, we report a systematic study of the response of a charged microparticle confined in an optical trap and driven by electric fields. The particle is embedded in a polar fluid, hence, the role of ions and counterions forming a double layer around the electrodes and the particle surface itself has been taken into account. We analyze two different cases: (i) electrodes energized by a step-wise voltage (DC mode) and (ii) electrodes driven by a sinusoidal voltage (AC mode). The experimental outcomes are analyzed in terms of a model that combines the electric response of the electrolytic cell and the motion of the trapped particle. In particular, for the DC mode we analyze the transient particle motion and correlate it with the electric current flowing in the cell. For the AC mode, the stochastic and deterministic motion of the trapped particle is analyzed either in the frequency domain (power spectral density, PSD) or in the time domain (autocorrelation function). Moreover, we will show how these different approaches (DC and AC modes) allow us, assuming predictable the applied electric field (here generated by plane parallel electrodes), to provide accurate estimation (3%) of the net charge carried by the microparticle. Vice versa, we also demonstrate how, once predetermined the charge, the trapped particle acts as a sensitive probe to reveal locally electric fields generated by arbitrary electrode geometries (in this work, wire-tip geometry).

Modeling realistic extracellular spiking activity in populations of neurons for the purpose of evaluating automatic spike-sorting algorithms

The emergence of silicon-based extracellular recording devices with large numbers of electrode contacts, such as multi-shank laminar electrodes or high-density multi-electrode arrays (MEA) now makes it possible to potentially record spiking activity from thousands of neurons simultaneously. With the concomitant increase in amounts and complexity of data, manual spike sorting is no longer an option, and there is a dire need for automatic spike-sorting methods. These methods must be able to correctly and efficiently resolve spikes of individual neurons from the recorded mixture, as discussed in a recent review [1]. For assessing the sorting quality, spike sorting methods should ideally be evaluated against test data with known ground truth, i.e., data for which the underlying spiking activity of each neuron in the recorded population is known. Unfortunately, such data sets cannot easily be acquired from experiments. One remedy is realistic, model-based simulations of extracellular recordings. Position-dependent spike shapes (Figure ​(Figure1A)1A) can straightforwardly be modeled in a biophysically realistic way by means of a recently released modeling tool, LFPy (compneuro.umb.no/LFPy), a Python implementation of a forward-modeling scheme [2] for extracellular potentials based on calculations of transmembrane currents in NEURON [3]. Figure 1 A. Position-dependent extracellular spike shapes in vicinity of a cat L5 pyramidal neuron, obtained using LFPy. B. Schematic of the evaluation of spike-sorting methods against ground-truth test data for a population of hippocampal pyramidal neurons. Test data for arbitrary electrode geometries, model neurons, noise levels and synchronicity levels can be produced at wish. Here we present example results relevant for tetrode and polytrode recordings in cortex and hippocampus. We also present test data for situations where prominent electrical boundary-condition effects significantly modify the recorded potentials, and FEM modeling must be used to solve the electrostatic problem. This is of particular relevance for cell cultures or retinal slices placed on high density MEAs. An algorithm evaluation website has been set up on http://www.g-node.org/spike to facilitate use of such benchmark data to evaluate the performance of spike sorting algorithms, as outlined in Figure ​Figure1B1B.

Computation of ac responses of arbitrary electrode geometries from the corresponding secondary current distributions: A method based on analytic continuation

A method of analytic continuation is advanced for computing ac responses of electrochemical systems with arbitrary electrode geometries and proposed as an exact alternative to the approximate and intuitive transmission line models (TLMs). Using a complex extension of the boundary element method, the small signal ac responses were computed for several Hull cell geometries, the rectangular pore, the saw-tooth and a fractal geometry. A comparison with the results of the TLMs for the rectangular pore and the saw-tooth reveal quantitative as well as qualitative differences. Besides providing a bench-mark for such approximate theories, the present method may well be the only option for system geometries not amenable to a TLM. An alternative approach to the study of the constant phase element based on analytic continuation is also sketched.

Analysis of semiconductor nuclear radiation detectors with arbitrary electrode geometries

This paper develops a theoretical framework and sets of differential and integral equations for analyzing the operating characteristics of semiconductor nuclear radiation detectors with arbitrary electrode geometries. Results provide a basis for conceptualization and numerical calculations and are relevant to recent substantial improvements in detector performance achieved through various single-carrier charge collection schemes based on special electrode configurations. During the course of the work, the approach known as static charge analysis is extended to three dimensions and placed on a firmer theoretical basis.

High order calculation of the multipole content of three dimensional electrostatic geometries

We present an accurate and simple method of 3-D multipole decomposition of the field of arbitrary electrode geometries. The induced charge on the surface is obtained by inverting the capacity matrix. The multipole moment decomposition of the resulting potential is readily accomplished using differential algebra methodology. The method is applied to the focussing lattice geometry of the MBE-4 accelerator at LBL. Multipole terms of up to the order 5 are computed, and a numerical accuracy of <1% is obtained. The effective quadrupole and dodecapole field strength are in good agreement with previous results.

Representation of reversible current for arbitrary electrode geometries and arbitrary potential modulation

For simple electron transfer O+ n e − ⇄ R with equal diffusion coefficients ( D o = D R), it is shown that reversible current can be expressed in terms of diffusion-limited current for arbitrary cell/electrode geometries and arbitrary time-dependent potentials. This result provides a better understanding of a formula due to Aoki and co-workers and suggests new experimental approaches which simplify interpretation of data obtained at microelectrodes.

Inhomogeneous field breakdown in GIS-the prediction of breakdown probabilities and voltages. I. Overview of a theory for inhomogeneous field breakdown in SF/sub 6/

Inhomogeneous field breakdown in SF/sub 6/ has been investigated, and a theory has been developed which predicts the breakdown voltage for fast-rising (rectangular) waveforms applied to arbitrary electrode geometries and gas pressures. This theory facilitates the analytical design aspects of many GIS components where previously, engineering judgement and development testing were necessary. It is suggested that extensions of the theory, will permit breakdown voltage prediction for an arbitrary surge waveform, which will facilitate the assessment of test waveform efficacy and the development of a more reliable field, factory, and type tests.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Simplifications in the theory of step experiments at microelectrodes

Theoretical studies of the chronoamperometry of the reaction O+ n e − ⇄ R often consider (1) the diffusion-limited reaction, (2) the totally irreversible reaction, and (3) the reversible reaction (governed by the Nernst equation), and these can all be considered as special limiting cases of (4) quasi-reversible reactions, electron transfer kinetics governed by the general current-potential characteristic. Cases (1) and (2) simplify to one-component diffusion systems for the concentration of O; cases (3) and (4) are necessarily two-component diffusion systems involving the concentrations of both O and R. We show that, when O and R have equal diffusion coefficients, the solution for the reversible reaction (3) can be expressed in terms of the solution for the diffusion-limited reaction (1) and that the solution for the quasi-reversible reaction (4) can be expressed in terms of the solution for the totally irreversible reaction (2). These results hold for arbitrary electrode geometries.

Analysis of a model for excitation of myelinated nerve.

Excellent models have been presented in the literature which relate membrane potential to transverse membrane current and which describe the propagation of action potentials along the axon, for both myelinated and nonmyelinated fibers. There is not, however, an adequate model for nerve excitation which allows one to compute the threshold of a nerve fiber for pulses of finite duration using electrodes that are not in direct contact with the fiber. This paper considers this problem and presents a model of the electrical properties of myelinated nerve which describes the time course of events following stimulus application up to the initiation of the action potential. The time-varying current and potential at all nodes can be computed from the model, and the strength-duration curve can be determined for arbitrary electrode geometries, although only the case of a monopolar electrode is considered in this paper. It is shown that even when the stimulus is a constant-current pulse, the membrane current at the nodes varies considerably with time. The strength-duration curve calculated from the model is consistent with previously published experimental data, and the model provides a quantitative relationship between threshold and fiber diameter which shows there is less selectivity among fibers of large diameter than those of small diameter.