Extracellular stimulation window explained by a geometry-based model of the neuron-electrode contact

A finite element method framework to model extracellular neural stimulation

OBJECTIVE

Increasing complexity in extracellular stimulation experiments and neural implant design also requires realistic computer simulations capable of modeling the neural activity of nerve cells under the influence of an electrical stimulus. Classical model approaches are often based on simplifications, are not able to correctly calculate the electric field generated by complex electrode designs, and do not consider electrical effects of the cell on its surrounding. A more accurate approach is the finite element method (FEM), which provides necessary techniques to solve the Poisson equation for complex geometries under consideration of electrical tissue properties. Especially in situations where neurons experience large and non-symmetric extracellular potential gradients, a FEM solution that implements the cell membrane model can improve the computer simulation results. To investigate the response of neurons in an electric field generated by complex electrode designs, a FEM framework for extracellular stimulation was developed in COMSOL.

APPROACH

Methods to implement morphologically- and biophysically-detailed neurons including active Hodgkin-Huxley (HH) cell membrane dynamics as well as the stimulation setup are described in detail. Covered methods are (i) development of cell and electrode geometries including meshing strategies, (ii) assignment of physics for the conducting spaces and the realization of active electrodes, (iii) implementation of the HH model, and (iv) coupling of the physics to get a fully described model.

MAIN RESULTS

Several implementation examples are briefly presented: (i) a full FEM implementation of a HH model cell stimulated with a honeycomb electrode, (ii) the electric field of a cochlear electrode placed inside the cochlea, and (iii) a proof of concept implementation of a detailed double-cable cell membrane model for myelinated nerve fibers.

SIGNIFICANCE

The presented concepts and methods provide basic and advanced techniques to realize a full FEM framework for innovative studies of neural excitation in response to extracellular stimulation.

Block Phenomena During Electric Micro-Stimulation of Pyramidal Cells and Retinal Ganglion Cells

Electric micro-stimulation of the nervous system is a means to restore various body functions. The stimulus amplitude necessary to generate action potentials, the lower threshold (LT), is well characterized for many neuronal populations. However, electric overstimulation above an upper threshold (UT) prevents action potential generation and therefore hinders optimal neuro-rehabilitation. Previous studies demonstrated the impact of the UT in micro-stimulation of retinal ganglion cells (RGCs). The observed phenomenon is mostly explained by (i) reversed sodium ion flow in the soma membrane, and (ii) anodal surround block that hinders spike conduction in strongly hyperpolarized regions of the axon at high stimulus intensities. However, up to now, no detailed study of the nature of these phenomena has been presented, particularly for different cell types. Here, we present computational analyses of LT and UT for layer 5 pyramidal cells (PCs) as well as alpha RGCs. Model neurons were stimulated in close vicinity to the cell body and LTs and UTs as well as the ratio UT/LT were compared. Aside from a simple point source electrode and monophasic stimuli also realistic electrode and pulse configurations were examined. The analysis showed: (i) in RGCs, the soma contributed to action potential initiation and block for small electrode distances, whereas in PCs the soma played no role in LTs or UTs. (ii) In both cell types, action potential always initiated within the axon initial segment at LT. (iii) In contrast to a complete block of spike conductance at UT that occurred in RGCs, an incomplete block of spiking appeared in PC axon collaterals. (iv) PC axon collateral arrangement influenced UTs but had small impact on LTs. (v) Population responses of RGCs change from circular regions of activation to ring-shaped patterns for increasing stimulus amplitude. A better understanding of the stimulation window that can reliably activate target neurons will benefit the future development of neuroprostheses.

Analysis of upper threshold mechanisms of spherical neurons during extracellular stimulation

Exceeding a certain stimulation strength can prevent the generation of somatic action potentials, as has been demonstrated in vitro with extracellularly stimulated dorsal root ganglion cells as well as retinal ganglion cells. This phenomenon, termed upper threshold, is currently thought to be a consequence of sodium current reversal in strongly depolarized regions. Here we analyze the contribution of membrane kinetics, using spherical model neurons that are stimulated externally with a microelectrode, in more detail. During extracellular pulse application, the electric field depolarizes one part and hyperpolarizes the other part of the cell. Strong transmembrane currents are generated only in the active depolarized region, changing the overall polarization level. The asymmetric membrane voltage distribution caused by the stimulus strongly influences the cell's behavior during and even after the stimulus. Effects on membrane voltage and transmembrane currents during and after the stimulus are shown and discussed in detail. Aside from the sodium current reversal, two more key mechanisms were identified in causing the upper threshold: strong potassium currents and inactivation of sodium channels. The contributions of the mechanisms involved strongly depend on cell properties, stimulus parameters, and other factors such as temperature. The conclusions presented here are based on several retinal ganglion cell models of the Fohlmeister group, a model with original Hodgkin-Huxley membrane, and a pyramidal cell model. NEW & NOTEWORTHY The upper threshold phenomenon in extracellular stimulation is analyzed in detail for spherical cells. Three main mechanisms were identified that prevent the generation of action potentials at high stimulation strengths: 1) strong potassium currents, 2) inactivating sodium ion channels, and 3) sodium current reversal. Ion channel kinetics in retinal ganglion cells, pyramidal cells, and the original Hodgkin-Huxley model were investigated under the influence of an extracellular stimulus.

The thermal voltage fluctuations in the planar core-coat conductor of a neuron-semiconductor interface

The extracellular electrical interfacing of nerve cells with metals or semiconductors is governed by the resistance of the cell-solid junction. With snail neurons on a CMOS chip, we have probed the thermal voltage fluctuations in the junction at a spatial resolution of 7.4 μm in a spectral range from 10 Hz to 1 MHz using an array of sensor transistors. The power spectral density (PSD) could be interpreted in terms of a Johnson-Nyquist noise if the distributed nature of the cell-solid junction and the size of the sensors were taken into account. The PSD over the whole spectral range as well as its spatial profile were matched by the thermal noise of a circular core-coat conductor with a homogeneous sheet resistance in the range of 100 MΩ. The quantitative interpretation of the thermal noise in a cell-solid junction provides a basis for applications of this noninvasive method in the characterization of biosensoric and neuroprosthetic devices.

Properties and application of a multichannel integrated circuit for low-artifact, patterned electrical stimulation of neural tissue

OBJECTIVE

Modern multielectrode array (MEA) systems can record the neuronal activity from thousands of electrodes, but their ability to provide spatio-temporal patterns of electrical stimulation is very limited. Furthermore, the stimulus-related artifacts significantly limit the ability to record the neuronal responses to the stimulation. To address these issues, we designed a multichannel integrated circuit for a patterned MEA-based electrical stimulation and evaluated its performance in experiments with isolated mouse and rat retina.

APPROACH

The Stimchip includes 64 independent stimulation channels. Each channel comprises an internal digital-to-analogue converter that can be configured as a current or voltage source. The shape of the stimulation waveform is defined independently for each channel by the real-time data stream. In addition, each channel is equipped with circuitry for reduction of the stimulus artifact.

MAIN RESULTS

Using a high-density MEA stimulation/recording system, we effectively stimulated individual retinal ganglion cells (RGCs) and recorded the neuronal responses with minimal distortion, even on the stimulating electrodes. We independently stimulated a population of RGCs in rat retina, and using a complex spatio-temporal pattern of electrical stimulation pulses, we replicated visually evoked spiking activity of a subset of these cells with high fidelity. Significance. Compared with current state-of-the-art MEA systems, the Stimchip is able to stimulate neuronal cells with much more complex sequences of electrical pulses and with significantly reduced artifacts. This opens up new possibilities for studies of neuronal responses to electrical stimulation, both in the context of neuroscience research and in the development of neuroprosthetic devices.

Upper threshold of extracellular neural stimulation

It is well known that spiking neurons can produce action potentials in response to extracellular stimulation above certain threshold. It is widely assumed that there is no upper limit to somatic stimulation, except for cellular or electrode damage. Here we demonstrate that there is an upper stimulation threshold, above which no action potential can be elicited, and it is below the threshold of cellular damage. Existence of this upper stimulation threshold was confirmed in retinal ganglion cells (RGCs) at pulse durations ranging from 5 to 500 μs. The ratio of the upper to lower stimulation thresholds varied typically from 1.7 to 7.6, depending on pulse duration. Computational modeling of extracellular RGC stimulation explained the upper limit by sodium current reversal on the depolarized side of the cell membrane. This was further confirmed by experiments in the medium with a low concentration of sodium. The limited width of the stimulation window may have important implications in design of the electro-neural interfaces, including neural prosthetics.

A topographically modified substrate-embedded MEA for directed myotube formation at electrode contact sites

Myoblast fusion into functionally distinct myotubes, and their subsequent integration with the nervous system, is a poorly understood phenomenon with important applications in basic science research, skeletal muscle tissue engineering, and cell-based biosensor development. We have previously demonstrated the ability of microelectrode arrays (MEAs) to record the extracellular action potentials of myotubes, and we have shown that this information reveals the presence of multiple, electrophysiologically independent myotubes even in unstructured cultures where there is extensive physical contact between cells (Langhammer et al., Biotechnol Prog 27:891-895, 2011). In this paper, we explore the ability of microscale topographical trenches to guide the myoblast alignment and fusion processes and use our findings to create a substrate-embedded MEA containing topographical trenches that are able to direct myotube contractility to specific locations. By combining substrate-embedded MEA technology with topographical patterns, we have developed a lab-on-a-chip test bed for the non-invasive examination of myotubes.

Modeling extracellular electrical neural stimulation: from basic understanding to MEA-based applications

Extracellular electrical stimulation of neural networks has been widely used empirically for decades with individual electrodes. Since recently, microtechnology provides advanced systems with high-density microelectrode arrays (MEAs). Taking the most of these devices for fundamental goals or developing neural prosthesis requires a good knowledge of the mechanisms underlying electrical stimulation. Here, we review modeling approaches used to determine (1) the electric potential field created by a stimulation and (2) the response of an excitable cell to an applied field. Computation of the potential field requires solving the Poisson equation. While this can be performed analytically in simple electrode-neuron configurations, numerical models are required for realistic geometries. In these models, special care must be taken to model the potential drop at the electrode/tissue interface using appropriate boundary conditions. The neural response to the field can then be calculated using compartmentalized cell models, by solving a cable equation, the source term of which (called activating function) is proportional to the second derivative of the extracellular field along the neural arborization. Analytical and numerical solutions to this equation are first presented. Then, we discuss the use of approximated solutions to intuitively predict the neuronal response: Either the "activating function" or the "mirror estimate", depending on the pulse duration and the cell space constant. Finally, we address the design of optimal electrode configurations allowing the selective activation of neurons near each stimulation site. This can be achieved using either multipolar configurations, or the "ground surface" configuration, which can be easily integrated in high-density MEAs. Overall, models highlighting the mechanisms of electrical microstimulation and improving stimulating devices should help understanding the influence of extracellular fields on neural elements and developing optimized neural prostheses for rehabilitation.

Fabrication and characterization of 3D micro- and nanoelectrodes for neuron recordings

In this paper we discuss the fabrication and characterization of three dimensional (3D) micro- and nanoelectrodes with the goal of using them for extra- and intracellular studies. Two different types of electrodes will be described: high aspect ratio microelectrodes for studying the communication between cells and ultimately for brain slice recordings and small nanoelectrodes for highly localized measurements and ultimately for intracellular studies. Electrical and electrochemical characterization of these electrodes as well as the results of PC12 cell differentiation on chip will be presented and discussed.

Iridium oxide microelectrode arrays for in vitro stimulation of individual rat neurons from dissociated cultures

We present the first in vitro extracellular stimulation of individual neurons from dissociated cultures with iridium oxide (IrO_x) electrodes. Microelectrode arrays with sputtered IrO_x films (SIROF) were developed for electrophysiological investigations with electrogenic cells. The microelectrodes were characterized with scanning electron and atomic force microscopy, revealing rough and porous electrodes with enlarged surface areas. As shown by cyclic voltammetry and electrochemical impedance spectroscopy, the large surface area in combination with the good electrochemical properties of SIROF resulted in high charge storage capacity and low electrode impedance. Thus, we could transfer the good properties of IrO_x as material for in vivo stimulation electrodes to multi-electrode arrays with electrode diameters as small as 10 μm for in vitro applications. Single rat cortical neurons from dissociated cultures were successfully stimulated to fire action potentials using single or trains of biphasic rectangular voltage-controlled stimulation pulses. The stimulated cell's membrane potential was simultaneously monitored using whole-cell current-clamp recordings. This experimental configuration allowed direct evaluation of the influence of pulse phase sequence, amplitude, and number on the stimulation success ratio and action potential latency. Negative phase first pulses were more effective for extracellular stimulation and caused reduced latency in comparison to positive phase first pulses. Increasing the pulse amplitude also improved stimulation reliability. However, in order to prevent cell or electrode damage, the pulse amplitude is limited to voltages below the threshold for irreversible electrochemical reactions at the electrode. As an alternative to increasing the amplitude, a higher number of stimulation pulses was also shown to increase stimulation success.

Improved focalization of electrical microstimulation using microelectrode arrays: a modeling study

Extracellular electrical stimulation (EES) of the central nervous system (CNS) has been used empirically for decades, with both fundamental and clinical goals. Currently, microelectrode arrays (MEAs) offer new possibilities for CNS microstimulation. However, although focal CNS activation is of critical importance to achieve efficient stimulation strategies, the precise spatial extent of EES remains poorly understood. The aim of the present work is twofold. First, we validate a finite element model to compute accurately the electrical potential field generated throughout the extracellular medium by an EES delivered with MEAs. This model uses Robin boundary conditions that take into account the surface conductance of electrode/medium interfaces. Using this model, we determine how the potential field is influenced by the stimulation and ground electrode impedances, and by the electrical conductivity of the neural tissue. We confirm that current-controlled stimulations should be preferred to voltage-controlled stimulations in order to control the amplitude of the potential field. Second, we evaluate the focality of the potential field and threshold-distance curves for different electrode configurations. We propose a new configuration to improve the focality, using a ground surface surrounding all the electrodes of the array. We show that the lower the impedance of this surface, the more focal the stimulation. In conclusion, this study proposes new boundary conditions for the design of precise computational models of extracellular stimulation, and a new electrode configuration that can be easily incorporated into future MEA devices, either in vitro or in vivo, for a better spatial control of CNS microstimulation.

Neural networks on chemically patterned electrode arrays: towards a cultured probe

One type of future, improved neural interfaces is the 'cultured probe'. It is a hybrid type of neural information transducer or prosthesis, for stimulation and/or recording of neural activity. It would consist of a micro-electrode array (MEA) on a planar substrate, each electrode being covered and surrounded by a local circularly confined network ('island') of cultured neurons. The main purpose of the local networks is that they act as bio-friendly intermediates for collateral sprouts from the in vivo system, thus allowing for an effective and selective neuron electrode interface. As a secondary purpose, one may envisage future information processing applications of these intermediary networks. In this chapter, first, progress is shown on how substrates can be chemically modified to confine developing networks, cultured from dissociated rat cortex cells, to 'islands' surrounding an electrode site. Additional coating of neurophobic, polyimide coated substrate by tri-block-copolymer coating enhances neurophilic-neurophobic adhesion contrast. Secondly, results are given on neuronal activity in patterned, unconnected and connected, circular 'island' networks. For connected islands, the larger the island diameter (50, 100 or 150 microm), the more spontaneous activity is seen. Also, activity may show a very high degree of synchronization between two islands. For unconnected islands, activity may start at 22 days in vitro (DIV), which is two weeks later than in unpatterned networks.

A CMOS-based microelectrode array for interaction with neuronal cultures

We report on the system integration of a CMOS chip that is capable of bidirectionally communicating (stimulation and recording) with electrogenic cells such as neurons or cardiomyocytes and that is targeted at investigating electrical signal propagation within cellular networks in vitro. The overall system consists of three major subunits: first, the core component is a 6.5 mm x 6.5 mm CMOS chip, on top of which the cells are cultured. It features 128 bidirectional electrodes, each equipped with dedicated analog filters and amplification stages and a stimulation buffer. The electrodes are sampled at 20 kHz with 8-bit resolution. The measured input-referred circuitry noise is 5.9 microV root mean square (10 Hz to 100 kHz), which allows to reliably detect the cell signals ranging from 1 mVpp down to 40 microVpp. Additionally, temperature sensors, a digital-to-analog converter for stimulation, and a digital interface for data transmission are integrated. Second, there is a reconfigurable logic device, which provides chip control, event detection, data buffering and an USB interface, capable of processing the 2.56 million samples per second. The third element includes software that is running on a standard PC performing data capturing, processing, and visualization. Experiments involving the stimulation of neurons with two different spatio-temporal patterns and the recording of the triggered spiking activity have been carried out. The response patterns have been successfully classified (83% correct) with respect to the different stimulation patterns. The advantages over current microelectrode arrays, as has been demonstrated in the experiments, include the capability to stimulate (voltage stimulation, 8 bit, 60 kHz) spatio-temporal patterns on arbitrary sets of electrodes and the fast stimulation reset mechanism that allows to record neuronal signals on a stimulating electrode 5 ms after stimulation (instantaneously on all other electrodes). Other advantages of the overall system include the small number of needed electrical connections due to the digital interface and the short latency time that allows to initiate a stimulation less than 2 ms after the detection of an action potential in closed-loop configurations.

The mechanism of extracellular stimulation of nerve cells on an electrolyte-oxide-semiconductor capacitor

Extracellular excitation of neurons is applied in studies of cultured networks and brain tissue, as well as in neuroprosthetics. We elucidate its mechanism in an electrophysiological approach by comparing voltage-clamp and current-clamp recordings of individual neurons on an insulated planar electrode. Noninvasive stimulation of neurons from pedal ganglia of Lymnaea stagnalis is achieved by defined voltage ramps applied to an electrolyte/HfO2/silicon capacitor. Effects on the smaller attached cell membrane and the larger free membrane are distinguished in a two-domain-stimulation model. Under current-clamp, we study the polarization that is induced for closed ion channels. Under voltage-clamp, we determine the capacitive gating of ion channels in the attached membrane by falling voltage ramps and for comparison also the gating of all channels by conventional variation of the intracellular voltage. Neuronal excitation is elicited under current-clamp by two mechanisms: Rising voltage ramps depolarize the free membrane such that an action potential is triggered. Falling voltage ramps depolarize the attached membrane such that local ion currents are activated that depolarize the free membrane and trigger an action potential. The electrophysiological analysis of extracellular stimulation in the simple model system is a basis for its systematic optimization in neuronal networks and brain tissue.

Three dimensional transport lattice model for describing action potentials in axons stimulated by external electrodes

Conditions that stimulate action potentials in one or more nerves is of widespread interest. Axon and nerve models are usually based on two dimensional pre-specified lumped equivalents that assume where currents will flow. In contrast, here we illustrate creation of three dimensional (3D) system models with a transport lattice of interconnected local models for external and internal electrolyte and axon membrane. The transport lattice solves Laplace's equation in the extracellular medium and is coupled to the Hodgkin-Huxley model at local membrane sites. These space-filling models incorporate the geometric scale, which allows explicit representation of confined axons and external electrodes. The present results demonstrate feasibility of the basic approach. These models are spatially coarse and approximate, but can be straightforwardly improved. The transport lattice system models are modular and multiscale (spatial scales ranging from the membrane thickness of 5 nm to the axon segment length of 2 cm).

Model of a confined spherical cell in uniform and heterogeneous applied electric fields

Cells exposed to electric fields are often confined to a small volume within a solid tissue or within or near a device. Here we report on an approach to describing the frequency and time domain electrical responses of a spatially confined spherical cell by using a transport lattice system model. Two cases are considered: (1) a uniform applied field created by parallel plane electrodes, and (2) a heterogeneous applied field created by a planar electrode and a sharp microelectrode. Here fixed conductivities and dielectric permittivities of the extra- and intracellular media and of the membrane are used to create local transport models that are interconnected to create the system model. Consistent with traditional analytical solutions for spherical cells in an electrolyte of infinite extent, in the frequency domain the field amplification, G(m) (f) is large at low frequencies, f<1 MHz. G(m) (f) gradually decreases above 1 MHz and reaches a lower plateau at about 300 MHz, with the cell becoming almost "electrically invisible". In the time domain the application of a field pulse can result in altered localized transmembrane voltage changes due to a single microelectrode. The transport lattice approach provides modular, multiscale modeling capability that here ranges from cell membranes (5 nm scale) to the cell confinement volume ( approximately 40 microm scale).

Geometry-based finite-element modeling of the electrical contact between a cultured neuron and a microelectrode

The electrical contact between a substrate embedded microelectrode and a cultured neuron depends on the geometry of the neuron-electrode interface. Interpretation and improvement of these contacts requires proper modeling of all coupling mechanisms. In literature, it is common practice to model the neuron-electrode contact using lumped circuits in which large simplifications are made in the representation of the interface geometry. In this paper, the finite-element method is used to model the neuron-electrode interface, which permits numerical solutions for a variety of interface geometries. The simulation results offer detailed spatial and temporal information about the combined electrical behavior of extracellular volume, electrode-electrolyte interface and neuronal membrane.