Electrode Spacing and Current Distribution in Electrical Stimulation of Peripheral Nerve: A Computational Modeling Study using Realistic Nerve Models

Electrical stimulation of peripheral nerves has long been used and proven effective in restoring function caused by disease or injury. Accurate placement of electrodes is often critical to properly excite the nerve and yield the desired outcome. Computational modeling is becoming an important tool that can guide the rapid development and optimization of such implantable neural stimulation devices. Here, we developed a heterogeneous very high-resolution computational model of a realistic peripheral nerve stimulated by a current source through cuff electrodes. We then calculated the current distribution inside the nerve and investigated the effect of electrodes spacing on current penetration. In the present study, we first describe model implementation and calibration; we then detail the methodology we use to calculate current distribution and apply it to characterize the effect of electrodes distance on current penetration. Our computational results indicate that when the source and return cuff electrodes are placed close to each other, the penetration depth in the nerve is shallower than the cases in which the electrode distance is larger. This study outlines the utility of the proposed computational methods and anatomically correct high-resolution models in guiding and optimizing experimental nerve stimulation protocols.

Electrical stimulation of cranial nerves in cognition and disease

The cranial nerves are the pathways through which environmental information (sensation) is directly communicated to the brain, leading to perception, and giving rise to higher cognition. Because cranial nerves determine and modulate brain function, invasive and non-invasive cranial nerve electrical stimulation methods have applications in the clinical, behavioral, and cognitive domains. Among other neuromodulation approaches such as peripheral, transcranial and deep brain stimulation, cranial nerve stimulation is unique in allowing axon pathway-specific engagement of brain circuits, including thalamo-cortical networks. In this review we amalgamate relevant knowledge of 1) cranial nerve anatomy and biophysics; 2) evidence of the modulatory effects of cranial nerves on cognition; 3) clinical and behavioral outcomes of cranial nerve stimulation; and 4) biomarkers of nerve target engagement including physiology, electroencephalography, neuroimaging, and behavioral metrics. Existing non-invasive stimulation methods cannot feasibly activate the axons of only individual cranial nerves. Even with invasive stimulation methods, selective targeting of one nerve fiber type requires nuance since each nerve is composed of functionally distinct axon-types that differentially branch and can anastomose onto other nerves. None-the-less, precisely controlling stimulation parameters can aid in affecting distinct sets of axons, thus supporting specific actions on cognition and behavior. To this end, a rubric for reproducible dose-response stimulation parameters is defined here. Given that afferent cranial nerve axons project directly to the brain, targeting structures (e.g. thalamus, cortex) that are critical nodes in higher order brain networks, potent effects on cognition are plausible. We propose an intervention design framework based on driving cranial nerve pathways in targeted brain circuits, which are in turn linked to specific higher cognitive processes. State-of-the-art current flow models that are used to explain and design cranial-nerve-activating stimulation technology require multi-scale detail that includes: gross anatomy; skull foramina and superficial tissue layers; and precise nerve morphology. Detailed simulations also predict that some non-invasive electrical or magnetic stimulation approaches that do not intend to modulate cranial nerves per se, such as transcranial direct current stimulation (tDCS) and transcranial magnetic stimulation (TMS), may also modulate activity of specific cranial nerves. Much prior cranial nerve stimulation work was conceptually limited to the production of sensory perception, with individual titration of intensity based on the level of perception and tolerability. However, disregarding sensory emulation allows consideration of temporal stimulation patterns (axon recruitment) that modulate the tone of cortical networks independent of sensory cortices, without necessarily titrating perception. For example, leveraging the role of the thalamus as a gatekeeper for information to the cerebral cortex, preventing or enhancing the passage of specific information depending on the behavioral state. We show that properly parameterized computational models at multiple scales are needed to rationally optimize neuromodulation that target sets of cranial nerves, determining which and how specific brain circuitries are modulated, which can in turn influence cognition in a designed manner.

Flat electrode contacts for vagus nerve stimulation

The majority of available systems for vagus nerve stimulation use helical stimulation electrodes, which cover the majority of the circumference of the nerve and produce largely uniform current density within the nerve. Flat stimulation electrodes that contact only one side of the nerve may provide advantages, including ease of fabrication. However, it is possible that the flat configuration will yield inefficient fiber recruitment due to a less uniform current distribution within the nerve. Here we tested the hypothesis that flat electrodes will require higher current amplitude to activate all large-diameter fibers throughout the whole cross-section of a nerve than circumferential designs. Computational modeling and in vivo experiments were performed to evaluate fiber recruitment in different nerves and different species using a variety of electrode designs. Initial results demonstrated similar fiber recruitment in the rat vagus and sciatic nerves with a standard circumferential cuff electrode and a cuff electrode modified to approximate a flat configuration. Follow up experiments comparing true flat electrodes to circumferential electrodes on the rabbit sciatic nerve confirmed that fiber recruitment was equivalent between the two designs. These findings demonstrate that flat electrodes represent a viable design for nerve stimulation that may provide advantages over the current circumferential designs for applications in which the goal is uniform activation of all fascicles within the nerve.

PyPNS: Multiscale Simulation of a Peripheral Nerve in Python

Bioelectronic Medicines that modulate the activity patterns on peripheral nerves have promise as a new way of treating diverse medical conditions from epilepsy to rheumatism. Progress in the field builds upon time consuming and expensive experiments in living organisms. To reduce experimentation load and allow for a faster, more detailed analysis of peripheral nerve stimulation and recording, computational models incorporating experimental insights will be of great help. We present a peripheral nerve simulator that combines biophysical axon models and numerically solved and idealised extracellular space models in one environment. We modelled the extracellular space as a three-dimensional resistive continuum governed by the electro-quasistatic approximation of the Maxwell equations. Potential distributions were precomputed in finite element models for different media (homogeneous, nerve in saline, nerve in cuff) and imported into our simulator. Axons, on the other hand, were modelled more abstractly as one-dimensional chains of compartments. Unmyelinated fibres were based on the Hodgkin-Huxley model; for myelinated fibres, we adapted the model proposed by McIntyre et al. in 2002 to smaller diameters. To obtain realistic axon shapes, an iterative algorithm positioned fibres along the nerve with a variable tortuosity fit to imaged trajectories. We validated our model with data from the stimulated rat vagus nerve. Simulation results predicted that tortuosity alters recorded signal shapes and increases stimulation thresholds. The model we developed can easily be adapted to different nerves, and may be of use for Bioelectronic Medicine research in the future.

On the parameters used in finite element modeling of compound peripheral nerves

OBJECTIVE

Computational modeling is an important tool for developing and optimizing implantable neural stimulation devices, but requires accurate electrical and geometrical parameter values to improve predictive value. We quantified the effects of perineurial (resistive sheath around each fascicle) and endoneurial (within each fascicle) parameter values for modeling peripheral nerve stimulation.

APPROACH

We implemented 3D finite element models of compound peripheral nerves and cuff electrodes to quantify activation and block thresholds of model axons. We also implemented a 2D finite element model of a bundle of axons to estimate the bulk transverse endoneurial resistivity; we compared numerical estimates to an analytical solution.

MAIN RESULTS

Since the perineurium is highly resistive, potentials were approximately constant over the cross section of a fascicle, and the perineurium resistivity, longitudinal endoneurial resistivity, and fascicle diameter had important effects on thresholds. Activation thresholds increased up to ~130% for higher perineurium resistivity (~400 versus 2200 Ω m) and by ~35%-250% for lower longitudinal endoneurial resistivity (3.5 versus 0.75 Ω m), with larger increases for smaller diameter axons and for axons in larger fascicles. Further, thresholds increased by ~30%-180% for larger fascicle radii, yielding a larger increase with higher perineurium resistivity. Thresholds were largely insensitive to the transverse endoneurial resistivity, but estimates of the bulk resistivity increased with extracellular resistivity and axonal area fraction; the numerical and analytical estimates were in strong agreement except at high axonal area fractions, where structured axon placements that achieved tighter packing produced electric field inhomogeneities.

SIGNIFICANCE

We performed a systematic investigation of the effects of values and methods for modeling the perineurium and endoneurium on thresholds for neural stimulation and block. These results provide guidance for future modeling studies, including parameter selection, data interpretation, and comparison to experimental results.

High-Resolution Multi-Scale Computational Model for Non-Invasive Cervical Vagus Nerve Stimulation

OBJECTIVES

To develop the first high-resolution, multi-scale model of cervical non-invasive vagus nerve stimulation (nVNS) and to predict vagus fiber type activation, given clinically relevant rheobase thresholds.

METHODS

An MRI-derived Finite Element Method (FEM) model was developed to accurately simulate key macroscopic (e.g., skin, soft tissue, muscle) and mesoscopic (cervical enlargement, vertebral arch and foramen, cerebral spinal fluid [CSF], nerve sheath) tissue components to predict extracellular potential, electric field (E-Field), and activating function along the vagus nerve. Microscopic scale biophysical models of axons were developed to compare axons of varying size (Aα-, Aβ- and Aδ-, B-, and C-fibers). Rheobase threshold estimates were based on a step function waveform.

RESULTS

Macro-scale accuracy was found to determine E-Field magnitudes around the vagus nerve, while meso-scale precision determined E-field changes (activating function). Mesoscopic anatomical details that capture vagus nerve passage through a changing tissue environment (e.g., bone to soft tissue) profoundly enhanced predicted axon sensitivity while encapsulation in homogenous tissue (e.g., nerve sheath) dulled axon sensitivity to nVNS.

CONCLUSIONS

These findings indicate that realistic and precise modeling at both macroscopic and mesoscopic scales are needed for quantitative predictions of vagus nerve activation. Based on this approach, we predict conventional cervical nVNS protocols can activate A- and B- but not C-fibers. Our state-of-the-art implementation across scales is equally valuable for models of spinal cord stimulation, cortex/deep brain stimulation, and other peripheral/cranial nerve models.

Simulation of effects of the electrode structure and material in the density measuring system of the peripheral nerve based on micro-electrical impedance tomography

The electrode structure in micro-electrical impedance tomography (MEIT) highly influences the measurement sensitivity and therefore the reconstructed image quality. Hence, optimizing the electrode structure leads to the improvement of image quality in the reconstruction procedure. Although there have been many investigations on electrical impedance tomography (EIT) electrodes, there is no comprehensive study on their influence on images of the peripheral nerve. In this paper, we present a simulation method to study the effects of the electrode structure in the density measurement system of the peripheral nerve based on MEIT. The influence of the electrode structure such as dimensions, material and the number of electrodes and also the recognition feature of different radii of fascicle and different locations of fascicles has been studied. Data were reconstructed from the real and imaginary parts of complex conductivity data, respectively. It has been shown that the material of the electrodes had no effect on the reconstructed images, while the dimensions of the electrodes significantly affected the image sensitivity and thus the image quality. An increase in the number of electrodes increased the amount of data and information content. However, as the number of electrodes increased due to the given perimeter of the peripheral nerve, the area of the electrodes was reduced. This reduction affects the reconstructed image quality. The real and imaginary parts of the data were separately reconstructed for each case. Although, in real EIT systems, the reconstructed images using the real part of the signal have a better signal-to-noise ratio (SNR), this study proved that for a density measuring system of the peripheral nerve, the reconstructed images using the imaginary part of the signal had better quality. This simulation study proposes the effects of the electrode size and material and obtained spatial resolution that was high enough to reconstruct fascicles in a peripheral nerve.

An improved method of crafting a multi-electrode spiral cuff for the selective

This article reviews an improved methodology and technology for crafting a multi-electrode spiral cuff for the selective activation of nerve fibres in particular superficial regions of a peripheral nerve. The analysis, structural and mechanical properties of the spot welds used for the interconnections between the stimulating electrodes and stainless-steel lead wires are presented. The cuff consisted of 33 platinum electrodes embedded within a self-curling 17-mm-long silicone spiral sheet with a nominal internal diameter of 2.5 mm. The weld was analyzed using scanning electron microscopy and nanohardness tests, while the interconnection was investigated using destructive load tests. The functionality of the cuff was tested in an isolated porcine vagus nerve. The results of the scanning electron microscopy show good alloying and none of the typical welding defects that occur between the wire and the platinum foil. The results of the destructive load tests show that the breaking loads were between 3.22 and 5 N. The results of the nanohardness testing show that the hardness of the weld was different for the particular sites on the weld sample. Finally, the results of the functional testing show that for different stimulation intensities both the compound action potential deflection and the shape are modulated.

Modeling the response of small myelinated axons in a compound nerve to kilohertz frequency signals

OBJECTIVE

There is growing interest in electrical neuromodulation of peripheral nerves, particularly autonomic nerves, to treat various diseases. Electrical signals in the kilohertz frequency (KHF) range can produce different responses, including conduction block. For example, EnteroMedics' vBloc® therapy for obesity delivers 5 kHz stimulation to block the abdominal vagus nerves, but the mechanisms of action are unclear.

APPROACH

We developed a two-part computational model, coupling a 3D finite element model of a cuff electrode around the human abdominal vagus nerve with biophysically-realistic electrical circuit equivalent (cable) model axons (1, 2, and 5.7 µm in diameter). We developed an automated algorithm to classify conduction responses as subthreshold (transmission), KHF-evoked activity (excitation), or block. We quantified neural responses across kilohertz frequencies (5-20 kHz), amplitudes (1-8 mA), and electrode designs.

MAIN RESULTS

We found heterogeneous conduction responses across the modeled nerve trunk, both for a given parameter set and across parameter sets, although most suprathreshold responses were excitation, rather than block. The firing patterns were irregular near transmission and block boundaries, but otherwise regular, and mean firing rates varied with electrode-fibre distance. Further, we identified excitation responses at amplitudes above block threshold, termed 're-excitation', arising from action potentials initiated at virtual cathodes. Excitation and block thresholds decreased with smaller electrode-fibre distances, larger fibre diameters, and lower kilohertz frequencies. A point source model predicted a larger fraction of blocked fibres and greater change of threshold with distance as compared to the realistic cuff and nerve model.

SIGNIFICANCE

Our findings of widespread asynchronous KHF-evoked activity suggest that conduction block in the abdominal vagus nerves is unlikely with current clinical parameters. Our results indicate that compound neural or downstream muscle force recordings may be unreliable as quantitative measures of neural activity for in vivo studies or as biomarkers in closed-loop clinical devices.

Analysis of compound action potentials elicited with specific current stimulating pulses in an isolated rat sciatic nerve

The ability to selectively stimulate Aα, Aβ-fibers and Aδ-fibers in an isolated rat sciatic nerve (SNR) was assessed. The stimulus used was a current, biphasic pulse with a quasitrapezoidal cathodic phase and rectangular anodic phase where parameters were systematically varied: intensity of the cathodic phase (i

Alternative paradigm of selective vagus nerve stimulation tested on an isolated porcine vagus nerve

Alternative paradigm for spatial and fibre-type selective vagus nerve stimulation (VNS) was developed using realistic structural topography and tested in an isolated segment of a porcine cervical left vagus nerve (LVN). A spiral cuff (cuff) containing a matrix of ninety-nine electrodes was developed for selective VNS. A quasitrapezoidal stimulating pulse (stimulus) was applied to the LVN via an appointed group of three electrodes (triplet). The triplet and stimulus were configured to predominantly stimulate the B-fibres, minimizing stimulation of the A-fibres and by-passing the stimulation of the C-fibres. To assess which fibres made the most probable contribution to the neural response (NR) during selective VNS, the distribution of conduction velocity (CV) within the LVN was considered. Experimental testing of the paradigm showed the existence of certain parameters and waveforms of the stimulus, for which the contribution of the A-fibres to the NR was slightly reduced and that of the B-fibres was slightly enlarged. The cuff provided satisfactory fascicle discrimination in selective VNS as well as satisfactory fascicle discrimination during NR recording. However, in the present stage of development, fibre-type VNS remained rather limited.

A simulation of current focusing and steering with penetrating optic nerve electrodes

OBJECTIVE

Current focusing and steering are both widely used to shape the electric field and increase the number of distinct perceptual channels in neural stimulation, yet neither technique has been used for an optic nerve (ON)-based visual prosthesis. In order to evaluate the effects of current focusing and steering in penetrative stimulation, we built an integrated computational model to simulate and investigate the influence of stimulating parameters on ON fibre recruitment.

APPROACH

Finite element models with extremely fine meshes were first established to compute the 3D electric potential distribution under different stimulating parameters. Then the external electric potential was fed to randomized multi-compartment cable models to predict the distribution of fibres generating an action potential. Finally a statistical process was conducted to quantify the recruitment region.

MAIN RESULTS

The simulation results show that a two-electrode mode is superior to a three-electrode mode in current steering. The three-electrode mode performs poorly in current focusing, albeit the localized recruitment from both configurations implies that current focusing might be unnecessary in penetrative ON stimulation.

SIGNIFICANCE

This study provides useful information for the optimized design of penetrating ON electrodes and stimulating strategies. The Monte Carlo style computation paradigm is designed to simulate neural responses of an ensemble of ON fibres, which can be immediately transferred to other similar problems.

Application of a computational model of vagus nerve stimulation

OBJECTIVES

The most widely used and studied neurostimulation procedure for medically refractory epilepsy is vagus nerve stimulation (VNS) Therapy. The goal of this study was to develop a computational model for improved understanding of the anatomy and neurophysiology of the vagus nerve as it pertains to the principles of electrical stimulation, aiming to provide clinicians with a systematic and rational understanding of VNS Therapy.

MATERIALS AND METHODS

Computational modeling allows the study of electrical stimulation of peripheral nerves. We used finite element electric field models of the vagus nerve with VNS Therapy electrodes to calculate the voltage field for several output currents and studied the effects of two programmable parameters (output current and pulse width) on optimal fiber activation.

RESULTS

The mathematical models correlated well with strength-duration curves constructed from actual patient data. In addition, digital constructs of chronic versus acute implant models demonstrated that at a given pulse width and current combination, presence of a 110-μm fibrotic tissue can decrease fiber activation by 50%. Based on our findings, a range of output current settings between 0.75 and 1.75 mA with pulse width settings of 250 or 500 μs may result in optimal stimulation.

CONCLUSIONS

The modeling illustrates how to achieve full or nearly full activation of the myelinated fibers of the vagus nerve through output current and pulse width settings. This knowledge will enable clinicians to apply these principles for optimal vagus nerve activation and proceed to adjust duty cycle and frequency to achieve effectiveness.

A simulation study of the combined thermoelectric extracellular stimulation of the sciatic nerve of the Xenopus laevis: the localized transient heat block

The electrical behavior of the Xenopus laevis nerve fibers was studied when combined electrical (cuff electrodes) and optical (infrared laser, low power sub-5 mW) stimulations are applied. Assuming that the main effect of the laser irradiation on the nerve tissue is the localized temperature increase, this paper analyzes and gives new insights into the function of the combined thermoelectric stimulation on both excitation and blocking of the nerve action potentials (AP). The calculations involve a finite-element model (COMSOL) to represent the electrical properties of the nerve and cuff. Electric-field distribution along the nerve was computed for the given stimulation current profile and imported into a NEURON model, which was built to simulate the electrical behavior of myelinated nerve fiber under extracellular stimulation. The main result of this study of combined thermoelectric stimulation showed that local temperature increase, for the given electric field, can create a transient block of both the generation and propagation of the APs. Some preliminary experimental data in support of this conclusion are also shown.

Computational modeling to evaluate helical electrode designs

Finite element models of helical electrodes were utilized in conjunction with nerve fiber models to determine the efficacy of various changes in helical electrode design in improving nerve fiber recruitment. It was determined that an increase in the helical overlap angle does not facilitate recruitment of smaller diameter nerve fibers. The simulations led to some strategies that could potentially improve the electrode design.

Fascicular perineurium thickness, size, and position affect model predictions of neural excitation

The number of applications using neural prosthetic interfaces is expanding. Computer models are a valuable tool to evaluate stimulation techniques and electrode designs. Although our understanding of neural anatomy has improved, its impact on the effects of neural stimulation is not well understood. This study evaluated the effects of fascicle perineurial thickness, diameter, and position on axonal excitation thresholds and population recruitment using finite element models and NEURON simulations. The perineurial thickness of human fascicles was found to be 3.0% +/- 1.0% of the fascicle diameter. Increased perineurial thickness and fascicle diameter increased activation thresholds. The presence of a large neighboring fascicle caused a significant change in activation of a smaller target fascicle by as much as 80% +/- 11% of the total axon population. Smaller fascicles were recruited at lower amplitudes than neighboring larger fascicles. These effects were further illustrated in a realistic model of a human femoral nerve surrounded by a nerve cuff electrode. The data suggest that fascicular selectivity is strongly dependent upon the anatomy of the nerve being stimulated. Therefore, accurate representations of nerve anatomy are required to develop more accurate computer models to evaluate and optimize nerve electrode designs for neural prosthesis applications.

Solution space reduction in the peripheral nerve source localization problem using forward field similarities

Improving our ability to localize bioelectric sources within a peripheral nerve would help us to monitor the control signals flowing to and from any limb or organ. This technology would provide a useful neuroscience tool, and could perhaps be incorporated into a neuroprosthesis interface. We propose to use measurements from a multi-contact nerve cuff to solve an inverse problem of bioelectric source localization within the peripheral nerve. Before the inverse problem can be addressed, the forward problem is solved using finite element modeling. A fine mesh improves the accuracy of the forward problem solution, but increases the number of variables to be solved for in the inverse problem. To alleviate this problem, variables corresponding to mesh elements that are not distinguishable by the measurement setup are grouped together, thus reducing the dimension of the inverse problem without impacting on the forward problem accuracy. A quantitative criterion for element distinguishability is derived using the columns of the leadfield matrix and information about the uncertainty in the measurements. Our results indicate that the number of variables in the inverse problem can be reduced by more than half using the proposed method, without having a detrimental impact on the quality of the localization.

Simulation of intra-orbital optic nerve electrical stimulation

In blind subjects who still have functional retinal ganglion cells, electrical stimuli applied to the optic nerve can produce localised visual sensations. This has been demonstrated with an intracranially implanted self-sizing spiral cuff electrode, but, to avoid skull opening, intra-orbital cuff implantation is now considered. In its orbital segment, the optic nerve is surrounded by subarachnoidal cerebrospinal fluid (CSF) and dura mater. Dura mater is a tough fibrous tissue that can impede electrical stimulation. In the study, the issue of whether or not to remove the dura mater at the implantation site was addressed using simulation on numerical models. Several volume conductor models were built representing, respectively: the cuff implanted directly around the nerve; the cuff over the nerve after connective tissue encapsulated the implant; and the cuff electrode placed around the dura mater. Stimulation-induced electric potential fields were computed for these configurations using a full 3D finite elements software. Responses of fibres within the nerve were computed. A large range of dural conductivities and several CSF thicknesses were considered. In all simulated conditions, the presence of dura mater around a layer of CSF increased excitation thresholds. Selectivity performance also decreased, but was found to be independent of the CSF thickness. However, simulations showed that, if the diameter of the cuff electrode is adapted to the target nerve, the injected charge associated with activation is limited within a reasonable range. Electrical stimulation of the optic nerve with a cuff electrode implanted around the dura mater should therefore be feasible.

Model-based evaluation of the short-circuited tripolar cuff configuration

Recordings of neural information for use as feedback in functional electrical stimulation are often contaminated with interfering signals from muscles and from stimulus pulses. The cuff electrode used for the neural recording can be optimized to improve the S/I ratio. In this work, we evaluate a model of both the nerve signal and the interfering signals recorded by a cuff, and subsequently use this model to study the signal to interference ratio of different cuff designs and to evaluate a recently introduced short-circuited tripolar cuff configuration. The results of the model showed good agreement with results from measurements in rabbits and confirmed the superior performance of the short-circuited tripolar configuration as compared with the traditionally used tripolar configuration.

Different pulse shapes for selective large fibre block in sacral nerve roots using a technique of anodal block: an experimental study

The aim of this study was experimentally to investigate whether it is possible to reduce the charge per phase that is applied during selective large fibre block. Sacral roots in pigs were stimulated. Sacral roots contain large somatic nerve fibres and small parasympathetic nerve fibres. Large nerve fibres that innervate the external urethral and external anal sphincters were selectively blocked using a technique of anodal block. In that way, selective activation of the detrusor muscle and the rectum innervated by parasympathetic fibres could be obtained. The square stimulation pulse was replaced with three different pulse shapes that had the same duration as the square pulse and consisted of a depolarising prepulse and a blocking part of the pulse. Compared with the square pulse, the charge per phase needed for anodal block could be reduced with all three pulse shapes. Maximum reduction of the charge per pulse was 17+/-6%. A lower charge might make anodal block safer in long-term applications.

Different Pulse Shapes to Obtain Small Fiber Selective Activation by Anodal Blocking— A Simulation Study

The aim of this study was to investigate whether it is possible to reduce a charge per pulse, which is needed for selective nerve stimulation. Simulation is performed using a two-part simulation model: a volume conductor model to calculate the electrical potential distribution inside a tripolar cuff electrode and a human fiber model to simulate the fiber response to simulation. Selective stimulation is obtained by anodal block. To obtain anodal block of large fibers, long square pulses (> 350 micros) with a relatively high currents (1-2.5 mA) are usually required. These pulses might not be safe for a long-term application because of a high charge per pulse. In this study, several pulse shapes are proposed that have less charge per pulse compared with the conventional square pulse and would therefore be safer in a chronic application. Compared with the conventional square pulse, it was possible to reduce the charge with all proposed pulse shapes, but the best results are obtained with a combination of a square depolarizing pulse and a blocking pulse. The charge per pulse was up to 32% less with that pulse shape than with a square pulse. Using a hyperpolarizing anodal prepulse preceding a square pulse, it was not possible to block nerve fibers in a whole nerve bundle and to obtain reduction of a charge per phase. Reduction of the charge could be achieved only with spatially selective blocking. The charge per phase was larger for the combination of a hyperpolarizing anodal prepulse and a two-step pulse than for the two-step pulse alone.

Selective electrical interfaces with the nervous system

To achieve selective electrical interfacing to the neural system it is necessary to approach neuronal elements on a scale of micrometers. This necessitates microtechnology fabrication and introduces the interdisciplinary field of neurotechnology, lying at the juncture of neuroscience with microtechnology. The neuroelectronic interface occurs where the membrane of a cell soma or axon meets a metal microelectrode surface. The seal between these may be narrow or may be leaky. In the latter case the surrounding volume conductor becomes part of the interface. Electrode design for successful interfacing, either for stimulation or recording, requires good understanding of membrane phenomena, natural and evoked action potential generation, volume conduction, and electrode behavior. Penetrating multimicroelectrodes have been produced as one-, two-, and three-dimensional arrays, mainly in silicon, glass, and metal microtechnology. Cuff electrodes circumvent a nerve; their selectivity aims at fascicles more than at nerve fibers. Other types of electrodes are regenerating sieves and cone-ingrowth electrodes. The latter may play a role in brain-computer interfaces. Planar substrate-embedded electrode arrays with cultured neural cells on top are used to study the activity and plasticity of developing neural networks. They also serve as substrates for future so-called cultured probes.

Modelling analysis of human optic nerve fibre excitation based on experimental data

The aim of the study is to determine which of the existing myelinated mammalian nerve fibre models better fits experimental data resulting from electrical stimulation of the human optic nerve and from propagation velocity measured on primates. The macroscopic electric potential is computed in a 3D, inhomogeneous and anisotropic nerve model. The Chiu-Sweeney (CS) and the Schwarz-Wesselink (SW) membrane descriptions are then considered. Variations in parameters that are not well established (encapsulation-tissue thickness, nerve-fascicle conductivity, geometric and electrochemical fibre cable parameters) are taken into account. Results demonstrate that the SW model predictions are in better agreement with the experimental data than those of the CS model, although thresholds are still too high. When channel densities are varied, the SW model turns out to be more robust than the CS model. For a suitable leakage channel density value (about 8% of the original one), the SW model predicts a conduction velocity of 11.4 ms-1 and an excitation threshold of 0.055 mA (for 0.1 ms pulse duration), which is in very good agreement with experimental values (11 ms-1 and 0.055 mA). Potassium current in the SW model is necessary for stability. Introduction of a potassium-like current can restore stability in the CS system.

Hybrid finite elements and spectral method for computation of the electric potential generated by a nerve cuff electrode

An original numerical method is developed to compute the 3D electric potential generated by a dot-contact cuff electrode implanted around an axisymmetrical, inhomogeneous, anisotropic nerve. The technique is based on a 2D finite-element approach coupled with a semi-analytical Fourier spectral decomposition to approximate the solution behaviour in the azymuthal direction. The method only requires a 2D FEM mesh and allows an accurate electrode description, with any number of contacts at different angular positions. Results show that the convergence of the Fourier series is very fast: typically, the relative error due to series truncation (estimated by the norm of the difference between the solution computed with M modes and the one computed with M-1 modes, normalised by the norm of the solution computed with M modes) reaches the order of 10(-3) with six spectral modes (M = 6). As a consequence, the whole algorithm has the complexity of a 2D approach.

Multigrid solution of the potential field in modeling electrical nerve stimulation

In this paper, multilevel techniques are introduced as a fast numerical method to compute 3-D potential field in nerve stimulation configurations. It is shown that with these techniques the computing time is reduced significantly compared to conventional methods. Consequently, these techniques greatly enhance the possibilities for parameter studies and electrode design. Following a general description of the model of nerve stimulation configurations, the basic principles of multilevel solvers for the numerical solution of partial differential equations are briefly summarized. Subsequently, some essential elements for successful application are discussed. Finally, results are presented for the potential field in a nerve bundle induced by tripolar stimulation with a cuff electrode surrounding part of the nerve.